LAGEOS geodetic analysis-SL7.1

NASA Technical Reports Server (NTRS)

Smith, D. E.; Kolenkiewicz, R.; Dunn, P. J.; Klosko, S. M.; Robbins, J. W.; Torrence, M. H.; Williamson, R. G.; Pavlis, E. C.; Douglas, N. B.; Fricke, S. K.

1991-01-01

Laser ranging measurements to the LAGEOS satellite from 1976 through 1989 are related via geodetic and orbital theories to a variety of geodetic and geodynamic parameters. The SL7.1 analyses are explained of this data set including the estimation process for geodetic parameters such as Earth's gravitational constant (GM), those describing the Earth's elasticity properties (Love numbers), and the temporally varying geodetic parameters such as Earth's orientation (polar motion and Delta UT1) and tracking site horizontal tectonic motions. Descriptions of the reference systems, tectonic models, and adopted geodetic constants are provided; these are the framework within which the SL7.1 solution takes place. Estimates of temporal variations in non-conservative force parameters are included in these SL7.1 analyses as well as parameters describing the orbital states at monthly epochs. This information is useful in further refining models used to describe close-Earth satellite behavior. Estimates of intersite motions and individual tracking site motions computed through the network adjustment scheme are given. Tabulations of tracking site eccentricities, data summaries, estimated monthly orbital and force model parameters, polar motion, Earth rotation, and tracking station coordinate results are also provided.

The effect of geocenter motion on Jason-2 orbits and the mean sea level

NASA Astrophysics Data System (ADS)

Melachroinos, S. A.; Lemoine, F. G.; Zelensky, N. P.; Rowlands, D. D.; Luthcke, S. B.; Bordyugov, O.

2013-04-01

We compute a series of Jason-2 GPS and SLR/DORIS-based orbits using ITRF2005 and the std0905 standards (Lemoine et al., 2010). Our GPS and SLR/DORIS orbit data sets span a period of 2 years from cycle 3 (July 2008) to cycle 74 (July 2010). We extract the Jason-2 orbit frame translational parameters per cycle by the means of a Helmert transformation between a set of reference orbits and a set of test orbits. We compare the annual terms of these time-series to the annual terms of two different geocenter motion models where biases and trends have been removed. Subsequently, we include the annual terms of the modeled geocenter motion as a degree-1 loading displacement correction to the GPS and SLR/DORIS tracking network of the POD process. Although the annual geocenter motion correction would reflect a stationary signal in time, under ideal conditions, the whole geocenter motion is a non-stationary process that includes secular trends. Our results suggest that our GSFC Jason-2 GPS-based orbits are closely tied to the center of mass (CM) of the Earth consistent with our current force modeling, whereas GSFC's SLR/DORIS-based orbits are tied to the origin of ITRF2005, which is the center of figure (CF) for sub-secular scales. We quantify the GPS and SLR/DORIS orbit centering and how this impacts the orbit radial error over the globe, which is assimilated into mean sea level (MSL) error, from the omission of the annual term of the geocenter correction. We find that for the SLR/DORIS std0905 orbits, currently used by the oceanographic community, only the negligence of the annual term of the geocenter motion correction results in a - 4.67 ± 3.40 mm error in the Z-component of the orbit frame which creates 1.06 ± 2.66 mm of systematic error in the MSL estimates, mainly due to the uneven distribution of the oceans between the North and South hemisphere.

The Effect of Geocenter Motion on Jason-2 Orbits and the Mean Sea Level

NASA Technical Reports Server (NTRS)

Melachroinos, S. A.; Lemoine, F. G.; Zelensky, N. P.; Rowlands, D. D.; Luthcke, S. B.; Bordyugov, O.

2012-01-01

We compute a series of Jason-2 GPS and SLR/DORIS-based orbits using ITRF2005 and the std0905 standards (Lemoine et al. 2010). Our GPS and SLR/DORIS orbit data sets span a period of 2 years from cycle 3 (July 2008) to cycle 74 (July 2010). We extract the Jason-2 orbit frame translational parameters per cycle by the means of a Helmert transformation between a set of reference orbits and a set of test orbits. We compare the annual terms of these time-series to the annual terms of two different geocenter motion models where biases and trends have been removed. Subsequently, we include the annual terms of the modeled geocenter motion as a degree-1 loading displacement correction to the GPS and SLR/DORIS tracking network of the POD process. Although the annual geocenter motion correction would reflect a stationary signal in time, under ideal conditions, the whole geocenter motion is a non-stationary process that includes secular trends. Our results suggest that our GSFC Jason-2 GPS-based orbits are closely tied to the center of mass (CM) of the Earth consistent with our current force modeling, whereas GSFC's SLR/DORIS-based orbits are tied to the origin of ITRF2005, which is the center of figure (CF) for sub-secular scales. We quantify the GPS and SLR/DORIS orbit centering and how this impacts the orbit radial error over the globe, which is assimilated into mean sea level (MSL) error, from the omission of the annual term of the geocenter correction. We find that for the SLR/DORIS std0905 orbits, currently used by the oceanographic community, only the negligence of the annual term of the geocenter motion correction results in a 4.67 plus or minus 3.40 mm error in the Z-component of the orbit frame which creates 1.06 plus or minus 2.66 mm of systematic error in the MSL estimates, mainly due to the uneven distribution of the oceans between the North and South hemisphere.

Spin-orbit coupling for tidally evolving super-Earths

NASA Astrophysics Data System (ADS)

Rodríguez, A.; Callegari, N.; Michtchenko, T. A.; Hussmann, H.

2012-12-01

We investigate the spin behaviour of close-in rocky planets and the implications for their orbital evolution. Considering that the planet rotation evolves under simultaneous actions of the torque due to the equatorial deformation and the tidal torque, both raised by the central star, we analyse the possibility of temporary captures in spin-orbit resonances. The results of the numerical simulations of the exact equations of motions indicate that, whenever the planet rotation is trapped in a resonant motion, the orbital decay and the eccentricity damping are faster than the ones in which the rotation follows the so-called pseudo-synchronization. Analytical results obtained through the averaged equations of the spin-orbit problem show a good agreement with the numerical simulations. We apply the analysis to the cases of the recently discovered hot super-Earths Kepler-10 b, GJ 3634 b and 55 Cnc e. The simulated dynamical history of these systems indicates the possibility of capture in several spin-orbit resonances; particularly, GJ 3634 b and 55 Cnc e can currently evolve under a non-synchronous resonant motion for suitable values of the parameters. Moreover, 55 Cnc e may avoid a chaotic rotation behaviour by evolving towards synchronization through successive temporary resonant trappings.

Tidal evolution of close binary asteroid systems

NASA Astrophysics Data System (ADS)

Taylor, Patrick A.; Margot, Jean-Luc

2010-12-01

We provide a generalized discussion of tidal evolution to arbitrary order in the expansion of the gravitational potential between two spherical bodies of any mass ratio. To accurately reproduce the tidal evolution of a system at separations less than 5 times the radius of the larger primary component, the tidal potential due to the presence of a smaller secondary component is expanded in terms of Legendre polynomials to arbitrary order rather than truncated at leading order as is typically done in studies of well-separated system like the Earth and Moon. The equations of tidal evolution including tidal torques, the changes in spin rates of the components, and the change in semimajor axis (orbital separation) are then derived for binary asteroid systems with circular and equatorial mutual orbits. Accounting for higher-order terms in the tidal potential serves to speed up the tidal evolution of the system leading to underestimates in the time rates of change of the spin rates, semimajor axis, and mean motion in the mutual orbit if such corrections are ignored. Special attention is given to the effect of close orbits on the calculation of material properties of the components, in terms of the rigidity and tidal dissipation function, based on the tidal evolution of the system. It is found that accurate determinations of the physical parameters of the system, e.g., densities, sizes, and current separation, are typically more important than accounting for higher-order terms in the potential when calculating material properties. In the scope of the long-term tidal evolution of the semimajor axis and the component spin rates, correcting for close orbits is a small effect, but for an instantaneous rate of change in spin rate, semimajor axis, or mean motion, the close-orbit correction can be on the order of tens of percent. This work has possible implications for the determination of the Roche limit and for spin-state alteration during close flybys.

Globular Clusters: Absolute Proper Motions and Galactic Orbits

NASA Astrophysics Data System (ADS)

Chemel, A. A.; Glushkova, E. V.; Dambis, A. K.; Rastorguev, A. S.; Yalyalieva, L. N.; Klinichev, A. D.

2018-04-01

We cross-match objects from several different astronomical catalogs to determine the absolute proper motions of stars within the 30-arcmin radius fields of 115 Milky-Way globular clusters with the accuracy of 1-2 mas yr-1. The proper motions are based on positional data recovered from the USNO-B1, 2MASS, URAT1, ALLWISE, UCAC5, and Gaia DR1 surveys with up to ten positions spanning an epoch difference of up to about 65 years, and reduced to Gaia DR1 TGAS frame using UCAC5 as the reference catalog. Cluster members are photometrically identified by selecting horizontal- and red-giant branch stars on color-magnitude diagrams, and the mean absolute proper motions of the clusters with a typical formal error of about 0.4 mas yr-1 are computed by averaging the proper motions of selected members. The inferred absolute proper motions of clusters are combined with available radial-velocity data and heliocentric distance estimates to compute the cluster orbits in terms of the Galactic potential models based on Miyamoto and Nagai disk, Hernquist spheroid, and modified isothermal dark-matter halo (axisymmetric model without a bar) and the same model + rotating Ferre's bar (non-axisymmetric). Five distant clusters have higher-than-escape velocities, most likely due to large errors of computed transversal velocities, whereas the computed orbits of all other clusters remain bound to the Galaxy. Unlike previously published results, we find the bar to affect substantially the orbits of most of the clusters, even those at large Galactocentric distances, bringing appreciable chaotization, especially in the portions of the orbits close to the Galactic center, and stretching out the orbits of some of the thick-disk clusters.

The Uncertain Nature of Cometary Motions

NASA Technical Reports Server (NTRS)

Yeomans, Donald K.

1997-01-01

The number of active short- and long-periodic comets crossing the Earth's orbit each year is less than 10 percent of the corresponding number of asteroids crossing the Earth's orbit. However, the higher relative velocities of comets with respect to the Earth and the uncertainties associated with accurately computing their future trajectories can cause considerable problems when assessing the risks of Earth-crossing objects. Unlike asteroids, the motions of active comets are often affected by so-called nongravitational (outgassing) forces that are imperfectly modeled. In addition, the astrometric optical observations that are used to refine a comet's orbit are often imprecise because a comet's center of mass can be hidden by atmospheric gas and dust. For long-period comets, there is the additional problem of having to base orbital solutions on relatively short observational data intervals. Long-term numerical integrations extending two centuries into the future have been carried out to investigate upcoming Earth-close approaches by known periodic comets. Error analyses and impact probabilities have been computed for those comets that will pass closest to the Earth. Although there are no known comets that will make dangerously close Earth approaches in the next two centuries, there are a few objects that warrant future monitoring.

Spectroscopic orbits of symbiotic stars - Preliminary results

NASA Technical Reports Server (NTRS)

Garcia, M. R.

1986-01-01

The present search for radial velocity variations due to orbital motions in symbiotic stars involved observations of 17 such stars at approximately 1-month intervals, as well as of radial velocity variations in the M-giant primary in nine stars. The observed radial velocity curves are commensurate with those expected from a group of binaries having random sin i and about 20 km/sec orbital velocities. Four of the orbital periods thus suggested for seven stars confirm previously known photometric periods, while one confirms a previously known orbital period and two are completely new. Knowledge of the orbits allows identification of those symbiotics that are close to filling their Roche lobes.

Secular motion around synchronously orbiting planetary satellites.

PubMed

Lara, Martin; San-Juan, Juan F; Ferrer, Sebastián

2005-12-01

We investigate the secular motion of a spacecraft around the natural satellite of a planet. The satellite rotates synchronously with its mean motion around the planet. Our model takes into account the gravitational potential of the satellite up to the second order, and the third-body perturbation in Hill's approximation. Close to the satellite, the ratio of rotation rate of the satellite to mean motion of the orbiter is small. When considering this ratio as a small parameter, the Coriolis effect is a first-order perturbation, while the third-body tidal attraction, the ellipticity effect, and the oblateness perturbation remain at higher orders. Then, we apply perturbation theory and find that a third-order approach is enough to show the influence of the satellite's ellipticity in the pericenter dynamics. Finally, we discuss the averaged system in the three-dimensional parametric space, and provide a global description of the flow.

Parametric control of maneuver of a space tether system

NASA Astrophysics Data System (ADS)

Bezglasnyi, S. P.; Piyakina, E. E.

2015-07-01

Planar motion of a space tether system (STS) simulated by a massless rod with two masses fixed on its edges and a third mass moving along the rod is considered. An equation of the pendulum-controlled motion of the system in an elliptical orbit is obtained. Problems of parametric control that takes the STS from one stable radial equilibrium state to another and stabilizes it with respect to planar excitations of two diametrically opposite positions of the relative equilibrium of the STS in a circular orbit are investigated. The control is a continuous law of motion for a moving mass along the tether on the swing principle. The solution is obtained in a closed form based on the second method of the classical stability theory by the construction of the corresponding Lyapunov functions. Asymptotic convergence of solutions is confirmed by the results of numerical modeling of the system motion.

The Eccentric Behavior of Nearly Frozen Orbits

NASA Technical Reports Server (NTRS)

Sweetser, Theodore H.; Vincent, Mark A.

2013-01-01

Frozen orbits are orbits which have only short-period changes in their mean eccentricity and argument of periapse, so that they basically keep a fixed orientation within their plane of motion. Nearly frozen orbits are those whose eccentricity and argument of periapse have values close to those of a frozen orbit. We call them "nearly" frozen because their eccentricity vector (a vector whose polar coordinates are eccentricity and argument of periapse) will stay within a bounded distance from the frozen orbit eccentricity vector, circulating around it over time. For highly inclined orbits around the Earth, this distance is effectively constant over time. Furthermore, frozen orbit eccentricity values are low enough that these orbits are essentially eccentric (i.e., off center) circles, so that nearly frozen orbits around Earth are bounded above and below by frozen orbits.

Hypervelocity stars from young stellar clusters in the Galactic Centre

NASA Astrophysics Data System (ADS)

Fragione, G.; Capuzzo-Dolcetta, R.; Kroupa, P.

2017-05-01

The enormous velocities of the so-called hypervelocity stars (HVSs) derive, likely, from close interactions with massive black holes, binary stars encounters or supernova explosions. In this paper, we investigate the origin of HVSs as consequence of the close interaction between the Milky Way central massive black hole and a passing-by young stellar cluster. We found that both single and binary HVSs may be generated in a burst-like event, as the cluster passes near the orbital pericentre. High-velocity stars will move close to the initial cluster orbital plane and in the direction of the cluster orbital motion at the pericentre. The binary fraction of these HVS jets depends on the primordial binary fraction in the young cluster. The level of initial mass segregation determines the value of the average mass of the ejected stars. Some binary stars will merge, continuing their travel across and out of the Galaxy as blue stragglers.

The motion of a vortex on a closed surface of constant negative curvature.

PubMed

Ragazzo, C Grotta

2017-10-01

The purpose of this work is to present an algorithm to determine the motion of a single hydrodynamic vortex on a closed surface of constant curvature and of genus greater than one. The algorithm is based on a relation between the Laplace-Beltrami Green function and the heat kernel. The algorithm is used to compute the motion of a vortex on the Bolza surface. This is the first determination of the orbits of a vortex on a closed surface of genus greater than one. The numerical results show that all the 46 vortex equilibria can be explicitly computed using the symmetries of the Bolza surface. Some of these equilibria allow for the construction of the first two examples of infinite vortex crystals on the hyperbolic disc. The following theorem is proved: 'a Weierstrass point of a hyperellitic surface of constant curvature is always a vortex equilibrium'.

A dynamical study of the multiple system 17 Cygni ABFG

NASA Astrophysics Data System (ADS)

Romanenko, L. G.

2017-03-01

Adynamical study of the relative motions of the components of the inner pairs AB (ADS 12913) and FG (ADS 12889) of the quadruple heirarchical system 17 Cygni (WDS 19464+3344) is presented, as well as analysis of themotions of the outer pair AB-FG. The study is based on CCD observations obtained on the 26-inch refractor of the Pulkovo Observatory (2003-2013), position observations from the WDS catalog, Hipparcos parallaxes, and radial velocities of the components from literature data. A family of orbits for 17 Cyg AB is obtained for the first time, and has a most probable period of 6200 yrs. The apparent motion parameters (AMP) method is used, since the entire visible arc of the orbit over 1832-2013 is only 4°. The AMP method is also used to calculate the orbit of the 17 Cyg FG pair, which has a period of 238 yrs, yielding results in good agreement with the orbits derived in other studies. The ephemerides of the obtained AMP orbits, the position data for the AF pair from the WDS catalog (11 positions during 1893-2002), and Pulkovo CCD observations for 2007-2013 are used to calculate the apparent motion parameters of AB-FG outer pair, as well as a family of close-to-parabolic orbits with periods of 3.7 million years ormore. All the orbits (for both the inner and the outer pairs) are steeply inclined to theGalactic plane. Monte Carlo simulations are used to compute the probability that the outer pair is gravitationally bound, which is 47%. The similarity of the proper motions and radial velocities of all the components provides evidence that they all belong to a single stellar stream. Data from the CNS3 catalog are used to compose a list of candidate members of this stream.

Analytical modeling of soliton interactions in a nonlocal nonlinear medium analogous to gravitational force

NASA Astrophysics Data System (ADS)

Zeng, Shihao; Chen, Manna; Zhang, Ting; Hu, Wei; Guo, Qi; Lu, Daquan

2018-01-01

We illuminate an analytical model of soliton interactions in lead glass by analogizing to a gravitational force system. The orbits of spiraling solitons under a long-range interaction are given explicitly and demonstrated to follow Newton's second law of motion and the Binet equation by numerical simulations. The condition for circular orbits is obtained and the oscillating orbits are proved not to be closed. We prove the analogy between the nonlocal nonlinear optical system and gravitational system and specify the quantitative relation of the quantity between the two models.

Expansion of the gravitational potential with computerized Poisson series

NASA Technical Reports Server (NTRS)

Broucke, R.

1976-01-01

The paper describes a recursive formulation for the expansion of the gravitational potential valid for both the tesseral and zonal harmonics. The expansion is primarily in rectangular coordinates, but the classical orbit elements or equinoctial orbit elements can be easily substituted. The equations of motion for the zonal harmonics in both classical and equinoctial orbital elements are described in a form which will result in closed-form expressions for the first-order perturbations. In order to achieve this result, the true longitude or true anomaly have to be used as independent variables.

Transiting circumbinary planets Kepler-34 b and Kepler-35 b

DOE Office of Scientific and Technical Information (OSTI.GOV)

Welsh, William F.; Orosz, Jerome A.; Carter, Joshua A.

Most Sun-like stars in the Galaxy reside in gravitationally-bound pairs of stars called 'binary stars'. While long anticipated, the existence of a 'circumbinary planet' orbiting such a pair of normal stars was not definitively established until the discovery of Kepler-16. Incontrovertible evidence was provided by the miniature eclipses ('transits') of the stars by the planet. However, questions remain about the prevalence of circumbinary planets and their range of orbital and physical properties. Here we present two additional transiting circumbinary planets, Kepler-34 and Kepler-35. Each is a low-density gas giant planet on an orbit closely aligned with that of its parentmore » stars. Kepler-34 orbits two Sun-like stars every 289 days, while Kepler-35 orbits a pair of smaller stars (89% and 81% of the Sun's mass) every 131 days. Due to the orbital motion of the stars, the planets experience large multi-periodic variations in incident stellar radiation. The observed rate of circumbinary planets implies > ~1% of close binary stars have giant planets in nearly coplanar orbits, yielding a Galactic population of at least several million.« less

A drag-free Lo-Lo satellite system for improved gravity field measurements

NASA Technical Reports Server (NTRS)

Fischell, R. E.; Pisacane, V. L.

1978-01-01

At very low altitudes, the effect of atmospheric drag results in drastically reduced orbit lifetimes and considerable uncertainty in satellite motions. The concept suggested herein employs a DISturbance COmpensation System (DISCOS) on each of a pair of satellites at very low altitudes to provide refined measurements of the earth's gravitational field. The DISCOS maintains the satellites in orbit and essentially eliminates motion uncertainties due mostly to drag and to a lesser extent from solar radiation pressure. By a closed-loop measurement of the relative rangerate between the two low satellites, one can determine the earth's gravitational field with a considerably greater accuracy than could be obtained by tracking a single satellite.

DROMO formulation for planar motions: solution to the Tsien problem

NASA Astrophysics Data System (ADS)

Urrutxua, Hodei; Morante, David; Sanjurjo-Rivo, Manuel; Peláez, Jesús

2015-06-01

The two-body problem subject to a constant radial thrust is analyzed as a planar motion. The description of the problem is performed in terms of three perturbation methods: DROMO and two others due to Deprit. All of them rely on Hansen's ideal frame concept. An explicit, analytic, closed-form solution is obtained for this problem when the initial orbit is circular (Tsien problem), based on the DROMO special perturbation method, and expressed in terms of elliptic integral functions. The analytical solution to the Tsien problem is later used as a reference to test the numerical performance of various orbit propagation methods, including DROMO and Deprit methods, as well as Cowell and Kustaanheimo-Stiefel methods.

Orbital resonances, unusual configurations and exotic rotation states among planetary satellites

NASA Technical Reports Server (NTRS)

Peale, S. J.

1986-01-01

The origin of orbital resonances is shown in the demonstration of the evolution of a pair of planetary satellites through a commensurability of the mean motions by a sequence of diagrams of constant energy curves in a two-dimensional phase space; the closed curve corresponding to the motion in each successive diagram is identified by its adiabatically conserved area. It is found that two-body resonances serve as a basis in the solution of the problem of the origin and evolution of the three-body Laplace resonance among the Galilean satellites of Jupiter. The unusual rotation state of Saturn's satellite Hyperion which is expected to tumble chaotically for an indefinite amount of time is discussed.

Observational signatures of spherically-symmetric black hole spacetimes

NASA Astrophysics Data System (ADS)

De Laurentis, Mariafelicia; Younsi, Ziri; Porth, Oliver; Mizuno, Yosuke; Fromm, Christian; Rezzolla, Luciano; Olivares, Hector

2017-12-01

A binary system composed of a supermassive black hole and a pulsar orbiting around it is studied. The motivation for this study arises from the fact that pulsar timing observations have proven to be a powerful tool in identifying physical features of the orbiting companion. In this study, taking into account a general spherically-symmetric metric, we present analytic calculations of the geodesic motion, and the possible deviations with respect to the standard Schwarzschild case of General Relativity. In particular, the advance at periastron is studied with the aim of identifying corrections to General Relativity. A discussion of the motion of a pulsar very close the supermassive central black hole in our Galaxy (Sgr A*) is reported.

Orbit-attitude coupled motion around small bodies: Sun-synchronous orbits with Sun-tracking attitude motion

NASA Astrophysics Data System (ADS)

Kikuchi, Shota; Howell, Kathleen C.; Tsuda, Yuichi; Kawaguchi, Jun'ichiro

2017-11-01

The motion of a spacecraft in proximity to a small body is significantly perturbed due to its irregular gravity field and solar radiation pressure. In such a strongly perturbed environment, the coupling effect of the orbital and attitude motions exerts a large influence that cannot be neglected. However, natural orbit-attitude coupled dynamics around small bodies that are stationary in both orbital and attitude motions have yet to be observed. The present study therefore investigates natural coupled motion that involves both a Sun-synchronous orbit and Sun-tracking attitude motion. This orbit-attitude coupled motion enables a spacecraft to maintain its orbital geometry and attitude state with respect to the Sun without requiring active control. Therefore, the proposed method can reduce the use of an orbit and attitude control system. This paper first presents analytical conditions to achieve Sun-synchronous orbits and Sun-tracking attitude motion. These analytical solutions are then numerically propagated based on non-linear coupled orbit-attitude equations of motion. Consequently, the possibility of implementing Sun-synchronous orbits with Sun-tracking attitude motion is demonstrated.

A semi-analytic theory for the motion of a close-earth artificial satellite with drag

NASA Technical Reports Server (NTRS)

Liu, J. J. F.; Alford, R. L.

1979-01-01

A semi-analytic method is used to estimate the decay history/lifetime and to generate orbital ephemeris for close-earth satellites perturbed by the atmospheric drag and earth oblateness due to the spherical harmonics J2, J3, and J4. The theory maintains efficiency through the application of the theory of a method of averaging and employs sufficient numerical emphasis to include a rather sophisticated atmospheric density model. The averaged drag effects with respect to mean anomaly are evaluated by a Gauss-Legendre quadrature while the averaged variational equations of motion are integrated numerically with automatic step size and error control.

Review of investigations performed in the USSR on close approaches of comets to Jupiter and the evolution of cometary orbits

NASA Technical Reports Server (NTRS)

Kazimirchak-Polonskaya, E. I.

1976-01-01

Methods are reviewed for calculating the evolution of cometary orbits with emphasis on the orbital changes that take place when comets pass within the spheres of action of giant planets. Topics discussed include: differences and difficulties in methods used for the calculation of large perturbations by Jupiter; the construction of numerical theories of motion covering the whole period of observations of each comet, allowing for planetary perturbations and the effects of nongravitational forces; and investigations of the evolution of cometary orbits over the 400 year interval 1660-2060. The classical theory of cometary capture is briefly discussed.

Tidal interactions of a Maclaurin spheroid - II. Resonant excitation of modes by a close, misaligned orbit

NASA Astrophysics Data System (ADS)

Braviner, Harry J.; Ogilvie, Gordon I.

2015-02-01

We model a tidally forced star or giant planet as a Maclaurin spheroid, decomposing the motion into the normal modes found by Bryan. We first describe the general prescription for this decomposition and the computation of the tidal power. Although this formalism is very general, forcing due to a companion on a misaligned, circular orbit is used to illustrate the theory. The tidal power is plotted for a variety of orbital radii, misalignment angles, and spheroid rotation rates. Our calculations are carried out including all modes of degree l ≤ 4, and the same degree of gravitational forcing. Remarkably, we find that for close orbits (a/R* ≈ 3) and rotational deformations that are typical of giant planets (e ≈ 0.4) the l = 4 component of the gravitational potential may significantly enhance the dissipation through resonance with surface gravity modes. There are also a large number of resonances with inertial modes, with the tidal power being locally enhanced by up to three orders of magnitude. For very close orbits (a/R* ≈ 3), the contribution to the power from the l = 4 modes is roughly the same magnitude as that due to the l = 3 modes.

Near-parabolic comets observed in 2006-2010 - II. Their past and future motion under the influence of the Galaxy field and known nearby stars

NASA Astrophysics Data System (ADS)

Dybczyński, Piotr A.; Królikowska, Małgorzata

2015-03-01

In the first part of this research we extensively investigated and carefully determined osculating, original (when entering Solar system) and future (when leaving it), orbits of 22 near-parabolic comets with small perihelion distance (qosc < 3.1 au), discovered in years 2006-2010. Here, we continue this research with a detailed study of their past and future motion during previous and next orbital periods under the perturbing action of our Galactic environment. At all stages of our dynamical study, we precisely propagate in time the observational uncertainties of cometary orbits. For the first time in our calculations, we fully take into account individual perturbations from all known stars or stellar systems that closely (less than 3.5 pc) approach the Sun during the cometary motion in the investigated time interval of several million years. This is done by means of a direct numerical integration of the N-body system comprising of a comet, the Sun and 90 potential stellar perturbers. We show a full review of various examples of individual stellar action on cometary motion. We conclude that perturbations from all known stars or stellar systems do not change the overall picture of the past orbit evolution of long-period comets. Their future motion might be seriously perturbed during the predicted close approach of Gliese 710 star but we do not observe significant energy changes. The importance of stellar perturbations is tested on the whole sample of 108 comets investigated by us so far and our previous results, obtained with only Galactic perturbations included, are fully confirmed. We present how our results can be used to discriminate between dynamically new and old near-parabolic comets and discuss the relevance of the so-called Jupiter-Saturn barrier phenomenon. Finally, we show how the Oort spike in the 1/a-distribution of near-parabolic comets is built from both dynamically new and old comets. We also point out that C/2007 W1 seems to be the first serious candidate for interstellar provenance.

Orbital Disturbance Analysis due to the Lunar Gravitational Potential and Deviation Minimization through the Trajectory Control in Closed Loop

NASA Astrophysics Data System (ADS)

Gonçalves, L. D.; Rocco, E. M.; de Moraes, R. V.

2013-10-01

A study evaluating the influence due to the lunar gravitational potential, modeled by spherical harmonics, on the gravity acceleration is accomplished according to the model presented in Konopliv (2001). This model provides the components x, y and z for the gravity acceleration at each moment of time along the artificial satellite orbit and it enables to consider the spherical harmonic degree and order up to100. Through a comparison between the gravity acceleration from a central field and the gravity acceleration provided by Konopliv's model, it is obtained the disturbing velocity increment applied to the vehicle. Then, through the inverse problem, the Keplerian elements of perturbed orbit of the satellite are calculated allowing the orbital motion analysis. Transfer maneuvers and orbital correction of lunar satellites are simulated considering the disturbance due to non-uniform gravitational potential of the Moon, utilizing continuous thrust and trajectory control in closed loop. The simulations are performed using the Spacecraft Trajectory Simulator-STRS, Rocco (2008), which evaluate the behavior of the orbital elements, fuel consumption and thrust applied to the satellite over the time.

Synthesis of a controller for stabilizing the motion of a rigid body about a fixed point

NASA Astrophysics Data System (ADS)

Zabolotnov, Yu. M.; Lobanov, A. A.

2017-05-01

A method for the approximate design of an optimal controller for stabilizing the motion of a rigid body about a fixed point is considered. It is assumed that rigid body motion is nearly the motion in the classical Lagrange case. The method is based on the common use of the Bellman dynamic programming principle and the averagingmethod. The latter is used to solve theHamilton-Jacobi-Bellman equation approximately, which permits synthesizing the controller. The proposed method for controller design can be used in many problems close to the problem of motion of the Lagrange top (the motion of a rigid body in the atmosphere, the motion of a rigid body fastened to a cable in deployment of the orbital cable system, etc.).

Rotational behavior of comet nuclei under gravitational perturbations

NASA Technical Reports Server (NTRS)

Oberti, Pascal; Bois, E.; Froeschle, Claude

1992-01-01

A dynamical qualitative study of the rotational motion for cometary-type bodies submitted to gravitational perturbations has been performed by numerical simulations, including the Sun and Jupiter's disturbing torques in the model. Results show small gravitational disturbing effects from the Sun on Halley-type orbits, as well as from Jupiter on most close-approach configurations. Only a very close-approach induces notable effects, presenting then some interesting sensitivity to initial conditions.

Strong tidal dissipation in Io and Jupiter from astrometric observations.

PubMed

Lainey, Valéry; Arlot, Jean-Eudes; Karatekin, Ozgür; Van Hoolst, Tim

2009-06-18

Io is the volcanically most active body in the Solar System and has a large surface heat flux. The geological activity is thought to be the result of tides raised by Jupiter, but it is not known whether the current tidal heat production is sufficiently high to generate the observed surface heat flow. Io's tidal heat comes from the orbital energy of the Io-Jupiter system (resulting in orbital acceleration), whereas dissipation of energy in Jupiter causes Io's orbital motion to decelerate. Here we report a determination of the tidal dissipation in Io and Jupiter through its effect on the orbital motions of the Galilean moons. Our results show that the rate of internal energy dissipation in Io (k(2)/Q = 0.015 +/- 0.003, where k(2) is the Love number and Q is the quality factor) is in good agreement with the observed surface heat flow, and suggest that Io is close to thermal equilibrium. Dissipation in Jupiter (k(2)/Q = (1.102 +/- 0.203) x 10(-5)) is close to the upper bound of its average value expected from the long-term evolution of the system, and dissipation in extrasolar planets may be higher than presently assumed. The measured secular accelerations indicate that Io is evolving inwards, towards Jupiter, and that the three innermost Galilean moons (Io, Europa and Ganymede) are evolving out of the exact Laplace resonance.

Stable low-altitude orbits around Ganymede considering a disturbing body in a circular orbit

NASA Astrophysics Data System (ADS)

Cardoso dos Santos, J.; Carvalho, J. P. S.; Vilhena de Moraes, R.

2014-10-01

Some missions are being planned to visit Ganymede like the Europa Jupiter System Mission that is a cooperation between NASA and ESA to insert the spacecraft JGO (Jupiter Ganymede Orbiter) into Ganymedes orbit. This comprehension of the dynamics of these orbits around this planetary satellite is essential for the success of this type of mission. Thus, this work aims to perform a search for low-altitude orbits around Ganymede. An emphasis is given in polar orbits and it can be useful in the planning of space missions to be conducted around, with respect to the stability of orbits of artificial satellites. The study considers orbits of artificial satellites around Ganymede under the influence of the third-body (Jupiter's gravitational attraction) and the polygenic perturbations like those due to non-uniform distribution of mass (J_2 and J_3) of the main body. A simplified dynamic model for these perturbations is used. The Lagrange planetary equations are used to describe the orbital motion of the artificial satellite. The equations of motion are developed in closed form to avoid expansions in eccentricity and inclination. The results show the argument of pericenter circulating. However, low-altitude (100 and 150 km) polar orbits are stable. Another orbital elements behaved variating with small amplitudes. Thus, such orbits are convenient to be applied to future space missions to Ganymede. Acknowledgments: FAPESP (processes n° 2011/05671-5, 2012/12539-9 and 2012/21023-6).

Proper Motions of Dwarf Spheroidal Galaxies from Hubble Space Telescope Imaging. II. Measurement for Carina

NASA Astrophysics Data System (ADS)

Piatek, Slawomir; Pryor, Carlton; Olszewski, Edward W.; Harris, Hugh C.; Mateo, Mario; Minniti, Dante; Tinney, Christopher G.

2003-11-01

This article presents and discusses a measurement of the proper motion for the Carina dwarf spheroidal galaxy (dSph) from images in two distinct fields in the direction of Carina taken with the Hubble Space Telescope, at three epochs. Each field contains a confirmed quasi-stellar object that is the reference point for measuring the proper motion of the dSph. The consecutive epochs are 1-2 yr apart. The components of the measured proper motion for Carina, expressed in the equatorial coordinate system, are μα=22+/-9 mas century-1 and μδ=15+/-9 mas century-1. The quoted proper motion is a weighted mean of two independent measurements and has not been corrected for the motions of the Sun and of the local standard of rest. Given the proper motion and its uncertainty, integrating the family of possible orbits of Carina in a realistic gravitational potential for the Milky Way indicates that Carina is bound gravitationally to the Milky Way and is close to apogalacticon. The best estimate of, and the 95% confidence interval for, the apogalacticon of the orbit is 102 kpc and (102,113) kpc, for the perigalacticon is 20 kpc and (3.0,63) kpc, and for the orbital period is 1.4 Gyr and (1.3,2.0) Gyr. Carina does not seem to be on a polar orbit. The best estimate of the inclination of the orbit with respect to the Galactic plane is 39°, but the 95% confidence interval is so wide, (23°,102°), that it includes a polar orbit. We are unable to confirm or to rule out the membership of Carina in a ``stream'' of galaxies in the Galactic halo because the difference between the observed and predicted directions of the proper motion is 1.6 times the uncertainty of the difference. Carina must contain dark matter to have survived the tidal interaction with the Milky Way until the present. The triggering of star formation by perigalacticon passages and crossings of the Galactic disk do not explain the history of star formation in Carina. Based on observations with NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555.

Transiting circumbinary planets Kepler-34 b and Kepler-35 b.

PubMed

Welsh, William F; Orosz, Jerome A; Carter, Joshua A; Fabrycky, Daniel C; Ford, Eric B; Lissauer, Jack J; Prša, Andrej; Quinn, Samuel N; Ragozzine, Darin; Short, Donald R; Torres, Guillermo; Winn, Joshua N; Doyle, Laurance R; Barclay, Thomas; Batalha, Natalie; Bloemen, Steven; Brugamyer, Erik; Buchhave, Lars A; Caldwell, Caroline; Caldwell, Douglas A; Christiansen, Jessie L; Ciardi, David R; Cochran, William D; Endl, Michael; Fortney, Jonathan J; Gautier, Thomas N; Gilliland, Ronald L; Haas, Michael R; Hall, Jennifer R; Holman, Matthew J; Howard, Andrew W; Howell, Steve B; Isaacson, Howard; Jenkins, Jon M; Klaus, Todd C; Latham, David W; Li, Jie; Marcy, Geoffrey W; Mazeh, Tsevi; Quintana, Elisa V; Robertson, Paul; Shporer, Avi; Steffen, Jason H; Windmiller, Gur; Koch, David G; Borucki, William J

2012-01-11

Most Sun-like stars in the Galaxy reside in gravitationally bound pairs of stars (binaries). Although long anticipated, the existence of a 'circumbinary planet' orbiting such a pair of normal stars was not definitively established until the discovery of the planet transiting (that is, passing in front of) Kepler-16. Questions remained, however, about the prevalence of circumbinary planets and their range of orbital and physical properties. Here we report two additional transiting circumbinary planets: Kepler-34 (AB)b and Kepler-35 (AB)b, referred to here as Kepler-34 b and Kepler-35 b, respectively. Each is a low-density gas-giant planet on an orbit closely aligned with that of its parent stars. Kepler-34 b orbits two Sun-like stars every 289 days, whereas Kepler-35 b orbits a pair of smaller stars (89% and 81% of the Sun's mass) every 131 days. The planets experience large multi-periodic variations in incident stellar radiation arising from the orbital motion of the stars. The observed rate of circumbinary planets in our sample implies that more than ∼1% of close binary stars have giant planets in nearly coplanar orbits, yielding a Galactic population of at least several million.

A stability study of asteroid families near the 3:1 and 5:2 resonance with Jupiter

NASA Astrophysics Data System (ADS)

Hahn, G.; Lagerkvist, C.-I.; Lindblad, B. A.

1993-06-01

The stability and homogeneity of three asteroid families from Lindblad's list (1992) are studied using numerical integration techniques. These families include the Maria family, which lies close to the 3:1 mean motion resonance with Jupiter, the Oppavia-Gefion, and Dora families which are close to the 5:2 resonance. The study is based on a simplified solar system model, which takes into account the perturbations only by Jupiter and Saturn, and Everhart's variable stepsize integrator RA15. Preliminary results indicate that the stability of the orbits of all family members are not affected by the proximity to the 3:1 and 5:2 mean motion resonance with Jupiter.

Tribology experiment in zero gravity

NASA Technical Reports Server (NTRS)

Pan, C. H. T.; Gause, R. L.; Whitaker, A. F.

1984-01-01

A tribology experiment in zero gravity was performed during the orbital flight of Spacelab 1 to study the motion of liquid lubricants over solid surfaces. The absence of a significant gravitational force facilitates studies of the motion of liquid lubricants over solid surfaces as controlled by interfacial and capillary forces. Observations were made of phenomena associated with the liquid on one solid surface and also with the liquid between a pair of closely spaced surfaces. Typical photographic records obtained on Spacelab 1 are described.

ON THE DYNAMICS AND ORIGIN OF HAUMEA'S MOONS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ćuk, Matija; Ragozzine, Darin; Nesvorný, David, E-mail: mcuk@seti.org

2013-10-01

The dwarf planet Haumea has two large satellites, Namaka and Hi'iaka, which orbit at relatively large separations. Both moons have significant eccentricities and inclinations in a pattern that is consistent with a past orbital resonance. Based on our analysis, we find that the present system is not consistent with satellite formation close to the primary and tidal evolution through mean-motion resonances. We propose that Namaka experienced only limited tidal evolution, leading to the mutual 8:3 mean-motion resonance which redistributed eccentricities and inclinations between the moons. This scenario requires that the original orbit of Hi'iaka was mildly eccentric; we propose thatmore » this eccentricity was either primordial or acquired through encounters with other trans-Neptunian objects. Both dynamical stability and our preferred tidal evolution model imply that the moons' masses are only about one-half of previously estimated values, suggesting high albedos and low densities. Because the present orbits of the moons strongly suggest formation from a flat disk close to their present locations, we conclude that Hi'iaka and Namaka may be second-generation moons, formed after the breakup of a larger past moon, previously proposed as the parent body of the Haumea family. We derive plausible parameters of that moon, consistent with the current models of Haumea's formation. An interesting implication of this hypothesis is that Hi'iaka and Namaka may orbit retrograde with respect to Haumea's spin. Retrograde orbits of Haumea's moons would be in full agreement with available observations and our dynamical analysis, and could provide a unique confirmation of the ''disrupted satellite'' scenario for the origin of the family.« less

Fractional Whirl Motion in Wave Journal Bearings

NASA Technical Reports Server (NTRS)

Dimofte, Florin; Hendricks, Robert C.

1996-01-01

Unloaded gas, plain journal bearings experience sub-synchronous whirl motion due to fluid film instabilities and wall contact usually occurs immediately after the onset of the whirl motion. An alternative is the wave journal bearing which significantly improves bearing stability. The predicted threshold where the sub-synchronous whirl motion starts was well confirmed by the experimental observation. In addition, both a two-wave and a three-wave journal bearing can operate free of sub-synchronous whirl motion over a large range in speeds. When the sub-synchronous whirl motion occurs, both the two-wave and three-wave bearing can run in a whirl orbit well within the bearing clearance. At large clearances and wave amplitudes a two-wave bearing, unliKe other bearings, can exhibit a sub-synchronous whirl movement at both low and high speeds, but can run extremely stable and without whirl at intermediate speeds. Moreover, in these cases, the whirl frequencies are close to a quarter of the synchronous speed. The three-wave bearing can exhibit sub-synchronous whirl motion only after a specific threshold when the speed increases and the whirl frequencies are close to half of the synchronous speed.

Operating Small Sat Swarms as a Single Entity: Introducing SODA

NASA Technical Reports Server (NTRS)

Conn, Tracie; Plice, Laura; Dono Perez, Andres; Ho, Michael

2017-01-01

NASA's decadal survey determined that simultaneous measurements from a 3D volume of space are advantageous for a variety of studies in space physics and Earth science. Therefore, swarm concepts with multiple spacecraft in close proximity are a growing topic of interest in the small satellite community. Among the capabilities needed for swarm missions is a means to maintain operator-specified geometry, alignment, or separation. Swarm stationkeeping poses a planning challenge due to the limited scalability of ground resources. To address scalable control of orbital dynamics, we introduce SODA - Swarm Orbital Dynamics Advisor - a tool that accepts high-level configuration commands and provides the orbital maneuvers needed to achieve the desired type of swarm relative motion. Rather than conventional path planning, SODA's innovation is the use of artificial potential functions to define boundaries and keepout regions. The software architecture includes high fidelity propagation, accommodates manual or automated inputs, displays motion animations, and returns maneuver commands and analytical results. Currently, two swarm types are enabled: in-train distribution and an ellipsoid volume container. Additional swarm types, simulation applications, and orbital destinations are in planning stages.

Motion of dust in a planetary magnetosphere - Orbit-averaged equations for oblateness, electromagnetic, and radiation forces with application to Saturn's E ring

NASA Technical Reports Server (NTRS)

Hamilton, Douglas P.

1993-01-01

The orbital dynamics of micrometer-sized dust grains is explored numerically and analytically, treating the strongest perturbation forces acting on close circumplanetary dust grains: higher-order gravity, radiation pressure, and the electromagnetic force. The appropriate orbit-average equations are derived and applied to the E ring. Arguments are made for the existence of azimuthal and vertical asymmetries in the E ring. New understanding of the dynamics of E ring dust grains is applied to problems of the ring's breadth and height. The possibility for further ground-based and spacecraft observations is considered.

Reconnaissance of the HR 8799 Exosolar System. II. Astrometry and Orbital Motion

NASA Astrophysics Data System (ADS)

Pueyo, L.; Soummer, R.; Hoffmann, J.; Oppenheimer, R.; Graham, J. R.; Zimmerman, N.; Zhai, C.; Wallace, J. K.; Vescelus, F.; Veicht, A.; Vasisht, G.; Truong, T.; Sivaramakrishnan, A.; Shao, M.; Roberts, L. C., Jr.; Roberts, J. E.; Rice, E.; Parry, I. R.; Nilsson, R.; Lockhart, T.; Ligon, E. R.; King, D.; Hinkley, S.; Hillenbrand, L.; Hale, D.; Dekany, R.; Crepp, J. R.; Cady, E.; Burruss, R.; Brenner, D.; Beichman, C.; Baranec, C.

2015-04-01

We present an analysis of the orbital motion of the four substellar objects orbiting HR 8799. Our study relies on the published astrometric history of this system augmented with an epoch obtained with the Project 1640 coronagraph with an integral field spectrograph (IFS) installed at the Palomar Hale telescope. We first focus on the intricacies associated with astrometric estimation using the combination of an extreme adaptive optics system (PALM-3000), a coronagraph, and an IFS. We introduce two new algorithms. The first one retrieves the stellar focal plane position when the star is occulted by a coronagraphic stop. The second one yields precise astrometric and spectrophotometric estimates of faint point sources even when they are initially buried in the speckle noise. The second part of our paper is devoted to studying orbital motion in this system. In order to complement the orbital architectures discussed in the literature, we determine an ensemble of likely Keplerian orbits for HR 8799bcde, using a Bayesian analysis with maximally vague priors regarding the overall configuration of the system. Although the astrometric history is currently too scarce to formally rule out coplanarity, HR 8799d appears to be misaligned with respect to the most likely planes of HR 8799bce orbits. This misalignment is sufficient to question the strictly coplanar assumption made by various authors when identifying a Laplace resonance as a potential architecture. Finally, we establish a high likelihood that HR 8799de have dynamical masses below 13 MJup, using a loose dynamical survival argument based on geometric close encounters. We illustrate how future dynamical analyses will further constrain dynamical masses in the entire system.

Safety Ellipse Motion with Coarse Sun Angle Optimization

NASA Technical Reports Server (NTRS)

Naasz, Bo

2005-01-01

The Hubble Space Telescope Robotic Servicing and De-orbit Mission (HRSDM) was t o be performed by the unmanned Hubble Robotic Vehicle (HRV) consisting of a Deorbit Module (DM), responsible for the ultimate disposal of Hubble Space Telescope (HST) at the end of science operations, and an Ejection Module (EM), responsible for robotically servicing the HST to extend its useful operational lifetime. HRSDM consisted of eight distinct phases, including: launch, pursuit, proximity operations, capture, servicing, EM jettison and disposal, science operations, and deorbit. The scope of this paper is limited to the Proximity Operations phase of HRSDM. It introduces a relative motion strategy useful for Autonomous Rendezvous and Docking (AR&D) or Formation Flying missions where safe circumnavigation trajectories, or close proximity operations (tens or hundreds of meters) are required for extended periods of time. Parameters and algorithms used to model the relative motion of HRV with respect to HST during the Proximity Operations phase of the HRSDM are described. Specifically, the Safety Ellipse (SE) concept, convenient parameters for describing SE motion, and a concept for initializing SE motion around a target vehicle to coarsely optimize sun and relative navigation sensor angles are presented. The effects of solar incidence angle variations on sun angle optimization, and the effects of orbital perturbations and navigation uncertainty on long term SE motion are discussed.

Reference equations of motion for automatic rendezvous and capture

NASA Technical Reports Server (NTRS)

Henderson, David M.

1992-01-01

The analysis presented in this paper defines the reference coordinate frames, equations of motion, and control parameters necessary to model the relative motion and attitude of spacecraft in close proximity with another space system during the Automatic Rendezvous and Capture phase of an on-orbit operation. The relative docking port target position vector and the attitude control matrix are defined based upon an arbitrary spacecraft design. These translation and rotation control parameters could be used to drive the error signal input to the vehicle flight control system. Measurements for these control parameters would become the bases for an autopilot or feedback control system (FCS) design for a specific spacecraft.

Dynamics of Space Particles and Spacecrafts Passing by the Atmosphere of the Earth

PubMed Central

Prado, Antonio Fernando Bertachini de Almeida; Golebiewska, Justyna

2013-01-01

The present research studies the motion of a particle or a spacecraft that comes from an orbit around the Sun, which can be elliptic or hyperbolic, and that makes a passage close enough to the Earth such that it crosses its atmosphere. The idea is to measure the Sun-particle two-body energy before and after this passage in order to verify its variation as a function of the periapsis distance, angle of approach, and velocity at the periapsis of the particle. The full system is formed by the Sun, the Earth, and the particle or the spacecraft. The Sun and the Earth are in circular orbits around their center of mass and the motion is planar for all the bodies involved. The equations of motion consider the restricted circular planar three-body problem with the addition of the atmospheric drag. The initial conditions of the particle or spacecraft (position and velocity) are given at the periapsis of its trajectory around the Earth. PMID:24396298

Dynamics of space particles and spacecrafts passing by the atmosphere of the Earth.

PubMed

Gomes, Vivian Martins; Prado, Antonio Fernando Bertachini de Almeida; Golebiewska, Justyna

2013-01-01

The present research studies the motion of a particle or a spacecraft that comes from an orbit around the Sun, which can be elliptic or hyperbolic, and that makes a passage close enough to the Earth such that it crosses its atmosphere. The idea is to measure the Sun-particle two-body energy before and after this passage in order to verify its variation as a function of the periapsis distance, angle of approach, and velocity at the periapsis of the particle. The full system is formed by the Sun, the Earth, and the particle or the spacecraft. The Sun and the Earth are in circular orbits around their center of mass and the motion is planar for all the bodies involved. The equations of motion consider the restricted circular planar three-body problem with the addition of the atmospheric drag. The initial conditions of the particle or spacecraft (position and velocity) are given at the periapsis of its trajectory around the Earth.

Derivation of capture probabilities for the corotation eccentric mean motion resonances

NASA Astrophysics Data System (ADS)

El Moutamid, Maryame; Sicardy, Bruno; Renner, Stéfan

2017-08-01

We study in this paper the capture of a massless particle into an isolated, first-order corotation eccentric resonance (CER), in the framework of the planar, eccentric and restricted three-body problem near a m + 1: m mean motion commensurability (m integer). While capture into Lindblad eccentric resonances (where the perturber's orbit is circular) has been investigated years ago, capture into CER (where the perturber's orbit is elliptic) has not yet been investigated in detail. Here, we derive the generic equations of motion near a CER in the general case where both the perturber and the test particle migrate. We derive the probability of capture in that context, and we examine more closely two particular cases: (I) if only the perturber is migrating, capture is possible only if the migration is outward from the primary. Notably, the probability of capture is independent of the way the perturber migrates outward; (II) if only the test particle is migrating, then capture is possible only if the algebraic value of its migration rate is a decreasing function of orbital radius. In this case, the probability of capture is proportional to the radial gradient of migration. These results differ from the capture into Lindblad eccentric resonance (LER), where it is necessary that the orbits of the perturber and the test particle converge for capture to be possible.

Intrawave sand suspension in the shoaling and surf zone of a field-scale laboratory beach

NASA Astrophysics Data System (ADS)

Brinkkemper, J. A.; de Bakker, A. T. M.; Ruessink, B. G.

2017-01-01

Short-wave sand transport in morphodynamic models is often based solely on the near-bed wave-orbital motion, thereby neglecting the effect of ripple-induced and surface-induced turbulence on sand transport processes. Here sand stirring was studied using measurements of the wave-orbital motion, turbulence, ripple characteristics, and sand concentration collected on a field-scale laboratory beach under conditions ranging from irregular nonbreaking waves above vortex ripples to plunging waves and bores above subdued bed forms. Turbulence and sand concentration were analyzed as individual events and in a wave phase-averaged sense. The fraction of turbulence events related to suspension events is relatively high (˜50%), especially beneath plunging waves. Beneath nonbreaking waves with vortex ripples, the sand concentration close to the bed peaks right after the maximum positive wave-orbital motion and shows a marked phase lag in the vertical, although the peak in concentration at higher elevations does not shift to beyond the positive to negative flow reversal. Under plunging waves, concentration peaks beneath the wavefront without any notable phase lags in the vertical. In the inner-surf zone (bores), the sand concentration remains phase coupled to positive wave-orbital motion, but the concentration decreases with distance toward the shoreline. On the whole, our observations demonstrate that the wave-driven suspended load transport is onshore and largest beneath plunging waves, while it is small and can also be offshore beneath shoaling waves. To accurately predict wave-driven sand transport in morphodynamic models, the effect of surface-induced turbulence beneath plunging waves should thus be included.

Long term evolution of planetary systems with a terrestrial planet and a giant planet.

NASA Astrophysics Data System (ADS)

Georgakarakos, Nikolaos; Dobbs-Dixon, Ian; Way, Michael J.

2017-06-01

We study the long term orbital evolution of a terrestrial planet under the gravitational perturbations of a giant planet. In particular, we are interested in situations where the two planets are in the same plane and are relatively close. We examine both possible configurations: the giant planet orbit being either outside or inside the orbit of the smaller planet. The perturbing potential is expanded to high orders and an analytical solution of the terrestrial planetary orbit is derived. The analytical estimates are then compared against results from the numerical integration of the full equations of motion and we find that the analytical solution works reasonably well. An interesting finding is that the new analytical estimates improve greatly the predictions for the timescales of the orbital evolution of the terrestrial planet compared to an octupole order expansion.

Optimal Lorentz-augmented spacecraft formation flying in elliptic orbits

NASA Astrophysics Data System (ADS)

Huang, Xu; Yan, Ye; Zhou, Yang

2015-06-01

An electrostatically charged spacecraft accelerates as it moves through the Earth's magnetic field due to the induced Lorentz force, providing a new means of propellantless electromagnetic propulsion for orbital maneuvers. The feasibility of Lorentz-augmented spacecraft formation flying in elliptic orbits is investigated in this paper. Assuming the Earth's magnetic field as a tilted dipole corotating with Earth, a nonlinear dynamical model that characterizes the orbital motion of Lorentz spacecraft in the vicinity of arbitrary elliptic orbits is developed. To establish a predetermined formation configuration at given terminal time, pseudospectral method is used to solve the optimal open-loop trajectories of hybrid control inputs consisted of Lorentz acceleration and thruster-generated control acceleration. A nontilted dipole model is also introduced to analyze the effect of dipole tilt angle via comparisons with the tilted one. Meanwhile, to guarantee finite-time convergence and system robustness against external perturbations, a continuous fast nonsingular terminal sliding mode controller is designed and the closed-loop system stability is proved by Lyapunov theory. Numerical simulations substantiate the validity of proposed open-loop and closed-loop control schemes, and the results indicate that an almost propellantless formation establishment can be achieved by choosing appropriate objective function in the pseudospectral method. Furthermore, compared to the nonsingular terminal sliding mode controller, the closed-loop controller presents superior convergence rate with only a bit more control effort. And the proposed controller can be applied in other Lorentz-augmented relative orbital control problems.

Wide Binaries in TGAS: Search Method and First Results

NASA Astrophysics Data System (ADS)

Andrews, Jeff J.; Chanamé, Julio; Agüeros, Marcel A.

2018-04-01

Half of all stars reside in binary systems, many of which have orbital separations in excess of 1000 AU. Such binaries are typically identified in astrometric catalogs by matching the proper motions vectors of close stellar pairs. We present a fully Bayesian method that properly takes into account positions, proper motions, parallaxes, and their correlated uncertainties to identify widely separated stellar binaries. After applying our method to the >2 × 106 stars in the Tycho-Gaia astrometric solution from Gaia DR1, we identify over 6000 candidate wide binaries. For those pairs with separations less than 40,000 AU, we determine the contamination rate to be ~5%. This sample has an orbital separation (a) distribution that is roughly flat in log space for separations less than ~5000 AU and follows a power law of a -1.6 at larger separations.

Analytical method for the effects of the asteroid belt on planetary orbits

NASA Technical Reports Server (NTRS)

Mayo, A. P.

1979-01-01

Analytic expressions are derived for the perturbation of planetary orbits due to a thick constant-density asteroid belt. The derivations include extensions and adaptations of Plakhov's (1968) analytic expressions for the perturbations in five of the orbital elements for closed orbits around Saturn's rings. The equations of Plakhov are modified to include the effect of ring thickness, and additional equations are derived for the perturbations in the sixth orbital element, the mean anomaly. The gravitational potential and orbital perturbations are derived for the asteroid belt with and without thickness, and for a hoop approximation to the belt. The procedures are also applicable to Saturn's rings and the newly discovered rings of Uranus. The effects of the asteroid belt thickness on the gravitational potential coefficients and the orbital motions are demonstrated. Comparisons between the Mars orbital perturbations obtained by using the analytic expressions and those obtained by numerical integration are discussed. The effects of the asteroid belt on earth-based ranging to Mars are also demonstrated.

Vestibular selection criteria development. [assessing susceptability to motion sickness during orbital space flight

NASA Technical Reports Server (NTRS)

Lackner, J. R.

1981-01-01

The experimental elicitation of motion sickness using a short arm centrifuge or a rotating chair surrounded by a striped cylindrical enclosure failed to reveal any systematic group or consistent individual relationship between changes in heart rate, blood pressure, and body temperature and the appearance of symptoms of motion sickness. A study of the influence of vision on susceptability to motion sickness during sudden stop simulation shows that having the eyes open during any part of the sudden stop assessment is more stressful than having them closed throughout the test. Subjects were found to be highly susceptible to motion sickness when tested in free fall and in high force phases of flight. The effect of touch and pressure cues on body orientation during rotation and in parabolic flight are considered as sensory as well as motor adaptation.

Families of periodic orbits in Hill's problem with solar radiation pressure: application to Hayabusa 2

NASA Astrophysics Data System (ADS)

Giancotti, Marco; Campagnola, Stefano; Tsuda, Yuichi; Kawaguchi, Jun'ichiro

2014-11-01

This work studies periodic solutions applicable, as an extended phase, to the JAXA asteroid rendezvous mission Hayabusa 2 when it is close to target asteroid 1999 JU3. The motion of a spacecraft close to a small asteroid can be approximated with the equations of Hill's problem modified to account for the strong solar radiation pressure. The identification of families of periodic solutions in such systems is just starting and the field is largely unexplored. We find several periodic orbits using a grid search, then apply numerical continuation and bifurcation theory to a subset of these to explore the changes in the orbit families when the orbital energy is varied. This analysis gives information on their stability and bifurcations. We then compare the various families on the basis of the restrictions and requirements of the specific mission considered, such as the pointing of the solar panels and instruments. We also use information about their resilience against parameter errors and their ground tracks to identify one particularly promising type of solution.

Dynamical Chaos in the Wisdom-Holman Integrator: Origins and Solutions

NASA Technical Reports Server (NTRS)

Rauch, Kevin P.; Holman, Matthew

1999-01-01

We examine the nonlinear stability of the Wisdom-Holman (WH) symplectic mapping applied to the integration of perturbed, highly eccentric (e-0.9) two-body orbits. We find that the method is unstable and introduces artificial chaos into the computed trajectories for this class of problems, unless the step size chosen 1s small enough that PeriaPse is always resolved, in which case the method is generically stable. This 'radial orbit instability' persists even for weakly perturbed systems. Using the Stark problem as a fiducial test case, we investigate the dynamical origin of this instability and argue that the numerical chaos results from the overlap of step-size resonances; interestingly, for the Stark-problem many of these resonances appear to be absolutely stable. We similarly examine the robustness of several alternative integration methods: a time-regularized version of the WH mapping suggested by Mikkola; the potential-splitting (PS) method of Duncan, Levison, Lee; and two original methods incorporating approximations based on Stark motion instead of Keplerian motion. The two fixed point problem and a related, more general problem are used to conduct a comparative test of the various methods for several types of motion. Among the algorithms tested, the time-transformed WH mapping is clearly the most efficient and stable method of integrating eccentric, nearly Keplerian orbits in the absence of close encounters. For test particles subject to both high eccentricities and very close encounters, we find an enhanced version of the PS method-incorporating time regularization, force-center switching, and an improved kernel function-to be both economical and highly versatile. We conclude that Stark-based methods are of marginal utility in N-body type integrations. Additional implications for the symplectic integration of N-body systems are discussed.

Analytic expressions for perturbations and partial derivatives of range and range rate of a spacecraft with respect to the coefficient of the second harmonic

NASA Technical Reports Server (NTRS)

Georgevic, R. M.

1973-01-01

Closed-form analytic expressions for the time variations of instantaneous orbital parameters and of the topocentric range and range rate of a spacecraft moving in the gravitational field of an oblate large body are derived using a first-order variation of parameters technique. In addition, the closed-form analytic expressions for the partial derivatives of the topocentric range and range rate are obtained, with respect to the coefficient of the second harmonic of the potential of the central body (J sub 2). The results are applied to the motion of a point-mass spacecraft moving in the orbit around the equatorially elliptic, oblate sun, with J sub 2 approximately equal to .000027.

N-Body Simulations of Planetary Accretion Around M Dwarf Stars

NASA Astrophysics Data System (ADS)

Ogihara, Masahiro; Ida, Shigeru

2009-07-01

We have investigated planetary accretion from planetesimals in terrestrial planet regions inside the ice line around M dwarf stars through N-body simulations including tidal interactions with disk gas. Because of low luminosity of M dwarfs, habitable zones (HZs) are located in inner regions (~0.1 AU). In the close-in HZ, type-I migration and the orbital decay induced by eccentricity damping are efficient according to the high disk gas density in the small orbital radii. Since the orbital decay is terminated around the disk inner edge and the disk edge is close to the HZ, the protoplanets accumulated near the disk edge affect formation of planets in the HZ. Ice lines are also in relatively inner regions at ~0.3 AU. Due to the small orbital radii, icy protoplanets accrete rapidly and undergo type-I migration before disk depletion. The rapid orbital decay, the proximity of the disk inner edge, and large amount of inflow of icy protoplanets are characteristic in planetary accretion in terrestrial planet regions around M dwarfs. In the case of full efficiency of type-I migration predicted by the linear theory, we found that protoplanets that migrate to the vicinity of the host star undergo close scatterings and collisions, and four to six planets eventually remain in mutual mean-motion resonances and their orbits have small eccentricities (lsim0.01) and they are stable both before and after disk gas decays. In the case of slow migration, the resonant capture is so efficient that densely packed ~40 small protoplanets remain in mutual mean-motion resonances. In this case, they start orbit crossing, after the disk gas decays and eccentricity damping due to tidal interaction with gas is no more effective. Through merging of the protoplanets, several planets in widely separated non-resonant orbits with relatively large eccentricities (~0.05) are formed. Thus, the final orbital configurations (separations, resonant or non-resonant, eccentricity, and distribution) of the terrestrial planets around M dwarfs sensitively depend on strength of type-I migration. We also found that large amount of water-ice is delivered by type-I migration from outer regions and final planets near the inner disk edge around M dwarfs are generally abundant in water-ice except for the innermost one that is shielded by the outer planets, unless type-I migration speed is reduced by a factor of more than 100 from that predicted by the linear theory.

Production of Star-Grazing and Star-Impacting Planetestimals via Orbital Migration of Extrasolar Planets

NASA Technical Reports Server (NTRS)

Quillen, A. C.; Holman, M.

2000-01-01

During the orbital migration of a giant extrasolar planet via ejection of planetesimals (as studied by Murray et al. in 1998), inner mean-motion resonances can be strong enough to cause planetesimals to graze or impact the star. We integrate numerically the motions of particles which pass through the 3:1 or 4:1 mean-motion resonances of a migrating Jupiter-mass planet. We find that many particles can be trapped in the 3:1 or 4:1 resonances and pumped to high enough eccentricities that they impact the star. This implies that for a planet migrating a substantial fraction of its semimajor axis, a fraction of its mass in planetesimals could impact the star. This process may be capable of enriching the metallicity of the star at a time when the star is no longer fully convective. Upon close approaches to the star, the surfaces of these planetesimals will be sublimated. Orbital migration should cause continuing production of evaporating bodies, suggesting that this process should be detectable with searches for transient absorption lines in young stars. The remainder of the particles will not impact the star but can be ejected subsequently by the planet as it migrates further inward. This allows the planet to migrate a substantial fraction of its initial semimajor axis by ejecting planetesimals.

Study of periodic motions of a satellite with a magnetic damper

NASA Technical Reports Server (NTRS)

Sadov, Y. A.; Teterin, A. D.

1979-01-01

The motion of a satellite with a magnetic damper in the plane of a circular polar orbit is studied. The asymptotics of periodic solutions are constructed for a satellite close to axisymmetric and the radius of convergence is evaluated for the power series obtained. In a broad range of values of parameters, a periodic solution is obtained by numerical integration of equations of motion of the satellite. The asymptotics of a bifurcated curve obtained (the curve on which origin of a pair of periodic solutions occurs) in the space of the parameters agrees well with the results of numerical computation with all physical values of these parameters. A breakdown is made of the space of the initial data of phase variables in the field of effect of different types of periodic motion.

The dynamics and control of large flexible space structures. Part B: Development of continuum model and computer simulation

NASA Technical Reports Server (NTRS)

Bainum, P. M.; Kumar, V. K.; James, P. K.

1978-01-01

The equations of motion of an arbitrary flexible body in orbit were derived. The model includes the effects of gravity with all its higher harmonics. As a specific example, the motion of a long, slender, uniform beam in circular orbit was modelled. The example considers both the inplane and three dimensional motion of the beam in orbit. In the case of planar motion with only flexible vibrations, the pitch motion is not influenced by the elastic motion of the beam. For large values of the square of the ratio of the structural modal frequency to the orbital angular rate the elastic motion was decoupled from the pitch motion. However, for small values of the ratio and small amplitude pitch motion, the elastic motion was governed by a Hill's 3 term equation. Numerical simulation of the equation indicates the possibilities of instability for very low values of the square of the ratio of the modal frequency to the orbit angular rate. Also numerical simulations of the first order nonlinear equations of motion for a long flexible beam in orbit were performed. The effect of varying the initial conditions and the number of modes was demonstrated.

Statistics and Machine Learning based Outlier Detection Techniques for Exoplanets

NASA Astrophysics Data System (ADS)

Goel, Amit; Montgomery, Michele

2015-08-01

Architectures of planetary systems are observable snapshots in time that can indicate formation and dynamic evolution of planets. The observable key parameters that we consider are planetary mass and orbital period. If planet masses are significantly less than their host star masses, then Keplerian Motion is defined as P^2 = a^3 where P is the orbital period in units of years and a is the orbital period in units of Astronomical Units (AU). Keplerian motion works on small scales such as the size of the Solar System but not on large scales such as the size of the Milky Way Galaxy. In this work, for confirmed exoplanets of known stellar mass, planetary mass, orbital period, and stellar age, we analyze Keplerian motion of systems based on stellar age to seek if Keplerian motion has an age dependency and to identify outliers. For detecting outliers, we apply several techniques based on statistical and machine learning methods such as probabilistic, linear, and proximity based models. In probabilistic and statistical models of outliers, the parameters of a closed form probability distributions are learned in order to detect the outliers. Linear models use regression analysis based techniques for detecting outliers. Proximity based models use distance based algorithms such as k-nearest neighbour, clustering algorithms such as k-means, or density based algorithms such as kernel density estimation. In this work, we will use unsupervised learning algorithms with only the proximity based models. In addition, we explore the relative strengths and weaknesses of the various techniques by validating the outliers. The validation criteria for the outliers is if the ratio of planetary mass to stellar mass is less than 0.001. In this work, we present our statistical analysis of the outliers thus detected.

Long Term Evolution of Planetary Systems with a Terrestrial Planet and a Giant Planet

NASA Technical Reports Server (NTRS)

Georgakarakos, Nikolaos; Dobbs-Dixon, Ian; Way, Michael J.

2016-01-01

We study the long term orbital evolution of a terrestrial planet under the gravitational perturbations of a giant planet. In particular, we are interested in situations where the two planets are in the same plane and are relatively close. We examine both possible configurations: the giant planet orbit being either outside or inside the orbit of the smaller planet. The perturbing potential is expanded to high orders and an analytical solution of the terrestrial planetary orbit is derived. The analytical estimates are then compared against results from the numerical integration of the full equations of motion and we find that the analytical solution works reasonably well. An interesting finding is that the new analytical estimates improve greatly the predictions for the timescales of the orbital evolution of the terrestrial planet compared to an octupole order expansion. Finally, we briefly discuss possible applications of the analytical estimates in astrophysical problems.

The research of the coupled orbital-attitude controlled motion of celestial body in the neighborhood of the collinear libration point L1

NASA Astrophysics Data System (ADS)

Shmyrov, A.; Shmyrov, V.; Shymanchuk, D.

2017-10-01

This article considers the motion of a celestial body within the restricted three-body problem of the Sun-Earth system. The equations of controlled coupled attitude-orbit motion in the neighborhood of collinear libration point L1 are investigated. The translational orbital motion of a celestial body is described using Hill's equations of circular restricted three-body problem of the Sun-Earth system. Rotational orbital motion is described using Euler's dynamic equations and quaternion kinematic equation. We investigate the problem of stability of celestial body rotational orbital motion in relative equilibrium positions and stabilization of celestial body rotational orbital motion with proposed control laws in the neighborhood of collinear libration point L1. To study stabilization problem, Lyapunov function is constructed in the form of the sum of the kinetic energy and special "kinematic function" of the Rodriguez-Hamiltonian parameters. Numerical modeling of the controlled rotational motion of a celestial body at libration point L1 is carried out. The numerical characteristics of the control parameters and rotational motion are given.

ORBITAL MOTION OF HR 8799 b, c, d USING HUBBLE SPACE TELESCOPE DATA FROM 1998: CONSTRAINTS ON INCLINATION, ECCENTRICITY, AND STABILITY

DOE Office of Scientific and Technical Information (OSTI.GOV)

Soummer, Remi; Hagan, J. Brendan; Pueyo, Laurent

2011-11-01

HR 8799 is currently the only multiple-planet system that has been detected with direct imaging, with four giant planets of masses 7-10 M{sub Jup} orbiting at large separations (15-68 AU) from this young late A star. Orbital motion provides insight into the stability and possible formation mechanisms of this planetary system. Dynamical studies can also provide constraints on the planets' masses, which help calibrate evolutionary models, yet measuring the orbital motion is a very difficult task because the long-period orbits (50-500 yr) require long time baselines and high-precision astrometry. This paper studies the three planets HR 8799b, c, and dmore » in the archival data set of HR 8799 obtained with the Hubble Space Telescope (HST) NICMOS coronagraph in 1998. The detection of all three planets is made possible by a careful optimization of the Locally Optimized Combination of Images algorithm, and we used a statistical analysis of a large number of reduced images. This work confirms previous astrometry for planet b and presents new detections and astrometry for planets c and d. These HST images provide a ten-year baseline with the discovery images from 2008, and therefore offer a unique opportunity to constrain their orbital motion now. Recent dynamical studies of this system show the existence of a few possible stable solutions involving mean motion resonances (MMRs), where the interaction between c and d plays a major role. We study the compatibility of a few of these stable scenarios (1d:1c, 1d:2c, or 1d:2c:4d) with the new astrometric data from HST. In the hypothesis of a 1d:2c:4b MMR our best orbit fit is close to the stable solution previously identified for a three-planet system and involves low eccentricity for planet d (e{sub d} = 0.10) and moderate inclination of the system (i = 28.0 deg), assuming a coplanar system, circular orbits for b and c, and exact resonance with integer period ratios. Under these assumptions, we can place strong constraints on the inclination of the system (27.3-31.4 deg) and on the eccentricity for d e{sub d} < 0.46. Our results are robust to small departures from exact integer period ratios and consistent with previously published results based on dynamical studies for a three-planet system prior to the discovery of the fourth planet.« less

Secular resonances between bodies on close orbits II: prograde and retrograde orbits for irregular satellites

NASA Astrophysics Data System (ADS)

Li, Daohai; Christou, Apostolos A.

2017-09-01

In extending the analysis of the four secular resonances between close orbits in Li and Christou (Celest Mech Dyn Astron 125:133-160, 2016) (Paper I), we generalise the semianalytical model so that it applies to both prograde and retrograde orbits with a one-to-one map between the resonances in the two regimes. We propose the general form of the critical angle to be a linear combination of apsidal and nodal differences between the two orbits b_1 Δ π + b_2 Δ Ω, forming a collection of secular resonances in which the ones studied in Paper I are among the strongest. Test of the model in the orbital vicinity of massive satellites with physical and orbital parameters similar to those of the irregular satellites Himalia at Jupiter and Phoebe at Saturn shows that {>}20 and {>}40% of phase space is affected by these resonances, respectively. The survivability of the resonances is confirmed using numerical integration of the full Newtonian equations of motion. We observe that the lowest order resonances with b_1+|b_2|≤ 3 persist, while even higher-order resonances, up to b_1+|b_2|≥ 7, survive. Depending on the mass, between 10 and 60% of the integrated test particles are captured in these secular resonances, in agreement with the phase space analysis in the semianalytical model.

One-Dimensional Spacecraft Formation Flight Testbed for Terrestrial Charged Relative Motion Experiments

NASA Astrophysics Data System (ADS)

Seubert, Carl R.

Spacecraft operating in a desired formation offers an abundance of attractive mission capabilities. One proposed method of controlling a close formation of spacecraft is with Coulomb (electrostatic) forces. The Coulomb formation flight idea utilizes charge emission to drive the spacecraft to kilovolt-level potentials and generate adjustable, micronewton- to millinewton-level Coulomb forces for relative position control. In order to advance the prospects of the Coulomb formation flight concept, this dissertation presents the design and implementation of a unique one-dimensional testbed. The disturbances of the testbed are identified and reduced below 1 mN. This noise level offers a near-frictionless platform that is used to perform relative motion actuation with electrostatics in a terrestrial atmospheric environment. Potentials up to 30 kV are used to actuate a cart over a translational range of motion of 40 cm. A challenge to both theoretical and hardware implemented electrostatic actuation developments is correctly modeling the forces between finite charged bodies, outside a vacuum. To remedy this, studies of Earth orbit plasmas and Coulomb force theory is used to derive and propose a model of the Coulomb force between finite spheres in close proximity, in a plasma. This plasma force model is then used as a basis for a candidate terrestrial force model. The plasma-like parameters of this terrestrial model are estimated using charged motion data from fixed-potential, single-direction experiments on the testbed. The testbed is advanced to the level of autonomous feedback position control using solely Coulomb force actuation. This allows relative motion repositioning on a flat and level track as well as an inclined track that mimics the dynamics of two charged spacecraft that are aligned with the principal orbit axis. This controlled motion is accurately predicted with simulations using the terrestrial force model. This demonstrates similarities between the partial charge shielding of space-based plasmas to the electrostatic screening in the laboratory atmosphere.

Satellite capture as a restricted 2 + 2 body problem

NASA Astrophysics Data System (ADS)

Kanaan, Wafaa; Farrelly, David; Lanchares, Víctor

2018-04-01

A restricted 2 + 2 body problem is proposed as a possible mechanism to explain the capture of small bodies by a planet. In particular, we consider two primaries revolving in a circular mutual orbit and two small bodies of equal mass, neither of which affects the motion of the primaries. If the small bodies are temporarily captured in the Hill sphere of the smaller primary, they may get close enough to each other to exchange energy in such a way that one of them becomes permanently captured. Numerical simulations show that capture is possible for both prograde and retrograde orbits.

The development of optimal control laws for orbiting tethered platform systems

NASA Technical Reports Server (NTRS)

Bainum, P. M.; Woodard, S.; Juang, J.-N.

1986-01-01

A mathematical model of the open and closed loop in-orbit plane dynamics of a space platform-tethered-subsatellite system is developed. The system consists of a rigid platform from which an (assumed massless) tether is deploying (retrieving) a subsatellite from an attachment point which is, in general, offset from the platform's mass center. A Lagrangian formulation yields equations describing platform pitch, subsatellite tether-line swing, and varying tether length motions. These equations are linearized about the nominal station keeping motion. Control can be provided by both modulation of the tether tension level and by a momentum type platform-mounted device; system controllability depends on the presence of both control inputs. Stability criteria are developed in terms of the control law gains, the platform inertia ratio, and tether offset parameter. Control law gains are obtained based on linear quadratic regulator techniques. Typical transient responses of both the state and required control effort are presented.

The development of optimal control laws for orbiting tethered platform systems

NASA Technical Reports Server (NTRS)

Bainum, P. M.

1986-01-01

A mathematical model of the open and closed loop in orbit plane dynamics of a space platform-tethered-subsatellite system is developed. The system consists of a rigid platform from which an (assumed massless) tether is deploying (retrieving) a subsatellite from an attachment point which is, in general, offset from the platform's mass center. A Langrangian formulation yields equations describing platform pitch, subsatellite tetherline swing, and varying tether length motions. These equations are linearized about the nominal station keeping motion. Control can be provided by both modulation of the tether tension level and by a momentum type platform-mounted device; system controllability depends on the presence of both control inputs. Stability criteria are developed in terms of the control law gains, the platform inertia ratio, and tether offset parameter. Control law gains are obtained based on linear quadratic regulator techniques. Typical transient responses of both the state and required control effort are presented.

The Dynamics of Objects in the Inner Edgeworth Kuiper Belt

NASA Astrophysics Data System (ADS)

Jones, Daniel C.; Williams, Iwan P.; Melita, Mario D.

2005-12-01

Objects in 3:2 mean motion resonance with Neptune are protected from close encounters with Neptune by the resonance. Bodies in orbits with semi-major axis between 39.5 and about 42 AU are not protected by the resonance; indeed due to overlapping secular resonances, the eccentricities of orbits in this region are driven up so that a close encounter with Neptune becomes inevitable. It is thus expected that such orbits are unstable. The list of known Trans-Neptunian objects shows a deficiency in the number of objects in this gap compared to the 43 50 AU region, but the gap is not empty. We numerically integrate models for the initial population in the gap, and also all known objects over the age of the Solar System to determine what fraction can survive. We find that this fraction is significantly less than the ratio of the population in the gap to that in the main belt, suggesting that some mechanism must exist to introduce new members into the gap. By looking at the evolution of the test body orbits, we also determine the manner in which they are lost. Though all have close encounters with Neptune, in most cases this does not lead to ejection from the Solar System, but rather to a reduced perihelion distance causing close encounters with some or all of the other giant planets before being eventually lost from the system, with Saturn appearing to be the cause of the ejection of most of the objects.

Analysis of the orbit distortion by the use of the wavelet transform

NASA Astrophysics Data System (ADS)

Matsushita, T.; Agui, A.; Yoshigoe, A.; Takao, M.; Aoyagi, H.; Takeuchi, M.; Nakatani, T.; Tanaka, H.

2004-05-01

We have adopted matching pursuit algorithm of discrete wavelet transform (DWT) for the analysis of the beam position shift correlated with the motion of insertion device(ID). The beam position data measured by the rf beam position monitors have included high-frequency `noises' and fluctuation of background level. Precise evaluation of the electron beam position shift correlated with the motion of the ID is required for estimation of the steering magnet currents in order to suppress the closed orbit distortion (COD). The DWT is a powerful tool for frequency analysis and data processing. The analysis of DWT was applied to the beam position shift correlated with the phase motion of APPLE-2 type undulator (ID23) in SPring-8. The result of the analysis indicated that `noises' are mainly composed of the components of 50 ˜ 6.25Hz and < 0.1Hz. We carried out the data processing to remove the `noises' by the matching pursuit algorithm. Then we have succeeded in suppressing the COD within 2 μm by the use of the steering magnet currents calculated from the processed data.

Long-Lived Near-Earth Asteroid 2013 RB6

NASA Astrophysics Data System (ADS)

Emel'yanenko, V. V.; Emel'yanenko, N. Yu.

2018-01-01

The search for asteroids that maintain stable motion in the zone between the Earth and Mars has been performed. The near-Earth object 2013 RB6, which has avoided close encounters with the planets for a long period of time, has been found. Integration of the equations of motion of the object shows that its dynamical lifetime in the zone between the Earth and Mars significantly exceeds 100 Myr. 2013 RB6 moves away from orbital resonances with the planets, but is in the secular resonance ν5. Solving the question of its origin requires further observations.

Recurrence spectra of a helium atom in parallel electric and magnetic fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Dehua; Department of Mathematics and Physics, Shandong Architecture and Engineering Institute, Jinan 250014, People's Republic of China; Ding, Shiliang

2003-08-01

A model potential for the general Rydberg atom is put forward, which includes not only the Coulomb interaction potential and the core-attractive potential, but also the exchange potential between the excited electron and other electrons. Using the region-splitting consistent and iterative method, we calculated the scaled recurrence spectra of the helium atom in parallel electric and magnetic fields and the closed orbits in the corresponding classical system have also been obtained. In order to remove the Coulomb singularity of the classical motion of Hamiltonian, we implement the Kustaanheimo-Stiefel transformation, which transforms the system from a three-dimensional to a four-dimensional one.more » The Fourier-transformed spectra of the helium atom has allowed direct comparison between peaks in such a plot and the scaled action values of closed orbits. Considering the exchange potential, the number of the closed orbits increased, which led to more peaks in the recurrence spectra. The results are compared with those of the hydrogen case, which shows that the core-scattered effects and the electron exchange potential play an important role in the multielectron Rydberg atom.« less

Design of relative trajectories for in orbit proximity operations

NASA Astrophysics Data System (ADS)

Opromolla, Roberto; Fasano, Giancarmine; Rufino, Giancarlo; Grassi, Michele

2018-04-01

This paper presents an innovative approach to design relative trajectories suitable for close-proximity operations in orbit, by assigning high-level constraints regarding their stability, shape and orientation. Specifically, this work is relevant to space mission scenarios, e.g. formation flying, on-orbit servicing, and active debris removal, which involve either the presence of two spacecraft carrying out coordinated maneuvers, or a servicing/recovery spacecraft (chaser) performing monitoring, rendezvous and docking with respect to another space object (target). In the above-mentioned scenarios, an important aspect is the capability of reducing collision risks and of providing robust and accurate relative navigation solutions. To this aim, the proposed approach exploits a relative motion model relevant to two-satellite formations, and developed in mean orbit parameters, which takes the perturbation effect due to secular Earth oblateness, as well as the motion of the target along a small-eccentricity orbit, into account. This model is used to design trajectories which ensure safe relative motion, to minimize collision risks and relax control requirements, providing at the same time favorable conditions, in terms of target-chaser relative observation geometry for pose determination and relative navigation with passive or active electro-optical sensors on board the chaser. Specifically, three design strategies are proposed in the context of a space target monitoring scenario, considering as design cases both operational spacecraft and debris, characterized by highly variable shape, size and absolute rotational dynamics. The effectiveness of the proposed design approach in providing favorable observation conditions for target-chaser relative pose estimation is demonstrated within a simulation environment which reproduces the designed target-chaser relative trajectory, the operation of an active LIDAR installed on board the chaser, and pose estimation algorithms.

Casimir energy in Kerr space-time

NASA Astrophysics Data System (ADS)

Sorge, F.

2014-10-01

We investigate the vacuum energy of a scalar massless field confined in a Casimir cavity moving in a circular equatorial orbit in the exact Kerr space-time geometry. We find that both the orbital motion of the cavity and the underlying space-time geometry conspire in lowering the absolute value of the (renormalized) Casimir energy ⟨ɛvac⟩ren , as measured by a comoving observer, with respect to whom the cavity is at rest. This, in turn, causes a weakening in the attractive force between the Casimir plates. In particular, we show that the vacuum energy density ⟨ɛvac⟩ren→0 when the orbital path of the Casimir cavity comes close to the corotating or counter-rotating circular null orbits (possibly geodesic) allowed by the Kerr geometry. Such an effect could be of some astrophysical interest on relevant orbits, such as the Kerr innermost stable circular orbits, being potentially related to particle confinement (as in some interquark models). The present work generalizes previous results obtained by several authors in the weak field approximation.

On the long-period evolution of the sun-synchronous orbits

NASA Astrophysics Data System (ADS)

Kuznetsov, E. D.; Jasim, A. T.

2016-05-01

The dynamic evolution of sun-synchronous orbits at a time interval of 20 years is considered. The numerical motion simulation has been carried out using the Celestial Mechanics software package developed at the Institute of Astronomy of the University of Bern. The dependence of the dynamic evolution on the initial value of the ascending node longitude is examined for two families of sun-synchronous orbits with altitudes of 751 and 1191 km. Variations of the semimajor axis and orbit inclination are obtained depending on the initial value of the ascending node longitude. Recommendations on the selection of orbits, in which spent sun-synchronous satellites can be moved, are formulated. Minimal changes of elements over a time interval of 20 years have been observed for orbits in which at the initial time the angle between the orbit ascending node and the direction of the Sun measured along the equator have been close to 90° or 270°. In this case, the semimajor axis of the orbit is not experiencing secular perturbations arising from the satellite's passage through the Earth's shadow.

Orbit classification in an equal-mass non-spinning binary black hole pseudo-Newtonian system

NASA Astrophysics Data System (ADS)

Zotos, Euaggelos E.; Dubeibe, Fredy L.; González, Guillermo A.

2018-07-01

The dynamics of a test particle in a non-spinning binary black hole system of equal masses is numerically investigated. The binary system is modelled in the context of the pseudo-Newtonian circular restricted three-body problem, such that the primaries are separated by a fixed distance and move in a circular orbit around each other. In particular, the Paczyński-Wiita potential is used for describing the gravitational field of the two non-Newtonian primaries. The orbital properties of the test particle are determined through the classification of the initial conditions of the orbits, using several values of the Jacobi constant, in the Hill's regions of possible motion. The initial conditions are classified into three main categories: (i) bounded, (ii) escaping, and (iii) displaying close encounters. Using the smaller alignment index chaos indicator, we further classify bounded orbits into regular, sticky, or chaotic. To gain a complete view of the dynamics of the system, we define grids of initial conditions on different types of two-dimensional planes. The orbital structure of the configuration plane, along with the corresponding distributions of the escape and collision/close encounter times, allow us to observe the transition from the classical Newtonian to the pseudo-Newtonian regime. Our numerical results reveal a strong dependence of the properties of the considered basins with the Jacobi constant as well as with the Schwarzschild radius of the black holes.

KEPLER ECLIPSING BINARIES WITH STELLAR COMPANIONS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gies, D. R.; Matson, R. A.; Guo, Z.

2015-12-15

Many short-period binary stars have distant orbiting companions that have played a role in driving the binary components into close separation. Indirect detection of a tertiary star is possible by measuring apparent changes in eclipse times of eclipsing binaries as the binary orbits the common center of mass. Here we present an analysis of the eclipse timings of 41 eclipsing binaries observed throughout the NASA Kepler mission of long duration and precise photometry. This subset of binaries is characterized by relatively deep and frequent eclipses of both stellar components. We present preliminary orbital elements for seven probable triple stars amongmore » this sample, and we discuss apparent period changes in seven additional eclipsing binaries that may be related to motion about a tertiary in a long period orbit. The results will be used in ongoing investigations of the spectra and light curves of these binaries for further evidence of the presence of third stars.« less

Long-term risk analysis associated with nuclear waste disposal in space

NASA Technical Reports Server (NTRS)

Friedlander, A. L.; Davis, D. R.

1979-01-01

An assessment and verification of previous analytic results on the long term risk of earth reentry for hazardous payloads is presented. The two areas were studied: (1) stability of nominal, near-circular storage orbits in the regions between Venus and earth and between earth and Mars, and (2) probability of earth reentry for off-nominal planet-crossing orbits resulting from deployment system failures. In the first area, numerical integrations of the equations of motion are compared with stability predications based on secular perturbation theory. The agreement is good in terms of the heliocentric distances covered and the general behavior of the orbital history, although certain near-resonance situations can lead to difficulty. In the second area, a Monte Carlo simulation of orbital evolution is used and the results compared with Opik's analytic theory of planetary encounters and collision statistics, with data verified to within a close order-of-magnitude.

Orbital motion in pre-main sequence binaries

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schaefer, G. H.; Prato, L.; Simon, M.

2014-06-01

We present results from our ongoing program to map the visual orbits of pre-main sequence (PMS) binaries in the Taurus star forming region using adaptive optics imaging at the Keck Observatory. We combine our results with measurements reported in the literature to analyze the orbital motion for each binary. We present preliminary orbits for DF Tau, T Tau S, ZZ Tau, and the Pleiades binary HBC 351. Seven additional binaries show curvature in their relative motion. Currently, we can place lower limits on the orbital periods for these systems; full solutions will be possible with more orbital coverage. Five othermore » binaries show motion that is indistinguishable from linear motion. We suspect that these systems are bound and might show curvature with additional measurements in the future. The observations reported herein lay critical groundwork toward the goal of measuring precise masses for low-mass PMS stars.« less

SHAPING POINT- AND MIRROR-SYMMETRIC PROTOPLANETARY NEBULAE BY THE ORBITAL MOTION OF THE CENTRAL BINARY SYSTEM

DOE Office of Scientific and Technical Information (OSTI.GOV)

Haro-Corzo, Sinhue A. R.; Velazquez, Pablo F.; Raga, Alejandro C.

We present three-dimensional hydrodynamical simulations of a jet launched from the secondary star of a binary system inside a protoplanetary nebula. The secondary star moves around the primary in a close eccentric orbit. From the gasdynamic simulations we compute synthetic [N II] lambda 6583 emission maps. Different jet axis inclinations with respect to the orbital plane, as well as different orientations of the flow with respect to the observer, are considered. For some parameter combinations, we obtain structures that show point- or mirror-symmetric morphologies depending on the orientation of the flow with respect to the observer. Furthermore, our models canmore » explain some of the emission distribution asymmetries that are summarized in the classification given by Soker and Hadar.« less

STABLE CONIC-HELICAL ORBITS OF PLANETS AROUND BINARY STARS: ANALYTICAL RESULTS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Oks, E.

2015-05-10

Studies of planets in binary star systems are especially important because it was estimated that about half of binary stars are capable of supporting habitable terrestrial planets within stable orbital ranges. One-planet binary star systems (OBSS) have a limited analogy to objects studied in atomic/molecular physics: one-electron Rydberg quasimolecules (ORQ). Specifically, ORQ, consisting of two fully stripped ions of the nuclear charges Z and Z′ plus one highly excited electron, are encountered in various plasmas containing more than one kind of ion. Classical analytical studies of ORQ resulted in the discovery of classical stable electronic orbits with the shape ofmore » a helix on the surface of a cone. In the present paper we show that despite several important distinctions between OBSS and ORQ, it is possible for OBSS to have stable planetary orbits in the shape of a helix on a conical surface, whose axis of symmetry coincides with the interstellar axis; the stability is not affected by the rotation of the stars. Further, we demonstrate that the eccentricity of the stars’ orbits does not affect the stability of the helical planetary motion if the center of symmetry of the helix is relatively close to the star of the larger mass. We also show that if the center of symmetry of the conic-helical planetary orbit is relatively close to the star of the smaller mass, a sufficiently large eccentricity of stars’ orbits can switch the planetary motion to the unstable mode and the planet would escape the system. We demonstrate that such planets are transitable for the overwhelming majority of inclinations of plane of the stars’ orbits (i.e., the projections of the planet and the adjacent start on the plane of the sky coincide once in a while). This means that conic-helical planetary orbits at binary stars can be detected photometrically. We consider, as an example, Kepler-16 binary stars to provide illustrative numerical data on the possible parameters and the stability of the conic-helical planetary orbits, as well as on the transitability. Then for the general case, we also show that the power of the gravitational radiation due to this planet can be comparable or even exceed the power of the gravitational radiation due to the stars in the binary. This means that in the future, with a progress of gravitational wave detectors, the presence of a planet in a conic-helical orbit could be revealed by the noticeably enhanced gravitational radiation from the binary star system.« less

Evanescent radiation, quantum mechanics and the Casimir effect

NASA Technical Reports Server (NTRS)

Schatten, Kenneth H.

1989-01-01

An attempt to bridge the gap between classical and quantum mechanics and to explain the Casimir effect is presented. The general nature of chaotic motion is discussed from two points of view: the first uses catastrophe theory and strange attractors to describe the deterministic view of this motion; the underlying framework for chaos in these classical dynamic systems is their extreme sensitivity to initial conditions. The second interpretation refers to randomness associated with probabilistic dynamics, as for Brownian motion. The present approach to understanding evanescent radiation and its relation to the Casimir effect corresponds to the first interpretation, whereas stochastic electrodynamics corresponds to the second viewpoint. The nonlinear behavior of the electromagnetic field is also studied. This well-understood behavior is utilized to examine the motions of two orbiting charges and shows a closeness between the classical behavior and the quantum uncertainty principle. The evanescent radiation is used to help explain the Casimir effect.

The structure of non-hierarchical triple system stability regions

NASA Astrophysics Data System (ADS)

Martynova, A. I.; Orlov, V. V.; Rubinov, A. V.

2009-08-01

A detailed study of the two-dimensional initial conditions region section in the planar three-body problem is performed. The initial conditions for the three well-known stable periodic orbits (the Schubart’s orbit, the Broucke’s orbit and the eight-like orbit) belong to this section. Continuous stability regions (for the fixed integration interval) generated by these periodic orbits are found. Zones of the quick stability violation are outlined. The analysis of some concrete trajectories coming from various stability regions is performed. In particular, trajectories possessing varying number of “eights” formed by moving triple system components are discovered. Orbits with librations are also found. The new periodic orbit originated from the zone siding with the Schubart’s orbit region is discovered. This orbit has reversibility points (each of the outer bodies possess a reversibility point) and two points of close double approach of the central body to each of the outer bodies. The influence of the numerical integration accuracy on the results is studied. The stability regions structure is preserved during calculations with different values of the precision parameter, numerical integration methods and regularization algorithms of the equations of motion.

NEMESIS: Near Encounters with M-dwarfs from an Enormous Sample and Integrated Simulations

NASA Astrophysics Data System (ADS)

Bochanski, John J.; Sanderson, R. E.; West, A. A.; Burgasser, A. J.

2011-01-01

The latest spectroscopic catalog of M dwarfs identified in the Sloan Digital Sky Survey provides radial velocities, proper motions and distances for nearly 40,000 low-mass stars. Using the full 6D phase space coverage and a realistic Galactic potential, we calculated orbits for each star in the sample. The sample consists of stars from both the thin and thick disks, and the orbital properties between the two groups are compared. We also examine trends in orbital properties with spectroscopic features, such as Balmer emission and molecular bands, that should correlate with age. In addition, we have identified a number of stars that will pass very close to the Sun within the next 1000 Myrs. These stars form the "Nemesis" family of orbits. Potential encounters with these stars could have a significant impact on orbits of Oort Cloud and Kuiper Belt members as well as the planets. We comment on the probability of a catastrophic encounter within the next 1000 Myrs.

Continued Kinematic and Photometric Investigations of Hierarchical Solar-type Multiple Star Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Roberts, Lewis C. Jr.; Marinan, Anne D.; Tokovinin, Andrei

2017-03-01

We observed 15 of the solar-type binaries within 67 pc of the Sun previously observed by the Robo-AO system in the visible, with the PHARO near-infrared camera and the PALM-3000 adaptive optics system on the 5 m Hale telescope. The physical status of the binaries is confirmed through common proper motion and detection of orbital motion. In the process, we detected a new candidate companion to HIP 95309. We also resolved the primary of HIP 110626 into a close binary, making that system a triple. These detections increase the completeness of the multiplicity survey of the solar-type stars within 67more » pc of the Sun. Combining our observations of HIP 103455 with archival astrometric measurements and RV measurements, we are able to compute the first orbit of HIP 103455, showing that the binary has a 68 year period. We place the components on a color–magnitude diagram and discuss each multiple system individually.« less

Slow Orbit Feedback at the ALS Using Matlab

DOE Office of Scientific and Technical Information (OSTI.GOV)

Portmann, G.

1999-03-25

The third generation Advanced Light Source (ALS) produces extremely bright and finely focused photon beams using undulatory, wigglers, and bend magnets. In order to position the photon beams accurately, a slow global orbit feedback system has been developed. The dominant causes of orbit motion at the ALS are temperature variation and insertion device motion. This type of motion can be removed using slow global orbit feedback with a data rate of a few Hertz. The remaining orbit motion in the ALS is only 1-3 micron rms. Slow orbit feedback does not require high computational throughput. At the ALS, the globalmore » orbit feedback algorithm, based on the singular valued decomposition method, is coded in MATLAB and runs on a control room workstation. Using the MATLAB environment to develop, test, and run the storage ring control algorithms has proven to be a fast and efficient way to operate the ALS.« less

Visual/infrared interferometry of Orion Trapezium stars: preliminary dynamical orbit and aperture synthesis imaging of the θ1 Orionis C system

NASA Astrophysics Data System (ADS)

Kraus, S.; Balega, Y. Y.; Berger, J.-P.; Hofmann, K.-H.; Millan-Gabet, R.; Monnier, J. D.; Ohnaka, K.; Pedretti, E.; Preibisch, Th.; Schertl, D.; Schloerb, F. P.; Traub, W. A.; Weigelt, G.

2007-05-01

Context: Located in the Orion Trapezium cluster, θ^1Ori C is one of the youngest and nearest high-mass stars (O5-O7) known. Besides its unique properties as a magnetic rotator, the system is also known to be a close binary. Aims: By tracing its orbital motion, we aim to determine the orbit and dynamical mass of the system, yielding a characterization of the individual components and, ultimately, also new constraints for stellar evolution models in the high-mass regime. Furthermore, a dynamical parallax can be derived from the orbit, providing an independent estimate for the distance of the Trapezium cluster. Methods: Using new multi-epoch visual and near-infrared bispectrum speckle interferometric observations obtained at the BTA 6 m telescope, and IOTA near-infrared long-baseline interferometry, we traced the orbital motion of the θ^1Ori C components over the interval 1997.8 to 2005.9, covering a significant arc of the orbit. Besides fitting the relative position and the flux ratio, we applied aperture synthesis techniques to our IOTA data to reconstruct a model-independent image of the θ^1Ori C binary system. Results: The orbital solutions suggest a highly eccentricity (e≈0.91) and short-period (P≈10.9 yrs) orbit. As the current astrometric data only allows rather weak constraints on the total dynamical mass, we present the two best-fit orbits. Of these two, the one implying a system mass of 48 M⊙ and a distance of 434 pc to the Trapezium cluster can be favored. When also taking the measured flux ratio and the derived location in the HR-diagram into account, we find good agreement for all observables, assuming a spectral type of O5.5 for θ^1Ori C1 (M = 34.0 M⊙, T_eff = 39 900 K) and O9.5 for C2 (M = 15.5 M⊙, T_eff = 31 900 K). Using IOTA, we also obtained first interferometric observations on θ^1Ori D, finding some evidence for a resolved structure, maybe by a faint, close companion. Conclusions: We find indications that the companion C2 is massive itself, which makes it likely that its contribution to the intense UV radiation field of the Trapezium cluster is non-negligible. Furthermore, the high eccentricity of the preliminary orbit solution predicts a very small physical separation during periastron passage (˜1.5 AU, next passage around 2007.5), suggesting strong wind-wind interaction between the two O stars.

Radiation Pressure, Poynting-Robertson Drag, and Solar Wind Drag in the Restricted Three-Body Problem

NASA Technical Reports Server (NTRS)

Liou, Jer-Chyi; Zook, Herbert A.; Jackson, A. A.

1995-01-01

In this paper, we examine the effects of radiation pressure, Poynting-Robertson (PR) drag, and solar wind drag on dust grains trapped in mean motion resonances with the Sun and Jupiter in the restricted (negligible dust mass) three-body Problem. We especially examine the evolution of dust grains in the 1:1 resonance. As a first step, the Sun and Jupiter are idealized to both be in circular orbit about a common center of mass (circular restricted three-body problem). From the equation of motion of the dust particle in the rotating reference frame, the drag-induced time rate of change of its Jacobi "constant," C, is then derived and expressed in spherical coordinates. This new mathematical expression in spherical coordinates shows that C, in the 1:1 resonance, both oscillates and secularly increases with increasing time. The new expression gives rise to an easy understanding of how an orbit evolves when the radiation force and solar wind drag are included. All dust grain orbits are unstable in time when PR and solar wind drag are included in the Sun-Jupiter-dust system. Tadpole orbits evolve into horseshoe orbits; and these orbits continuously expand in size to lead to close encounters with Jupiter. Permanent trapping is impossible. Orbital evolutions of a dust grain trapped in the 1:1 resonance in the planar circular, an inclined case, an eccentric case, and the actual Sun-Jupiter case are numerically simulated and compared with each other and show grossly similar time behavior. Resonances other than 1:1 are also explored with the new expression. Stable exterior resonance trapping may be possible under certain conditions. One necessary condition for such a trap is derived. Trapping in interior resonances is shown to be always unstable.

Orbital theory in terms of KS elements with luni-solar perturbations

NASA Astrophysics Data System (ADS)

Sellamuthu, Harishkumar; Sharma, Ram

2016-07-01

Precise orbit computation of Earth orbiting satellites is essential for efficient mission planning of planetary exploration, navigation and satellite geodesy. The third-body perturbations of the Sun and the Moon predominantly affect the satellite motion in the high altitude and elliptical orbits, where the effect of atmospheric drag is negligible. The physics of the luni-solar gravity effect on Earth satellites have been studied extensively over the years. The combined luni-solar gravitational attraction will induce a cumulative effect on the dynamics of satellite orbits, which mainly oscillates the perigee altitude. Though accurate orbital parameters are computed by numerical integration with respect to complex force models, analytical theories are highly valued for the manifold of solutions restricted to relatively simple force models. During close approach, the classical equations of motion in celestial mechanics are almost singular and they are unstable for long-term orbit propagation. A new singularity-free analytical theory in terms of KS (Kustaanheimo and Stiefel) regular elements with respect to luni-solar perturbation is developed. These equations are regular everywhere and eccentric anomaly is the independent variable. Plataforma Solar de Almería (PSA) algorithm and a Fourier series algorithm are used to compute the accurate positions of the Sun and the Moon, respectively. Numerical studies are carried out for wide range of initial parameters and the analytical solutions are found to be satisfactory when compared with numerically integrated values. The symmetrical nature of the equations allows only two of the nine equations to be solved for computing the state vectors and the time. Only a change in the initial conditions is required to solve the other equations. This theory will find multiple applications including on-board software packages and for mission analysis purposes.

Scalar self-force for highly eccentric equatorial orbits in Kerr spacetime

NASA Astrophysics Data System (ADS)

Thornburg, Jonathan; Wardell, Barry

2017-04-01

If a small "particle" of mass μ M (with μ ≪1 ) orbits a black hole of mass M , the leading-order radiation-reaction effect is an O (μ2) "self-force" acting on the particle, with a corresponding O (μ ) "self-acceleration" of the particle away from a geodesic. Such "extreme-mass-ratio inspiral" systems are likely to be important gravitational-wave sources for future space-based gravitational-wave detectors. Here we consider the "toy model" problem of computing the self-force for a scalar-field particle on a bound eccentric orbit in Kerr spacetime. We use the Barack-Golbourn-Vega-Detweiler effective-source regularization with a 4th-order puncture field, followed by an ei m ϕ ("m -mode") Fourier decomposition and a separate time-domain numerical evolution in 2 +1 dimensions for each m . We introduce a finite worldtube that surrounds the particle worldline and define our evolution equations in a piecewise manner so that the effective source is only used within the worldtube. Viewed as a spatial region, the worldtube moves to follow the particle's orbital motion. We use slices of constant Boyer-Lindquist time in the region of the particle's motion, deformed to be asymptotically hyperboloidal and compactified near the horizon and J+ . Our numerical evolution uses Berger-Oliger mesh refinement with 4th-order finite differencing in space and time. Our computational scheme allows computation for highly eccentric orbits and should be generalizable to orbital evolution in the future. Our present implementation is restricted to equatorial geodesic orbits, but this restriction is not fundamental. We present numerical results for a number of test cases with orbital eccentricities as high as 0.98. In some cases we find large oscillations ("wiggles") in the self-force on the outgoing leg of the orbit shortly after periastron passage; these appear to be caused by the passage of the orbit through the strong-field region close to the background Kerr black hole.

Discovery, Orbit and Orbital Evolution of the Distant Object (463368) 2012 VU85

NASA Astrophysics Data System (ADS)

Wlodarczyk, I.; Černis, K.; Boyle, R. P.

2017-03-01

We present the discovery and time evolution of orbital elements of the distant Centaur-type object (463368) 2012 VU85. From all 2135 distant objects listed in the Minor Planet Center we select all 347 numbered distant object and integrate their equations of motion in the 1 Gyr forward and backward integration. The asteroid (463368) 2012 VU85 lies on the border of the group of 347 distant objects, which have a semimajor axis about 44 a.u., eccentricity 0.1 and inclination between 0° and 30°. We show that after 1 Gyr of forward integration, about half of the objects are expelled from the Solar System, \\ie their median lifetime is about 1 Gyr. We note that the long-lived distant objects are mainly located between the regions where Neptune controls aphelia of asteroids and the asteroids are in the mean motion resonance 2/3 with Neptune. We find eight almost regular approaches of clones of the asteroid (463368) 2012 VU85 to Neptune and several generally shorter in time regular approaches to Uranus. For other outer planets we did not detect any approaches below 5 a.u. for a period of 15 000 yr in forward and backward integrations. In our calculations we find eight episodes, each lasting about 3000 yr when the value of inclination oscillates around its average. These changes look similar to the changes of semimajor axis during the occurrence of orbital mean motion resonance with a planet. We find that half of the clones of the asteroid (463368) 2012 VU85 remain in the Solar System for a forward integration of 44 Myr, and for a backward integration of 34 Myr. This is a significantly shorter escape time as compared to the group of distant objects. Almost all long-lived clones have value of Tisserand parameter with respect to Neptune smaller than 3 during the whole 1 Gyr forward and backward integrations. This implies that there are several clones of the asteroid (463368) 2012 VU85 that cross the orbits of Neptune and Uranus. We find many orbital mean motion resonances lasting up to several Myr in the motion of the asteroid (463368) 2012 VU85. According to our computations the presence of the Kozai resonance protects the asteroid from the close approaches with Uranus and Neptune. The Lyapunov time for the asteroid (463368) 2012 VU85 is equal to 4260 years.

Stable Orbits in the Didymos Binary Asteroid System - Useful Platforms for Exploration

NASA Astrophysics Data System (ADS)

Damme, Friedrich; Hussmann, Hauke; Wickhusen, Kai; Enrico, Mai; Oberst, Jürgen

2016-04-01

We have analyzed particle motion in binary asteroid systems to search for stable orbits. In particular, we studied the motion of particles near the asteroid 1996 GT (Didymos), proposed as a target for the AIDA mission. The combined gravity fields of the odd-shaped rotating objects moving about each other are complex. In addition, orbiting spacecraft or dust particles are affected by radiation pressure, possibly exceeding the faint gravitational forces. For the numerical integrations, we adopt parameters for size, shape, and rotation from telescopic observations. To simulate the effect of radiation pressure during a spacecraft mission, we apply a spacecraft wing-box shape model. Integrations were carried out beginning in near-circular orbits over 11 days, during which the motion of the particles were examined. Most orbits are unstable with particles escaping quickly or colliding with the asteroid bodies. However, with carefully chosen initial positions, we found stable motion (in the orbiting plane of the secondary) associated with the Lagrangian points (L4 and L5), in addition to horseshoe orbits, where particles move from one of the Lagrangian point to the other. Finally, we examined orbits in 1:2 resonances with the motion of the orbital period of the secondary. Stable conditions depend strongly on season caused by the inclination of the mutual orbit plane with respect to Didymos solar orbit. At larger distance from the asteroid pair, we find the well-known terminator orbits where gravitational attraction is balanced against radiation pressure. Stable orbits and long motion arcs are useful for long tracking runs by radio or Laser instruments and are well-suited for modelling of the ephemerides of the asteroid pair and gravity field mapping. Furthermore, these orbits may be useful as observing posts or as platforms for approach. These orbits may also represent traps for dust particles, an opportunity for dust collection - or possibly a hazard to spacecraft operation.

Orbit classification in an equal-mass non-spinning binary black hole pseudo-Newtonian system

NASA Astrophysics Data System (ADS)

Zotos, Euaggelos E.; Dubeibe, F. L.; González, Guillermo A.

2018-04-01

The dynamics of a test particle in a non-spinning binary black hole system of equal masses is numerically investigated. The binary system is modeled in the context of the pseudo-Newtonian circular restricted three-body problem, such that the primaries are separated by a fixed distance and move in a circular orbit around each other. In particular, the Paczyński-Wiita potential is used for describing the gravitational field of the two non-Newtonian primaries. The orbital properties of the test particle are determined through the classification of the initial conditions of the orbits, using several values of the Jacobi constant, in the Hill's regions of possible motion. The initial conditions are classified into three main categories: (i) bounded, (ii) escaping and (iii) displaying close encounters. Using the smaller alignment index (SALI) chaos indicator, we further classify bounded orbits into regular, sticky or chaotic. To gain a complete view of the dynamics of the system, we define grids of initial conditions on different types of two-dimensional planes. The orbital structure of the configuration plane, along with the corresponding distributions of the escape and collision/close encounter times, allow us to observe the transition from the classical Newtonian to the pseudo-Newtonian regime. Our numerical results reveal a strong dependence of the properties of the considered basins with the Jacobi constant as well as with the Schwarzschild radius of the black holes.

Mercury in Retrograde: Shaking Up the Study of Orbital Motion with Kinesthetic Learning

NASA Astrophysics Data System (ADS)

DeStefano, Paul; Allen, Thomas; Widenhorn, Ralf

2018-06-01

We are investigating the use of kinesthetic activities to teach the orbital motion of planets at the introductory astronomy level. In addition to breaking the monotony of traditional classroom settings, kinesthetic activities can allow novel connections to form between the student and the material, as established in a recent study. In our example active learning activity, two students walk along predetermined paths in the classroom, simulating the dynamics of any two real or fictional bodies in orbital motion about a common object. Each student carries a short-range, local positioning device that records its 2D position, continuously. The position data from both devices are collected on a single computer. After acquisition, the data can be used to highlight interesting features of orbital dynamics. For example, we demonstrate a particular transformation of the data that shows apparent retrograde motion arising directly from the relative motion of two bodies orbiting a common object. This activity provides students with the opportunity to observe interesting orbital dynamics on a human scale.

The Orbital Evolution of Near-Earth Asteroid 3753

NASA Astrophysics Data System (ADS)

Wiegert, Paul A.; Innanen, Kimmo A.; Mikkola, Seppo

1998-06-01

Asteroid 3753 (1986 TO) is in a 1:1 mean motion resonance with Earth, on a complex horseshoe-type orbit. Numerical experiments are performed to determine its medium-term stability and the means by which it may have entered its current orbit. Though 3753 moves primarily under the influence of the Sun and Earth, the giant planets (and Jupiter especially) play an important role by influencing, through torque-induced precession, the position of the asteroid's nodes. Variations in the nodal distance strongly affect the interaction of 3753 with Earth and may change or destroy the horseshoe-like behavior currently seen. This precession of the nodes provides a mechanism for placing minor planets into, or removing them from, a variety of horseshoe-type orbits. The chaotic nature of this asteroid's orbit makes predictions difficult on timescales longer than its Lyapunov time (~150 yr); therefore, ensembles of particles on orbits near that of 3753 are considered. The asteroid has a high probability of passing close to Venus and/or Mars on 10^4 yr timescales, pointing to a dynamical age much shorter than that of the solar system.

The structure of motion in a 4-component galaxy mass model

NASA Astrophysics Data System (ADS)

Caranicolas, N. D.

1996-03-01

We use a composite galaxy model consisting of a disk-halo, bulge, nucleus and dark-halo components in order to investigate the motion of stars in ther-z plane. It is observed that high angular momentum stars move in regular orbits. The majority of orbits are box orbits. There are also banana-like orbits. For a given value of energy, only a fraction of the low angular momentum stars — those going near the nucleus — show chaotic motion while the rest move in regular orbits. Again one observes the above two kinds of orbits. In addition to the above one can also see orbits with the characteristics of the 2/3 and 3/4 resonance. It is also shown that, in the absence of the bulge component, the area of chaotic motion in the surface of section increases, significantly. This suggests that a larger number of low angular momentum stars are in chaotic orbits in galaxies with massive nuclei and no bulge components.

a Numerical Study of Close Approaches for a Cloud of Debris Considering Atmospheric Drag and Lift

NASA Astrophysics Data System (ADS)

Gomes, Vivian; Golebiewska, Justyna; Prado, Antonio

The present paper study close approaches between a group of debris and a planet. The dynamical model considers the atmosphere of the planet, both in terms of drag as well as lift. This cloud is created during the passage of the spacecraft by the atmosphere of the planet, which is the responsible by the explosion of the spacecraft. The dynamical system is compos by the planet, the Sun, and the spacecraft, which explodes and becomes a cloud of debris. The planet and the Sun are in circular planar orbits. The equations of motion are the ones of the circular planar restricted three-body problem with the addition of the forces given by the atmospheric: drag and lift. The planet Jupiter is used for the numerical simulations. The initial conditions of the spacecraft and the debris are specified at the periapsis, which is the point where the explosion occurs. The equations of motion are numerically integrated forward in time for each particle, until a point where the particle is at a distance that can be considered far enough from the planet and it is possible to disregard the effects of the planet and consider the Sun-particle as a two-body system. Then we compute the velocity, energy and angular momentum after the passage by the planet, for each particle, based in the two-body celestial mechanics. From those results, the eccentricity and the semi-major axis of each particle can be obtained. Then, the orbit of the spacecraft is integrated backwards in time, as a single body. The difference from the usual close approaches technique is the presence of the atmosphere of the planet, which generates a drag and a lift forces in the spacecraft, which causes the explosion and modifies the trajectories of the debris generated by the explosion. The primary objective of the present paper is to map the modifications of the orbits of the debris that compose the cloud due to the close approach with the planet. Emphasis is given to map the orbital parameters of the debris after the close approach with the planet. Then, the effects are compared with the same maneuvers performed without the inclusion of the atmosphere. This type of research is useful, because it helps to obtain the size and density of the cloud of debris after the passage, as a function of time. That information has impact on the evaluations of the risks that spacecrafts suffer when passing by shorter distances from this cloud.

Orbital motions of bubbles in an acoustic field

NASA Astrophysics Data System (ADS)

Shirota, Minori; Yamashita, Ko; Inamura, Takao

2012-09-01

This experimental study aims to clarify the mechanism of orbital motion of two oscillating bubbles in an acoustic field. Trajectory of the orbital motion on the wall of a spherical levitator was observed using a high-speed video camera. Because of a good repeatability in volume oscillation of bubbles, we were also able to observe the radial motion driven at 24 kHz by stroboscopic like imaging technique. The orbital motions of bubbles raging from 0.13 to 0.18 mm were examined with different forcing amplitude and in different viscous oils. As a result, we found that pairs of bubbles revolve along an elliptic orbit around the center of mass of the bubbles. We also found that the two bubbles perform anti-phase radial oscillation. Although this radial oscillation should result in a repulsive secondary Bjerknes force, the bubbles kept a constant separate distance of about 1 mm, which indicates the existence of centripetal primary Bjerknes force.

Calculation of precision satellite orbits with nonsingular elements /VOP formulation/

NASA Technical Reports Server (NTRS)

Velez, C. E.; Cefola, P. J.; Long, A. C.; Nimitz, K. S.

1974-01-01

Review of some results obtained in an effort to develop efficient, high-precision trajectory computation processes for artificial satellites by optimum selection of the form of the equations of motion of the satellite and the numerical integration method. In particular, the matching of a Gaussian variation-of-parameter (VOP) formulation is considered which is expressed in terms of equinoctial orbital elements and partially decouples the motion of the orbital frame from motion within the orbital frame. The performance of the resulting orbit generators is then compared with the popular classical Cowell/Gauss-Jackson formulation/integrator pair for two distinctly different orbit types - namely, the orbit of the ATS satellite at near-geosynchronous conditions and the near-circular orbit of the GEOS-C satellite at 1000 km.

The orbital mechanics of flight mechanics

NASA Technical Reports Server (NTRS)

Dunning, R. S.

1973-01-01

A reference handbook on modern dynamic orbit theory is presented. Starting from the most basic inverse-square law, the law of gravity for a sphere is developed, and the motion of point masses under the influence of a sphere is considered. The reentry theory and the orbital theory are discussed along with the relative motion between two bodies in orbit about the same planet. Relative-motion equations, rectangular coordinates, and the mechanics of simple rigid bodies under the influence of a gravity gradient field are also discussed.

Star-planet interactions. IV. Possibility of detecting the orbit-shrinking of a planet around a red giant

NASA Astrophysics Data System (ADS)

Meynet, Georges; Eggenberger, Patrick; Privitera, Giovanni; Georgy, Cyril; Ekström, Sylvia; Alibert, Yann; Lovis, Christophe

2017-06-01

The surface rotations of some red giants are so fast that they must have been spun up by tidal interaction with a close companion, either another star, a brown dwarf, or a planet. We focus here on the case of red giants that are spun up by tidal interaction with a planet. When the distance between the planet and the star decreases, the spin period of the star decreases, the orbital period of the planet decreases, and the reflex motion of the star increases. We study the change rate of these three quantities when the circular orbit of a planet of 15 MJ that initially orbits a 2 M⊙ star at 1 au shrinks under the action of tidal forces during the red giant phase. We use stellar evolution models coupled with computations of the orbital evolution of the planet, which allows us to follow the exchanges of angular momentum between the star and the orbit in a consistent way. We obtain that the reflex motion of the red giant star increases by more than 1 m s-1 per year in the last 40 yr before the planet engulfment. During this phase, the reflex motion of the star is between 660 and 710 m s-1. The spin period of the star increases by more than about 10 min per year in the last 3000 yr before engulfment. During this period, the spin period of the star is shorter than 0.7 yr. During this same period, the variation in orbital period, which is shorter than 0.18 yr, is on the same order of magnitude. Changes in reflex-motion and spin velocities are very small and thus most likely out of reach of being observed. The most promising way of detecting this effect is through observations of transiting planets, that is, through changes of the beginning or end of the transit. For the relatively long orbital periods expected around red giants, long observing runs of typically a few years are needed. Interesting star-planet systems that currently are in this stage of orbit-shrinking would be red giants with fast rotation (above typically 4-5 km s-1), a low surface gravity (log g lower than 2), and having a planet at a distance typically smaller than about 0.4-1 au, depending on log g. A space mission like PLATO might be of great interest for detecting planets that are on the verge of being engulfed by red giants. The discovery of a few systems, even only one, would provide very interesting clues about the physics of tidal interaction between a red giant and a planet.

Periastron shifts of stellar orbits near the Galactic Center

NASA Astrophysics Data System (ADS)

Rubilar, G. F.; Eckart, A.

2001-07-01

The presence of a 2.9+/-0.4 million solar mass object in the central stellar cluster of the Milky Way has recently been demonstrated via measurements of the stellar proper motions and radial velocities. This mass is located at the position of the compact radio source Sagittarius A* (Sgr A*) at a distance of Ro=8.0 kpc and is most likely present in the form of a massive black hole (BH). Some of the stars have a projected distance to Sgr A* of <=0.005 pc and have proper motion velocities of up to 1400 km s-1. Recent measurements indicate that their orbits show significant curvatures indicating that the stars indeed orbit the central compact object. Detailed measurements of the stellar orbits close to Sgr A* will allow us to precisely determine the distribution of this mass. With an increased point source sensitivity due to the combination of large telescope apertures, adaptive optics, and - in the very near future - NIR interferometry it is likely that stars with orbital time scales of the order of one year will be detected. Theses sources, however, will most likely not be on simple Keplerian orbits. The effects of measurable prograde relativistic and retrograde Newtonian periastron shifts will result in rosetta shaped orbits. A substantial Newtonian periastron rotation can already be expected if only a few percent of the central mass are extended. We discuss the conditions under which an extended mass can (over-) compensate the relativistic periastron shift. We also demonstrate that measuring a single periastron shift is not sufficient to determine the distribution of an extended mass component. A periastron shift will allow us to determine the inclination of the stellar orbits and to derive inclination corrected shift values. These have to be acquired for three stars on orbits with different energy or angular momentum in order to unambiguously solve for the compactness, extent and shape of any extended mass contribution.

Relative motion of orbiting satellites

NASA Technical Reports Server (NTRS)

Eades, J. B., Jr.

1972-01-01

The relative motion problem is analyzed, as a linearized case, and as a numerically determined solution to provide a time history of the geometries representing the motion state. The displacement history and the hodographs for families of solutions are provided, analytically and graphically, to serve as an aid to understanding this problem area. Linearized solutions to relative motion problems of orbiting particles are presented for the impulsive and fixed thrust cases. Second order solutions are described to enhance the accuracy of prediction. A method was developed to obtain accurate, numerical solutions to the intercept and rendezvous problem; and, special situations are examined. A particular problem related to relative motions, where the motion traces develop a cusp, is examined in detail. This phenomenon is found to be dependent on a particular relationship between orbital eccentricity and the inclination between orbital planes. These conditions are determined, and, example situations are presented and discussed.

Proceedings from the 2nd International Symposium on Formation Flying Missions and Technologies

NASA Technical Reports Server (NTRS)

2004-01-01

Topics discussed include: The Stellar Imager (SI) "Vision Mission"; First Formation Flying Demonstration Mission Including on Flight Nulling; Formation Flying X-ray Telescope in L2 Orbit; SPECS: The Kilometer-baseline Far-IR Interferometer in NASA's Space Science Roadmap Presentation; A Tight Formation for Along-track SAR Interferometry; Realization of the Solar Power Satellite using the Formation Flying Solar Reflector; SIMBOL-X : Formation Flying for High-Energy Astrophysics; High Precision Optical Metrology for DARWIN; Close Formation Flight of Micro-Satellites for SAR Interferometry; Station-Keeping Requirements for Astronomical Imaging with Constellations of Free-Flying Collectors; Closed-Loop Control of Formation Flying Satellites; Formation Control for the MAXIM Mission; Precision Formation Keeping at L2 Using the Autonomous Formation Flying Sensor; Robust Control of Multiple Spacecraft Formation Flying; Virtual Rigid Body (VRB) Satellite Formation Control: Stable Mode-Switching and Cross-Coupling; Electromagnetic Formation Flight (EMFF) System Design, Mission Capabilities, and Testbed Development; Navigation Algorithms for Formation Flying Missions; Use of Formation Flying Small Satellites Incorporating OISL's in a Tandem Cluster Mission; Semimajor Axis Estimation Strategies; Relative Attitude Determination of Earth Orbiting Formations Using GPS Receivers; Analysis of Formation Flying in Eccentric Orbits Using Linearized Equations of Relative Motion; Conservative Analytical Collision Probabilities for Orbital Formation Flying; Equations of Motion and Stability of Two Spacecraft in Formation at the Earth/Moon Triangular Libration Points; Formations Near the Libration Points: Design Strategies Using Natural and Non-Natural Ares; An Overview of the Formation and Attitude Control System for the Terrestrial Planet Finder Formation Flying Interferometer; GVE-Based Dynamics and Control for Formation Flying Spacecraft; GNC System Design for a New Concept of X-Ray Distributed Telescope; GNC System for the Deployment and Fine Control of the DARWIN Free-Flying Interferometer; Formation Algorithm and Simulation Testbed; and PLATFORM: A Formation Flying, RvD and Robotic Validation Test-bench.

Resonances as the general cause of the outbursts in the symbiotic system AG Draconis

NASA Astrophysics Data System (ADS)

Gális, R.; Hric, L.; Friedjung, M.; Petrík, K.

1999-08-01

The general behaviour of the symbiotic system AG Dra is studied in the context of the long-term photometry monitoring and radial velocity analysis. Period analysis of the data gave two values of periods, 549fd73 +/- 1fd59 and 355fd27 +/- 1fd82 days for orbital motion and pulsations of cool giant respectively. The new orbital elements have been determined as well as the new orbital and pulsation ephemerides respectively. The ratio of the orbital to the pulsation period is actually very close to 14/9, so resonance might occur. We suggested, that this is the general cause of the recurrence time of the active stages. The pulsations of the cool component are very probably non-radial, so accretion by the white dwarf is particularly high when the material ejected due to the pulsations, is ejected in certain directions with respect to the line joining the two stars. The manifestations of this phenomena are the observed outbursts themselves.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Winn, Joshua N.; Albrecht, Simon; Johnson, John Asher

We show that the exoplanet HAT-P-7b has an extremely tilted orbit, with a true angle of at least 86 deg. with respect to its parent star's equatorial plane, and a strong possibility of retrograde motion. We also report evidence for an additional planet or companion star. The evidence for the unparalleled orbit and the third body is based on precise observations of the star's apparent radial velocity (RV). The anomalous RV due to rotation (the Rossiter-McLaughlin effect) was found to be a blueshift during the first half of the transit and a redshift during the second half, an inversion ofmore » the usual pattern, implying that the angle between the sky-projected orbital and stellar angular momentum vectors is 182.{sup 0}5 +- 9.{sup 0}4. The third body is implicated by excess RV variation of the host star over 2 yr. Some possible explanations for the tilted orbit of HAT-P-7b are a close encounter with another planet, the Kozai effect, and resonant capture by an inward-migrating outer planet.« less

Orbital Decay in Binaries with Evolved Stars

NASA Astrophysics Data System (ADS)

Sun, Meng; Arras, Phil; Weinberg, Nevin N.; Troup, Nicholas; Majewski, Steven R.

2018-01-01

Two mechanisms are often invoked to explain tidal friction in binary systems. The ``dynamical tide” is the resonant excitation of internal gravity waves by the tide, and their subsequent damping by nonlinear fluid processes or thermal diffusion. The ``equilibrium tide” refers to non-resonant excitation of fluid motion in the star’s convection zone, with damping by interaction with the turbulent eddies. There have been numerous studies of these processes in main sequence stars, but less so on the subgiant and red giant branches. Motivated by the newly discovered close binary systems in the Apache Point Observatory Galactic Evolution Experiment (APOGEE-1), we have performed calculations of both the dynamical and equilibrium tide processes for stars over a range of mass as the star’s cease core hydrogen burning and evolve to shell burning. Even for stars which had a radiative core on the main sequence, the dynamical tide may have very large amplitude in the newly radiative core in post-main sequence, giving rise to wave breaking. The resulting large dynamical tide dissipation rate is compared to the equilibrium tide, and the range of secondary masses and orbital periods over which rapid orbital decay may occur will be discussed, as well as applications to close APOGEE binaries.

Launch window analysis in a new perspective with examples of departures from Earth to Mars

NASA Technical Reports Server (NTRS)

Thibodeau, J. R., III; Bond, V. R.

1972-01-01

Earth-departure windows are investigated for two round trip stopover missions to Mars. These are the 1981 inbound Venus swingby mission and the 1986 direct minimum-energy mission. The secular effects of planetary oblateness are used to predict the motion of the parking orbit. A procedure is developed for matching the motion of the parking orbit and the escape asymptote. Earth-departure velocity penalties, caused by orbital plane misalinement, are reduced by synchronizing the motion of the parking orbit and the escape trajectory.

Numerical modeling of on-orbit propellant motion resulting from an impulsive acceleration

NASA Technical Reports Server (NTRS)

Aydelott, John C.; Mjolsness, Raymond C.; Torrey, Martin D.; Hochstein, John I.

1987-01-01

In-space docking and separation maneuvers of spacecraft that have large fluid mass fractions may cause undesirable spacecraft motion in response to the impulsive-acceleration-induced fluid motion. An example of this potential low gravity fluid management problem arose during the development of the shuttle/Centaur vehicle. Experimentally verified numerical modeling techniques were developed to establish the propellant dynamics, and subsequent vehicle motion, associated with the separation of the Centaur vehicle from the shuttle orbiter cargo bay. Although the shuttle/Centaur development activity was suspended, the numerical modeling techniques are available to predict on-orbit liquid motion resulting from impulsive accelerations for other missions and spacecraft.

Propulsion Trade Studies for Spacecraft Swarm Mission Design

NASA Technical Reports Server (NTRS)

Dono, Andres; Plice, Laura; Mueting, Joel; Conn, Tracie; Ho, Michael

2018-01-01

Spacecraft swarms constitute a challenge from an orbital mechanics standpoint. Traditional mission design involves the application of methodical processes where predefined maneuvers for an individual spacecraft are planned in advance. This approach does not scale to spacecraft swarms consisting of many satellites orbiting in close proximity; non-deterministic maneuvers cannot be preplanned due to the large number of units and the uncertainties associated with their differential deployment and orbital motion. For autonomous small sat swarms in LEO, we investigate two approaches for controlling the relative motion of a swarm. The first method involves modified miniature phasing maneuvers, where maneuvers are prescribed that cancel the differential delta V of each CubeSat's deployment vector. The second method relies on artificial potential functions (APFs) to contain the spacecraft within a volumetric boundary and avoid collisions. Performance results and required delta V budgets are summarized, indicating that each method has advantages and drawbacks for particular applications. The mini phasing maneuvers are more predictable and sustainable. The APF approach provides a more responsive and distributed performance, but at considerable propellant cost. After considering current state of the art CubeSat propulsion systems, we conclude that the first approach is feasible, but the modified APF method of requires too much control authority to be enabled by current propulsion systems.

Making the cold Kuiper belt in a planetary instability migration model

NASA Astrophysics Data System (ADS)

Gomes, Rodney S.

2017-06-01

Numerical integrations of the equations of motion of Jupiter, Saturn, three ice cores and a disk of planetesimals are undertaken. Two of the ice planets stand for Uranus and Neptune and a third one is expected to be ejected from the solar system. The planets start in compact cold orbits and each one is in mean motion resonance with its neighbor(s). The disk of planetesimals is placed just outside the outermost planet and is extended to 45 au. Five hundred integrations are done for each of four masses assigned to the disk, which are 25, 30, 35 and 40 Earth masses. The integrations are extended to 100 My. After that, I choose the successful runs in which there are four planets left in closed orbits around the Sun and I separate the good runs among the successful ones, defined by semi-major axes ranges around and not too far from the real ones. Among these good runs, I further choose by visual inspection those that yield an orbital distribution of planetesimals at the Kuiper belt region that resembles the real cold Kuiper belt. I extend these runs to 1 Gy and, after that, to 4.5 Gy. These last integrations for 3.5 Gy are done after replacing the orbits of the planets in the end of the 1 Gy integrations by their current orbits, changing the semi-major axes of the planetesimals so as to keep the same mean motion ratio with Neptune and assigning null masses for the planetesimals. Orbital distributions of the cold Kuiper belt obtained in some of the runs at 4.5 Gy are quite similar to that of the real cold Kuiper belt. The mass in the Kuiper belt region can be dynamically eroded to up to 90% of the original mass. The main conclusion is that the cold Kuiper belt is compatible with a past planetary instability phase even though in some of these runs Neptune's semi-major axis and eccentricity attained values simultaneously larger than 20 au and 0.2 for over 1 My.

orbit-estimation: Fast orbital parameters estimator

NASA Astrophysics Data System (ADS)

Mackereth, J. Ted; Bovy, Jo

2018-04-01

orbit-estimation tests and evaluates the Stäckel approximation method for estimating orbit parameters in galactic potentials. It relies on the approximation of the Galactic potential as a Stäckel potential, in a prolate confocal coordinate system, under which the vertical and horizontal motions decouple. By solving the Hamilton Jacobi equations at the turning points of the horizontal and vertical motions, it is possible to determine the spatial boundary of the orbit, and hence calculate the desired orbit parameters.

AMD-stability in the presence of first-order mean motion resonances

NASA Astrophysics Data System (ADS)

Petit, A. C.; Laskar, J.; Boué, G.

2017-11-01

The angular momentum deficit (AMD)-stability criterion allows to discriminate between a priori stable planetary systems and systems for which the stability is not granted and needs further investigations. AMD-stability is based on the conservation of the AMD in the averaged system at all orders of averaging. While the AMD criterion is rigorous, the conservation of the AMD is only granted in absence of mean-motion resonances (MMR). Here we extend the AMD-stability criterion to take into account mean-motion resonances, and more specifically the overlap of first-order MMR. If the MMR islands overlap, the system will experience generalized chaos leading to instability. The Hamiltonian of two massive planets on coplanar quasi-circular orbits can be reduced to an integrable one degree of freedom problem for period ratios close to a first-order MMR. We use the reduced Hamiltonian to derive a new overlap criterion for first-order MMR. This stability criterion unifies the previous criteria proposed in the literature and admits the criteria obtained for initially circular and eccentric orbits as limit cases. We then improve the definition of AMD-stability to take into account the short term chaos generated by MMR overlap. We analyze the outcome of this improved definition of AMD-stability on selected multi-planet systems from the Extrasolar Planets Encyclopædia.

Nasa s near earth object program office

NASA Astrophysics Data System (ADS)

Yeomans, D.; Chamberlin, A.; Chesley, S.; Chodas, P.; Giorgini, J.; Keesey, M.

In 1998, NASA formed the Near-Earth Object Program Office at JPL to provide a focal point for NASA's efforts to discover and monitor the motions of asteroids and comets that can approach the Earth. This office was charged with 1.) facilitating communication between the near-Earth object (NEO) community and the public, 2.) helping coordinate the search efforts for NEOs, 3.) monitoring the progress in finding NEOs at NASA -supported sites, and 4.) monitoring the future motions of all known NEOs and cataloging their orbits. There are far more near-Earth asteroids (NEAs) than near-Earth comets and one of the driving motivations for NASA's NEO Program is the Spaceguard Goal to find 90% of the NEAs larger than one kilometer by 2008. While the total population of NEAs is not clearly established, the consensus opinion seems to be that the total population of NEAs larger than one kilometer is about 1000 (with a range of perhaps 800 - 1200). By April 2002, nearly 60% of the total population of large NEAs had been discovered and while the discovery rate will likely drop off as the easy ones are found, these early discovery efforts are encouraging. The five NASA-supported NEO discovery teams are the Lincoln Laboratory Near-Earth Asteroid Research effort (LINEAR, Grant Stokes, Principal Investigator), the Near-Earth Asteroid Tracking team at JPL (NEAT, Eleanor Helin, P.I.), the Lowell Observatory Near-Earth Object Search (LONEOS, E. Bowell, P.I.), and two discovery teams near Tucson Arizona - the Spacewatch effort (R. McMillan, P.I.) and the Catalina Sky Survey group (S. Larson, P.I.). Mention should also be made of the Japanese Spaceguard discovery site at Bisei Japan (S. Isobe, P.I.). A substantial portion of the critical follow-up observations necessary to secure the orbits of NEOs and provide information on their physical characteristics is provided by a group of very sophisticated amateur astronomers who might better be described as unfunded professionals. After nearly two years in development, the JPL SENTRY system has been brought on line to provide automatic updates of near-Earth asteroid (NEA) orbits and to predict future close Earth approaches along with their associated impact probabilities. For those NEAs that can approach the Earth, a Palermo Scale risk number is computed based upon the object's impact probability at a particular time, the energy upon impact and the time interval before the potential impact. A Palermo Scale number larger than zero implies the predicted impact event has risen above the expected background level of impacts that could occur between now and the predicted time of impact from all NEAs of the same size or larger. Computed Palermo Scale values are used to prioritize automatic Monte Carlo numerical integration runs to determine robust impact probabilities for those NEAs where a future impact cannot be ruled out - usually because of poor orbits and/or close planetary encounters. Our interactive web site at http://neo.jpl.nasa.gov will allow the user access to the latest information on NEOs including coming close Earth approaches, the risk page for poorly determined orbits, the progress toward meeting the Spaceguard Goal, links to the web sites of the NEO search teams, the rationale for studying NEOs, space missions to NEOs, as well as information on the characteristics, future motions, orbits and orbital movies for well over 120,000 comets and asteroids.

An introduction to shuttle/LDEF retrieval operations: The R-bar approach option. [orbital mechanics and braking schedule

NASA Technical Reports Server (NTRS)

Hall, W. M.

1978-01-01

Simulated orbiter direct approaches during long duration exposure facility (LDEF) retrieval operations reveal that the resultant orbiter jet plume fields can significantly disturb LDEF. An alternate approach technique which utilizes orbital mechanics forces in lieu of jets to brake the final orbiter/LDEF relative motion during the final approach, is described. Topics discussed include: rendezvous operations from the terminal phase initiation burn through braking at some standoff distance from LDEF, pilot and copilot activities, the cockpit instrumentation employed, and a convenient coordinate frame for studying the relative motion between two orbiting bodies. The basic equations of motion for operating on the LDEF radius vector are introduced. Practical considerations of implementing an R-bar approach, namely, orbiter/LDEF relative state uncertainties and orbiter control system limitations are explored. A possible R-bar approach strategy is developed and demonstrated.

Natural motion around the Martian moon Phobos: the dynamical substitutes of the Libration Point Orbits in an elliptic three-body problem with gravity harmonics

NASA Astrophysics Data System (ADS)

Zamaro, M.; Biggs, J. D.

2015-07-01

The Martian moon Phobos is becoming an appealing destination for future scientific missions. The orbital dynamics around this planetary satellite is particularly complex due to the unique combination of both small mass-ratio and length-scale of the Mars-Phobos couple: the resulting sphere of influence of the moon is very close to its surface, therefore both the classical two-body problem and circular restricted three-body problem (CR3BP) do not provide an accurate approximation to describe the spacecraft's dynamics in the vicinity of Phobos. The aim of this paper is to extend the model of the CR3BP to consider the orbital eccentricity and the highly-inhomogeneous gravity field of Phobos, by incorporating the gravity harmonics series expansion into an elliptic R3BP, named ER3BP-GH. Following this, the dynamical substitutes of the Libration Point Orbits (LPOs) are computed in this more realistic model of the relative dynamics around Phobos, combining methodologies from dynamical systems theory and numerical continuation techniques. Results obtained show that the structure of the periodic and quasi-periodic LPOs differs substantially from the classical case without harmonics. Several potential applications of these natural orbits are presented to enable unique low-cost operations in the proximity of Phobos, such as close-range observation, communication, and passive radiation shielding for human spaceflight. Furthermore, their invariant manifolds are demonstrated to provide high-performance natural landing and take-off pathways to and from Phobos' surface, and transfers from and to Martian orbits. These orbits could be exploited in upcoming and future space missions targeting the exploration of this Martian moon.

Matrix Formalism of Synchrobetatron Coupling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huang, Xiaobiao; /SLAC

In this paper we present a complete linear synchrobetatron coupling formalism by studying the transfer matrix which describes linear horizontal and longitudinal motions. With the technique established in the linear horizontal-vertical coupling study [D. Sagan and D. Rubin, Phys. Rev. ST Accel. Beams 2, 074001 (1999)], we found a transformation to block diagonalize the transfer matrix and decouple the betatron motion and the synchrotron motion. By separating the usual dispersion term from the horizontal coordinate first, we were able to obtain analytic expressions of the transformation under reasonable approximations. We also obtained the perturbations to the betatron tune and themore » Courant-Snyder functions. The closed orbit changes due to finite energy gains at rf cavities and radiation energy losses were also studied by the 5 x 5 extended transfer matrix with the fifth column describing kicks in the 4-dimension phase space.« less

Tribology Experiment in Zero Gravity

NASA Technical Reports Server (NTRS)

Pan, C. H. T.; Gause, R. L.; Whitaker, A. F.; Finckenor, M. M.

2015-01-01

A tribology experiment in zero gravity was performed during the orbital flight of Spacelab 1 to study the motion of liquid lubricants over solid surfaces. The absence of a significant gravitational force facilitates observation of such motions as controlled by interfacial and capillary forces. Two experimental configurations were used. One deals with the liquid on one solid surface, and the other with the liquid between a pair of closed spaced surfaces. Time sequence photographs of fluid motion on a solid surface yielded spreading rate data of several fluid-surface combinations. In general, a slow spreading process as governed by the tertiary junction can be distinguished from a more rapid process which is driven by surface tension controlled internal fluid pressure. Photographs were also taken through the transparent bushings of several experimental journal bearings. Morphology of incomplete fluid films and its fluctuation with time suggest the presence or absence of unsteady phenomena of the bearing-rotor system in various arrangements.

Numerical verification of bounce-harmonic resonances in neoclassical toroidal viscosity for tokamaks.

PubMed

Kim, Kimin; Park, Jong-Kyu; Boozer, Allen H

2013-05-03

This Letter presents the first numerical verification for the bounce-harmonic (BH) resonance phenomena of the neoclassical transport in a tokamak perturbed by nonaxisymmetric magnetic fields. The BH resonances were predicted by analytic theories of neoclassical toroidal viscosity (NTV), as the parallel and perpendicular drift motions can be resonant and result in a great enhancement of the radial momentum transport. A new drift-kinetic δf guiding-center particle code, POCA, clearly verified that the perpendicular drift motions can reduce the transport by phase-mixing, but in the BH resonances the motions can form closed orbits and particles radially drift out fast. The POCA calculations on resulting NTV torque are largely consistent with analytic calculations, and show that the BH resonances can easily dominate the NTV torque when a plasma rotates in the perturbed tokamak and therefore, is a critical physics for predicting the rotation and stability in the International Thermonuclear Experimental Reactor.

Astronomy Simulation with Computer Graphics.

ERIC Educational Resources Information Center

Thomas, William E.

1982-01-01

"Planetary Motion Simulations" is a system of programs designed for students to observe motions of a superior planet (one whose orbit lies outside the orbit of the earth). Programs run on the Apple II microcomputer and employ high-resolution graphics to present the motions of Saturn. (Author/JN)

Molecular Gas Clumps from the Destruction of Icy Bodies in the beta Pictoris Debris Disk

NASA Technical Reports Server (NTRS)

Dent, W. R. F.; Wyatt, M. C.; Roberge, A.; Augereau, J. -C.; Casassus, S.; Corder, S.; Greaves, J. S.; DeGregorio-Monsalvo, I.; Hales, A.; Jackson, A. P.;

The disruption of multiplanet systems through resonance with a binary orbit.

PubMed

Touma, Jihad R; Sridhar, S

2015-08-27

Most exoplanetary systems in binary stars are of S-type, and consist of one or more planets orbiting a primary star with a wide binary stellar companion. Planetary eccentricities and mutual inclinations can be large, perhaps forced gravitationally by the binary companion. Earlier work on single planet systems appealed to the Kozai-Lidov instability wherein a sufficiently inclined binary orbit excites large-amplitude oscillations in the planet's eccentricity and inclination. The instability, however, can be quenched by many agents that induce fast orbital precession, including mutual gravitational forces in a multiplanet system. Here we report that orbital precession, which inhibits Kozai-Lidov cycling in a multiplanet system, can become fast enough to resonate with the orbital motion of a distant binary companion. Resonant binary forcing results in dramatic outcomes ranging from the excitation of large planetary eccentricities and mutual inclinations to total disruption. Processes such as planetary migration can bring an initially non-resonant system into resonance. As it does not require special physical or initial conditions, binary resonant driving is generic and may have altered the architecture of many multiplanet systems. It can also weaken the multiplanet occurrence rate in wide binaries, and affect planet formation in close binaries.

The Propeller and the Frog

NASA Astrophysics Data System (ADS)

Pan, Margaret; Chiang, Eugene

2010-10-01

"Propellers" in planetary rings are disturbances in ring material excited by moonlets that open only partial gaps. We describe a new type of co-orbital resonance that can explain the observed non-Keplerian motions of propellers. The resonance is between the moonlet underlying the propeller and co-orbiting ring particles downstream of the moonlet where the gap closes. The moonlet librates within the gap about an equilibrium point established by co-orbiting material and stabilized by the Coriolis force. In the limit of small libration amplitude, the libration period scales linearly with the gap azimuthal width and inversely as the square root of the co-orbital mass. The new resonance recalls but is distinct from conventional horseshoe and tadpole orbits; we call it the "frog" resonance, after the relevant term in equine hoof anatomy. For a ring surface density and gap geometry appropriate for the propeller Blériot in Saturn's A ring, our theory predicts a libration period of ~4 years, similar to the ~3.7 year period over which Blériot's orbital longitude is observed to vary. These librations should be subtracted from the longitude data before any inferences about moonlet migration are made.

THE PROPELLER AND THE FROG

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pan, Margaret; Chiang, Eugene, E-mail: mpan@astro.berkeley.ed

2010-10-20

'Propellers' in planetary rings are disturbances in ring material excited by moonlets that open only partial gaps. We describe a new type of co-orbital resonance that can explain the observed non-Keplerian motions of propellers. The resonance is between the moonlet underlying the propeller and co-orbiting ring particles downstream of the moonlet where the gap closes. The moonlet librates within the gap about an equilibrium point established by co-orbiting material and stabilized by the Coriolis force. In the limit of small libration amplitude, the libration period scales linearly with the gap azimuthal width and inversely as the square root of themore » co-orbital mass. The new resonance recalls but is distinct from conventional horseshoe and tadpole orbits; we call it the 'frog' resonance, after the relevant term in equine hoof anatomy. For a ring surface density and gap geometry appropriate for the propeller Bleriot in Saturn's A ring, our theory predicts a libration period of {approx}4 years, similar to the {approx}3.7 year period over which Bleriot's orbital longitude is observed to vary. These librations should be subtracted from the longitude data before any inferences about moonlet migration are made.« less

Orbit Determination for the Lunar Reconnaissance Orbiter Using an Extended Kalman Filter

NASA Technical Reports Server (NTRS)

Slojkowski, Steven; Lowe, Jonathan; Woodburn, James

2015-01-01

Orbit determination (OD) analysis results are presented for the Lunar Reconnaissance Orbiter (LRO) using a commercially available Extended Kalman Filter, Analytical Graphics' Orbit Determination Tool Kit (ODTK). Process noise models for lunar gravity and solar radiation pressure (SRP) are described and OD results employing the models are presented. Definitive accuracy using ODTK meets mission requirements and is better than that achieved using the operational LRO OD tool, the Goddard Trajectory Determination System (GTDS). Results demonstrate that a Vasicek stochastic model produces better estimates of the coefficient of solar radiation pressure than a Gauss-Markov model, and prediction accuracy using a Vasicek model meets mission requirements over the analysis span. Modeling the effect of antenna motion on range-rate tracking considerably improves residuals and filter-smoother consistency. Inclusion of off-axis SRP process noise and generalized process noise improves filter performance for both definitive and predicted accuracy. Definitive accuracy from the smoother is better than achieved using GTDS and is close to that achieved by precision OD methods used to generate definitive science orbits. Use of a multi-plate dynamic spacecraft area model with ODTK's force model plugin capability provides additional improvements in predicted accuracy.

Chaos and nonlinear dynamics of single-particle orbits in a magnetotaillike magnetic field

NASA Technical Reports Server (NTRS)

Chen, J.; Palmadesso, P. J.

1986-01-01

The properties of charged-particle motion in Hamiltonian dynamics are studied in a magnetotaillike magnetic field configuration. It is shown by numerical integration of the equation of motion that the system is generally nonintegrable and that the particle motion can be classified into three distinct types of orbits: bounded integrable orbits, unbounded stochastic orbits, and unbounded transient orbits. It is also shown that different regions of the phase space exhibit qualitatively different responses to external influences. The concept of 'differential memory' in single-particle distributions is proposed. Physical implications for the dynamical properties of the magnetotail plasmas and the possible generation of non-Maxwellian features in the distribution functions are discussed.

First-order analytic propagation of satellites in the exponential atmosphere of an oblate planet

NASA Astrophysics Data System (ADS)

Martinusi, Vladimir; Dell'Elce, Lamberto; Kerschen, Gaëtan

2017-04-01

The paper offers the fully analytic solution to the motion of a satellite orbiting under the influence of the two major perturbations, due to the oblateness and the atmospheric drag. The solution is presented in a time-explicit form, and takes into account an exponential distribution of the atmospheric density, an assumption that is reasonably close to reality. The approach involves two essential steps. The first one concerns a new approximate mathematical model that admits a closed-form solution with respect to a set of new variables. The second step is the determination of an infinitesimal contact transformation that allows to navigate between the new and the original variables. This contact transformation is obtained in exact form, and afterwards a Taylor series approximation is proposed in order to make all the computations explicit. The aforementioned transformation accommodates both perturbations, improving the accuracy of the orbit predictions by one order of magnitude with respect to the case when the atmospheric drag is absent from the transformation. Numerical simulations are performed for a low Earth orbit starting at an altitude of 350 km, and they show that the incorporation of drag terms into the contact transformation generates an error reduction by a factor of 7 in the position vector. The proposed method aims at improving the accuracy of analytic orbit propagation and transforming it into a viable alternative to the computationally intensive numerical methods.

Proper motion and secular variations of Keplerian orbital elements

NASA Astrophysics Data System (ADS)

Butkevich, Alexey G.

2018-05-01

High-precision observations require accurate modelling of secular changes in the orbital elements in order to extrapolate measurements over long time intervals, and to detect deviation from pure Keplerian motion caused, for example, by other bodies or relativistic effects. We consider the evolution of the Keplerian elements resulting from the gradual change of the apparent orbit orientation due to proper motion. We present rigorous formulae for the transformation of the orbit inclination, longitude of the ascending node and argument of the pericenter from one epoch to another, assuming uniform stellar motion and taking radial velocity into account. An approximate treatment, accurate to the second-order terms in time, is also given. The proper motion effects may be significant for long-period transiting planets. These theoretical results are applicable to the modelling of planetary transits and precise Doppler measurements as well as analysis of pulsar and eclipsing binary timing observations.

Tethered body problems and relative motion orbit determination

NASA Technical Reports Server (NTRS)

Eades, J. B., Jr.; Wolf, H.

1972-01-01

Selected problems dealing with orbiting tethered body systems have been studied. In addition, a relative motion orbit determination program was developed. Results from these tasks are described and discussed. The expected tethered body motions were examined, analytically, to ascertain what influence would be played by the physical parameters of the tether, the gravity gradient and orbit eccentricity. After separating the motion modes these influences were determined; and, subsequently, the effects of oscillations and/or rotations, on tether force, were described. A study was undertaken, by examining tether motions, to see what type of control actions would be needed to accurately place a mass particle at a prescribed position relative to a main vehicle. Other applications for tethers were studied. Principally these were concerned with the producing of low-level gee forces by means of stabilized tether configurations; and, the initiation of free transfer trajectories from tether supported vehicle relative positions.

On the Long Period Luni-Solar Effect in the Motion of an Artificial Satellite

NASA Technical Reports Server (NTRS)

Musen, Peter

1961-01-01

Two systems of formulas are presented for the determination of the long period perturbations caused by the Sun and the Moon in the motion of an artificial satellite. The first system can be used to determine the lunar effect for all satellites. The second method is more convenient for finding the lunar effect for close satellites and the solar effect for all satellites. Knowledge of these effects is essential for determining the stability of the satellite orbit. The basic equations of both systems are arranged in a form which permits the use of numerical integration. The two theories are more accurate and more adaptable to the use of electronic machines than the analytical developments obtained previously.

Geocenter motion estimated from GRACE orbits: The impact of F10.7 solar flux

NASA Astrophysics Data System (ADS)

Tseng, Tzu-Pang; Hwang, Cheinway; Sośnica, Krzysztof; Kuo, Chung-Yen; Liu, Ya-Chi; Yeh, Wen-Hao

2017-06-01

We assess the impact of orbit modeling on the origin offsets between GRACE kinematic and reduced-dynamic orbits. The origin of the kinematic orbit is the center of IGS network (CN), whereas the origin of the reduced-dynamic orbit is assumed to be the center of mass of the Earth (CM). Theoretically, the origin offset between these two orbits is associated with the geocenter motion. However, the dynamic property of the reduced-dynamic orbit is highly related to orbit parameterizations. The assessment of the F10.7 impact on the geocenter motion is implemented by using different orbit parameterization setups in the reduced-dynamic method. We generate two types of reduced-dynamic orbits using 15 and 240 empirical parameters per day from 2005 to 2012. The empirical parameter used in Bernese GNSS Software is called piece-wise constant empirical acceleration (PCA) and is mainly to absorb the non-gravitational forces mostly related to the atmospheric drag and solar radiation pressure. The differences between kinematic and dynamic orbits can serve as a measurement for geocenter. The RMS value of the geocenter measurement in the 15-PCA case is approximately 3.5 cm and approximately 2 cm in the 240-PCA case. The correlation between the orbit difference and F10.7 is about 0.90 in the 15-PCA case and -0.10 to 0 in the 240-PCA case. This implies that the reduced-dynamic orbit modeled with 240 PCAs absorbs the F10.7 variation, which aliases to the 15-PCA orbit solution. The annual amplitudes of the geocenter motion are 3.1, 3.1 and 2.5 mm in the 15-PCA case, compared to 0.9, 2.0 and 1.3 mm in the 240-PCA case in the X, Y and Z components, respectively. The 15-PCA solution is thus closer to the geocenter motions derived from other space-geodetic techniques. The proposed method is limited to the parameterizations in the reduced-dynamic approach.

Analytical and numerical construction of vertical periodic orbits about triangular libration points based on polynomial expansion relations among directions

NASA Astrophysics Data System (ADS)

Qian, Ying-Jing; Yang, Xiao-Dong; Zhai, Guan-Qiao; Zhang, Wei

2017-08-01

Innovated by the nonlinear modes concept in the vibrational dynamics, the vertical periodic orbits around the triangular libration points are revisited for the Circular Restricted Three-body Problem. The ζ -component motion is treated as the dominant motion and the ξ and η -component motions are treated as the slave motions. The slave motions are in nature related to the dominant motion through the approximate nonlinear polynomial expansions with respect to the ζ -position and ζ -velocity during the one of the periodic orbital motions. By employing the relations among the three directions, the three-dimensional system can be transferred into one-dimensional problem. Then the approximate three-dimensional vertical periodic solution can be analytically obtained by solving the dominant motion only on ζ -direction. To demonstrate the effectiveness of the proposed method, an accuracy study was carried out to validate the polynomial expansion (PE) method. As one of the applications, the invariant nonlinear relations in polynomial expansion form are used as constraints to obtain numerical solutions by differential correction. The nonlinear relations among the directions provide an alternative point of view to explore the overall dynamics of periodic orbits around libration points with general rules.

A new release of the mean orbital motion theory, and a new tool provided by CNES for long term analysis of disposal orbits and re-entry predictions

NASA Astrophysics Data System (ADS)

Deleflie, Florent; Wailliez, Sébastien; Portmann, Christophe; Gilles, M.; Vienne, Alain; Berthier, J.; Valk, St; Hautesserres, Denis; Martin, Thierry; Fraysse, Hubert

To perform an orbit modelling accurate enough to provide a good estimate of the lifetime of a satellite, or to ensure the stability of a disposal orbit through centuries, we built a new orbit propagator based on the theory of mean orbital motion. It is named SECS-SD2 , for Simplified and Extended CODIOR Software -Space Debris Dedicated . The CODIOR software propagates numerically averaged equations of motion, with a typical integration step size on the order of a few hours, and was originally written in classical orbital elements. The so-called Space Debris -dedicated version is written in orbital elements suitable for orbits with small eccentricities and inclinations, so as to characterize the main dynamic properties of the motion within the LEO, MEO, and GEO regions. The orbital modelling accounts for the very first terms of the geopotential, the perturbations induced by the luni-solar attraction, the solar radiation pressure, and the atmospheric drag (using classical models). The new software was designed so as to ensure short computation times, even over periods of decades or centuries. This paper aims first at describing and validating the main functionalities of the software: we explain how the simplified averaged equations of motion were built, we show how we get sim-plified luni-solar ephemerides without using any huge file for orbit propagations over centuries, and we show how we averaged and simulated the solar flux. We show as well how we expressed short periodic terms to be added to the mean equations of motion, in order to get orbital ele-ments comparable to those deduced from the classical numerical integration of the oscultating equations of motion. The second part of the paper sheds light on some dynamical properties of space debris flying in the LEO and GEO regions, which were obtained from the new software. Knowing that each satellite in the LEO region is now supposed to re-enter the atmosphere within a period of 25 years, we estimated in various dynamical configurations the lifetime of LEO objects depending on their initial conditions of motion, on the solar flux models applied through decades, and on the atmospheric density models and also the satellite area-to-mass ratio. In the GEO region, we investigated the dynamical reasons that can cause space debris re-entering the GEO-protected region after the passivation of a disposal spacecraft.

View of Arabella, one of two Skylab spiders and her web

NASA Technical Reports Server (NTRS)

1973-01-01

A close-up view of Arabella, one of the two Skylab 3 common cross spiders 'aranous diadematus,' and the web it had spun in the zero gravity of space aboard the Skylab space station cluster in Earth orbit. During the 59 day Skylab 3 mission the two spiders Arabella and Anita, were housed in an enclosure onto which a motion picture and still camera were attached to record the spiders' attempts to build a web in the weightless environment.

Motion of the moonlet in the binary system 243 Ida

NASA Astrophysics Data System (ADS)

Lan, L.; Ni, Y.; Jiang, Y.; Li, J.

2018-02-01

The motion of the moonlet Dactyl in the binary system 243 Ida is investigated in this paper. First, periodic orbits in the vicinity of the primary are calculated, including the orbits around the equilibrium points and large-scale orbits. The Floquet multipliers' topological cases of periodic orbits are calculated to study the orbits' stabilities. During the continuation of the retrograde near-circular orbits near the equatorial plane, two period-doubling bifurcations and one Neimark-Sacker bifurcation occur one by one, leading to two stable regions and two unstable regions. Bifurcations occur at the boundaries of these regions. Periodic orbits in the stable regions are all stable, but in the unstable regions are all unstable. Moreover, many quasi-periodic orbits exist near the equatorial plane. Long-term integration indicates that a particle in a quasi-periodic orbit runs in a space like a tire. Quasi-periodic orbits in different regions have different styles of motion indicated by the Poincare sections. There is the possibility that moonlet Dactyl is in a quasi-periodic orbit near the stable region I, which is enlightening for the stability of the binary system.

The analysis of influence of field of co-rotation on motion of submicronic particles in the Earth's plasmasphere

NASA Astrophysics Data System (ADS)

Yakovlev, A. B.

2018-05-01

The analysis of the motion of micro-particles with radii of several dozens of nanometers in the Earth's plasmasphere has confirmed that the earlier proved statement about conservation of the form for an orbit of a particle with constant electric charge which moves in superposition of the central gravitational field and the field of a magnetic dipole is true also for the case of a quasi-equilibrium electric charge. For a wide range of altitudes and the sizes of micro-particles other forces that act on the charged grain make considerably smaller impact on its motion. On the basis of numerical simulation it has been shown that for motion in an equatorial plane the field of co-rotation leads to very small monotonous growth of the semimajor axis and an orbit eccentricity, and for not-equatorial orbits there are fluctuations of the semimajor axis, an eccentricity and an inclination of an orbit with the period that considerably exceeds the period of orbital motion. In this paper, on the basis of the analysis of the canonical equations of the motion of a micro-particle in superposition of the central gravitational field and the field of co-rotation the explanation of the time dependences obtained numerically for the basic characteristics of an orbit of a micro-particle is proposed.

Operating Small Sat Swarms as a Single Entity: Introducing SODA

NASA Technical Reports Server (NTRS)

Conn, Tracie; Dono Perez, Andres

2017-01-01

Swarm concepts are a growing topic of interest in the small satellite community. Compared to a small satellite constellation, a swarm has the distinction of being multiple spacecraft in close proximity, in approximately the same orbit. Furthermore, we envision swarms to have capabilities for cross-link communication and station-keeping. Of particular interest is a means to maintain operator-specified geometry, alignment, and/or separation.From NASA's decadal survey, it is clear that simultaneous measurements from a 3D volume of space are desired for a variety of Earth scientific studies. As this mission concept is ultimately extended to deep space, some degree of local control for the swarm to self-correct its configuration is required. We claim that the practicality of ground commanding each individual satellite in the swarm is simply not a feasible concept of operations. In other words, the current state-of-practice does not scale to very large swarms (e.g. 100 spacecraft or more) without becoming cost prohibitive. To contain the operations costs and complexity, a new approach is required: the swarm must be operated as a unit, responding to high-level specifications for relative position and velocity.The Mission Design Division at NASA Ames Research Center is looking to the near future for opportunities to develop satellite swarm technology. As part of this effort, we are developing SODA (Swarm Orbital Dynamics Advisor), a tool that provides the orbital maneuvers required to achieve a desired type of relative swarm motion. The purpose of SODA is two-fold. First, it encompasses the algorithms and orbital dynamics model to enable the desired relative motion of the swarm satellites. The process starts with the user specifying the properties of a swarm configuration. This could be as simple as varying in-track spacing of the swarm in one orbit, or as complex as maintaining a specified 3D geometrical orientation. We presume that science objectives will drive this choice. Given these inputs, the tool provides the most efficient maneuver(s) to achieve the objective.Second, SODA provides a variety of visualization tools. We acknowledge that the relationship between a desired relative motion amongst the swarm, and the corresponding orbital parameters for each individual satellite may not be immediately apparent for ground controllers and mission planners. The purpose of SODA's visualization tools is to illustrate this concept clearly with a variety of graphics and animations. After computing the optimal orbital maneuvers to modify the swarm, these results are simulated to demonstrate successful swarm control.Our emphasis in this paper is on the importance of relating the desired motion of the swarm satellites relative to one another with the required orbital element changes. One cannot joystick a drifting swarm satellite back into position; the underlying orbital mechanics dictate the most efficient recovery maneuvers. To illustrate this point, results from several case study simulations are presented. We conclude with our forward work for ongoing SODA development and potential science applications.

Intrinsic Magnetic Flux of the Electron's Orbital and Spin Motion

NASA Astrophysics Data System (ADS)

Wan, K. K.; Saglam, M.

2006-06-01

In analogy with the fact that there are magnetic moments associated respectively with the electron's orbital and spin motion in an atom we present several analyses on a proposal to introduce a concept of intrinsic magnetic flux associated with the electron's orbital and spin motion. It would be interesting to test or to demonstrate Faraday's and Lenz's laws of electromagnetic induction arising directly from the flux change due to transition of states in an atom and to examine applications of this concept of intrinsic flux.

Gravitational orientation of the orbital complex, Salyut-6--Soyuz

NASA Technical Reports Server (NTRS)

Grecho, G. M.; Sarychev, V. A.; Legostayev, V. P.; Sazonov, V. V.; Gansvind, I. N.

1983-01-01

A simple mathematical model is proposed for the Salyut-6-Soyuz orbital complex motion with respect to the center of mass under the one-axis gravity-gradient orientation regime. This model was used for processing the measurements of the orbital complex motion parameters when the above orientation region was implemented. Some actual satellite motions are simulated and the satellite's aerodynamic parameters are determined. Estimates are obtained for the accuracy of measurements as well as that of the mathematical model.

Long Term Missions at the Sun-Earth Libration Point L1: ACE, SOHO, and WIND

NASA Technical Reports Server (NTRS)

Roberts, Craig E.

2011-01-01

Three heliophysics missions -- the Advanced Composition Explorer (ACE), Solar Heliospheric Observatory (SOHO), and the Global Geoscience WIND -- have been orbiting the Sun-Earth interior libration point L1 continuously since 1997, 1996, and 2004, respectively. ACE and WIND (both NASA missions) and SOHO (an ESA-NASA joint mission) are all operated from the NASA Goddard Space Flight Center (GSFC). While ACE and SOHO have been dedicated libration point orbiters since their launches, WIND has had also a remarkable 10-year career flying a deep-space, multiple lunar-flyby trajectory prior to 2004. That era featured 36 targeted lunar flybys with excursions to both L1 and L2 before its final insertion in L1 orbit. A figure depicts the orbits of the three spacecraft, showing projections of the orbits onto the orthographic planes of a solar rotating ecliptic frame of reference. The SOHO orbit is a quasi-periodic halo orbit, where the frequencies of the in-plane and out-of-plane motions are practically equal. Such an orbit is seen to repeat itself with a period of approximately 178 days. For ACE and WIND, the frequencies of the in-plane and out-of-plane motions are unequal, giving rise to the characteristic Lissajous motion. ACE's orbit is of moderately small amplitude, whereas WIND's orbit is a large-amplitude Lissajous of dimensions close to those of the SOHO halo orbit. As motion about the collinear points is inherently unstable, stationkeeping maneuvers are necessary to prevent orbital decay and eventual escape from the L1 region. Though the three spacecraft are dissimilar (SOHO is a 3-axis stabilized Sun pointer, WIND is a spin-stabilized ecliptic pole pointer, and ACE is also spin-stabilized with its spin axis maintained between 4 and 20 degrees of the Sun), the stationkeeping technique for the three is fundamentally the same. The technique consists of correcting the energy of the orbit via a delta-V directed parallel or anti-parallel to the Spacecraft-to-Sun line. SOHO achieves this using thrusters oriented in line with the solar direction. WIND achieves the delta-V via pulsing radial thrusters when aligned with the Sun. ACE uses axial thrusters to apply delta-V with a component that is 94% or more aligned with the ACE-Sun line. Sunward thrust adds energy to the orbit preventing decay back toward Earth. Thrust directed anti-Sunward takes energy out of the L1 orbit, thereby preventing escape from the Earth-Moon system into independent heliocentric orbit. Libration point orbit stationkeeping delta-V costs grow exponentially with time elapsed from the last maneuver performed. The doubling time constant is approximately 16 days. For the sake of fuel conservation, and for limiting the absolute magnitude of propulsion performance errors, stationkeeping maneuvers should be performed before the delta-V grows too large; for our purposes 'too large' is considered to be greater than 0.5 m/sec. In practice, the typical interval between burns for this trio is about three months, and the typical delta-V is much smaller than 0.5 m/sec. Typical annual stationkeeping costs have been around 1.0 m/sec for ACE and WIND, and much less than that for SOHO. All three spacecraft have ample fuel remaining; barring contingencies all three could, in principle, be maintained at L1 for decades to come. This paper will review the L1 orbits and the mission history of ACE, WIND, and SOHO, and describe the stationkeeping techniques and orbit maneuver experience. The Lissajous phase control that was practiced for ACE during the period from 1999 to 2001 will also be briefly discussed. The final section will consider the future of these ongoing missions.

Distant retrograde orbits for the Moon's exploration

NASA Astrophysics Data System (ADS)

Sidorenko, Vladislav

We discuss the properties of the distant retrograde orbits (which are called quasi-satellite orbits also) around Moon. For the first time the distant retrograde orbits were described by J.Jackson in studies on restricted three body problem at the beginning of 20th century [1]. In the synodic (rotating) reference frame distant retrograde orbit looks like an ellipse whose center is slowly drifting in the vicinity of minor primary body while in the inertial reference frame the third body is orbiting the major primary body. Although being away the Hill sphere the third body permanently stays close enough to the minor primary. Due to this reason the distant retrograde orbits are called “quasi-satellite” orbits (QS-orbits) too. Several asteroids in solar system are in a QS-orbit with respect to one of the planet. As an example we can mention the asteroid 2002VE68 which circumnavigates Venus [2]. Attention of specialists in space flight mechanics was attracted to QS-orbits after the publications of NASA technical reports devoted to periodic moon orbits [3,4]. Moving in QS-orbit the SC remains permanently (or at least for long enough time) in the vicinity of small celestial body even in the case when the Hill sphere lies beneath the surface of the body. The properties of the QS-orbit can be studied using the averaging of the motion equations [5,6,7]. From the theoretical point of view it is a specific case of 1:1 mean motion resonance. The integrals of the averaged equations become the parameters defining the secular evolution of the QS-orbit. If the trajectory is robust enough to small perturbations in the simplified problem (i.e., restricted three body problem) it may correspond to long-term stability of the real-world orbit. Our investigations demonstrate that under the proper choice of the initial conditions the QS-orbits don’t escape from Moon or don’t impact Moon for long enough time. These orbits can be recommended as a convenient technique for the large scale browsing of the Moon’s environment. [1] Jackson, J. (1913) MNRAS, 74, 62-82. [2] Mikkola, S., Brasser, R., Wiegert, P., Innanen, K. (2004) MNRAS, 351, L63-L65. [3] Broucke, R.A. (1968) NASA Technical Report 32-1168, JPL. [4] Broucke, R.A. (1969) NASA Technical Report 32-1360, JPL. [5] Kogan, A.I. (1989) Cosmic Research, 26, 705-710. [6] Namouni, F. (1999) Icarus, 6, 293-314. [7] Sidorenko, V.V., Neishtadt, A.I., Artemyev, A.V., Zelenyi, L.M. (2013) Doklady Physics, 58, 207-211.

Projectile Motion in the "Language" of Orbital Motion

ERIC Educational Resources Information Center

Zurcher, Ulrich

2011-01-01

We consider the orbit of projectiles launched with arbitrary speeds from the Earth's surface. This is a generalization of Newton's discussion about the transition from parabolic to circular orbits, when the launch speed approaches the value [image omitted]. We find the range for arbitrary launch speeds and angles, and calculate the eccentricity of…

The Orbit of Water Droplets around Charged Rod

ERIC Educational Resources Information Center

Ferstl, Andrew; Burns, Andrew

2013-01-01

The motion of charges around a centrally charged object is often compared to gravitational orbits (such as satellites around planets). Recently, a video taken by astronaut Don Pettit onboard the International Space Station shows water droplets orbiting a charged knitting needle. Here we attempt to model this motion and estimate the charges on the…

Steady Motions of Rigid Body Satellites in a Central Gravitational Field

DTIC Science & Technology

1993-12-01

been explored for several centuries. Orbiting bodies investigated include point masses, spheres, cylinders, rods, ball-and-socket connected objects...of the satellite model relative to its orbit radius could lead to 5 its treatment as a point mass, doing so would prevent analysis of satellite...8217 librational ’ motion ... and internal elastic forces in the structure balance the orbital dynamic accelerations tending to separate masses orbiting at

The Roles of Tidal Evolution and Evaporative Mass Loss in the Origin of CoRoT-7 b

NASA Technical Reports Server (NTRS)

Jackson, Brian; Miller, Neil; Barnes, Rory; Raymond, Sean N.; Fortney, Jonathan J.; Greenberg, Richard

2010-01-01

CoRoT-7 b is the first confirmed rocky exoplanet, but, with an orbital semimajor axis of 0.0172 au, its origins may be unlike any rocky planet in our Solar System. In this study, we consider the roles of tidal evolution and evaporative mass loss in CoRoT-7 b's history, which together have modified the planet's mass and orbit. If CoRoT-7 b has always been a rocky body, evaporation may have driven off almost half its original mass, but the mass loss may depend sensitively on the extent of tidal decay of its orbit. As tides caused CoRoT-7 b's orbit to decay, they brought the planet closer to its host star, thereby enhancing the mass loss rate. Such a large mass loss also suggests the possibility that CoRoT-7 b began as a gas giant planet and had its original atmosphere completely evaporated. In this case, we find that CoRoT-7 b's original mass probably did not exceed 200 Earth masses (about two-third of a Jupiter mass). Tides raised on the host star by the planet may have significantly reduced the orbital semimajor axis, perhaps causing the planet to migrate through mean-motion resonances with the other planet in the system, CoRoT-7 c. The coupling between tidal evolution and mass loss may be important not only for CoRoT-7 b but also for other close-in exoplanets, and future studies of mass loss and orbital evolution may provide insight into the origin and fate of close-in planets, both rocky and gaseous.

Stability of the Kepler-11 system and its origin

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mahajan, Nikhil; Wu, Yanqin

2014-11-01

A significant fraction of Kepler systems are closely packed, largely coplanar, and circular. We study the stability of a six-planet system, Kepler-11, to gain insights on the dynamics and formation history of such systems. Using a technique called 'frequency maps' as fast indicators of long-term stability, we explore the stability of the Kepler-11 system by analyzing the neighborhood space around its orbital parameters. Frequency maps provide a visual representation of chaos and stability, and their dependence on orbital parameters. We find that the current system is stable, but lies within a few percent of several dynamically dangerous two-body mean-motion resonances.more » Planet eccentricities are restricted below a small value, ∼0.04, for long-term stability, but planet masses can be more than twice their reported values (thus allowing for the possibility of mass loss by past photoevaporation). Based on our frequency maps, we speculate on the origin of instability in closely packed systems. We then proceed to investigate how the system could have been assembled. The stability constraints on Kepler-11 (mainly eccentricity constraints) suggest that if the system were assembled in situ, a dissipation mechanism must have been at work to neutralize the eccentricity excitation. On the other hand, if migration was responsible for assembling the planets, there has to be little differential migration among the planets to avoid them either getting trapped into mean motion resonances, or crashing into each other.« less

Typical motions in multiple systems

NASA Technical Reports Server (NTRS)

Anosova, Joanna P.

1990-01-01

In very old times, people counted - one, two, many. The author wants to show that they were right. Consider the motions of isolated bodies: (1) N = 1 - simple motion; (2) N = 2 - Keplerian orbits; and (3) N = 3 - this is the difficult problem. In general, this problem can be studied only by computer simulations. The author studied this problem over many years (see, e.g., Agekian and Anosova, 1967; Anosova, 1986, 1989 a,b). The principal result is that two basic types of dynamics take place in triple systems. The first special type is the stable hierarchical systems with two almost Keplerian orbits. The second general type is the unstable triple systems with complicated motions of the bodies. By random choice of the initial conditions, by the Monte-Carlo method, the stable systems comprised about approx. 10% of the examined cases; the unstable systems comprised the other approx. 90% of cases under consideration. In N greater than 3, the studies of dynamics of such systems by computer simulations show that we have in general also the motions roughly as at the cases 1 - 3 with the relative negative or positive energies of the bodies. In the author's picture, the typical trajectories of the bodies in unstable triple systems of the general type of dynamics are seen. Such systems are disrupted always after close triple approaches of the bodies. These approaches play a role like the gravitational slingshot. Often, the velocities of escapers are very large. On the other hand, the movie also shows the dynamical processes of a formation, dynamical evolution and disruption of the temporary wide binaries in triples and a formation of final hard massive binaries in the final evolution of triples.

RESONANT CLUMPING AND SUBSTRUCTURE IN GALACTIC DISKS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Molloy, Matthew; Smith, Martin C.; Shen, Juntai

2015-05-10

We describe a method to extract resonant orbits from N-body simulations, exploiting the fact that they close in frames rotating with a constant pattern speed. Our method is applied to the N-body simulation of the Milky Way by Shen et al. This simulation hosts a massive bar, which drives strong resonances and persistent angular momentum exchange. Resonant orbits are found throughout the disk, both close to the bar and out to the very edges of the disk. Using Fourier spectrograms, we demonstrate that the bar is driving kinematic substructure even in the very outer parts of the disk. We identifymore » two major orbit families in the outskirts of the disk, one of which makes significant contributions to the kinematic landscape, namely, the m:l = 3:−2 family, resonating with the bar. A mechanism is described that produces bimodal distributions of Galactocentric radial velocities at selected azimuths in the outer disk. It occurs as a result of the temporal coherence of particles on the 3:−2 resonant orbits, which causes them to arrive simultaneously at pericenter or apocenter. This resonant clumping, due to the in-phase motion of the particles through their epicycle, leads to both inward and outward moving groups that belong to the same orbital family and consequently produce bimodal radial velocity distributions. This is a possible explanation of the bimodal velocity distributions observed toward the Galactic anticenter by Liu et al. Another consequence is that transient overdensities appear and dissipate (in a symmetric fashion), resulting in a periodic pulsing of the disk’s surface density.« less

Multi-instrumental observations of the 2014 Ursid meteor outburst

NASA Astrophysics Data System (ADS)

Moreno-Ibáñez, Manuel; Trigo-Rodríguez, Josep M.; Madiedo, José María; Vaubaillon, Jérémie; Williams, Iwan P.; Gritsevich, Maria; Morillas, Lorenzo G.; Blanch, Estefanía; Pujols, Pep; Colas, François; Dupouy, Philippe

2017-06-01

The Ursid meteor shower is an annual shower that usually shows little activity. However, its Zenith hourly rate sometimes increases, usually either when its parent comet, 8P/Tuttle, is close to its perihelion or its aphelion. Outbursts when the comet is away from perihelion are not common and outbursts when the comet is close to aphelion are extremely rare. The most likely explanation offered to date is based on the orbital mean motion resonances. The study of the aphelion outburst of 2000 December provided a means of testing that hypothesis. A new aphelion outburst was predicted for 2014 December. The SPanish Meteor Network, in collaboration with the French Fireball Recovery and InterPlanetary Observation Network, set up a campaign to monitor this outburst and eventually retrieve orbital data that expand and confirm previous preliminary results and predictions. Despite unfavourable weather conditions over the south of Europe over the relevant time period, precise trajectories from multistation meteor data recorded over Spain were obtained, as well as orbital and radiant information for four Ursid meteors. The membership of these four meteors to the expected dust trails that were to provoke the outburst is discussed, and we characterize the origin of the outburst in the dust trail produced by the comet in the year ad 1392.

SKYLAB (SL)-3 - TELEVISION

NASA Image and Video Library

1973-09-29

S73-34619 (28 July 1973) --- A composite of four frames taken from 16mm movie camera footage showing an overhead view of the Skylab space station cluster in Earth orbit. The Maurer motion picture camera scenes were being filmed during the Skylab 3 Command/Service Module's (CSM) first "fly around" inspection of the space station. Close comparison of the four frames reveals movement of the improvised parasol solar shield over the Orbital Workshop (OWS). The "flapping" of the sun shade was caused from the exhaust of the reaction control subsystem (RCS) thrusters of the Skylab 3 CSM. The one remaining solar array system wing on the OWS is in the lower left background. The solar panel in the lower left foreground is on the Apollo Telescope Mount (ATM). Photo credit: NASA

Studying the energy variation in the powered Swing-By in the Sun-Mercury system

NASA Astrophysics Data System (ADS)

Ferreira, A. F. S.; Prado, A. F. B. A.; Winter, O. C.; Santos, D. P. S.

2017-10-01

A maneuver where a spacecraft passes close to Mercury and uses the gravity of this body combined with an impulse applied at the periapsis, with different magnitudes and directions, is presented. The main objective of this maneuver is the fuel economy in space missions. Using this maneuver, it is possible to insert the spacecraft into an orbit captured around the Sun or Mercury. Trajectories escaping the Solar System are also obtained and mapped. Maps of the spacecraft energy variation relative to the Sun and the types of orbits resulting from the maneuver are presented, based in numerical integrations. The results show that applying the impulse out of the direction of motion can optimize the maneuver due to the effect of the combination of the impulse and the gravity.

Orbit Correction for the Newly Developed Polarization-Switching Undulator

NASA Astrophysics Data System (ADS)

Obina, Takashi; Honda, Tohru; Shioya, Tatsuro; Kobayashi, Yukinori; Tsuchiya, Kimichika; Yamamoto, Shigeru

2007-01-01

A new scheme of undulator magnet arrangements has been proposed and developed as a polarization-switching radiation source, and its test-stand was installed in the 2.5-GeV Photon Factory storage ring (PF ring) in order to investigate the effects on the beam orbit. The closed orbit distortion (COD) over 200 μm was produced in a vertical direction when we switched the polarization of the radiation from the test-stand. In a horizontal direction, the COD was less than 50μm. The results agreed well with the predictions from the magnetic-field measurement on the bench. In order to suppress the CODs and realize a stable operation of the ring with the polarization-switching, we developed an orbit correction system which consists of an encoder to detect motion of magnets, a pair of beam position monitors (BPMs), signal processing parts, and a pair of steering magnets. We succeeded in suppressing the CODs to the level below 3μm using the system even when we switch the polarization at a maximum frequency of 0.8 Hz.

The orbital evolution of NEA 30825 1900 TG1

NASA Astrophysics Data System (ADS)

Timoshkova, E. I.

2008-02-01

The orbital evolution of the near-Earth asteroid (NEA) 30825 1990 TG1 has been studied by numerical integration of the equations of its motion over the 100 000-year time interval with allowance for perturbations from eight major planets and Pluto, and the variations in its osculating orbit over this time interval were determined. The numerical integrations were performed using two methods: the Bulirsch-Stoer method and the Everhart method. The comparative analysis of the two resulting orbital evolutions of motion is presented for the time interval examined. The evolution of the asteroid motion is qualitatively the same for both variants, but the rate of evolution of the orbital elements is different. Our research confirms the known fact that the application of different integrators to the study of the long-term evolution of the NEA orbit may lead to different evolution tracks.

Analysis of Scanned Probe Images for Magnetic Focusing in Graphene

DOE PAGES

Bhandari, Sagar; Lee, Gil-Ho; Kim, Philip; ...

2017-02-21

We have used cooled scanning probe microscopy (SPM) to study electron motion in nanoscale devices. The charged tip of the microscope was raster-scanned at constant height above the surface as the conductance of the device was measured. The image charge scatters electrons away, changing the path of electrons through the sample. Using this technique, we imaged cyclotron orbits that flow between two narrow contacts in the magnetic focusing regime for ballistic hBN–graphene–hBN devices. We present herein an analysis of our magnetic focusing imaging results based on the effects of the tip-created charge density dip on the motion of ballistic electrons.more » The density dip locally reduces the Fermi energy, creating a force that pushes electrons away from the tip. When the tip is above the cyclotron orbit, electrons are deflected away from the receiving contact, creating an image by reducing the transmission between contacts. The data and our analysis suggest that the graphene edge is rather rough, and electrons scattering off the edge bounce in random directions. However, when the tip is close to the edge, it can enhance transmission by bouncing electrons away from the edge, toward the receiving contact. Our results demonstrate that cooled SPM is a promising tool to investigate the motion of electrons in ballistic graphene devices.« less

Analysis of Scanned Probe Images for Magnetic Focusing in Graphene

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bhandari, Sagar; Lee, Gil-Ho; Kim, Philip

We have used cooled scanning probe microscopy (SPM) to study electron motion in nanoscale devices. The charged tip of the microscope was raster-scanned at constant height above the surface as the conductance of the device was measured. The image charge scatters electrons away, changing the path of electrons through the sample. Using this technique, we imaged cyclotron orbits that flow between two narrow contacts in the magnetic focusing regime for ballistic hBN–graphene–hBN devices. We present herein an analysis of our magnetic focusing imaging results based on the effects of the tip-created charge density dip on the motion of ballistic electrons.more » The density dip locally reduces the Fermi energy, creating a force that pushes electrons away from the tip. When the tip is above the cyclotron orbit, electrons are deflected away from the receiving contact, creating an image by reducing the transmission between contacts. The data and our analysis suggest that the graphene edge is rather rough, and electrons scattering off the edge bounce in random directions. However, when the tip is close to the edge, it can enhance transmission by bouncing electrons away from the edge, toward the receiving contact. Our results demonstrate that cooled SPM is a promising tool to investigate the motion of electrons in ballistic graphene devices.« less

Dynamical evolution of differentiated asteroid families

NASA Astrophysics Data System (ADS)

Martins-Filho, W. S.; Carvano, J.; Mothe-Diniz, T.; Roig, F.

2014-10-01

The project aims to study the dynamical evolution of a family of asteroids formed from a fully differentiated parent body, considering family members with different physical properties consistent with what is expected from the break up of a body formed by a metallic nucleus surrounded by a rocky mantle. Initially, we study the effects of variations in density, bond albedo, and thermal inertia in the semi-major axis drift caused by the Yarkovsky effect. The Yarkovsky effect is a non-conservative force caused by the thermal re-radiation of the solar radiation by an irregular body. In Solar System bodies, it is known to cause changes in the orbital motions (Peterson, 1976), eventually bringing asteroids into transport routes to near-Earth space, such as some mean motion resonances. We expressed the equations of variation of the semi-major axis directly in terms of physical properties (such as the mean motion, frequency of rotation, conductivity, thermal parameter, specific heat, obliquity and bond albedo). This development was based on the original formalism for the Yarkovsky effect (i.e., Bottke et al., 2006 and references therein). The derivation of above equations allowed us to closely study the variation of the semi-major axis individually for each physical parameter, clearly showing that the changes in semi-major axis for silicate bodies is twice or three times greater than for metal bodies. The next step was to calculate the orbital elements of a synthetic family after the break-up. That was accomplished assuming that the catastrophic disruption energy is given by the formalism described by Stewart and Leinhardt (2009) and assuming an isotropic distribution of velocities for the fragments of the nucleus and the mantle. Finally, the orbital evolution of the fragments is implemented using a simpletic integrator, and the result compared with the distribution of real asteroid families.

Longitudinal control effectiveness and entry dynamics of a single-stage-to-orbit vehicle

NASA Technical Reports Server (NTRS)

Vinh, N. X.; Lin, C. F.

1982-01-01

The classical theory of flight dynamics for airplane longitudinal stability and control analysis was extended to the case of a hypervelocity reentry vehicle. This includes the elements inherent in supersonic and hypersonic flight such as the influence of the Mach number on aerodynamic characteristics, and the effect of the reaction control system and aerodynamic controls on the trim condition through a wide range of speed. Phugoid motion and angle of attack oscillation for typical cases of cruising flight, ballistic entry, and glide entry are investigated. In each case, closed form solutions for the variations in altitude, flight path angle, speed and angle of attack are obtained. The solutions explicitly display the influence of different regions design parameters and trajectory variables on the stability of the motion.

Orbital fitting of imaged planetary companions with high eccentricities and unbound orbits. Their application to Fomalhaut b and PZ Telecopii B

NASA Astrophysics Data System (ADS)

Beust, H.; Bonnefoy, M.; Maire, A.-L.; Ehrenreich, D.; Lagrange, A.-M.; Chauvin, G.

2016-03-01

Context. Regular follow-up of imaged companions to main-sequence stars often allows a projected orbital motion to be detected. Markov chain Monte Carlo (MCMC) has become very popular recent years for fitting and constraining their orbits. Some of these imaged companions appear to move on very eccentric, possibly unbound orbits. This is, in particular, the case for the exoplanet Fomalhaut b and the brown dwarf companion PZ Tel B on which we focus here. Aims: For these orbits, standard MCMC codes that assume only bound orbits may be inappropriate. Our goal is to develop a new MCMC implementation that is able to handle both bound and unbound orbits in a continuous manner, and to apply this to the cases of Fomalhaut b and PZ Tel B. Methods: We present here this code, based on the use of universal Keplerian variables and Stumpff functions. We present two versions of this code, the second one using a different set of angular variables that were designed to avoid degeneracies arising when the projected orbital motion is quasi-radial, as is the case for PZ Tel B. We also present additional observations of PZ Tel B. Results: The code is applied to Fomalhaut b and PZ Tel B. We confirm previous results in relation to, but we show that on the sole basis of the astrometric data, open orbital solutions are also possible. The eccentricity distribution nevertheless still peaks around ~0.9 in the bound regime. We present a first successful orbital fit of PZ Tel B, which shows in particular that, while both bound and unbound orbital solutions are equally possible, the eccentricity distribution presents a sharp peak very close to e = 1, meaning a quasi-parabolic orbit. Conclusions: It has recently been suggested that the presence of unseen inner companions to imaged ones may lead orbital fitting algorithms to artificially give very high eccentricities. We show that this caveat is unlikely to apply to Fomalhaut b. Concerning PZ Tel B, we derive a possible solution, which involves an inner ~12 MJup companion, that would mimic a e = 1 orbit, despite a real eccentricity of around 0.7, but a dynamical analysis reveals that this type of system would not be stable. We thus conclude that our orbital fit is robust. Based on observations collected at the European Organisation for Astronomical Research in the Southern Hemisphere, Chile (Program ID: 085.C-0867(B) and 085.C-0277(B)).

The influence of orbit selection on the accuracy of the Stanford Relativity gyroscope experiment

NASA Technical Reports Server (NTRS)

Vassar, R.; Everitt, C. W. F.; Vanpatten, R. A.; Breakwell, J. V.

1980-01-01

This paper discusses an error analysis for the Stanford Relativity experiment, designed to measure the precession of a gyroscope's spin-axis predicted by general relativity. Measurements will be made of the spin-axis orientations of 4 superconducting spherical gyroscopes carried by an earth-satellite. Two relativistic precessions are predicted: a 'geodetic' precession associated with the satellite's orbital motion and a 'motional' precession due to the earth's rotation. Using a Kalman filter covariance analysis with a realistic error model we have computed the error in determining the relativistic precession rates. Studies show that a slightly off-polar orbit is better than a polar orbit for determining the 'motional' drift.

Dynamic trajectory analysis of superparamagnetic beads driven by on-chip micromagnets

PubMed Central

Abedini-Nassab, Roozbeh; Lim, Byeonghwa; Yang, Ye; Howdyshell, Marci; Sooryakumar, Ratnasingham; Yellen, Benjamin B.

2015-01-01

We investigate the non-linear dynamics of superparamagnetic beads moving around the periphery of patterned magnetic disks in the presence of an in-plane rotating magnetic field. Three different dynamical regimes are observed in experiments, including (1) phase-locked motion at low driving frequencies, (2) phase-slipping motion above the first critical frequency fc1, and (3) phase-insulated motion above the second critical frequency fc2. Experiments with Janus particles were used to confirm that the beads move by sliding rather than rolling. The rest of the experiments were conducted on spherical, isotropic magnetic beads, in which automated particle position tracking algorithms were used to analyze the bead dynamics. Experimental results in the phase-locked and phase-slipping regimes correlate well with numerical simulations. Additional assumptions are required to predict the onset of the phase-insulated regime, in which the beads are trapped in closed orbits; however, the origin of the phase-insulated state appears to result from local magnetization defects. These results indicate that these three dynamical states are universal properties of bead motion in non-uniform oscillators. PMID:26648596

Tides and the evolution of planetary habitability.

PubMed

Barnes, Rory; Raymond, Sean N; Jackson, Brian; Greenberg, Richard

2008-06-01

Tides raised on a planet by the gravity of its host star can reduce the planet's orbital semi-major axis and eccentricity. This effect is only relevant for planets orbiting very close to their host stars. The habitable zones of low-mass stars are also close in, and tides can alter the orbits of planets in these locations. We calculate the tidal evolution of hypothetical terrestrial planets around low-mass stars and show that tides can evolve planets past the inner edge of the habitable zone, sometimes in less than 1 billion years. This migration requires large eccentricities (>0.5) and low-mass stars ( less or similar to 0.35 M(circle)). Such migration may have important implications for the evolution of the atmosphere, internal heating, and the Gaia hypothesis. Similarly, a planet that is detected interior to the habitable zone could have been habitable in the past. We consider the past habitability of the recently discovered, approximately 5 M(circle) planet, Gliese 581 c. We find that it could have been habitable for reasonable choices of orbital and physical properties as recently as 2 Gyr ago. However, when constraints derived from the additional companions are included, most parameter choices that indicate past habitability require the two inner planets of the system to have crossed their mutual 3:1 mean motion resonance. As this crossing would likely have resulted in resonance capture, which is not observed, we conclude that Gl 581 c was probably never habitable.

Spin, tumble, and twirl - beyond Jeffery orbits in the rotation of real-world particles

NASA Astrophysics Data System (ADS)

Variano, E. A.; Pujara, N.

2016-12-01

The classical theory of particle rotation explained by Jeffery's 1922 paper has guided how people think about the motion of non-spherical particles. The resulting concept of Jeffery orbits has been useful in guiding intuition, but is limited by some restrictive assumptions. We present a picture of what happens when some of these restrictions are relaxed. First, we review recent results from a variety of researchers showing how inertia causes Jeffery orbits to collapse. Next, we present our results from numerical simulations of particle particle motion in turbulence to show how Jeffery orbits `survive' in unsteady flows. Finally, we combine the two and discuss the motion expected for inertial particles in turbulent flow. The presentation uses a number of videos to illustrate these motions, and indicates a youtube channel on which they can be accessed for teaching purposes.

Probing the holographic principle using dynamical gauge effects from open spin-orbit coupling

NASA Astrophysics Data System (ADS)

Zhao, Jianshi; Price, Craig; Liu, Qi; Gemelke, Nathan

2016-05-01

Dynamical gauge fields result from locally defined symmetries and an effective over-labeling of quantum states. Coupling atoms weakly to a reservoir of laser modes can create an effective dynamical gauge field purely due to the disregard of information in the optical states. Here we report measurements revealing effects of open spin-orbit coupling in a system where an effective model can be formed from a non-abelian SU(2) × U(1) field theory following the Yang-Mills construct. Forming a close analogy to dynamical gauge effects in quantum chromodynamics, we extract a measure of atomic motion which reveals the analog of a closing mass gap for the relevant gauge boson, shedding insight on long standing open problems in gauge-fixing scale anomalies. Using arguments following the holographic principle, we measure scaling relations which can be understood by quantifying information present in the local potential. New prospects using these techniques for developing fractionalization of multi-particle and macroscopic systems using dissipative and non-abelian gauge fields will also be discussed. We acknowledge support from NSF Award No. 1068570, and the Charles E. Kaufman Foundation.

HP-9810A calculator programs for plotting the 2-dimensional motion of cyclindrical payloads relative to the shuttle orbiter

NASA Technical Reports Server (NTRS)

Wilson, S. W.

1976-01-01

The HP-9810A calculator programs described provide the capability to generate HP-9862A plotter displays which depict the apparent motion of a free-flying cyclindrical payload relative to the shuttle orbiter body axes by projecting the payload geometry into the orbiter plane of symmetry at regular time intervals.

Impact of Eccentricity on East-west Stationkeeping for GPS Class of Orbits

NASA Technical Reports Server (NTRS)

Ely, Todd A.

1999-01-01

There exists a strong relationship between eccentricity and the potential for a repeating groundtrack orbit to exhibit chaotic motion. This is true at all values of eccentricity, but, perhaps most dramatic, is that it is true even for orbits that are nearly circular. These complex motions can have a significant impact on the east-west stationkeeping process for maintaining the repeating groundtrack property of a commensurate orbit. Ely and Howell have shown that traditional stationkeeping (SK) methods are unable to maintain a repeating groundtrack in the presence of complex dynamics, such as with chaotic motion. They developed an alternate SK method that is able to maintain a repeating groundtrack for eccentric, commensurate orbits. The focus of the current study is to investigate orbits with characteristics that are similar to GPS satellites except with modestly larger eccentricities. It will be shown that at eccentricities larger than approx. .01 the chaotic regions become significant, and the need arises for a robust stationkeeping approach, such as developed in. FurtheRmore, the investigation will reveal that the influence of luni-solar perturbations contributes to the growth of eccentricity, thus increasing the probability of encountering chaotic motion during a typical satellite lifetime.

View of Arabella, one of the two Skylab 3 spiders used in experiment

NASA Technical Reports Server (NTRS)

1973-01-01

A close-up view of Arabella, one of the two Skylab 3 common cross spiders 'Araneus diadematus,' and the web it had spun in the zero gravity of space aboard the Skylab space station cluster in Earth orbit. This is a photographic reproduction made from a color television transmission aboard Skylab. Arabella and Anita, were housed in an enclosure onto which a motion picture camera and a still camera were attached to record the spiders' attempts to build a web in the weightless environment.

Optimum solar electric interplanetary mission opportunities from 1975 to 1990

NASA Technical Reports Server (NTRS)

Mann, F. I.; Horsewood, J. L.

1971-01-01

A collection of optimum trajectory and spacecraft data is presented for unmanned interplanetary missions from 1975 to 1990 using solar electric propulsion. Data are presented for one-way flyby and orbiter missions from Earth to Venus, Mars, Jupiter, Saturn, Uranus, Neptune, and Pluto. The solar system model assumes planetary ephemerides which very closely approximate the true motion of the planets. Direct and indirect flight profiles are investigated. Data are presented for two representative flight times for each mission. The launch vehicle is the Titan 3 B (core)/Centaur, and a constant jet exhaust speed solar electric propulsion system having a specific mass of 30 kg/kw is completely optimized in terms of power level and jet exhaust speed to yield maximum net spacecraft mass. The hyperbolic excess speeds at departure and arrival and the launch date are optimized for each mission. For orbiter missions, a chemical retro stage is used to brake the spacecraft into a highly eccentric capture orbit about the target planet.

Various oscillation patterns in phase models with locally attractive and globally repulsive couplings.

PubMed

Sato, Katsuhiko; Shima, Shin-ichiro

2015-10-01

We investigate a phase model that includes both locally attractive and globally repulsive coupling in one dimension. This model exhibits nontrivial spatiotemporal patterns that have not been observed in systems that contain only local or global coupling. Depending on the relative strengths of the local and global coupling and on the form of global coupling, the system can show a spatially uniform state (in-phase synchronization), a monotonically increasing state (traveling wave), and three types of oscillations of relative phase difference. One of the oscillations of relative phase difference has the characteristic of being locally unstable but globally attractive. That is, any small perturbation to the periodic orbit in phase space destroys its periodic motion, but after a long time the system returns to the original periodic orbit. This behavior is closely related to the emergence of saddle two-cluster states for global coupling only, which are connected to each other by attractive heteroclinic orbits. The mechanism of occurrence of this type of oscillation is discussed.

MT Ser, a binary blue subdwarf

NASA Astrophysics Data System (ADS)

Shimanskii, V. V.; Borisov, N. V.; Sakhibullin, N. A.; Sheveleva, D. V.

2008-06-01

We have classified and determined the parameters of the evolved close binary MT Ser. Our moderate-resolution spectra covering various phases of the orbital period were taken with the 6-m telescope of the Special Astrophysical Observatory. The spectra of MT Ser freed from the contribution of the surrounding nebula Abell 41 contained no emission lines due to the reflection effect. The radial velocities measured from lines of different elements showed them to be constant on a time scale corresponding to the orbital period. At the same time, we find effects of broadening for the HeII absorption lines, due to the orbital motion of two hot stars of similar types. As a result, we classify MT Ser as a system with two blue subdwarfs after the common-envelope stage. We estimate the component masses and the distance to the object from the Doppler broadening of the HeII lines. We demonstrate that the age of the ambient nebula, Abell 41, is about 35 000 years.

A Gauge-generalized Solution for Non-Keplerian Motion in the Frenet-Serret Frame

NASA Astrophysics Data System (ADS)

Garber, Darren D.

2009-05-01

The customary modeling of perturbed planetary and spacecraft motion as a continuous sequence of unperturbed two-body orbits (instantaneous ellipses) is conveniently assigned a physical interpretation through the Keplerian and Delaunay elements and complemented mathematically by the Lagrange-type equations which describe the evolution of these variables. If however the actual motion is very non-Keplerian (i.e. the perturbed orbit varies greatly from a two-body orbit), then its modeling by a sequence of conics is not necessarily optimal in terms of its mathematical description and its resulting physical interpretation. Since, in principle a curve of any type can be represented as a sequence of points from a family of curves of any other type (Efroimsky 2005), alternate non-conic curves can be utilized to better describe the perturbed non-Keplerian motion of the body both mathematically and with a physically relevant interpretation. Non-Keplerian motion exists in both celestial mechanics and astrodynamics as evident by the complex interactions within star clusters and also as the result of a spacecraft accelerating via ion propulsion, solar sails and electro-dynamic tethers. For these cases, the sequence of simple orbits to describe the motion is not based on conics, but instead a family of spirals. The selection of spirals as the underlying simple motion is supported by the fact that it is unnecessary to describe the motion in terms of instantaneous orbits tangent to the actual trajectory (Efroimsky 2002, Newman & Efroimsky 2003) and at times there is an advantage to deviate from osculation, in order to greatly simplify the resulting mathematics via gauge freedom (Efroimsky & Goldreich 2003, Slabinski 2003, Gurfil 2004). From these two principles, (1) spirals as instantaneous orbits, and (2) controlled deviation from osculation, new planetary equations are derived for new non-osculating elements in the Frenet-Serret frame with the gauge function as a measure of non-osculation.

Radiation of a nonrelativistic particle during its finite motion in a central field

DOE Office of Scientific and Technical Information (OSTI.GOV)

Karnakov, B. M., E-mail: karnak@theor.mephi.ru; Korneev, Ph. A., E-mail: korneev@theor.mephi.ru; Popruzhenko, S. V.

The spectrum and expressions for the intensity of dipole radiation lines are obtained for a classical nonrelativistic charged particle that executes a finite aperiodic motion in an arbitrary central field along a non-closed trajectory. It is shown that, in this case of a conditionally periodic motion, the radiaton spectrum consists of two series of equally spaced lines. It is pointed out that, according to the correspondence principle, the rise of two such series in the classical theory corresponds to the well-known selection rule |{delta}l = 1 for the dipole radiation in a central field in quantum theory, where l ismore » the orbital angular momentum of the particle. The results obtained can be applied to the description of the radiation and the absorption of a classical collisionless electron plasma in nanoparticles irradiated by an intense laser field. As an example, the rate of collisionless absorption of electromagnetic wave energy in equilibrium isotropic nanoplasma is calculated.« less

Equation-of-motion coupled-cluster method for doubly ionized states with spin-orbit coupling.

PubMed

Wang, Zhifan; Hu, Shu; Wang, Fan; Guo, Jingwei

2015-04-14

In this work, we report implementation of the equation-of-motion coupled-cluster method for doubly ionized states (EOM-DIP-CC) with spin-orbit coupling (SOC) using a closed-shell reference. Double ionization potentials (DIPs) are calculated in the space spanned by 2h and 3h1p determinants with the EOM-DIP-CC approach at the CC singles and doubles level (CCSD). Time-reversal symmetry together with spatial symmetry is exploited to reduce computational effort. To circumvent the problem of unstable dianion references when diffuse basis functions are included, nuclear charges are scaled. Effect of this stabilization potential on DIPs is estimated based on results from calculations using a small basis set without diffuse basis functions. DIPs and excitation energies of some low-lying states for a series of open-shell atoms and molecules containing heavy elements with two unpaired electrons have been calculated with the EOM-DIP-CCSD approach. Results show that this approach is able to afford a reliable description on SOC splitting. Furthermore, the EOM-DIP-CCSD approach is shown to provide reasonable excitation energies for systems with a dianion reference when diffuse basis functions are not employed.

Equation-of-motion coupled-cluster method for doubly ionized states with spin-orbit coupling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Zhifan; Hu, Shu; Guo, Jingwei

2015-04-14

In this work, we report implementation of the equation-of-motion coupled-cluster method for doubly ionized states (EOM-DIP-CC) with spin-orbit coupling (SOC) using a closed-shell reference. Double ionization potentials (DIPs) are calculated in the space spanned by 2h and 3h1p determinants with the EOM-DIP-CC approach at the CC singles and doubles level (CCSD). Time-reversal symmetry together with spatial symmetry is exploited to reduce computational effort. To circumvent the problem of unstable dianion references when diffuse basis functions are included, nuclear charges are scaled. Effect of this stabilization potential on DIPs is estimated based on results from calculations using a small basis setmore » without diffuse basis functions. DIPs and excitation energies of some low-lying states for a series of open-shell atoms and molecules containing heavy elements with two unpaired electrons have been calculated with the EOM-DIP-CCSD approach. Results show that this approach is able to afford a reliable description on SOC splitting. Furthermore, the EOM-DIP-CCSD approach is shown to provide reasonable excitation energies for systems with a dianion reference when diffuse basis functions are not employed.« less

Approximate approach for optimization space flights with a low thrust on the basis of sufficient optimality conditions

NASA Astrophysics Data System (ADS)

Salmin, Vadim V.

2017-01-01

Flight mechanics with a low-thrust is a new chapter of mechanics of space flight, considered plurality of all problems trajectory optimization and movement control laws and the design parameters of spacecraft. Thus tasks associated with taking into account the additional factors in mathematical models of the motion of spacecraft becomes increasingly important, as well as additional restrictions on the possibilities of the thrust vector control. The complication of the mathematical models of controlled motion leads to difficulties in solving optimization problems. Author proposed methods of finding approximate optimal control and evaluating their optimality based on analytical solutions. These methods are based on the principle of extending the class of admissible states and controls and sufficient conditions for the absolute minimum. Developed procedures of the estimation enabling to determine how close to the optimal founded solution, and indicate ways to improve them. Authors describes procedures of estimate for approximately optimal control laws for space flight mechanics problems, in particular for optimization flight low-thrust between the circular non-coplanar orbits, optimization the control angle and trajectory movement of the spacecraft during interorbital flights, optimization flights with low-thrust between arbitrary elliptical orbits Earth satellites.

Self-attraction into spinning eigenstates of a mobile wave source by its emission back-reaction

NASA Astrophysics Data System (ADS)

Labousse, Matthieu; Perrard, Stéphane; Couder, Yves; Fort, Emmanuel

2016-10-01

The back-reaction of a radiated wave on the emitting source is a general problem. In the most general case, back-reaction on moving wave sources depends on their whole history. Here we study a model system in which a pointlike source is piloted by its own memory-endowed wave field. Such a situation is implemented experimentally using a self-propelled droplet bouncing on a vertically vibrated liquid bath and driven by the waves it generates along its trajectory. The droplet and its associated wave field form an entity having an intrinsic dual particle-wave character. The wave field encodes in its interference structure the past trajectory of the droplet. In the present article we show that this object can self-organize into a spinning state in which the droplet possesses an orbiting motion without any external interaction. The rotation is driven by the wave-mediated attractive interaction of the droplet with its own past. The resulting "memory force" is investigated and characterized experimentally, numerically, and theoretically. Orbiting with a radius of curvature close to half a wavelength is shown to be a memory-induced dynamical attractor for the droplet's motion.

Real-time approximate optimal guidance laws for the advanced launch system

NASA Technical Reports Server (NTRS)

Speyer, Jason L.; Feeley, Timothy; Hull, David G.

1989-01-01

An approach to optimal ascent guidance for a launch vehicle is developed using an expansion technique. The problem is to maximize the payload put into orbit subject to the equations of motion of a rocket over a rotating spherical earth. It is assumed that the thrust and gravitational forces dominate over the aerodynamic forces. It is shown that these forces can be separated by a small parameter epsilon, where epsilon is the ratio of the atmospheric scale height to the radius of the earth. The Hamilton-Jacobi-Bellman or dynamic programming equation is expanded in a series where the zeroth-order term (epsilon = 0) can be obtained in closed form. The zeroth-order problem is that of putting maximum payload into orbit subject to the equations of motion of a rocket in a vacuum over a flat earth. The neglected inertial and aerodynamic terms are included in higher order terms of the expansion, which are determined from the solution of first-order linear partial differential equations requiring only quadrature integrations. These quadrature integrations can be performed rapidly, so that real-time approximate optimization can be used to construct the launch guidance law.

Topology of the Relative Motion: Circular and Eccentric Reference Orbit Cases

NASA Technical Reports Server (NTRS)

FontdecabaiBaig, Jordi; Metris, Gilles; Exertier, Pierre

2007-01-01

This paper deals with the topology of the relative trajectories in flight formations. The purpose is to study the different types of relative trajectories, their degrees of freedom, and to give an adapted parameterization. The paper also deals with the research of local circular motions. Even if they exist only when the reference orbit is circular, we extrapolate initial conditions to the eccentric reference orbit case.This alternative approach is complementary with traditional approaches in terms of cartesian coordinates or differences of orbital elements.

Effects of spacecraft motions on fluids experiments

NASA Technical Reports Server (NTRS)

Gans, R. F.

1981-01-01

The equations of motion governing an incompressible fluid contained in an orbiting laboratory were examined to isolate various fictitious forces and their relative influence on the fluid. The forces are divided into those arising from the orbital motions and those arising from small local motions of the spacecraft about its center of mass. The latter dominate the nonrotating experiments. Both are important for rotating experiments. A brief discussion of the onset of time-dependence and violent instability in earth-based rotating and processing systems is given.

Geodesic motion around traversable wormholes supported by a massless conformally coupled scalar field

NASA Astrophysics Data System (ADS)

Willenborg, Felix; Grunau, Saskia; Kleihaus, Burkhard; Kunz, Jutta

2018-06-01

We consider a traversable wormhole solution of Einstein's gravity conformally coupled to a massless scalar field, a solution derived by Barcelo and Visser based on the Janis-Newman-Winicour-Wyman spacetime. We study the geodesic motion of timelike and spacelike particles in this spacetime. We solve the equations of motion analytically in terms of the Weierstraß functions and discuss all possible orbit types and their parameter dependence. Interestingly, bound orbits occur for timelike geodesics only in one of the two worlds. Moreover, under no conditions there exist timelike two world bound orbits.

Analytical solution of perturbed relative motion: an application of satellite formations to geodesy

NASA Astrophysics Data System (ADS)

Wnuk, Edwin

In the upcoming years, several space missions will be operated using a number of spacecraft flying in formation. Clusters of spacecraft with a carefully designed orbits and optimal formation geometry enable a wide variety of applications ranging from remote sensing to astronomy, geodesy and basic physics. Many of the applications require precise relative navigation and autonomous orbit control of satellites moving in a formation. For many missions a centimeter level of orbit control accuracy is required. The GRACE mission, since its launch in 2002, has been improving the Earth's gravity field model to a very high level of accuracy. This mission is a formation flying one consisting of two satellites moving in coplanar orbits and provides range and range-rate measurements between the satellites in the along-track direction. Future geodetic missions probably will employ alternative architectures using additional satellites and/or performing out-of-plane motion, e.g cartwheel orbits. The paper presents an analytical model of a satellite formation motion that enables propagation of the relative spacecraft motion. The model is based on the analytical theory of satellite relative motion that was presented in the previous our papers (Wnuk and Golebiewska, 2005, 2006). This theory takes into account the influence of the following gravitational perturbation effects: 1) zonal and tesseral harmonic geopotential coefficients up to arbitrary degree and order, 2) Lunar gravity, 3) Sun gravity. Formulas for differential perturbations were derived with any restriction concerning a plane of satellite orbits. They can be applied in both: in plane and out of plane cases. Using this propagator we calculated relative orbits and future relative satellite positions for different types of formations: in plane, out of plane, cartwheel and others. We analyzed the influence of particular parts of perturbation effects and estimated the accuracy of predicted relative spacecrafts positions. References 1,Wnuk E., Golebiewska J.,2005, ,,The relative motion of Earth's orbiting satellites", Celestial Mechanics, 91, 373-389. 2.Wnuk E., Golebiewska J.,2006, "Differential Perturbations and Semimajor Axis Estimation for Satellite Formation Orbits", American Institute of Aeronautics and Astronautics, Electronic Library, 2006, 6018.

Orbital motion of the solar power satellite

NASA Technical Reports Server (NTRS)

Graf, O. F., Jr.

1977-01-01

A study on the effects of solar radiation pressure on the SPS orbit is documented. It was shown that the eccentricity of the orbit can increase from initially being zero. The SPS configuration is primarily considered but the results are applicable to any geosynchronous satellite that resembles a flat surface continually facing the sun. The orbital evolution of the SPS was investigated over its expected 30 year lifetime and the satellite was assumed to be in free flight. The satellite's motion was described with analytical formulae which could be used to develop an orbit control theory in order to minimize station keeping costs.

Ray-tracing in pseudo-complex General Relativity

NASA Astrophysics Data System (ADS)

Schönenbach, T.; Caspar, G.; Hess, P. O.; Boller, T.; Müller, A.; Schäfer, M.; Greiner, W.

2014-07-01

Motivated by possible observations of the black hole candidate in the centre of our Galaxy and the galaxy M87, ray-tracing methods are applied to both standard General Relativity (GR) and a recently proposed extension, the pseudo-complex GR (pc-GR). The correction terms due to the investigated pc-GR model lead to slower orbital motions close to massive objects. Also the concept of an innermost stable circular orbit is modified for the pc-GR model, allowing particles to get closer to the central object for most values of the spin parameter a than in GR. Thus, the accretion disc, surrounding a massive object, is brighter in pc-GR than in GR. Iron Kα emission-line profiles are also calculated as those are good observables for regions of strong gravity. Differences between the two theories are pointed out.

The MillSOT-A Spiral Orbit Tribometer on a Milling Machine

NASA Technical Reports Server (NTRS)

Pepper, Stephen V.

2014-01-01

A spiral orbit tribometer (SOT) intended to characterize friction and wear phenomena has been constructed on a milling machine. The instrument, essentially a retainerless thrust bearing with one ball and flat races, is exceedingly simple and inexpensive to construct. The capabilities of the tribometer to measure both the coefficient of friction and contact electrical resistance are demonstrated with clean specimens as well as with well known lubricants such as molybdenum disulphide and Krytox oil. Operation in a purged environment of inert gas is also demonstrated. The results with these lubricants are quite close to what is obtained by other methods. Suggestions for extending the capabilities of the tribometer are given. This arrangement may find use in university mechanical engineering laboratories to introduce and study rolling contact motion as well as for research in contact mechanics and tribology.

Quantum entanglement and quantum information in biological systems (DNA)

NASA Astrophysics Data System (ADS)

Hubač, Ivan; Švec, Miloslav; Wilson, Stephen

2017-12-01

Recent studies of DNA show that the hydrogen bonds between given base pairs can be treated as diabatic systems with spin-orbit coupling. For solid state systems strong diabaticity and spin-orbit coupling the possibility of forming Majorana fermions has been discussed. We analyze the hydrogen bonds in the base pairs in DNA from this perspective. Our analysis is based on a quasiparticle supersymmetric transformation which couples electronic and vibrational motion and includes normal coordinates and the corresponding momenta. We define qubits formed by Majorana fermions in the hydrogen bonds and also discuss the entangled states in base pairs. Quantum information and quantum entropy are introduced. In addition to the well-known classical information connected with the DNA base pairs, we also consider quantum information and show that the classical and quantum information are closely connected.

Modeling Attitude Dynamics in Simulink: A Study of the Rotational and Translational Motion of a Spacecraft Given Torques and Impulses Generated by RMS Hand Controllers

NASA Technical Reports Server (NTRS)

Mauldin, Rebecca H.

2010-01-01

In order to study and control the attitude of a spacecraft, it is necessary to understand the natural motion of a body in orbit. Assuming a spacecraft to be a rigid body, dynamics describes the complete motion of the vehicle by the translational and rotational motion of the body. The Simulink Attitude Analysis Model applies the equations of rigid body motion to the study of a spacecraft?s attitude in orbit. Using a TCP/IP connection, Matlab reads the values of the Remote Manipulator System (RMS) hand controllers and passes them to Simulink as specified torque and impulse profiles. Simulink then uses the governing kinematic and dynamic equations of a rigid body in low earth orbit (LE0) to plot the attitude response of a spacecraft for five seconds given known applied torques and impulses, and constant principal moments of inertia.

The rotational motion of an earth orbiting gyroscope according to the Einstein theory of general relativity

NASA Technical Reports Server (NTRS)

Hoots, F. R.; Fitzpatrick, P. M.

1979-01-01

The classical Poisson equations of rotational motion are used to study the attitude motions of an earth orbiting, rapidly spinning gyroscope perturbed by the effects of general relativity (Einstein theory). The center of mass of the gyroscope is assumed to move about a rotating oblate earth in an evolving elliptic orbit which includes all first-order oblateness effects produced by the earth. A method of averaging is used to obtain a transformation of variables, for the nonresonance case, which significantly simplifies the Poisson differential equations of motion of the gyroscope. Long-term solutions are obtained by an exact analytical integration of the simplified transformed equations. These solutions may be used to predict both the orientation of the gyroscope and the motion of its rotational angular momentum vector as viewed from its center of mass. The results are valid for all eccentricities and all inclinations not near the critical inclination.

Accurate orbit propagation in the presence of planetary close encounters

NASA Astrophysics Data System (ADS)

Amato, Davide; Baù, Giulio; Bombardelli, Claudio

2017-09-01

We present an efficient strategy for the numerical propagation of small Solar system objects undergoing close encounters with massive bodies. The trajectory is split into several phases, each of them being the solution of a perturbed two-body problem. Formulations regularized with respect to different primaries are employed in two subsequent phases. In particular, we consider the Kustaanheimo-Stiefel regularization and a novel set of non-singular orbital elements pertaining to the Dromo family. In order to test the proposed strategy, we perform ensemble propagations in the Earth-Sun Circular Restricted 3-Body Problem (CR3BP) using a variable step size and order multistep integrator and an improved version of Everhart's radau solver of 15th order. By combining the trajectory splitting with regularized equations of motion in short-term propagations (1 year), we gain up to six orders of magnitude in accuracy with respect to the classical Cowell's method for the same computational cost. Moreover, in the propagation of asteroid (99942) Apophis through its 2029 Earth encounter, the position error stays within 100 metres after 100 years. In general, as to improve the performance of regularized formulations, the trajectory must be split between 1.2 and 3 Hill radii from the Earth. We also devise a robust iterative algorithm to stop the integration of regularized equations of motion at a prescribed physical time. The results rigorously hold in the CR3BP, and similar considerations may apply when considering more complex models. The methods and algorithms are implemented in the naples fortran 2003 code, which is available online as a GitHub repository.

RXJ0440.9+4431: a Persistent Be-x-ray Binary in Outburst

NASA Technical Reports Server (NTRS)

Ferrigno, C.; Farinelli, R.; Bozzo, E.; Pottschmidt, K.; Klochkov, D.; Kretschmar, P.

2013-01-01

The persistent Be/X-ray binary RXJ0440.9+4431 flared in 2010 and 2011 and has been followed by various X-ray facilities (Swift, RXTE, XMM-Newton, and INTEGRAL).We studied the source timing and spectral properties as a function of its X-ray luminosity to investigate the transition from normal to flaring activity and the dynamical properties of the system. We have determined the orbital period from the long-term Swift/BAT light curve, but our determinations of the spin-period are not precise enough to constrain any orbital solution. The source spectrum can always be described by a bulk-motion Comptonization model of black body seed photons attenuated by a moderate photoelectric absorption. At the highest luminosity, we measured a curvature of the spectrum, which we attribute to a significant contribution of the radiation pressure in the accretion process. This allows us to estimate that the transition from a bulk-motion-dominated flow to a radiatively dominated one happens at a luminosity of approx 2 × 10(exp 36) erg/ s. The luminosity dependency of the size of the black body emission region is found to be r(sub BB) varies as L(sub x) (exp 0.39 +/- 0.02). This suggests that either matter accreting onto the neutron star hosted in RXJ0440.9+4431 penetrates through closed magnetic field lines at the border of the compact object magnetosphere or that the structure of the Neutron star magnetic field is more complicated than a simple dipole close to the surface.

Nodding motions of accretion rings and disks - A short-term period in SS 433

NASA Technical Reports Server (NTRS)

Katz, J. I.; Anderson, S. F.; Grandi, S. A.; Margon, B.

1982-01-01

It is pointed out that accretion disks and rings in mass transfer binaries have been observed spectroscopically and calculated theoretically for many years. The present investigation is partly based on the availability of several years of spectroscopic observations of the Doppler shifts of the moving lines in SS433. A formalism is presented to compute frequencies and amplitudes of short-term 'nodding' motions in precessing accretion disks in close binary systems. This formalism is applied to an analysis of the moving-line Doppler shifts in SS433. The 35d X-ray cycle of Hercules X-1 is also discussed. In the considered model, the companion star exerts a gravitational torque on the disk rim. Averaged over the binary orbit, this yields a steady torque which results in the mean driven counterprecession of the disk.

Self-focusing skyrmion racetracks in ferrimagnets

NASA Astrophysics Data System (ADS)

Kim, Se Kwon; Lee, Kyung-Jin; Tserkovnyak, Yaroslav

2017-04-01

We theoretically study the dynamics of ferrimagnetic skyrmions in inhomogeneous metallic films close to the angular momentum compensation point. In particular, it is shown that the line of the vanishing angular momentum can be utilized as a self-focusing racetrack for skyrmions. To that end, we begin by deriving the equations of motion for the dynamics of collinear ferrimagnets in the presence of a charge current. The obtained equations of motion reduce to those of ferromagnets and antiferromagnets at two special limits. In the collective coordinate approach, a skyrmion behaves as a massive charged particle moving in a viscous medium subjected to a magnetic field. Analogous to the snake orbits of electrons in a nonuniform magnetic field, we show that a ferrimagnet with nonuniform angular momentum density can exhibit the snake trajectories of skyrmions, which can be utilized as racetracks for skyrmions.

Dynamics of the retrograde 1/1 mean motion resonance

NASA Astrophysics Data System (ADS)

Huang, Yukun; Li, Miao; Li, Junfeng; Gong, Shengping

2018-04-01

Mean motion resonances are very common in the solar system. Asteroids in mean motion resonances with giant planets have been studied for centuries. But it was not until recently that asteroids in retrograde mean motion resonances with Jupiter and Saturn were discovered. The newly discovered asteroid, 2015 BZ509 is confirmed to be the first asteroid in retrograde 1:1 mean motion resonance (or retrograde co-orbital resonance) with Jupiter, which gives rise to our interests in its unique resonant dynamics. In this study, we thoroughly investigate the phase-space structure of the retrograde 1:1 resonance within the framework of the circular restricted three-body problem. We begin by constructing a simple integrable approximation for the planar retrograde resonance with the Hamiltonian approach and show that the variables definition of the retrograde resonance is very different to the prograde one. When it comes to the disturbing function, we abandon the classical series expansion approach, whereas numerically carry out the averaging process on the disturbing function in closed form. The phase portrait of the retrograde 1:1 resonance is depicted with the level curves of the averaged Hamiltonian. We find that the topological structure of phase space for the retrograde 1:1 resonance is very different to other resonances, due to the consistent existence of the collision separatrix. And the surprising bifurcation of equilibrium point around 180° (i.e., the apocentric libration center) has never been found in any other mean motion resonances before. We thoroughly analyze the novel apocentric librations and find that close encounter with the planet does not always lead to the disruption of a stable apocentric libration. Afterwards, we examine the Kozai dynamics inside the mean motion resonance with the similar Hamiltonian approach and explain why the exact resonant point does not exist in the 3D retrograde 1:1 resonance model.

The stability of steady motion of magnetic domain wall: Role of higher-order spin-orbit torques

DOE Office of Scientific and Technical Information (OSTI.GOV)

He, Peng-Bin, E-mail: hepengbin@hnu.edu.cn; Yan, Han; Cai, Meng-Qiu

The steady motion of magnetic domain wall driven by spin-orbit torques is investigated analytically in the heavy/ferromagnetic metal nanowires for three cases with a current transverse to the in-plane and perpendicular easy axis, and along the in-plane easy axis. By the stability analysis of Walker wall profile, we find that if including the higher-order spin-orbit torques, the Walker breakdown can be avoided in some parameter regions of spin-orbit torques with a current transverse to or along the in-plane easy axis. However, in the case of perpendicular anisotropy, even considering the higher-order spin-orbit torques, the velocity of domain wall cannot bemore » efficiently enhanced by the current. Furthermore, the direction of wall motion is dependent on the configuration and chirality of domain wall with a current along the in-plane easy axis or transverse to the perpendicular one. Especially, the direction of motion can be controlled by the initial chirality of domain wall. So, if only involving the spin-orbit mechanism, it is preferable to adopt the scheme of a current along the in-plane easy axis for enhancing the velocity and controlling the direction of domain wall.« less

Measurement and Compensation of BPM Chamber Motion in HLS

NASA Astrophysics Data System (ADS)

Li, J. W.; Sun, B. G.; Cao, Y.; Xu, H. L.; Lu, P.; Li, C.; Xuan, K.; Wang, J. G.

2010-06-01

Significant horizontal drifts in the beam orbit in the storage ring of HLS (Hefei Light Source) have been seen for many years. What leads to the motion of Beam Position Monitor (BPM) chamber is thermal expansion mainly caused by the synchrotron light. To monitor the BPM chamber motions for all BPMs, a BPM chamber motion measurement system is built in real-time. The raster gauges are used to measure the displacements. The results distinctly show the relation between the BPM chamber motion and the beam current. To suppress the effect of BPM chamber motion, a compensation strategy is implemented at HLS. The horizontal drifts of beam orbit have been really suppressed within 20μm without the compensation of BPM chamber motion in the runtime.

Identification of new orbits to enable future mission opportunities for the human exploration of the Martian moon Phobos

NASA Astrophysics Data System (ADS)

Zamaro, Mattia; Biggs, James D.

2016-02-01

One of the paramount stepping stones towards NASA's long-term goal of undertaking human missions to Mars is the exploration of the Martian moons. Since a precursor mission to Phobos would be easier than landing on Mars itself, NASA is targeting this moon for future exploration, and ESA has also announced Phootprint as a candidate Phobos sample-and-return mission. Orbital dynamics around small planetary satellites are particularly complex because many strong perturbations are involved, and the classical circular restricted three-body problem (R3BP) does not provide an accurate approximation to describe the system's dynamics. Phobos is a special case, since the combination of a small mass-ratio and length-scale means that the sphere-of-influence of the moon moves very close to its surface. Thus, an accurate nonlinear model of a spacecraft's motion in the vicinity of this moon must consider the additional perturbations due to the orbital eccentricity and the complete gravity field of Phobos, which is far from a spherical-shaped body, and it is incorporated into an elliptic R3BP using the gravity harmonics series-expansion (ER3BP-GH). In this paper, a showcase of various classes of non-keplerian orbits is identified and a number of potential mission applications in the Mars-Phobos system are proposed: these results could be exploited in upcoming unmanned missions targeting the exploration of this Martian moon. These applications include: low-thrust hovering and orbits around Phobos for close-range observations; the dynamical substitutes of periodic and quasi-periodic Libration Point Orbits in the ER3BP-GH to enable unique low-cost operations for space missions in the proximity of Phobos; their manifold structure for high-performance landing/take-off maneuvers to and from Phobos' surface and for transfers from and to Martian orbits; Quasi-Satellite Orbits for long-period station-keeping and maintenance. In particular, these orbits could exploit Phobos' occulting bulk and shadowing wake as a passive radiation shield during future manned flights to Mars to reduce human exposure to radiation, and the latter orbits can be used as an orbital garage, requiring no orbital maintenance, where a spacecraft could make planned pit-stops during a round-trip mission to Mars.

Proper Motions of Dwarf Spheroidal Galaxies from Hubble Space Telescope Imaging. III. Measurement for Ursa Minor

NASA Astrophysics Data System (ADS)

Piatek, Slawomir; Pryor, Carlton; Bristow, Paul; Olszewski, Edward W.; Harris, Hugh C.; Mateo, Mario; Minniti, Dante; Tinney, Christopher G.

2005-07-01

This article presents a measurement of the proper motion of the Ursa Minor dwarf spheroidal galaxy determined from images taken with the Hubble Space Telescope in two distinct fields. Each field contains a quasi-stellar object that serves as the ``reference point.'' The measured proper motion for Ursa Minor, expressed in the equatorial coordinate system, is (μα,μδ)=(-50+/-17,22+/-16) mas century-1. Removing the contributions of the solar motion and the motion of the local standard of rest yields the proper motion in the Galactic rest frame: (μGrfα,μGrfδ)=(-8+/-17,38+/-16) mas century-1. The implied space velocity with respect to the Galactic center has a radial component of Vr=-75+/-44 km s-1 and a tangential component of Vt=144+/-50 km s-1. Integrating the motion of Ursa Minor in a realistic potential for the Milky Way produces orbital elements. The perigalacticon and apogalacticon are 40 (10, 76) and 89 (78, 160) kpc, respectively, where the values in the parentheses represent the 95% confidence intervals derived from Monte Carlo experiments. The eccentricity of the orbit is 0.39 (0.09, 0.79), and the orbital period is 1.5 (1.1, 2.7) Gyr. The orbit is retrograde and inclined by 124° (94°, 136°) to the Galactic plane. Ursa Minor is not a likely member of a proposed stream of galaxies on similar orbits around the Milky Way, nor is the plane of its orbit coincident with a recently proposed planar alignment of galaxies around the Milky Way. Comparing the orbits of Ursa Minor and Carina shows no reason for the different star formation histories of these two galaxies. Ursa Minor must contain dark matter to have a high probability of having survived disruption by the Galactic tidal force until the present. Based on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555.

On the Early In Situ Formation of Pluto’s Small Satellites

NASA Astrophysics Data System (ADS)

Woo, Jason Man Yin; Lee, Man Hoi

2018-04-01

The formation of Pluto’s small satellites—Styx, Nix, Keberos, and Hydra—remains a mystery. Their orbits are nearly circular and are near mean-motion resonances and nearly coplanar with Charon’s orbit. One scenario suggests that they all formed close to their current locations from a disk of debris that was ejected from the Charon-forming impact before the tidal evolution of Charon. The validity of this scenario is tested by performing N-body simulations with the small satellites treated as test particles and Pluto–Charon evolving tidally from an initial orbit at a few Pluto radii with initial eccentricity e C = 0 or 0.2. After tidal evolution, the free eccentricities e free of the test particles are extracted by applying fast Fourier transformation to the distance between the test particles and the center of mass of the system and compared with the current eccentricities of the four small satellites. The only surviving test particles with e free matching the eccentricities of the current satellites are those not affected by mean-motion resonances during the tidal evolution in a model with Pluto’s effective tidal dissipation function Q = 100 and an initial e C = 0.2 that is damped down rapidly. However, these test particles do not have any preference to be in or near 4:1, 5:1, and 6:1 resonances with Charon. An alternative scenario may be needed to explain the formation of Pluto’s small satellites.

From Measure Zero to Measure Hero: Periodic Kerr Orbits and Gravitational Wave Physics

NASA Astrophysics Data System (ADS)

Perez-Giz, Gabriel

2011-12-01

A direct observational detection of gravitational waves -- perhaps the most fundamental prediction of a theory of curved spacetime -- looms close at hand. Stellar mass compact objects spiraling into supermassive black holes have received particular attention as sources of gravitational waves detectable by space-based gravitational wave observatories. A well-established approach models such an extreme mass ratio inspirals (EMRI) as an adiabatic progression through a series of Kerr geodesics. Thus, the direct detection of gravitational radiation from EMRIs and the extraction of astrophysical information from those waveforms require a thorough knowledge of the underlying geodesic dynamics. This dissertation adopts a dynamical systems approach to the study of Kerr orbits, beginning with equatorial orbits. We deduce a topological taxonomy of orbits that hinges on a correspondence between periodic orbits and rational numbers. The taxonomy defines the entire dynamics, including aperiodic motion, since every orbit is in or near the periodic set. A remarkable implication of this periodic orbit taxonomy is that the simple precessing ellipse familiar from planetary orbits is not allowed in the strong-field regime. Instead, eccentric orbits trace out precessions of multi-leaf clovers in the final stages of inspiral. Furthermore, for any black hole, there is some orbital angular momentum value in the strong-field regime below which zoom-whirl behavior becomes unavoidable. We then generalize the taxonomy to help identify nonequatorial orbits whose radial and polar frequencies are rationally related, or in resonance. The thesis culminates by describing how those resonant orbits can be leveraged for an order of magnitude or more reduction in the computational cost of adiabatic order EMRI trajectories, which are so prohibitively expensive that no such relativistically correct inspirals have been generated to date.

VizieR Online Data Catalog: Double stars with wide separations in the AGK3 (Halbwachs+, 2016)

NASA Astrophysics Data System (ADS)

Halbwachs, J. L.; Mayor, M.; Udry, S.

2016-10-01

A large list of common proper motion stars selected from the third Astronomischen Gesellschaft Katalog (AGK3) was monitored with the CORAVEL (for COrrelation RAdial VELocities) spectrovelocimeter, in order to prepare a sample of physical binaries with very wide separations. In paper I,66 stars received special attention, since their radial velocities (RV) seemed to be variable. These stars were monitored over several years in order to derive the elements of their spectroscopic orbits. In addition, 10 of them received accurate RV measurements from the SOPHIE spectrograph of the T193 telescope at the Observatory of Haute-Provence. For deriving the orbital elements of double-lined spectroscopic binaries (SB2s), a new method was applied, which assumed that the RV of blended measurements are linear combinations of the RV of the components. 13 SB2 orbits were thus calculated. The orbital elements were eventually obtained for 52 spectroscopic binaries (SBs), two of them making a triple system. 40 SBs received their first orbit and the orbital elements were improved for 10 others. In addition, 11 SBs were discovered with very long periods for which the orbital parameters were not found. It appeared that HD 153252 has a close companion, which is a candidate brown dwarf with a minimum mass of 50 Jupiter masses. In paper II, 80 wide binaries (WBs) were detected, and 39 optical pairs were identified. Adding CPM stars with separations close enough to be almost certain they are physical, a "bias-controlled" sample of 116 wide binaries was obtained, and used to derive the distribution of separations from 100 to 30,000 au. The distribution obtained doesn't match the log-constant distribution, but is in agreement with the log-normal distribution. The spectroscopic binaries detected among the WB components were used to derive statistical informations about the multiple systems. The close binaries in WBs seem to be similar to those detected in other field stars. As for the WBs, they seem to obey the log-normal distribution of periods. The number of quadruple systems is in agreement with the "no correlation" hypothesis; this indicates that an environment conducive to the formation of WBs doesn't favor the formation of subsystems with periods shorter than 10 years. (9 data files).

Spaceborne Autonomous and Ground Based Relative Orbit Control for the TerraSAR-X/TanDEM-X Formation

NASA Technical Reports Server (NTRS)

Ardaens, J. S.; D'Amico, S.; Kazeminejad, B.; Montenbruck, O.; Gill, E.

2007-01-01

TerraSAR-X (TSX) and TanDEM-X (TDX) are two advanced synthetic aperture radar (SAR) satellites flying in formation. SAR interferometry allows a high resolution imaging of the Earth by processing SAR images obtained from two slightly different orbits. TSX operates as a repeat-pass interferometer in the first phase of its lifetime and will be supplemented after two years by TDX in order to produce digital elevation models (DEM) with unprecedented accuracy. Such a flying formation makes indeed possible a simultaneous interferometric data acquisition characterized by highly flexible baselines with range of variations between a few hundreds meters and several kilometers [1]. TSX has been successfully launched on the 15th of June, 2007. TDX is expected to be launched on the 31st of May, 2009. A safe and robust maintenance of the formation is based on the concept of relative eccentricity/inclination (e/i) vector separation whose efficiency has already been demonstrated during the Gravity Recovery and Climate Experiment (GRACE) [2]. Here, the satellite relative motion is parameterized by mean of relative orbit elements and the key idea is to align the relative eccentricity and inclination vectors to minimize the hazard of a collision. Previous studies have already shown the pertinence of this concept and have described the way of controlling the formation using an impulsive deterministic control law [3]. Despite the completely different relative orbit control requirements, the same approach can be applied to the TSX/TDX formation. The task of TDX is to maintain the close formation configuration by actively controlling its relative motion with respect to TSX, the leader of the formation. TDX must replicate the absolute orbit keeping maneuvers executed by TSX and also compensate the natural deviation of the relative e/i vectors. In fact the relative orbital elements of the formation tend to drift because of the secular non-keplerian perturbations acting on both satellites. The goal of the ground segment is thus to regularly correct this configuration by performing small orbit correction maneuvers on TDX. The ground station contacts are limited due to the geographic position of the station and the costs for contact time. Only with a polar ground station a contact visibility is possible every orbit for LEO satellites. TSX and TDX use only the Weilheim ground station (in the southern part of Germany) during routine operations. This station allows two scheduled contact per day for the nominal orbit configuration, meaning that the satellite conditions can be checked with an interval of 12 hours. While this limitation is usually not critical for single satellite operations, the visibility constraints drive the achievable orbit control accuracy for a LEO formation if a ground based approach is chosen. Along-track position uncertainties and maneuver execution errors affect the relative motion and can be compensated only after a ground station contact.

Rendezvous and docking tracker

NASA Technical Reports Server (NTRS)

Ray, Art J.; Ross, Susan E.; Deming, Douglas R.

1986-01-01

A conceptual solid-state rendezvous and docking tracker (RDT) has been devised for generating range and attitude data for a docking vehicle relative to a target vehicle. Emphasis is placed on the approach of the Orbiter to a link with the Space Station. Three laser illuminators ring the optical axis of the lens a directed toward retroreflectors on the target vehicle. Each retroreflector is equipped with a bandpass filter for a designated illumination frequency. Data are collected sequentially over a 20 deg field of view as the range closes to 100-1000 m. A fourth ranging retroreflector 0.3 m from center is employed during close-in maneuvers. The system provides tracking data on motions with 6 deg of freedom, and furnishes 500 msec updates (to be enhanced to 100 msec) to the operator at a computer console.

Twist-induced guidance in coreless photonic crystal fiber: A helical channel for light.

PubMed

Beravat, Ramin; Wong, Gordon K L; Frosz, Michael H; Xi, Xiao Ming; Russell, Philip St J

2016-11-01

A century ago, Einstein proposed that gravitational forces were the result of the curvature of space-time and predicted that light rays would deflect when passing a massive celestial object. We report that twisting the periodically structured "space" within a coreless photonic crystal fiber creates a helical channel where guided modes can form despite the absence of any discernible core structure. Using a Hamiltonian optics analysis, we show that the light rays follow closed spiral or oscillatory paths within the helical channel, in close analogy with the geodesics of motion in a two-dimensional gravitational field. The mode diameter shrinks, and its refractive index rises, as the twist rate increases. The birefringence, orbital angular momentum, and dispersion of these unusual modes are explored.

Study of a close-grid geodynamic measurement system

NASA Technical Reports Server (NTRS)

1977-01-01

The Clogeos (Close-Grid Geodynamic Measurement System) concept, a complete range or range-rate measurement terminal installed in a satellite in a near-polar orbit with a network of relatively simple transponders or retro-reflectors on the ground at intervals of 0.1 to 10 km was reviewed. The distortion of the grid was measured in three dimensions to accuracies of + or - 1 cm with important applications to geodynamics, glaciology, and geodesy. User requirements are considered, and a typical grid, designed for earthquake prediction, was laid out along the San Andreas, Hayward, and Calaceras faults in southern California. The sensitivity of both range and range-rate measurements to small grid motions was determined by a simplified model. Variables in the model are satellite altitude and elevation angle plus grid displacements in latitude, and height.

Exact Delaunay normalization of the perturbed Keplerian Hamiltonian with tesseral harmonics

NASA Astrophysics Data System (ADS)

Mahajan, Bharat; Vadali, Srinivas R.; Alfriend, Kyle T.

2018-03-01

A novel approach for the exact Delaunay normalization of the perturbed Keplerian Hamiltonian with tesseral and sectorial spherical harmonics is presented in this work. It is shown that the exact solution for the Delaunay normalization can be reduced to quadratures by the application of Deprit's Lie-transform-based perturbation method. Two different series representations of the quadratures, one in powers of the eccentricity and the other in powers of the ratio of the Earth's angular velocity to the satellite's mean motion, are derived. The latter series representation produces expressions for the short-period variations that are similar to those obtained from the conventional method of relegation. Alternatively, the quadratures can be evaluated numerically, resulting in more compact expressions for the short-period variations that are valid for an elliptic orbit with an arbitrary value of the eccentricity. Using the proposed methodology for the Delaunay normalization, generalized expressions for the short-period variations of the equinoctial orbital elements, valid for an arbitrary tesseral or sectorial harmonic, are derived. The result is a compact unified artificial satellite theory for the sub-synchronous and super-synchronous orbit regimes, which is nonsingular for the resonant orbits, and is closed-form in the eccentricity as well. The accuracy of the proposed theory is validated by comparison with numerical orbit propagations.

Compensator-based 6-DOF control for probe asteroid-orbital-frame hovering with actuator limitations

NASA Astrophysics Data System (ADS)

Liu, Xiaosong; Zhang, Peng; Liu, Keping; Li, Yuanchun

2016-05-01

This paper is concerned with 6-DOF control of a probe hovering in the orbital frame of an asteroid. Considering the requirements of the scientific instruments pointing direction and orbital position in practical missions, the coordinate control of relative attitude and orbit between the probe and target asteroid is imperative. A 6-DOF dynamic equation describing the relative translational and rotational motion of a probe in the asteroid's orbital frame is derived, taking the irregular gravitation, model and parameter uncertainties and external disturbances into account. An adaptive sliding mode controller is employed to guarantee the convergence of the state error, where the adaptation law is used to estimate the unknown upper bound of system uncertainty. Then the controller is improved to deal with the practical problem of actuator limitations by introducing a RBF neural network compensator, which is used to approximate the difference between the actual control with magnitude constraint and the designed nominal control law. The closed-loop system is proved to be asymptotically stable through the Lyapunov stability analysis. Numerical simulations are performed to compare the performances of the preceding designed control laws. Simulation results demonstrate the validity of the control scheme using the compensator-based adaptive sliding mode control law in the presence of actuator limitations, system uncertainty and external disturbance.

Bondi-Hoyle-Lyttleton Accretion onto Binaries

NASA Astrophysics Data System (ADS)

Antoni, Andrea; MacLeod, Morgan; Ramírez-Ruiz, Enrico

2018-01-01

Binary stars are not rare. While only close binary stars will eventually interact with one another, even the widest binary systems interact with their gaseous surroundings. The rates of accretion and the gaseous drag forces arising in these interactions are the key to understanding how these systems evolve. This poster examines accretion flows around a binary system moving supersonically through a background gas. We perform three-dimensional hydrodynamic simulations of Bondi-Hoyle-Lyttleton accretion using the adaptive mesh refinement code FLASH. We simulate a range of values of semi-major axis of the orbit relative to the gravitational focusing impact parameter of the pair. On large scales, gas is gravitationally focused by the center-of-mass of the binary, leading to dynamical friction drag and to the accretion of mass and momentum. On smaller scales, the orbital motion imprints itself on the gas. Notably, the magnitude and direction of the forces acting on the binary inherit this orbital dependence. The long-term evolution of the binary is determined by the timescales for accretion, slow down of the center-of-mass, and decay of the orbit. We use our simulations to measure these timescales and to establish a hierarchy between them. In general, our simulations indicate that binaries moving through gaseous media will slow down before the orbit decays.

The Improvement of Efficiency in the Numerical Computation of Orbit Trajectories

NASA Technical Reports Server (NTRS)

Dyer, J.; Danchick, R.; Pierce, S.; Haney, R.

1972-01-01

An analysis, system design, programming, and evaluation of results are described for numerical computation of orbit trajectories. Evaluation of generalized methods, interaction of different formulations for satellite motion, transformation of equations of motion and integrator loads, and development of efficient integrators are also considered.

Experimental investigation of the abrasive crown dynamics in orbital atherectomy.

PubMed

Zheng, Yihao; Belmont, Barry; Shih, Albert J

2016-07-01

Orbital atherectomy is a catheter-based minimally invasive procedure to modify the plaque within atherosclerotic arteries using a diamond abrasive crown. This study was designed to investigate the crown motion and its corresponding contact force with the vessel. To this end, a transparent arterial tissue-mimicking phantom made of polyvinyl chloride was developed, a high-speed camera and image processing technique were utilized to visualize and quantitatively analyze the crown motion in the vessel phantom, and a piezoelectric dynamometer measured the forces on the phantom during the procedure. Observed under typical orbital atherectomy rotational speeds of 60,000, 90,000, and 120,000rpm in a 4.8mm caliber vessel phantom, the crown motion was a combination of high-frequency rotation at 1000, 1500, and 1660.4-1866.1Hz and low-frequency orbiting at 18, 38, and 40Hz, respectively. The measured forces were also composed of these high and low frequencies, matching well with the rotation of the eccentric crown and the associated orbital motion. The average peak force ranged from 0.1 to 0.4N at different rotational speeds. Copyright © 2016 IPEM. Published by Elsevier Ltd. All rights reserved.

Accuracy of Estimating Solar Radiation Pressure for GEO Debris with Tumbling Effect

NASA Astrophysics Data System (ADS)

Chao, Chia-Chun George

2009-03-01

The accuracy of estimating solar radiation pressure for GEO debris is examined and demonstrated, via numerical simulations, by fitting a batch (months) of simulated position vectors. These simulated position vectors are generated from a "truth orbit" with added white noise using high-precision numerical integration tools. After the long-arc fit of the simulated observations (position vectors), one can accurately and reliably determine how close the estimated value of solar radiation pressure is to the truth. Results of this study show that the inherent accuracy in estimating the solar radiation pressure coefficient can be as good as 1% if a long-arc fit span up to 180 days is used and the satellite is not tumbling. The corresponding position prediction accuracy can be as good as, in maximum error, 1 km along in-track, 0.3 km along radial and 0.1 km along cross-track up to 30 days. Similar accuracies can be expected when the object is tumbling as long as the rate of attitude change is different from the orbit rate. Results of this study reveal an important phenomenon that the solar radiation pressure significantly affects the orbit motion when the spin rate is equal to the orbit rate.

A machine learns to predict the stability of circumbinary planets

NASA Astrophysics Data System (ADS)

Lam, Christopher; Kipping, David

2018-06-01

Long-period circumbinary planets appear to be as common as those orbiting single stars and have been found to frequently have orbital radii just beyond the critical distance for dynamical stability. Assessing the stability is typically done either through N-body simulations or using the classic stability criterion first considered by Dvorak and later developed by Holman and Wiegert: a second-order polynomial calibrated to broadly match numerical simulations. However, the polynomial is unable to capture islands of instability introduced by mean motion resonances, causing the accuracy of the criterion to approach that of a random coin-toss when close to the boundary. We show how a deep neural network (DNN) trained on N-body simulations generated with REBOUND is able to significantly improve stability predictions for circumbinary planets on initially coplanar, circular orbits. Specifically, we find that the accuracy of our DNN never drops below 86 per cent, even when tightly surrounding the boundary of instability, and is fast enough to be practical for on-the-fly calls during likelihood evaluations typical of modern Bayesian inference. Our binary classifier DNN is made publicly available at https://github.com/CoolWorlds/orbital-stability.

On orbital stability of planar oscillations of a satellite in a circular orbit on the boundary of the parametric resonance

NASA Astrophysics Data System (ADS)

Bardin, B. S.; Chekina, E. A.

2018-05-01

We consider the motion of a satellite about its center of mass in a circular orbit. We study the problem of orbital stability for planar pendulum-like oscillations of the satellite. It is supposed that the satellite is a rigid body whose mass geometry is that of a plate. For the unperturbed motion the plane of the satellite-plate is perpendicular to the plane of the orbit. We perform a nonlinear analysis of the orbital stability of planar pendulum-like oscillations for previously unexplored parameter values corresponding to the combination resonance. It appears that in this case both formal orbital stability and instability can take place. The results of stability study are shown in stability diagrams.

Formation of close binary black holes merging due to gravitational-wave radiation

NASA Astrophysics Data System (ADS)

Tutukov, A. V.; Cherepashchuk, A. M.

2017-10-01

The conditions for the formation of close-binary black-hole systems merging over the Hubble time due to gravitational-wave radiation are considered in the framework of current ideas about the evolution of massive close-binary systems. The original systems whose mergers were detected by LIGO consisted of main-sequence stars with masses of 30-100 M ⊙. The preservation of the compactness of a binary black hole during the evolution of its components requires either the formation of a common envelope, probably also with a low initial abundance of metals, or the presence of a "kick"—a velocity obtained during a supernova explosion accompanied by the formation of a black hole. In principle, such a kick can explain the relatively low frequency of mergers of the components of close-binary stellar black holes, if the characteristic speed of the kick exceeds the orbital velocities of the system components during the supernova explosion. Another opportunity for the components of close-binary systems to approach each other is related to their possible motion in a dense molecular cloud.

Preadapting to Weightlessness

NASA Technical Reports Server (NTRS)

Reschke, M. F.; Parker, D. E.; Arrott, A. P.

1986-01-01

Report discusses physiological and physical concepts of proposed training system to precondition astronauts to weightless environment. System prevents motion sickness, often experienced during early part of orbital flight. Also helps prevent seasickness and other forms of terrestrial motion sickness, often experienced during early part of orbital flight. Training affects subject's perception of inner-ear signals, visual signals, and kinesthetic motion perception. Changed perception resembles that of astronauts who spent many days in space and adapted to weightlessness.

Fuel-efficient feedback control of orbital motion around irregular-shaped asteroids

NASA Astrophysics Data System (ADS)

Winkler, Timothy Michael

Unmanned probes are the primary technologies used when exploring celestial bodies in our solar system. As these deep space exploration missions are becoming more and more complex, there is a need for advanced autonomous operation capabilities in order to meet mission objectives. These autonomous capabilities are required as ground-based guidance and navigation commands will not be able to be issued in real time due to the large distance from the Earth. For long-duration asteroid exploration missions, this also entails how to keep the spacecraft around or on the body in order for the mission to be successfully completed. Unlike with larger bodies such as planets, though, the dynamical environment around these smaller bodies can be difficult to characterize. The weak gravitational fields are not uniform due to irregular shapes and non-homogeneous mass distribution, especially when orbiting in close-proximity to the body. On top of that, small perturbation forces such as solar radiation pressure can be strong enough to destabilize an orbit around an asteroid. The best solution for keeping a spacecraft in orbit about a small body is to implement some form of control technique. With conventional propulsion thrusters, active control algorithms tend to have a higher than acceptable propellant requirements for long-duration asteroid exploration missions, which has led to much research being devoted to finding open-loop solutions to long-term stable orbits about small bodies. These solutions can prove to be highly sensitive to the orbit's initial conditions, making them potentially unreliable in the presence of orbit injection errors. This research investigates a fuel-efficient, active control scheme to safely control a spacecraft's orbit in close-proximity to an asteroid. First, three different gravitational models capable of simulating the non-homogeneous gravity fields of asteroids are presented: the polyhedron gravity shape model, a spherical harmonics expansion, and an inertia dyadic gravity model. Then a simple feedback controller augmented by a disturbance-accommodating filter is employed to ensure orbital stability. Using these models and controller, several orbiting cases as well as body-frame hovering are investigated to test the viability and fuel-efficiency of the proposed control system. The ultimate goal is to design an active orbit control system with minimum DeltaV expenditure.

Computer Controlled Optical Surfacing With Orbital Tool Motion

NASA Astrophysics Data System (ADS)

Jones, Robert A.

1985-11-01

Asymmetric aspheric optical surfaces are very difficult to fabricate using classical techniques and laps the same size as the workpiece. Opticians can produce such surfaces by hand grinding and polishing, using small laps with orbital tool motion. However, this is a time consuming process unsuitable for large optical elements.

Measurement and Compensation of BPM Chamber Motion in HLS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, J. W.; Sun, B. G.; Cao, Y.

2010-06-23

Significant horizontal drifts in the beam orbit in the storage ring of HLS (Hefei Light Source) have been seen for many years. What leads to the motion of Beam Position Monitor (BPM) chamber is thermal expansion mainly caused by the synchrotron light. To monitor the BPM chamber motions for all BPMs, a BPM chamber motion measurement system is built in real-time. The raster gauges are used to measure the displacements. The results distinctly show the relation between the BPM chamber motion and the beam current. To suppress the effect of BPM chamber motion, a compensation strategy is implemented at HLS.more » The horizontal drifts of beam orbit have been really suppressed within 20{mu}m without the compensation of BPM chamber motion in the runtime.« less

Chaotic motion of comets in near-parabolic orbit: Mapping aproaches

NASA Astrophysics Data System (ADS)

Liu, Jie; Sun, Yi-Sui

1994-09-01

There exist many comets with near-parabolic orbits in the solar system. Among various theories proposed to explain their origin, the Oort cloud hypothesis seems to be the most reasonable. The theory assumes that there is a cometary cloud at a distance 103 to 107 from the sun and that perturbing forces from planets or stars make orbits of some of these comets become the near-parabolic type. Concerning the evolution of these orbits under planetary perturbations, we can raise the question: Will they stay in the solar system forever or will they escape from it? This is an attractive dynamical problem. If we go ahead by directly solving the dynamical differential equations, we may encounter the difficulty of long-time computation. For the orbits of these comets are near-parabolic and their periods are too long to study on their long-term evolution. With mapping approaches the difficulty will be overcome. In another aspect, the study of this model has special meaning for chaotic dynamics. We know that in the neighborhood of any separatrix i.e. the trajectory with zero frequency of the uperturbed motion of a Hamiltonian system, some chaotic motions have to be expected. Actually, the simplest example of separatrix is the parabolic trajectory of the two-body problem which separates the bounded and unbounded motion. From this point of view, the dynamical study of near-parabolic motion is very important. Petrosky's elegant but more abstract deduction gives a Kepler mapping which describes the dynamics of the cometary motion. In this paper we derive a similar mapping directly and discuss its dynamical characters.

Vision sensing techniques in aeronautics and astronautics

NASA Technical Reports Server (NTRS)

Hall, E. L.

1988-01-01

The close relationship between sensing and other tasks in orbital space, and the integral role of vision sensing in practical aerospace applications, are illustrated. Typical space mission-vision tasks encompass the docking of space vehicles, the detection of unexpected objects, the diagnosis of spacecraft damage, and the inspection of critical spacecraft components. Attention is presently given to image functions, the 'windowing' of a view, the number of cameras required for inspection tasks, the choice of incoherent or coherent (laser) illumination, three-dimensional-to-two-dimensional model-matching, edge- and region-segmentation techniques, and motion analysis for tracking.

KSC-08pd3279

NASA Image and Video Library

2008-10-20

CAPE CANAVERAL, Fla. - In the Vehicle Assembly Building's high bay 3 at NASA's Kennedy Space Center in Florida, a worker closely observes space shuttle Atlantis as it rolls in after leaving Launch Pad 39A. In the VAB, Atlantis will await launch on its STS-125 mission to repair NASA's Hubble Space Telescope. First motion of Atlantis off the pad was at 6:48 a.m. EDT. Atlantis' targeted launch on Oct. 14 was delayed when a system that transfers science data from the orbiting observatory to Earth malfunctioned on Sept. 27. The new target launch date is under review. Photo credit: NASA/Kim Shiflett

Runge-Lenz vector, accidental SU(2) symmetry, and unusual multiplets for motion on a cone

DOE Office of Scientific and Technical Information (OSTI.GOV)

Al-Hashimi, M.H.; Wiese, U.-J.

2008-01-15

We consider a particle moving on a cone and bound to its tip by 1/r or harmonic oscillator potentials. When the deficit angle of the cone divided by 2{pi} is a rational number, all bound classical orbits are closed. Correspondingly, the quantum system has accidental degeneracies in the discrete energy spectrum. An accidental SU(2) symmetry is generated by the rotations around the tip of the cone as well as by a Runge-Lenz vector. Remarkably, some of the corresponding multiplets have fractional 'spin' and unusual degeneracies.

The eivaN: A forward-looking interactive orbital trajectory plotting tool for use with proximity operations (PROX OPS) and other maneuvers: Description and user's manual

NASA Technical Reports Server (NTRS)

Brody, Adam R.

1988-01-01

The results of vehicle burns on-orbit are very difficult to anticipate because of nonlinearities in the equations of motion governing orbiting bodies. This confusion was noticed firsthand in prior experimentation. Out of plane motion is relatively simple as it is uncoupled from the other two degrees of freedom. However, in plane thrusts are more complex because the motions resulting from these inputs are coupled. An interactive planning device, eivaN, was developed to plot resulting trajectories, to provide a better comprehension of orbital mechanics effects, and to help the user to develop heuristics for on-orbit mission planning. The eivaN runs with Microsoft Excel on a Macintosh computer. It provides a forward looking display: burn parameters in the three orthogonal axes in addition to time inputted, and the resultant trajectory is then plotted. Position and velocity components for any burn at any user specified time are readily available. A new area of research related to the human factors of real time, on-orbit mission planning was identified and is currently being investigated.

Determining Our Motion Through the Galaxy

NASA Astrophysics Data System (ADS)

Kohler, Susanna

2016-12-01

Though we dont notice it from our point of view, were hurtling through space at breakneck speed and one of the contributors to our overall motion through the universe is the Suns revolutionaround the center of our galaxy. A recent study uses an unusual approach to measure the speed of this rotation.Moving While Sitting StillWe know that the Sun zips rapidly around the center of the Milky Way our orbitalspeed is somewhere around250 km/s, or 560,000 mph! Getting a precise measurement of this velocity is useful because we can combine it with the observed proper motion of Sgr A*, the black hole at the center of our galaxy, to determine the distance from us to the center of the Milky Way. This is an important baseline for lots of other measurements.Example particle orbits modeled within the galactic potential. The top panel represents a starwith zero angular momentum, which is scattered into a chaotic orbit after interacting with the galactic nucleus. [Hunt et al. 2016]But how can we measure the Suns revolutionspeed accurately? A team of scientists led by Jason Hunt (Dunlap Institute at University of Toronto, Canada) have suggested a unique approach to pin down this value: look for missing stars in the solar neighborhood.Missing StarsThe stars around us should exhibit a distribution of velocities describing their orbits about the galactic center but those stars with zero angular momentum should have plunged directly into the galactic center long ago. These stars would have been scattered onto chaotic halo orbits after their plunge, resulting in a dearth of stars with zero angular momentum around us today.By looking at the relative speeds of the stars moving around us, then, we should see a dip in the velocity distribution corresponding to the missing zero-angular-momentum stars. By noting the relative velocity at which that dip occurs, we cleverly reveal the negative of our motion around the galactic center.Velocity distribution for stars within 700 pc of the Sun. A dip in the distribution (marked with an arrow) is noticeable between 210 and 270 km/s. [Hunt et al. 2016]Where Are We and How Fast Are We Going?Hunt and collaborators use a combination of the first data release from ESAs Gaia mission and a star catalog from the Radial Velocity Experiment to examine the motions of a total of over 200,000 stars in the solar neighborhood. They find that there is indeed a lack of disk stars with velocities close to zero angular momentum. They then compare modeled stellar orbits to the data to estimate the relative speed at which the dip in the velocity distribution occurs.From this information, the authors obtain a measurement of 2399 km/s for the Suns revolutionvelocity around the galactic center. They combine this value with a proper motion measurement of Sgr A* to calculate the distance to the galactic center: 7.90.3 kpc (or about 26,000 light-years).Both of these measurements can be improved with future Gaia data releases, which will contain many orders of magnitude more stars. This clever technique, therefore, proves a useful way of better constraining our position and motion through the Milky Way.CitationJason A. S. Hunt et al 2016 ApJL 832 L25. doi:10.3847/2041-8205/832/2/L25

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pilat-Lohinger, E.; Bazsó, A.; Funk, B.

Gravitational perturbations in multi-planet systems caused by an accompanying star are the subject of this investigation. Our dynamical model is based on the binary star HD 41004 AB where a giant planet orbits HD 41004 A. We modify the orbital parameters of this system and analyze the motion of a hypothetical test planet surrounding HD 41004 A on an interior orbit to the detected giant planet. Our numerical computations indicate perturbations due to mean motion and secular resonances (SRs). The locations of these resonances are usually connected to high eccentricity and highly inclined motion depending strongly on the binary-planet architecture.more » As the positions of mean motion resonances can easily be determined, the main purpose of this study is to present a new semi-analytical method to determine the location of an SR without huge computational effort.« less

Motion Parameters Determination of the SC and Phobos in the Project Phobos-Grunt

NASA Technical Reports Server (NTRS)

Akim, E. L.; Stepanyants, V. A.; Tuchin, A. G.; Shishov, V. A.

2007-01-01

The SC "Phobos-Grunt" flight is planned to 2009 in Russia with the purpose to deliver to the Earth the soil samples of the Mars satellite Phobos. The mission will pass under the following scheme [1-4]: the SC flight from the Earth to the Mars, the SC transit on the Mars satellite orbit, the motion round the Mars on the observation orbit and on the quasi-synchronous one [5], landing on Phobos, taking of a ground and start in the direction to the Earth. The implementation of complicated dynamical operations in the Phobos vicinity is foreseen by the project. The SC will be in a disturbance sphere of gravitational fields from the Sun, the Mars and the Phobos. The SC orbit determination is carried out on a totality of trajectory measurements executed from ground tracking stations and measurements of autonomous systems onboard space vehicle relatively the Phobos. As ground measurements the radio engineering measurements of range and range rate are used. There are possible as onboard optical observations of the Phobos by a television system and ranges from the SC up to the Phobos surface by laser locator. As soon as the Phobos orbit accuracy is insufficient for a solution of a problem of landing its orbit determination will be carried out together with determination of the SC orbit. Therefore the algorithms for joint improving of initial conditions of the SC and the Phobos are necessary to determine parameters of the SC relative the Phobos motion within a single dynamical motion model. After putting on the martial satellite orbit, on the Phobos observation orbit, on the quasi-synchronous orbit in the Phobos vicinity the equipment guidance and the following process of the SC orbit determination relatively Phobos requires a priori knowledge of the Phobos orbit parameters with sufficiently high precision. These parameters should be obtained beforehand using both all modern observations and historical ones.

Meanest foundations and nobler superstructures: Hooke, Newton and the "compounding of the celestiall motions of the planets

NASA Astrophysics Data System (ADS)

Gal, Ofer

This book is a historical-epistemological study of one the most consequential idea of early modern celestial mechanics: Robert Hooke's proposal to "compoun[d] the celestial motions of the planets of a direct motion by the tangent & an attractive motion towards a central body," a proposal which Isaac Newton adopted and realized in his Principia. Hooke's Programme was revolutionary both cosmologically and mathematically. It presented "the celestial motions," the proverbial symbol of stability and immutability, as a process of continuous change, and prescribed only parameters of rectilinear motions and rectilinear attractions for calculating their closed curved orbits. Yet the traces of Hooke's construction of his Programme for the heavens lead through his investigations in such earthly disciplines as microscopy, practical optics and horology, and the mathematical tools developed by Newton to accomplish it appear no less local and goal-oriented than Hooke's lenses and springs. This transgression of the boundaries between the theoretical, experimental and technological realms is reminiscent of Hooke's own free excursions in and out of the circles occupied by gentlemen-philosophers, university mathematicians, instrument makers, technicians and servants. It presents an opportunity to examine the social and epistemological distinctions, relations and hierarchies between those realms and their inhabitants, and compels a critical assessment of the philosophical categories they embody.

ECCENTRICITY EVOLUTION THROUGH ACCRETION OF PROTOPLANETS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Matsumoto, Yuji; Nagasawa, Makiko; Ida, Shigeru, E-mail: yuji.matsumoto@nao.ac.jp, E-mail: nagasawa.m.ad@m.titech.ac.jp, E-mail: ida@elsi.jp

2015-09-10

Most super-Earths detected by the radial velocity (RV) method have significantly smaller eccentricities than the eccentricities corresponding to velocity dispersion equal to their surface escape velocity (“escape eccentricities”). If orbital instability followed by giant impacts among protoplanets that have migrated from outer regions is considered, it is usually considered that eccentricities of the merged bodies become comparable to those of orbital crossing bodies, which are excited up to their escape eccentricities by close scattering. However, the eccentricity evolution in the in situ accretion model has not been studied in detail. Here, we investigate the eccentricity evolution through N-body simulations. Wemore » have found that the merged planets tend to have much smaller eccentricities than escape eccentricities due to very efficient collision damping. If the protoplanet orbits are initially well separated and their eccentricities are securely increased, an inner protoplanet collides at its apocenter with an outer protoplanet at its pericenter. The eccentricity of the merged body is the smallest for such configurations. Orbital inclinations are also damped by this mechanism and planets tend to share a same orbital plane, which is consistent with Kepler data. Such efficient collision damping is not found when we start calculations from densely packed orbits of the protoplanets. If the protoplanets are initially in the mean-motion resonances, which corresponds to well separated orbits, the in situ accretion model well reproduces the features of eccentricities and inclinations of multiple super-Earths/Earth systems discovered by RV and Kepler surveys.« less

Observational Evidence for Tidal Interaction in Close Binary Systems

NASA Astrophysics Data System (ADS)

Mazeh, T.

This paper reviews the rich corpus of observational evidence for tidal effects, mostly based on photometric and radial-velocity measurements. This is done in a period when the study of binaries is being revolutionized by large-scaled photometric surveys that are detecting many thousands of new binaries and tens of extrasolar planets. We begin by examining the short-term effects, such as ellipsoidal variability and apsidal motion. We next turn to the long-term effects, of which circularization was studied the most: a transition period between circular and eccentric orbits has been derived for eight coeval samples of binaries. The study of synchronization and spin-orbit alignment is less advanced. As binaries are supposed to reach synchronization before circularization, one can expect finding eccentric binaries in pseudo-synchronization state, the evidence for which is reviewed. We also discuss synchronization in PMS and young stars, and compare the emerging timescale with the circularization timescale. We next examine the tidal interaction in close binaries that are orbited by a third distant companion, and review the effect of pumping the binary eccentricity by the third star. We elaborate on the impact of the pumped eccentricity on the tidal evolution of close binaries residing in triple systems, which may shrink the binary separation. Finally we consider the extrasolar planets and the observational evidence for tidal interaction with their parent stars. This includes a mechanism that can induce radial drift of short-period planets, either inward or outward, depending on the planetary radial position relative to the corotation radius. Another effect is the circularization of planetary orbits, the evidence for which can be found in eccentricity-versus-period plot of the planets already known. Whenever possible, the paper attempts to address the possible confrontation between theory and observations, and to point out noteworthy cases and observations that can be performed in the future and may shed some light on the key questions that remain open.

Minimum Propellant Low-Thrust Maneuvers near the Libration Points

NASA Astrophysics Data System (ADS)

Marinescu, A.; Dumitrache, M.

The impulse technique certainly can bring the vehicle on orbits around the libration points or close to them. The question that aries is, by what means can the vehicle arrive in such cases at the libration points? A first investigation carried out in this paper can give an answer: the use of the technique of low-thrust, which, in addition, can bring the vehicle from the libration points near to or into orbits around these points. This aspect is considered in this present paper where for the applications we have considered the transfer for orbits of the equidistant point L4 and of the collinear point L2, from Earth-moon system. This transfer maneuver can be used to insertion one satellite on libration points orbits. In Earth- moon system the points L 4 and L 5 because an vehicle in on of the equidistant points in quite stable and remains in its vicinity of perturbed, have potential interest for the establishment of transporder satellite for interplanetary tracking. In contrast an vehicle in one of the collinear points is quite instable and it will oscillate along the Earth-moon-axis at increasing amplitude and gradually escape from the libration point. Let use assume that a space vehicle equipped with a low-thrust propulsion is near a libration point L. We consider the planar motion in the restricted frame of the three bodies in the rotating system L, where the Earth-moon distance D=l. The unit of time T is period of the moon's orbit divided by 2 and multiplied by the square root of the quantity one plus the moon/Earth mass ratio, and the unit of mass is the Earth's mass. With these predictions the motion equatios of the vehicle equiped with a low-thrust propulsion installation in the linear approximation near the libration point, have been established. The parameters of the motion at the beginning and the end of these maneuvers are known, the variational problem has been formulated as a Lagrange type problem with fixed extremities. On established the differential equations of the extremals and integrating these differential equations we obtain the desired extremals which characterize the minimum propellant optimal manoeuvres of transfer from libration points to their orbits. By means of Legendre conditions for weak minimum and Weierstrass condition for strong minimum, is demonstrated that variational problem so formulated has sense and is a problem of minimum. The integration of extremal's differential equations system can not lead to analytical solutions easily to obtain and for this we have directed to a numerical integration. The problem is a bilocal one because the motion parameter values are predicted at the beginning and of the maneuver (the manoeuvre duration coincides with the combustion duration) the values of the Lagrange multipliers not being specified at the beginning and end of the manoeuvre. For determination of the velocities at any point on the libration point L4 and L2 has been elaborated the program of calculus on the integration of the motion equations without accelerations due thrust during a revolution period the coordinates and velocities to be equal, with which have been calculated the velocities at the apoapsis A and respectively A'. With these specifications, the final conditions (at the end of the maneuver) could be established, and the determination of optimal transfer parameters in the specified points could be determined. The calculus performed for the transfer from the libration points L4 and L2 to their orbits, shows that the evolution velocities on the orbits are in general small, the velocities on the L2 orbits being greater than the velocities on L 4 orbits having the same semimajor axis. This fact is explicable because the period of evolution on orbits of libration point L4 is greater than the period of orbits of the libration point L2. For the transfer in the apoapsis of both orbits (the points A. and A') on can remarque the fact the accelerations due thrust are greater for orbits around the libration point L2 comparatively with orbits having the same semimajor axis around the libration point L 4 ( maneuver duration = 106 s = 11.574 days for L 4 and = 105 s = 1.157 days for L2 ). Considering orbits around libration points L4 and L2 with semimajor axis between 150-15000 km the components of acceleration due thrust have values between 10-2 -10-5 m/S2 which lays in the range of performances of law thrust propulsion installations (the D, T units have been converted in m, s). *Senior Scientist. Member AIAA **Researche Engineer

The dynamical connection between Phaethon and Pallas

NASA Astrophysics Data System (ADS)

Todorović, Nataša

2018-03-01

Phaethon (3200) is an active Near Earth Asteroid classified as a B-type object and a suspected former member of the Pallas family. In this article, we search for sources of Phaethon-like orbits originating from the two strongest resonances in the region of the Pallas family; namely, the 5:2 and 8:3 mean motion resonances with Jupiter, located at a ˜ 2.82 au and a ˜ 2.70 au, respectively. The probability for this dynamical connection observed in De León et al. (2010) was close to 2 per cent. Using sophisticated numerical methods, we found a highly efficient dynamical flow between Pallas and Phaethon. As many as 43.6 per cent of test particles placed in the 5:2 resonance were able to reach the orbit of Phaethon; whereas, for the 8:3 resonance, this percentage was 46.9 per cent.

Colloidal Bandpass and Bandgap Filters

NASA Astrophysics Data System (ADS)

Yellen, Benjamin; Tahir, Mukarram; Ouyang, Yuyu; Nori, Franco

2013-03-01

Thermally or deterministically-driven transport of objects through asymmetric potential energy landscapes (ratchet-based motion) is of considerable interest as models for biological transport and as methods for controlling the flow of information, material, and energy. Here, we provide a general framework for implementing a colloidal bandpass filter, in which particles of a specific size range can be selectively transported through a periodic lattice, whereas larger or smaller particles are dynamically trapped in closed-orbits. Our approach is based on quasi-static (adiabatic) transition in a tunable potential energy landscape composed of a multi-frequency magnetic field input signal with the static field of a spatially-periodic magnetization. By tuning the phase shifts between the input signal and the relative forcing coefficients, large-sized particles may experience no local energy barriers, medium-sized particles experience only one local energy barrier, and small-sized particles experience two local energy barriers. The odd symmetry present in this system can be used to nudge the medium-sized particles along an open pathway, whereas the large or small beads remain trapped in a closed-orbit, leading to a bandpass filter, and vice versa for a bandgap filter. NSF CMMI - 0800173, Youth 100 Scholars Fund

Long period nodal motion of sun synchronous orbits

NASA Technical Reports Server (NTRS)

Duck, K. I.

1975-01-01

An approximative model is formulated for assessing these perturbations that significantly affect long term modal motion of sun synchronous orbits. Computer simulations with several independent computer programs consider zonal and tesseral gravitational harmonics, third body gravitational disturbances induced by the sun and the moon, and atmospheric drag. A pendulum model consisting of evenzonal harmonics through order 4 and solar gravity dominated nodal motion approximation. This pendulum motion results from solar gravity inducing an inclination oscillation which couples into the nodal precession induced by the earth's oblateness. The pendulum model correlated well with simulations observed flight data.

Determination of Non-gravitational Effects in the Motion of Near-Sun Objects 321P, 322P, 323P, and 342P

NASA Astrophysics Data System (ADS)

Emel'yanenko, V. V.; Naroenkov, S. A.

2018-01-01

At the beginning of this century, the SOHO space observatory discovered near-Sun comets with perihelion distances q ≈ 0.05 AU, which remained observable over several close encounters with the Sun. This became one of the surprises in studying the small bodies of the Solar System. Currently, there are objects that have already been observed in four (342P) and five (321P, 322P, and 323P) apparitions. In the present work, the estimates of nongravitational effects are obtained for these objects based on the pair-wise linkage of the apparitions. The calculations show that the observations of these objects are poorly represented if solely the gravitational forces are considered. The magnitude of nongravitational effects in the semimajor axis noticeably changes with time. The motion of all comets is significantly affected by the components of nongravitational forces that are perpendicular to the orbital plane.

An analytic method to account for drag in the Vinti Satellite theory

NASA Technical Reports Server (NTRS)

Watson, J. S.; Mistretta, G. D.; Bonavito, N. L.

1974-01-01

To retain separability in the Vinti theory of earth satellite motion when a nonconservative force such as air drag is considered, a set of variational equations for the orbital elements are introduced, and expressed as functions of the transverse, radial, and normal components of the nonconservative forces acting on the system. In this approach, the Hamiltonian is preserved in form, and remains the total energy, but the initial or boundary conditions and hence the Jacobi constants of the motion advance with time through the variational equations. In particular, the atmospheric density profile is written as a fitted exponential function of the eccentric anomaly, which adheres to tabular data at all altitudes and simultaneously reduced the variational equations to indefinite integrals with closed form evaluations. The values of the limits for any arbitrary time interval are obtained from the Vinti program.

Investigating the dynamical history of the interstellar object 'Oumuamua

NASA Astrophysics Data System (ADS)

Dybczyński, Piotr A.; Królikowska, Małgorzata

2018-02-01

Here we try to find the origin of 1I/2017 U1 'Oumuamua, the first interstellar object recorded inside the solar system. To this aim, we searched for close encounters between 'Oumuamua and all nearby stars with known kinematic data during their past motion. We had checked over 200 thousand stars and found just a handful of candidates. If we limit our investigation to within a 60 pc sphere surrounding the Sun, then the most probable candidate for the 'Oumuamua parent stellar habitat is the star UCAC4 535-065571. However GJ 876 is also a favourable candidate. However, the origin of 'Oumuamua from a much more distant source is still an open question. Additionally, we found that the quality of the original orbit of 'Oumuamua is accurate enough for such a study and that none of the checked stars had perturbed its motion significantly. All numerical results of this research are available in the appendix.

March of the Planets

ERIC Educational Resources Information Center

Thompson, Bruce

2007-01-01

The motion of the planets in their orbits can be demonstrated to students by using planetarium software programs. These allow time to be sped up so that the relative motions are readily observed. However, it is also valuable to have the students understand the real speed of the planets in their orbits. This paper describes an exercise that gives…

Student Ideas about Kepler's Laws and Planetary Orbital Motions

ERIC Educational Resources Information Center

Yu, Ka Chun; Sahami, Kamran; Denn, Grant

2010-01-01

We present the analysis of oral interviews with 112 undergraduate nonmajor students during the first week of a General Education Introduction to Astronomy class before they had received any instruction. The students were asked questions relating to Kepler's three Laws of Motion, as well as their understanding of what keeps planets in orbit around…

A spectroscopic search for colliding stellar winds in O-type close binary systems. III - 29 UW Canis Majoris

NASA Technical Reports Server (NTRS)

Wiggs, Michael S.; Gies, Douglas R.

1993-01-01

The orbital-phase variations in the optical emission lines and UV P Cygni lines of the massive O-type binary 29 UW Canis Majoris are investigated in a search for evidence of colliding winds. High SNR spectra of the H-alpha and He I 6678-A emission lines are presented, and radial velocity curves for several features associated with the photosphere of the more luminous primary star are given. The H-alpha features consists of a P Cygni component that shares the motion of the primary, and which probably originates at the base of its wind, and a broad, stationary emission component. It is proposed that the broad emission forms in a plane midway between the stars where the winds collide. A simple geometric model is used to show that this placement of the broad component can explain the lack of orbital velocity shifts, the near-constancy of the emission strength throughout the orbit, the large velocities associated with the H-alpha wings, and the constancy of the velocity range observed.

Controlling the motion of a spacecraft when approaching a large object of space debris

NASA Astrophysics Data System (ADS)

Baranov, A. A.; Budyanskiy, A. A.; Razumnyi, Yu. N.

2017-07-01

The problem of calculating the parameters of maneuvering a spacecraft as it approaches a large object of space debris (LOSD) in close near-circular noncoplanar orbits has been considered. In [1-4], the results of analyzing the problem of the flyby of the separated LOSD groups have been presented. It has been assumed that a collector spacecraft approaches the LOSD and captures it or it is inserted into the nozzle of a small spacecraft that has a proper propulsion system (PS). However, in these papers, the flight from one object to another was only analyzed and the problem of approaching to LOSD with a given accuracy was not considered. This paper is a supplement to the cycle of papers [1-4]. It is assumed that, the final stage of approaching the LOSD is implemented by maneuvering in many orbits (up to several dozens) with low-thrust engines, but the PS operating time is fairly small compared with the orbit period in order to make it possible to use impulse approximation in the calculations.

Deriving analytic solutions for compact binary inspirals without recourse to adiabatic approximations

NASA Astrophysics Data System (ADS)

Galley, Chad R.; Rothstein, Ira Z.

2017-05-01

We utilize the dynamical renormalization group formalism to calculate the real space trajectory of a compact binary inspiral for long times via a systematic resummation of secularly growing terms. This method generates closed form solutions without orbit averaging, and the accuracy can be systematically improved. The expansion parameter is v5ν Ω (t -t0) where t0 is the initial time, t is the time elapsed, and Ω and v are the angular orbital frequency and initial speed, respectively. ν is the binary's symmetric mass ratio. We demonstrate how to apply the renormalization group method to resum solutions beyond leading order in two ways. First, we calculate the second-order corrections of the leading radiation reaction force, which involves highly nontrivial checks of the formalism (i.e., its renormalizability). Second, we show how to systematically include post-Newtonian corrections to the radiation reaction force. By avoiding orbit averaging, we gain predictive power and eliminate ambiguities in the initial conditions. Finally, we discuss how this methodology can be used to find analytic solutions to the spin equations of motion that are valid over long times.

A real-time approximate optimal guidance law for flight in a plane

NASA Technical Reports Server (NTRS)

Feeley, Timothy S.; Speyer, Jason L.

1990-01-01

A real-time guidance scheme is presented for the problem of maximizing the payload into orbit subject to the equations of motion of a rocket over a nonrotating spherical earth. The flight is constrained to a path in the equatorial plane while reaching an orbital altitude at orbital injection speeds. The dynamics of the problem can be separated into primary and perturbation effects by a small parameter, epsilon, which is the ratio of the atmospheric scale height to the radius of the earth. The Hamilton-Jacobi-Bellman or dynamic programming equation is expanded in an asymptotic series where the zeroth-order term (epsilon = 0) can be obtained in closed form. The neglected perturbation terms are included in the higher-order terms of the expansion, which are determined from the solution of first-order linear partial differential equations requiring only integrations which are quadratures. The quadratures can be performed rapidly with emerging computer capability, so that real-time approximate optimization can be used to construct the launch guidance law. The application of this technique to flight in three-dimensions is made apparent from the solution presented.

Studies of perturbed three vortex dynamics

NASA Astrophysics Data System (ADS)

Blackmore, Denis; Ting, Lu; Knio, Omar

2007-06-01

It is well known that the dynamics of three point vortices moving in an ideal fluid in the plane can be expressed in Hamiltonian form, where the resulting equations of motion are completely integrable in the sense of Liouville and Arnold. The focus of this investigation is on the persistence of regular behavior (especially periodic motion) associated with completely integrable systems for certain (admissible) kinds of Hamiltonian perturbations of the three vortex system in a plane. After a brief survey of the dynamics of the integrable planar three vortex system, it is shown that the admissible class of perturbed systems is broad enough to include three vortices in a half plane, three coaxial slender vortex rings in three space, and "restricted" four vortex dynamics in a plane. Included are two basic categories of results for admissible perturbations: (i) general theorems for the persistence of invariant tori and periodic orbits using Kolmogorov-Arnold-Moser- and Poincaré-Birkhoff-type arguments and (ii) more specific and quantitative conclusions of a classical perturbation theory nature guaranteeing the existence of periodic orbits of the perturbed system close to cycles of the unperturbed system, which occur in abundance near centers. In addition, several numerical simulations are provided to illustrate the validity of the theorems as well as indicating their limitations as manifested by transitions to chaotic dynamics.

SPICE SDM: Innovative Approaches for Linear Motion and Heat Management

NASA Astrophysics Data System (ADS)

Relecom, Ken; Larcheveque, Cyril; Constant, Joël; Autissier, Nordahl; Pornin, Arnaud; Martini, Nicolas

2015-09-01

The SPICE Door Mechanism (SDM) is foreseen to be flown on Solar Orbiter, to close the SPICE instrument aperture and shield it from the solar flux and from contamination. The environment it is exposed to is particularly extreme, as the Solar Orbiter mission will reach a distance of 0.28 AU (41’887’403.8 km) to the Sun, and the SPICE instrument will be looking directly at it. Because of its position at the far end of a cantilevered structure, the SDM is also exposed to amplified launch loads and must remain very light and compact. The cleanliness constraints are also very tight, as the mechanism is positioned directly at the aperture of the SPICE spectrometer.To tackle these issues, two novelties were introduced on the SPICE Door Mechanism:- A specifically engineered reflective coating toprotect the Aluminium door from the heat generatedby the solar flux- The use of miniature profile rail type linearbearings to support the door during launch andallow its motion during the missionThis paper details the design and verification approach applied for these two innovations and for the mechanism as a whole, as well as the results and findings from the testing carried out on the Bread Board, Qualification and Flight models.

Proper-Motion Study of the Magellanic Clouds Using SPM Material

DTIC Science & Technology

2010-12-01

F. VAN ALTENA I, NORBERT ZACHARIAS2, DANA I. CASETTI-DINESCU I, VLADIMIR I. KORCHAGIN I, iMANTSPLATAIS3, DAVID G. MONE -r4, CARLOS E. LOPEZ5, DAVID...difference of the two clouds to within ±54 km S-I. The absolute proper-motion results are consistent with the Clouds’ orbits being marginally bound...consistent with the Clouds’ orbits being marginally bound to the Milky Way, albeit on an elongated orbit. The inferred relative velocity between the

Position of planet X obtained from motion of near-parabolic comets

NASA Astrophysics Data System (ADS)

Medvedev, Yurii; Vavilov, Dmitrii

2016-10-01

The authors of paper (Batygin and Brown, 2016) proposed that a planet with 10 earth's mass and an orbit of 700 AU semi major axis and 0.6 eccentricity can explain the observed distribution of Kuiper Belt objects around Sedna. Then Fienga et al.(2016) used the INPOP planetary ephemerides model as a sensor for testing for an additional body in the solar system. They defined the planet position on the orbit using the most sensitive data set, the Cassini radio ranging data.Here we use near-parabolic comets for determination of the planet's position on the orbit. Assuming that some comets approached the planet in the past, we made a search for the comets with low Minimum Orbit Intersection Distance (MOID) with the planet's orbit. From the list of 768 near-parabolic comets five "new" comets with hyperbolic orbits were chosen. We considered two cases of the planet's motion: the direct and the inverse ones. In case of the direct motion the true anomaly of the planet lies in interval [1760, 1840] and, thus, the right ascension, the declination and geocentric distance of the planet are in intervals [830, 900], [80,100], and [1110, 1120] AU, correspondingly. In case of the inverse motion the true anomaly is in [2120, 2230] and the other values are in intervals [480, 580], [-120,-60] and [790, 910] AU. For comparison with the direct motion the true anomaly for the inverse motion, v, should be transformed by 3600-v. That gives us the interval [1370, 1480] that belongs to the intervals of the true anomaly of possible planet's position given by Fienga et al.(2016).ReferencesBatygin, K. & Brown, M. E., 2016, Evidence for a distant giant planet in the Solar system, Astronomical Journal, v. 151, 22Fienga A. A. Fienga1,J. Laskar, H. Manche, and M. Gastineau, 2016, Constraints on the location of a possible 9th planet derived from the Cassini data , Astronomy & Astrophysics, v. 587, L8

Obliquity evolution of the minor satellites of Pluto and Charon

NASA Astrophysics Data System (ADS)

Quillen, Alice C.; Nichols-Fleming, Fiona; Chen, Yuan-Yuan; Noyelles, Benoît

2017-09-01

New Horizons mission observations show that the small satellites Styx, Nix, Kerberos and Hydra, of the Pluto-Charon system, have not tidally spun-down to near synchronous spin states and have high obliquities with respect to their orbit about the Pluto-Charon binary (Weaver, 2016). We use a damped mass-spring model within an N-body simulation to study spin and obliquity evolution for single spinning non-round bodies in circumbinary orbit. Simulations with tidal dissipation alone do not show strong obliquity variations from tidally induced spin-orbit resonance crossing and this we attribute to the high satellite spin rates and low orbital eccentricities. However, a tidally evolving Styx exhibits intermittent obliquity variations and episodes of tumbling. During a previous epoch where Charon migrated away from Pluto, the minor satellites could have been trapped in orbital mean motion inclination resonances. An outward migrating Charon induces large variations in Nix and Styx's obliquities. The cause is a commensurability between the mean motion resonance frequency and the spin precession rate of the spinning body. As the minor satellites are near mean motion resonances, this mechanism could have lifted the obliquities of all four minor satellites. The high obliquities need not be primordial if the minor satellites were at one time captured into mean motion resonances.

Testing a satellite automatic nutation control system. [on synchronous meteorological satellite

NASA Technical Reports Server (NTRS)

Hrasiar, J. A.

1974-01-01

Testing of a particular nutation control system for the synchronous meteorological satellite (SMS) is described. The test method and principles are applicable to nutation angle control for other satellites with similar requirements. During its ascent to synchronous orbit, a spacecraft like the SMS spins about its minimum-moment-of-inertia axis. An uncontrolled spacecraft in this state is unstable because torques due to fuel motion increase the nutation angle. However, the SMS is equipped with an automatic nutation control (ANC) system which will keep the nutation angle close to zero. Because correct operation of this system is critical to mission success, it was tested on an air-bearing table. The ANC system was mounted on the three-axis air-bearing table which was scaled to the SMS and equipped with appropriate sensors and thrusters. The table was spun up in an altitude chamber and nutation induced so that table motion simulated spacecraft motion. The ANC system was used to reduce the nutation angle. This dynamic test of the ANC system met all its objectives and provided confidence that the ANC system will control the SMS nutation angle.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pavlovski, K.; Kolbas, V.; Southworth, J.

We present a spectroscopic study of the eclipsing binary system AS Camelopardalis, the first such study based on phase-resolved CCD echelle spectra. Via a spectral disentangling analysis we measure the minimum masses of the stars to be M{sub A}sin {sup 3} i = 3.213 {+-} 0.032 M{sub sun} and M{sub B}sin {sup 3} i = 2.323 {+-} 0.032 M{sub sun}, their effective temperatures to be T{sub eff}(A) = 12, 840 {+-} 120 K and T{sub eff}(B) = 10, 580 {+-} 240 K, and their projected rotational velocities to be v{sub A}sin i{sub A} = 14.5 {+-} 0.1 km s{sup -1}more » and v{sub B}sin i{sub B} {<=} 4.6 {+-} 0.1 km s{sup -1}. These projected rotational velocities appear to be much lower than the synchronous values. We show that measurements of the apsidal motion of the system suffer from a degeneracy between orbital eccentricity and apsidal motion rate. We use our spectroscopically measured e = 0.164 {+-} 0.004 to break this degeneracy and measure {omega}-dot{sub obs} = 0{sup 0}.133{+-}0{sup 0}.010 yr{sup -1}. Subtracting the relativistic contribution of {omega}-dot{sub GR} = 0{sup 0}.0963{+-}0{sup 0}0002 yr{sup -1} yields the contribution due to tidal torques: {omega}-dot{sub cl} = 0{sup 0}.037{+-}0{sup 0}.010 yr{sup -1}. This value is much smaller than the rate predicted by stellar theory, 0.{sup 0}40-0.{sup 0}87 yr{sup -1}. We interpret this as a misalignment between the orbital axis of the close binary and the rotational axes of its component stars, which also explains their apparently low rotational velocities. The observed and predicted apsidal motion rates could be brought into agreement if the stars were rotating three times faster than synchronous about axes perpendicular to the orbital axis. Measurement of the Rossiter-McLaughlin effect can be used to confirm this interpretation.« less

Advanced dynamical models for very well observed asteroids : perturbations from small bodies, relativity, non - gravitational effects.

NASA Astrophysics Data System (ADS)

Bernardi, Fabrizio; Farnocchia, Davide; Milani, Andrea

2012-08-01

The availability of radar data and high precision optical observations has increased the number of objects with a very well constrained orbit, especially for those objects with a long observed arc. In these cases, the uncertainty of orbital predictions is often dominated by the inaccuracy of the dynamical model. However, the motion of small solar system bodies poses a serious challenge in modeling their dynamics. In particular, for those objects with a chaotic motion small differences in the model are amplified with propagation. Thus, we need to take into account small perturbations too, especially for long - term prediction. An improved dynamical model is relevant in several applications such as assessing the risk of an impact between an asteroid and the Earth. The N - body model describing the motion of a small solar system body includes the Newtonian attraction of the planets. The contribution o f other perturbing bodies has to be taken into account. We propose to include the Moon, two dwarf planets (Ceres and Pluto) and fifteen asteroids (Pallas, Vesta, Juno, Metis, Hygiea, Eunomia, Psyche, Amphitrite, Euphrosyne, Europa, Cybele, Sylvia, Davida, Herculina, Interamnia). The next step is the introduction of the relativity terms due to both the Sun and the planets . Despite their small magnitude, planetary relativistic terms turn out to be relevant for objects experiencing close approaches with a planet. Finally, we discuss non - gravitational effects such as solar radiation pressure and the Yarkovsky effect. In particular, the latter acts as a tiny but secular semimajor axis drift that may decisively drive long - term predictions. These non - gravitational effects are difficult to model as they depend on object ’ s physical properties that are typically unknown. However, a very well observed object can have an orbit precise enough to allow the determination of the parameters defining a non - gravitational perturbation and thus the modeling of the corresponding acceleration.

The effects of the stellar wind and orbital motion on the jets of high-mass microquasars

NASA Astrophysics Data System (ADS)

Bosch-Ramon, V.; Barkov, M. V.

2016-05-01

Context. High-mass microquasar jets propagate under the effect of the wind from the companion star, and the orbital motion of the binary system. The stellar wind and the orbit may be dominant factors determining the jet properties beyond the binary scales. Aims: This is an analytical study, performed to characterise the effects of the stellar wind and the orbital motion on the jet properties. Methods: Accounting for the wind thrust transferred to the jet, we derive analytical estimates to characterise the jet evolution under the impact of the stellar wind. We include the Coriolis force effect, induced by orbital motion and enhanced by the wind's presence. Large-scale evolution of the jet is sketched, accounting for wind-to-jet thrust transfer, total energy conservation, and wind-jet flow mixing. Results: If the angle of the wind-induced jet bending is larger than its half-opening angle, the following is expected: (I) a strong recollimation shock; (II) bending against orbital motion, caused by Coriolis forces and enhanced by the wind presence; and (III) non-ballistic helical propagation further away. Even if disrupted, the jet can re-accelerate due to ambient pressure gradients, but wind entrainment can weaken this acceleration. On large scales, the opening angle of the helical structure is determined by the wind-jet thrust relation, and the wind-loaded jet flow can be rather slow. Conclusions: The impact of stellar winds on high-mass microquasar jets can yield non-ballistic helical jet trajectories, jet partial disruption and wind mixing, shocks, and possibly non-thermal emission. Among other observational diagnostics, such as radiation variability at any band, the radio morphology on milliarcsecond scales can be informative on the wind-jet interaction.

Closed-loop suppression of chaos in nonlinear driven oscillators

NASA Astrophysics Data System (ADS)

Aguirre, L. A.; Billings, S. A.

1995-05-01

This paper discusses the suppression of chaos in nonlinear driven oscillators via the addition of a periodic perturbation. Given a system originally undergoing chaotic motions, it is desired that such a system be driven to some periodic orbit. This can be achieved by the addition of a weak periodic signal to the oscillator input. This is usually accomplished in open loop, but this procedure presents some difficulties which are discussed in the paper. To ensure that this is attained despite uncertainties and possible disturbances on the system, a procedure is suggested to perform control in closed loop. In addition, it is illustrated how a model, estimated from input/output data, can be used in the design. Numerical examples which use the Duffing-Ueda and modified van der Pol oscillators are included to illustrate some of the properties of the new approach.

Simulating the Librational Behaviour of Propeller Moons In The Saturnian Ring System

NASA Astrophysics Data System (ADS)

Seiler, Michael; Seiss, Martin; Hoffmann, Holger; Spahn, Frank

2016-10-01

The propeller structure Blériot orbiting in the outer A ring of the Saturnian ring system has been one of the tremendous discoveries of the spacecraft Cassini [Tiscareno et al., 2010, ApJL]. The reconstruction of the orbital evolution of Blériot from recurrent observations in the ISS images yielded a systematic offset motion from the expected Keplerian orbit. This offset motion can be well described by three sinusoidal harmonics with amplitudes and periods of 1845, 152, 58 km and 11.1, 3.7 and 2.2 years, respectively [Sremčević et al., 2014, EPSC]. Oscillatory deviations from the Keplerian orbit are a known phenomenon for the Saturnian moons, which can be explained by resonant interactions with other moons [Spitale et al., 2006, AJ] and which look similar to the observation of Blériot.In this work we present our results from N-Body simulations, where we integrated the orbital evolution of a test particle, orbiting at the radial position of the propeller Blériot and 15 other moons of Saturn. Our simulation yield, that gravitational interactions with the larger moons result in reasonable and observable frequencies, but the resulting amplitudes of the librations are by far too small to explain the observations. Further mechanisms are needed, to amplify the amplitudes of the forced librations -- as e.g. by moonlet-ring interactions. Inspired by the recent work of Pan and Chiang [2010, ApJL; 2012, AJ] we introduce an alternative, physically more reasonable model. In our model, the moonlet is allowed to be slightly displaced with respect to its created gaps, resulting in a repulsive force. As a result, the moonlet's longitude starts to oscillate. In the presence of the additional external forcing by the outer moons the libration amplitude gets amplified, if the forcing frequency is close to the eigenfrequency of the system. Applying our model to Blériot, we can indeed reproduce a libration period of 13 years with an amplitude of about 2000 km.

Cassini's motions and resonant librations of synchronous satellites of big planets

NASA Astrophysics Data System (ADS)

Barkin, Yu. V.

2008-09-01

Introduction. In the paper the rotations of synchronous satellites of the Jupiter, Saturn, Uran and Neptune are studied. On the base theory of resonant rotation of the rigid satellite on precessing elliptical orbit [1], [2] parameters of Cassini's motions and periods of free resonant librations have been determined for big grope of satellites of planets considered as rigid non-spherical bodies. Here I use observed values of coefficients of second harmonics of gravitational potensials ( 2 J and 22 C ) and of dimension less moment of inertia I = C / ?mr 2 ? of Io, Europa, Ganimede, Callisto and also Rhea and Titan, obtained on the base of data of space missions to these bodies [3]. Here C is the polar moment of inertia, m and r is the mass and the mean radius of satellite. Mentioned parameters 2 J , 22 C and I also have been evaluated for a wide set of another's satellites of big planets for their models as homogeneous ellipsoids of known forms and sizes (www.nasa.gov). These models also have been obtained here effective applications. For corresponding models the notation (e) is used here. For another from considered satellites (without indexes) we use also ellipsoidal models of hydrostatic equilibrium state of synchronous satellite [4]. The full list of discussed parameters for satellites of planets is presented in the paper [5]. Perturbed orbital motions of considered satellites we discribe by mean orbital elements reffered to local Laplacian planes of corresponding satellites ( http://ssd.jpl.nasa. gov/sat_elem. html). From them: the eccentricity ( e ), the inclination of orbit plane ( i ), the mean orbital motion and its period ( n and n T ), the angular velocity and period of preseccion of orbit plane of satellite on local Laplacian plane ( n? and T? ). In our approach all mentioned parameters are considered as constants and more fine effects in orbital motions of satellites do not take into account in this paper. The purpose of paper is to study syncronous motions of satellites in Solar system and for each of them to determine the values of the basic Cassini's parameter 0 ? (it is the average angle of inclination of the axis of rotation relatively to normal of the precessing orbit plane) and the periods of resonant librations in the longitude ( g T ), in the pole wobble ( l T ) and period of space precession ( h T ) (and their errors). Here we use the analytical formulas for mentioned parameters which were developed by study of the Moon Cassini's motion in my early papers [1], [2]. Specially for the case of small eccentricities and inclinations of orbits of synchronous satellites we have obtained the simple reduced formulas for all four considered parameters.

On periodic motions of an orbital dumbbell-shaped body with a cabin-elevator

NASA Astrophysics Data System (ADS)

Burov, A. A.; Kosenko, I. I.; Troger, H.

2012-05-01

The motion of a dumbbell-shaped body (a pair of massive points connected with each other by a weightless rod along which the elevator, i.e., a third point, is moving according to a given law) in an attractive Newtonian central field is considered. In particular, such a mechanical system can be considered as a simplified model of an orbital cable system equipped with an elevator. The practically most interesting case where the cabin performs periodic "shuttle"motions is studied. Under the assumption that the elevator mass is small compared with the dumbbell mass, the Poincaré theory is used to determine the conditions for the existence of families of system periodic motions analytically depending on the arising small parameter and passing into some stable radial steady-state motion of the unperturbed problem as the small parameter tends to zero. It is also proved that, for sufficiently small parameter values, each of the radial relative equilibria generates exactly one family of such periodic motions. The stability of the obtained periodic solutions is studied in the linear approximation, and these solutions themselves are calculated up to terms of the firstorder in the small parameter. The contemporary studies of the motion of orbital dumbbell systems apparently originated in Okunev's papers [1, 2]. These studies were continued in [3], where plane motions of an orbit tether (represented as a dumbbell-shaped satellite) in a circular orbit were considered in the satellite approximation. In [4], in the case of equal masses and in the unbounded statement, the energy-momentum method was used to perform the dynamic reduction of the problem and analyze the stability of relative equilibria. A similar technique was used in [5], where, in contrast to the above-mentioned problems, the massive points were connected by an elastic spring resisting to compression and forming a dumbbell with elastic properties. Under such assumptions, the stability of radial configurations was investigated in that paper. The bifurcations and stability of steady-state configurations of a deformable elastic dumbbell were also studied in [6]. Various obstacles arising in the construction of orbital cable systems, in particular, the strong deformability of known materials, were discussed in [7]. In [8], the problem of orbital motion of a pair of massive points connected by an inextensible weightless cable was considered in the exact statement. In other words, it was assumed that a unilateral constraint is imposed on themassive points. The conditions of stability of vertical positions of the relative equilibria of the cable system, which were obtained in [8], can be used for any ratio of the subsatellite and station masses. In turn, these results agree well with the results obtained earlier in the studies of stability of vertical configurations in the case of equal masses of the system end bodies [3, 4]. One of the basic papers in the dynamics of three-body orbital cable systems is the paper [9]. The steady-state motions and their bifurcations and stability were studied depending on the elevator cabin position in [10].

Proper Motions of Dwarf Spheroidal Galaxies from Hubble Space Telescope Imaging. 3; Measurement for URSA Minor

NASA Technical Reports Server (NTRS)

Piatek, Slawomir; Pryor, Carlton; Bristow, Paul; Olszewski, Edward W.; Harris, Hugh C.; Mateo, Mario; Minniti, Dante; Tinney, Christopher G.

2005-01-01

This article presents a measurement of the proper motion of the Ursa Minor dwarf spheroidal galaxy determined from images taken with the Hubble Space Telescope in two distinct fields. Each field contains a quasi-stellar object that serves as the "reference point". Integrating the motion of Ursa Minor in a realistic potential for the Milky Way produces orbital elements. The perigalacticon and apogalacticon are 40 (10, 76) and 89 (78, 160) kpc, respectively, where the values in the parentheses represent the 95% confidence intervals derived from Monte Carlo experiments. The eccentricity of the orbit is 0.39 (0.09, 0.79), and the orbital period is 1.5 (1.1, 2.7) Gyr. The orbit is retrograde and inclined by 124 degrees (94 deg, 36 deg ) to the Galactic plane. Ursa Minor is not a likely member of a proposed stream of galaxies on similar orbits around the Milky Way, nor is the plane of its orbit coincident with a recently proposed planar alignment of galaxies around the Milky Way. Comparing the orbits of Ursa Minor and Carina shows no reason for the different star formation histories of these two galaxies. Ursa Minor must contain dark matter to have a high probability of having survived disruption by the Galactic tidal force until the present.

Solar radiation pressure application for orbital motion stabilization near the Sun-Earth collinear libration point

NASA Astrophysics Data System (ADS)

Polyakhova, Elena; Shmyrov, Alexander; Shmyrov, Vasily

2018-05-01

Orbital maneuvering in a neighborhood of the collinear libration point L1 of Sun-Earth system has specific properties, primarily associated with the instability L1. For a long stay in this area of space the stabilization problem of orbital motion requires a solution. Numerical experiments have shown that for stabilization of motion it is requires very small control influence in comparison with the gravitational forces. On the other hand, the stabilization time is quite long - months, and possibly years. This makes it highly desirable to use solar pressure forces. In this paper we illustrate the solar sail possibilities for solving of stabilization problem in a neighborhood L1 with use of the model example.

The long-term motion of comet Halley

NASA Technical Reports Server (NTRS)

Yeomans, D. K.; Kiang, T.

1981-01-01

The orbital motion of comet Halley is numerically integrated back to 1404 BC. Starting with an orbit based on the 1759, 1682, and 1607 observations of the comet, the integration was run back in time with full planetary perturbations and nongravitational forces taken into account at each 0.5 day time-step. Small empirical corrections were made to the computed perihelion passage time in 837 and to the osculating orbital eccentricity in 800. In nine cases, the perihelion passage times calculated by Kiang (1971) from Chinese observations have been redetermined, and osculating orbital elements are given at each apparition from 1910 back to 1404 BC.

A new method for computing the gyrocenter orbit in the tokamak configuration

NASA Astrophysics Data System (ADS)

Xu, Yingfeng

2013-10-01

Gyrokinetic theory is an important tool for studying the long-time behavior of magnetized plasmas in Tokamaks. The gyrocenter trajectory determined by the gyrocenter equations of motion can be computed by using a special kind of the Lie-transform perturbation method. The corresponding Lie-transform called I-transform makes that the transformed equations of motion have the same form as the unperturbed ones. The gyrocenter trajectory in short time is divided into two parts. One is along the unperturbed orbit. The other one, which is related to perturbation, is determined by the I-transform generating vector. The numerical gyrocenter orbit code based on this new method has been developed in the tokamak configuration and benchmarked with the other orbit code in some simple cases. Furthermore, it is clearly demonstrated that this new method for computing gyrocenter orbit is equivalent to the gyrocenter Hamilton equations of motion up to the second order in timestep. The new method can be applied to the gyrokinetic simulation. The gyrocenter orbit of the unperturbed part determined by the equilibrium fields can be computed previously in the gyrokinetic simulation, and the corresponding time consumption is neglectable.

A Potential Proxy of the Second Integral of Motion (I2) in a Rotating Barred Potential

NASA Astrophysics Data System (ADS)

Shen, Juntai; Qin, Yujing

2017-06-01

The only analytically known integral of motion in a 2-D rotating barred potential is the Jacobi constant (EJ). In addition to EJ, regular orbits also obey a second integral of motion (I2) whose analytical form is unknown. We show that the time-averaged characteristics of angular momentum in a rotating bar potential resemble the behavior of the analytically-unknown I2. For a given EJ, regular orbits of various families follow a continuous sequence in the space of net angular momentum and its dispersion ("angular momentum space"). In the limiting case where regular orbits of the well-known x1/x4 orbital families dominate the phase space, the orbital sequence can be monotonically traced by a single parameter, namely the ratio of mean angular momentum to its dispersion. This ratio behaves well even in the 3-D case, and thus may be used as a proxy of I2. The potential proxy of I2 may be used as an efficient way to probe the phase space structure, and a convenient new scheme of orbit classification in addition to the frequency mapping technique.

The Influence of Orbital Resonances on the Water Transport to Objects in the Circumprimary Habitable Zone of Binary Star Systems

NASA Astrophysics Data System (ADS)

Bancelin, David; Pilat-Lohinger, Elke; Maindl, Thomas I.; Ragossnig, Florian; Schäfer, Christoph

2017-06-01

We investigate the role of secular and mean motion resonances on the water transport from a belt of icy asteroids onto planets or embryos orbiting inside the circumprimary habitable zone (HZ) of a binary star system. In addition, the host-star has an accompanying gas giant planet. For a comparison, we perform two case studies where a secular resonance (SR) is located either inside the HZ close to 1.0 au (causing eccentric motion of a planet or embryos therein) or in the asteroid belt, beyond the snow line. In the latter case, a higher flux of icy objects moving toward the HZ is expected. Collisions between asteroids and objects in the HZ are treated analytically. Our purely dynamical study shows that the SR in the HZ boosts the water transport however, collisions can occur at very high impact speeds. In this paper, we treat for the first time, realistic collisions using a GPU 3D-SPH code to assess the water loss in the projectile. Including the water loss into the dynamical results, we get more realistic values for the water mass fraction of the asteroid during an impact. We highlight that collisions occurring at high velocities greatly reduce the water content of the projectile and thus the amount of water transported to planets or embryos orbiting inside the HZ. Moreover, we discuss other effects that could modify our results, namely the asteroid’s surface rate recession due to ice sublimation and the atmospheric drag contribution on the asteroids’ mass loss.

Constraints on the perturbed mutual motion in Didymos due to impact-induced deformation of its primary after the DART impact

NASA Astrophysics Data System (ADS)

Hirabayashi, Masatoshi; Schwartz, Stephen R.; Yu, Yang; Davis, Alex B.; Chesley, Steven R.; Fahnestock, Eugene G.; Michel, Patrick; Richardson, Derek C.; Naidu, Shantanu P.; Scheeres, Daniel J.; Cheng, Andrew F.; Rivkin, Andrew S.; Benner, Lance A. M.

2017-12-01

Binary near-Earth asteroid (65803) Didymos is the target of the proposed NASA Double Asteroid Redirection Test (DART), part of the Asteroid Impact & Deflection Assessment (AIDA) mission concept. In this mission, the DART spacecraft is planned to impact the secondary body of Didymos, perturbing mutual dynamics of the system. The primary body is currently rotating at a spin period close to the spin barrier of asteroids, and materials ejected from the secondary due to the DART impact are likely to reach the primary. These conditions may cause the primary to reshape, due to landslides or internal deformation, changing the permanent gravity field. Here, we propose that if shape deformation of the primary occurs, the mutual orbit of the system would be perturbed due to a change in the gravity field. We use a numerical simulation technique based on the full two-body problem to investigate the shape effect on the mutual dynamics in Didymos after the DART impact. The results show that under constant volume, shape deformation induces strong perturbation in the mutual motion. We find that the deformation process always causes the orbital period of the system to become shorter. If surface layers with a thickness greater than ∼0.4 m on the poles of the primary move down to the equatorial region due to the DART impact, a change in the orbital period of the system and in the spin period of the primary will be detected by ground-based measurement.

Origin of the Local Group satellite planes

NASA Astrophysics Data System (ADS)

Banik, Indranil; O'Ryan, David; Zhao, Hongsheng

2018-04-01

We attempt to understand the planes of satellite galaxies orbiting the Milky Way (MW) and M31 in the context of Modified Newtonian Dynamics (MOND), which implies a close MW-M31 flyby occurred ≈8 Gyr ago. Using the timing argument, we obtain MW-M31 trajectories consistent with cosmological initial conditions and present observations. We adjust the present M31 proper motion within its uncertainty in order to simulate a range of orbital geometries and closest approach distances. Treating the MW and M31 as point masses, we follow the trajectories of surrounding test particle disks, thereby mapping out the tidal debris distribution. Around each galaxy, the resulting tidal debris tends to cluster around a particular orbital pole. We find some models in which these preferred spin vectors align fairly well with those of the corresponding observed satellite planes. The radial distributions of material in the simulated satellite planes are similar to what we observe. Around the MW, our best-fitting model yields a significant fraction (0.22) of counter-rotating material, perhaps explaining why Sculptor counter-rotates within the MW satellite plane. In contrast, our model yields no counter-rotating material around M31. This is testable with proper motions of M31 satellites. In our best model, the MW disk is thickened by the flyby 7.65 Gyr ago to a root mean square height of 0.75 kpc. This is similar to the observed age and thickness of the Galactic thick disk. Thus, the MW thick disk may have formed together with the MW and M31 satellite planes during a past MW-M31 flyby.

Origin of the Local Group satellite planes

NASA Astrophysics Data System (ADS)

Banik, Indranil; O'Ryan, David; Zhao, Hongsheng

2018-07-01

We attempt to understand the planes of satellite galaxies orbiting the Milky Way (MW) and M31 in the context of Modified Newtonian Dynamics, which implies a close MW-M31 flyby occurred ≈8 Gyr ago. Using the timing argument, we obtain MW-M31 trajectories consistent with cosmological initial conditions and present observations. We adjust the present M31 proper motion within its uncertainty in order to simulate a range of orbital geometries and closest approach distances. Treating the MW and M31 as point masses, we follow the trajectories of surrounding test particle discs, thereby mapping out the tidal debris distribution. Around each galaxy, the resulting tidal debris tends to cluster around a particular orbital pole. We find some models in which these preferred spin vectors align fairly well with those of the corresponding observed satellite planes. The radial distributions of material in the simulated satellite planes are similar to what we observe. Around the MW, our best-fitting model yields a significant fraction (0.22) of counter-rotating material, perhaps explaining why Sculptor counter-rotates within the MW satellite plane. In contrast, our model yields no counter-rotating material around M31. This is testable with proper motions of M31 satellites. In our best model, the MW disc is thickened by the flyby 7.65 Gyr ago to a root mean square height of 0.75 kpc. This is similar to the observed age and thickness of the Galactic thick disc. Thus, the MW thick disc may have formed together with the MW and M31 satellite planes during a past MW-M31 flyby.

Proper Motions of Dwarf Spheroidal Galaxies from Hubble Space Telescope Imaging. V. Final Measurement for Fornax

NASA Astrophysics Data System (ADS)

Piatek, Slawomir; Pryor, Carlton; Bristow, Paul; Olszewski, Edward W.; Harris, Hugh C.; Mateo, Mario; Minniti, Dante; Tinney, Christopher G.

2007-03-01

The measured proper motion of Fornax, expressed in the equatorial coordinate system, is (μα,μδ)=(47.6+/-4.6,-36.0+/-4.1) mas century-1. This proper motion is a weighted mean of four independent measurements for three distinct fields. Each measurement uses a quasi-stellar object as a reference point. Removing the contribution of the motion of the Sun and of the local standard of rest to the measured proper motion produces a Galactic rest-frame proper motion of (μGrfα,μGrfδ)=(24.4+/-4.6,-14.3+/-4.1) mas century-1. The implied space velocity with respect to the Galactic center has a radial component of Vr=-31.8+/-1.7 km s-1 and a tangential component of Vt=196+/-29 km s-1. Integrating the motion of Fornax in a realistic potential for the Milky Way produces orbital elements. The perigalacticon and apogalacticon are 118 (66, 137) and 152 (144, 242) kpc, respectively, where the values in the parentheses represent the 95% confidence intervals derived from Monte Carlo experiments. The eccentricity of the orbit is 0.13 (0.11, 0.38), and the orbital period is 3.2 (2.5, 4.6) Gyr. The orbit is retrograde and inclined by 101° (94°, 107°) to the Galactic plane. Fornax could be a member of a proposed ``stream'' of galaxies and globular clusters; however, the membership of another proposed galaxy in the stream, Sculptor, has been previously ruled out. Fornax is in the Kroupa-Theis-Boily plane, which contains 11 of the Galactic satellite galaxies, but its orbit will take it out of that plane. Based on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555.

Proper motion of the Draco dwarf galaxy from Subaru Suprime-Cam data

NASA Astrophysics Data System (ADS)

Casetti-Dinescu, Dana I.; Girard, Terrence M.

2016-09-01

We have measured the absolute proper motion of the Draco dwarf spheroidal galaxy using Subaru Suprime-Cam images taken at three epochs, with time baselines of 4.4 and 7 yr. The magnitude limit of the proper-motion study is I = 25, thus allowing for thousands of background galaxies and Draco stars to be used to perform extensive astrometric tests and to derive the correction to an inertial reference frame. The derived proper motion is (μα, μδ) = (-0.284 ± 0.047, -0.289 ± 0.041) mas yr-1. This motion implies an orbit that takes Draco to a pericentre of ˜20 kpc; a somewhat disruptive orbit suggesting that tides might account for the rising velocity-dispersion profile of Draco seen in line-of-sight velocity studies. The orbit is only marginally consistent with Draco's membership to the vast polar structure of Galactic satellites, in contrast to a recent Hubble Space Telescope proper-motion measurement that finds alignment very likely. Our study is a test case to demonstrate that deep imaging with mosaic cameras of appropriate resolution can be used for high-accuracy, ground-based proper-motion measurement. As a useful by-product of the study, we also identify two faint brown-dwarf candidates in the foreground field.

Scout: orbit analysis and hazard assessment for NEOCP objects

NASA Astrophysics Data System (ADS)

Farnocchia, Davide; Chesley, Steven R.; Chamberlin, Alan B.

2016-10-01

It typically takes a few days for a newly discovered asteroid to be officially recognized as a real object. During this time, the tentative discovery is published on the Minor Planet Center's Near-Earth Object Confirmation Page (NEOCP) until additional observations confirm that the object is a real asteroid rather than an observational artifact or an artificial object. Also, NEOCP objects could have a limited observability window and yet be scientifically interesting, e.g., radar and lightcurve targets, mini-moons (temporary Earth captures), mission accessible targets, close approachers or even impactors. For instance, the only two asteroids discovered before an impact, 2008 TC3 and 2014 AA, both reached the Earth less than a day after discovery. For these reasons we developed Scout, an automated system that provides an orbital and hazard assessment for NEOCP objects within minutes after the observations are available. Scout's rapid analysis increases the chances of securing the trajectory of interesting NEOCP objects before the ephemeris uncertainty grows too large or the observing geometry becomes unfavorable. The generally short observation arcs, perhaps only a few hours or even less, lead severe degeneracies in the orbit estimation process. To overcome these degeneracies Scout relies on systematic ranging, a technique that derives possible orbits by scanning a grid in the poorly constrained space of topocentric range and range rate, while the plane-of-sky position and motion are directly tied to the recorded observations. This scan allows us to derive a distribution of the possible orbits and in turn identify the NEOCP objects of most interest to prioritize followup efforts. In particular, Scout ranks objects according to the likelihood of an impact, estimates the close approach distance, the Earth-relative minimum orbit intersection distance and v-infinity, and computes scores to identify objects more likely to be an NEO, a km-sized NEO, a Potentially Hazardous Asteroid, and those on a geocentric orbit. Moreover, Scout provides an ephemeris service that makes use of the statistical information to support observers in their followup efforts.

Outward Migration of Giant Planets in Orbital Resonance

NASA Astrophysics Data System (ADS)

D'Angelo, G.; Marzari, F.

2013-05-01

A pair of giant planets interacting with a gaseous disk may be subject to convergent orbital migration and become locked into a mean motion resonance. If the orbits are close enough, the tidal gaps produced by the planets in the disk may overlap. This represents a necessary condition to activate the outward migration of the pair. However, a number of other conditions must also be realized in order for this mechanism to operate. We have studied how disk properties, such as turbulence viscosity, temperature, surface density gradient, mass, and age, may affect the outcome of the outward migration process. We have also investigated the implications on this mechanism of the planets' gas accretion. If the pair resembles Jupiter and Saturn, the 3:2 orbital resonance may drive them outward until they reach stalling radii for migration, which are within ~10 AU of the star for disks representative of the early proto-solar nebula. However, planet post-formation conditions in the disk indicate that such planets become typically locked in the 1:2 orbital resonance, which does not lead to outward migration. Planet growth via gas accretion tends to alter the planets' mass-ratio and/or the disk accretion rate toward the star, reducing or inhibiting outward migration. Support from NASA Outer Planets Research Program and NASA Origins of Solar Systems Program is gratefully acknowledged.

Discovery and dynamical characterization of the Amor-class asteroid 2012 XH16

NASA Astrophysics Data System (ADS)

Wlodarczyk, I.; Cernis, K.; Boyle, R. P.; Laugalys, V.

2014-03-01

The near-Earth asteroid belt is continuously replenished with material originally moving in Amor-class orbits. Here, the orbit of the dynamically interesting Amor-class asteroid 2012 XH16 is analysed. This asteroid was discovered with the Vatican Advanced Technology Telescope (VATT) at the Mt Graham International Observatory as part of an ongoing asteroid survey focused on astrometry and photometry. The orbit of the asteroid was computed using 66 observations (57 obtained with VATT and 9 from the Lunar and Planetary Laboratory-Spacewatch II project) to give a = 1.63 au, e = 0.36, i = 3.76°. The absolute magnitude of the asteroid is 22.3 which translates into a diameter in the range 104-231 m, assuming the average albedos of S-type and C-type asteroids, respectively. We have used the current orbit to study the future dynamical evolution of the asteroid under the perturbations of the planets and the Moon, relativistic effects, and the Yarkovsky force. Asteroid 2012 XH16 is locked close to the strong 1:2 mean motion resonance with the Earth. The object shows stable evolution and could survive in near-resonance for a relatively long period of time despite experiencing frequent close encounters with Mars. Moreover, results of our computations show that the asteroid 2012 XH16 can survive in the Amor region at most for about 200-400 Myr. The evolution is highly chaotic with a characteristic Lyapunov time of 245 yr. Jupiter is the main perturber but the effects of Saturn, Mars and the Earth-Moon system are also important. In particular, secular resonances with Saturn are significant.

The rectilinear three-body problem as a basis for studying highly eccentric systems

NASA Astrophysics Data System (ADS)

Voyatzis, G.; Tsiganis, K.; Gaitanas, M.

2018-01-01

The rectilinear elliptic restricted three-body problem (TBP) is the limiting case of the elliptic restricted TBP when the motion of the primaries is described by a Keplerian ellipse with eccentricity e'=1, but the collision of the primaries is assumed to be a non-singular point. The rectilinear model has been proposed as a starting model for studying the dynamics of motion around highly eccentric binary systems. Broucke (AIAA J 7:1003-1009, 1969) explored the rectilinear problem and obtained isolated periodic orbits for mass parameter μ =0.5 (equal masses of the primaries). We found that all orbits obtained by Broucke are linearly unstable. We extend Broucke's computations by using a finer search for symmetric periodic orbits and computing their linear stability. We found a large number of periodic orbits, but only eight of them were found to be linearly stable and are associated with particular mean motion resonances. These stable orbits are used as generating orbits for continuation with respect to μ and e'<1. Also, continuation of periodic solutions with respect to the mass of the small body can be applied by using the general TBP. FLI maps of dynamical stability show that stable periodic orbits are surrounded in phase space with regions of regular orbits indicating that systems of very highly eccentric orbits can be found in stable resonant configurations. As an application we present a stability study for the planetary system HD7449.

The Quadruple-lined, Doubly Eclipsing System V482 Persei

NASA Astrophysics Data System (ADS)

Torres, Guillermo; Sandberg Lacy, Claud H.; Fekel, Francis C.; Wolf, Marek; Muterspaugh, Matthew W.

2017-09-01

We report spectroscopic and differential photometric observations of the A-type system V482 Per, which reveal it to be a rare hierarchical quadruple system containing two eclipsing binaries. One binary has the previously known orbital period of 2.4 days and a circular orbit, and the other a period of 6 days, a slightly eccentric orbit (e = 0.11), and shallow eclipses only 2.3% deep. The two binaries revolve around their common center of mass in a highly elongated orbit (e = 0.85) with a period of 16.67 yr. Radial velocities are measured for all components from our quadruple-lined spectra and are combined with the light curves and measurements of times of minimum light for the 2.4 day binary to solve for the elements of the inner and outer orbits simultaneously. The line-of-sight inclination angles of the three orbits are similar, suggesting they may be close to coplanar. The available observations appear to indicate that the 6 day binary experiences significant retrograde apsidal motion in the amount of about 60 deg per century. We derive absolute masses for the four stars good to better than 1.5%, along with radii with formal errors of 1.1% and 3.5% for the 2.4 day binary and ˜9% for the 6 day binary. A comparison of these and other physical properties with current stellar evolution models gives excellent agreement for a metallicity of [{Fe}/{{H}}]=-0.15 and an age of 360 Myr.

Stability of orbits around planetary satellites considering a disturbing body in an elliptical orbit: Applications to Europa and Ganymede

NASA Astrophysics Data System (ADS)

Cardoso dos Santos, Josué; Carvalho, Jean Paulo; Vilhena de Moraes, Rodolpho

Europa and Ganymede are two of the four Jupiter’s moons which compose the Galilean satellite. These ones are planetary satellites of greater interest at the present moment among the scientific community. There are some missions being planned to visit them and and the Jovian system. One of them is the cooperation between NASA and ESA for the Europa Jupiter System Mission (EJSM). In this mission are planned the insertion of the spacecrafts JEO (Jupiter Europa Orbiter) and JGO (Jupiter Ganymede Orbiter) into Europa and Ganymede’s orbit. Thus, there is a great necessity for having a better comprehension of the dynamics of the orbits around this planetary satellite. This comprehension is essential for the success of this type of mission. In this context, this work aims to perform a search for low-altitude orbits around these planetary satellites. An emphasis is given in polar orbits. These orbits can be useful in the planning of aerospace activities to be conducted around this planetary satellite, with respect to the stability of orbits of artificial satellites. The study considers orbits of an artificial satellite around Europa and Ganymede under the influence of the third-body perturbation (the gravitational attraction of Jupiter) and the polygenic perturbations. These last ones occur due to forces such as the non-uniform distribution of mass (J2 and J3) of the main (central) body. A simplified dynamic model for polygenic perturbations is used. A new model for the third-body disturbance is presented considering it in an elliptical orbit. The Lagrange planetary equations, which compose a system of nonlinear differential equations, are used to describe the orbital motion of the artificial satellite around Ganymede. The equations showed here are developed in closed form to avoid expansions in inclination and eccentricity.

Study of the detail content of Apollo orbital photography

NASA Technical Reports Server (NTRS)

Kinzly, R. E.

1972-01-01

The results achieved during a study of the Detail Content of Apollo Orbital Photography are reported. The effect of residual motion smear or image reproduction processes upon the detail content of lunar surface imagery obtained from the orbiting command module are assessed. Data and conclusions obtained from the Apollo 8, 12, 14 and 15 missions are included. For the Apollo 8, 12 and 14 missions, the bracket-mounted Hasselblad camera had no mechanism internal to the camera for motion compensation. If the motion of the command module were left totally uncompensated, these photographs would exhibit a ground smear varying from 12 to 27 meters depending upon the focal length of the lens and the exposure time. During the photographic sequences motion compensation was attempted by firing the attitude control system of the spacecraft at a rate to compensate for the motion relative to the lunar surface. The residual smear occurring in selected frames of imagery was assessed using edge analyses methods to obtain and achieved modulation transfer function (MTF) which was compared to a baseline MTF.

On a possible additional component in an eclipsing binary system HS 2231 + 2441

NASA Astrophysics Data System (ADS)

Vidmachenko, A. P.; Romanyuk, Ya. O.; Shliahetskaya, Ya. O.

2016-05-01

Timing method based on the registration period of variations of a periodic process, associated with the star. The study of stellar eclipsing binary system for a long time allows a series of several transits, depending on the orbital period of the satellite smaller. We present a photometric study of system of the type HW Vir HS 2231 + 2441. Photometric data processing was performed using C-MuniWin Version 1.2.30 program. The accuracy of values for each observation point is in the range 0,003...0,009m for different nights. The calculated ephemeris determined from the light curve by fitting of arc of minimums to the nuclei of primary and secondary eclipses. The amplitude of the periodic changes of minimums moments that arise from the orbital motion of a close pair of stars around the barycenter of the triple system, is less than 0.0008 days (1.15 minutes). It was found that the periodic variation of the orbital period can be explained by the gravitational influence of a third companion on the central binary system with an orbital period of about 97±10d. Periodogram analysis of the observational data series indicate also on the periodicity with values of 48±5d and 195±15d, but with substantially less reliably

Analysis of direct transfer trajectories from LL2 halo orbits to LLOs

NASA Astrophysics Data System (ADS)

Cao, Pengfei; He, Boyong; Li, Haiyang

2017-09-01

A convenient procedure for designing the direct transfer trajectory from lunar L2 point (LL2) halo orbit to a low lunar orbit (LLO) is presented in this paper. The trajectory characteristics are analyzed to support the manned lunar missions design aimed at lunar surface global access. The concise procedure is established based on the circular restricted three-body problem (CR3BP) model. An analytical algorithm is employed to estimate an initial maneuver vector for approaching the Moon in its close vicinity. An iteration process is adopted to generate favorable trajectory that satisfies the constraints at perilune. By introducing a number of intermediate coordinate frames, an algorithm to compute the arriving LLO inclination and right ascension of ascending node (RAAN) is proposed. The orbital inclination and RAAN in this paper are defined and established in the J2000 frame rather than in the synodical frame. Numerical results show that, regardless of value of out-of-plane amplitude (Az) of the halo orbit, the overall maneuver cost of the trajectory largely depends on departure position, and it has two minima around 0.65 km/s. Further study shows that the values of the arriving LLO inclination and RAAN largely depend on the choices of the departure time and the value of Az. The periodicity, due to the natural motion of the Moon, is discovered to play a role in this time dependency. It is concluded that the fuel optimal trajectory permits access to almost any final lunar orbit, including a polar orbit, by means of varying the departure time and Az value.

LONG-LIVED CHAOTIC ORBITAL EVOLUTION OF EXOPLANETS IN MEAN MOTION RESONANCES WITH MUTUAL INCLINATIONS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barnes, Rory; Deitrick, Russell; Quinn, Thomas R.

2015-03-10

We present N-body simulations of resonant planets with inclined orbits that show chaotically evolving eccentricities and inclinations that can persist for at least 10 Gyr. A wide range of behavior is possible, from fast, low amplitude variations to systems in which eccentricities reach 0.9999 and inclinations 179.°9. While the orbital elements evolve chaotically, at least one resonant argument always librates. We show that the HD 73526, HD 45364, and HD 60532 systems may be in chaotically evolving resonances. Chaotic evolution is apparent in the 2:1, 3:1, and 3:2 resonances, and for planetary masses from lunar- to Jupiter-mass. In some cases, orbital disruption occurs aftermore » several gigayears, implying the mechanism is not rigorously stable, just long-lived relative to the main sequence lifetimes of solar-type stars. Planet-planet scattering appears to yield planets in inclined resonances that evolve chaotically in about 0.5% of cases. These results suggest that (1) approximate methods for identifying unstable orbital architectures may have limited applicability, (2) the observed close-in exoplanets may be produced during epochs of high eccentricit induced by inclined resonances, (3) those exoplanets' orbital planes may be misaligned with the host star's spin axis, (4) systems with resonances may be systematically younger than those without, (5) the distribution of period ratios of adjacent planets detected via transit may be skewed due to inclined resonances, and (6) potentially habitable planets may have dramatically different climatic evolution than Earth. The Gaia spacecraft is capable of discovering giant planets in these types of orbits.« less

The first retrograde Trojan asteroid

NASA Astrophysics Data System (ADS)

Wiegert, Paul; Connors, Martin; Veillet, Christian

2018-04-01

There are about six thousand asteroids which share Jupiter's orbit around the Sun. Called the 'Trojan asteroids', they co-exist easily with this giant planet because they travel in the same direction as it ('direct' or 'prograde' motion), and remain roughly 60 degrees ahead of or behind it in its orbit. Newly discovered asteroid 2015 BZ509 is on a retrograde orbit, but is nonetheless in a state dynamically analogous to that of the prograde Trojans. The discovery circumstances and the nature of the motion of this curious asteroid -the first of its kind- will be outlined.

Comet Halley - The orbital motion

NASA Technical Reports Server (NTRS)

Yeomans, D. K.

1977-01-01

The orbital motion of Comet Halley is investigated over the interval from A.D. 837 to 2061. Using the observations from 1607 through 1911, least-squares differential orbit corrections were successfully computed using the existing model for the nongravitational forces. The nongravitational-force model was found to be consistent with the outgassing-rocket effect of a water-ice cometary nucleus and, prior to the 1910 return, these forces are time-independent for nearly a millennium. For the 1986 return, viewing conditions are outlined for the comet and the related Orionid and Eta Aquarid meteor showers.

Compensation of orbit distortion due to quadrupole motion using feed-forward control at KEK ATF

NASA Astrophysics Data System (ADS)

Bett, D. R.; Charrondière, C.; Patecki, M.; Pfingstner, J.; Schulte, D.; Tomás, R.; Jeremie, A.; Kubo, K.; Kuroda, S.; Naito, T.; Okugi, T.; Tauchi, T.; Terunuma, N.; Burrows, P. N.; Christian, G. B.; Perry, C.

2018-07-01

The high luminosity requirement for a future linear collider sets a demanding limit on the beam quality at the Interaction Point (IP). One potential source of luminosity loss is the motion of the ground itself. The resulting misalignments of the quadrupole magnets cause distortions to the beam orbit and hence an increase in the beam emittance. This paper describes a technique for compensating this orbit distortion by using seismometers to monitor the misalignment of the quadrupole magnets in real-time. The first demonstration of the technique was achieved at the Accelerator Test Facility (ATF) at KEK in Japan. The feed-forward system consisted of a seismometer-based quadrupole motion monitoring system, an FPGA-based feed-forward processor and a stripline kicker plus associated electronics. Through the application of a kick calculated from the position of a single quadruple, the system was able to remove about 80% of the component of the beam jitter that was correlated to the motion of the quadrupole. As a significant fraction of the orbit jitter in the ATF final focus is due to sources other than quadrupole misalignment, this amounted to an approximately 15% reduction in the absolute beam jitter.

Dynamics of vortex dipoles in anisotropic Bose-Einstein condensates

DOE PAGES

Goodman, Roy H.; Kevrekidis, P. G.; Carretero-González, R.

2015-04-14

We study the motion of a vortex dipole in a Bose-Einstein condensate confined to an anisotropic trap. We focus on a system of ODEs describing the vortices' motion, which is in turn a reduced model of the Gross-Pitaevskii equation describing the condensate's motion. Using a sequence of canonical changes of variables, we reduce the dimension and simplify the equations of motion. In this study, we uncover two interesting regimes. Near a family of periodic orbits known as guiding centers, we find that the dynamics is essentially that of a pendulum coupled to a linear oscillator, leading to stochastic reversals inmore » the overall direction of rotation of the dipole. Near the separatrix orbit in the isotropic system, we find other families of periodic, quasi-periodic, and chaotic trajectories. In a neighborhood of the guiding center orbits, we derive an explicit iterated map that simplifies the problem further. Numerical calculations are used to illustrate the phenomena discovered through the analysis. Using the results from the reduced system, we are able to construct complex periodic orbits in the original, PDE, mean-field model for Bose-Einstein condensates, which corroborates the phenomenology observed in the reduced dynamical equations.« less

Dynamics of vortex dipoles in anisotropic Bose-Einstein condensates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Goodman, Roy H.; Kevrekidis, P. G.; Carretero-González, R.

We study the motion of a vortex dipole in a Bose-Einstein condensate confined to an anisotropic trap. We focus on a system of ODEs describing the vortices' motion, which is in turn a reduced model of the Gross-Pitaevskii equation describing the condensate's motion. Using a sequence of canonical changes of variables, we reduce the dimension and simplify the equations of motion. In this study, we uncover two interesting regimes. Near a family of periodic orbits known as guiding centers, we find that the dynamics is essentially that of a pendulum coupled to a linear oscillator, leading to stochastic reversals inmore » the overall direction of rotation of the dipole. Near the separatrix orbit in the isotropic system, we find other families of periodic, quasi-periodic, and chaotic trajectories. In a neighborhood of the guiding center orbits, we derive an explicit iterated map that simplifies the problem further. Numerical calculations are used to illustrate the phenomena discovered through the analysis. Using the results from the reduced system, we are able to construct complex periodic orbits in the original, PDE, mean-field model for Bose-Einstein condensates, which corroborates the phenomenology observed in the reduced dynamical equations.« less

A robotic orbital emulator with lidar-based SLAM and AMCL for multiple entity pose estimation

NASA Astrophysics Data System (ADS)

Shen, Dan; Xiang, Xingyu; Jia, Bin; Wang, Zhonghai; Chen, Genshe; Blasch, Erik; Pham, Khanh

2018-05-01

This paper revises and evaluates an orbital emulator (OE) for space situational awareness (SSA). The OE can produce 3D satellite movements using capabilities generated from omni-wheeled robot and robotic arm motions. The 3D motion of satellite is partitioned into the movements in the equatorial plane and the up-down motions in the vertical plane. The 3D actions are emulated by omni-wheeled robot models while the up-down motions are performed by a stepped-motorcontrolled- ball along a rod (robotic arm), which is attached to the robot. Lidar only measurements are used to estimate the pose information of the multiple robots. SLAM (simultaneous localization and mapping) is running on one robot to generate the map and compute the pose for the robot. Based on the SLAM map maintained by the robot, the other robots run the adaptive Monte Carlo localization (AMCL) method to estimate their poses. The controller is designed to guide the robot to follow a given orbit. The controllability is analyzed by using a feedback linearization method. Experiments are conducted to show the convergence of AMCL and the orbit tracking performance.

Disturbing effects of attitude control maneuvers on the orbital motion of the Helios spacecraft

NASA Technical Reports Server (NTRS)

Georgevic, R. M.

1976-01-01

The position of the spin axis of the Helios A spacecraft has been maintained and updated by a series of attitude control maneuvers, by means of a sequence of unbalanced jet forces which produce an additional disturbed motion of the spacecraft's center of mass. The character of this motion, its magnitude and direction was studied. For practical purposes of the orbit determination of the spacecraft, a computer program is given which shows how the components of the disturbing acceleration in the spacecraft-fixed reference frame can be easily computed.

HP-9825A HFRMP trajectory processor (#TRAJ), detailed description. [relative motion of the space shuttle orbiter and a free-flying payload

NASA Technical Reports Server (NTRS)

Kindall, S. M.

1980-01-01

The computer code for the trajectory processor (#TRAJ) of the high fidelity relative motion program is described. The #TRAJ processor is a 12-degrees-of-freedom trajectory integrator (6 degrees of freedom for each of two vehicles) which can be used to generate digital and graphical data describing the relative motion of the Space Shuttle Orbiter and a free-flying cylindrical payload. A listing of the code, coding standards and conventions, detailed flow charts, and discussions of the computational logic are included.

A new method to compute lunisolar perturbations in satellite motions

NASA Technical Reports Server (NTRS)

Kozai, Y.

1973-01-01

A new method to compute lunisolar perturbations in satellite motion is proposed. The disturbing function is expressed by the orbital elements of the satellite and the geocentric polar coordinates of the moon and the sun. The secular and long periodic perturbations are derived by numerical integrations, and the short periodic perturbations are derived analytically. The perturbations due to the tides can be included in the same way. In the Appendix, the motion of the orbital plane for a synchronous satellite is discussed; it is concluded that the inclination cannot stay below 7 deg.

Modeling circumbinary planets: The case of Kepler-38

NASA Astrophysics Data System (ADS)

Kley, Wilhelm; Haghighipour, Nader

2014-04-01

Context. Recently, a number of planets orbiting binary stars have been discovered by the Kepler space telescope. In a few systems the planets reside close to the dynamical stability limit. Owing to the difficulty of forming planets in such close orbits, it is believed that they have formed farther out in the disk and migrated to their present locations. Aims: Our goal is to construct more realistic models of planet migration in circumbinary disks and to determine the final position of these planets more accurately. In our work, we focus on the system Kepler-38 where the planet is close to the stability limit. Methods: The evolution of the circumbinary disk is studied using two-dimensional hydrodynamical simulations. We study locally isothermal disks as well as more realistic models that include full viscous heating, radiative cooling from the disk surfaces, and radiative diffusion in the disk midplane. After the disk has been brought into a quasi-equilibrium state, a 115 Earth-mass planet is embedded and its evolution is followed. Results: In all cases the planets stop inward migration near the inner edge of the disk. In isothermal disks with a typical disk scale height of H/r = 0.05, the final outcome agrees very well with the observed location of planet Kepler-38b. For the radiative models, the disk thickness and location of the inner edge is determined by the mass in the system. For surface densities on the order of 3000 g/cm2 at 1 AU, the inner gap lies close to the binary and planets stop in the region between the 5:1 and 4:1 mean-motion resonances with the binary. A model with a disk with approximately a quarter of the mass yields a final position very close to the observed one. Conclusions: For planets migrating in circumbinary disks, the final position is dictated by the structure of the disk. Knowing the observed orbits of circumbinary planets, radiative disk simulations with embedded planets can provide important information on the physical state of the system during the final stages of its evolution. Movies are available in electronic form at http://www.aanda.org

Attitude dynamics and control of a spacecraft like a robotic manipulator when implementing on-orbit servicing

NASA Astrophysics Data System (ADS)

Da Fonseca, Ijar M.; Goes, Luiz C. S.; Seito, Narumi; da Silva Duarte, Mayara K.; de Oliveira, Élcio Jeronimo

2017-08-01

In space the manipulators working space is characterized by the microgravity environment. In this environment the spacecraft floats and its rotational/translational motion may be excited by any internal and external disturbances. The complete system, i.e., the spacecraft and the associated robotic manipulator, floats and is sensitive to any reaction force and torque related to the manipulator's operation. In this sense the effort done by the robot may result in torque about the system center of mass and also in forces changing its translational motion. This paper analyzes the impact of the robot manipulator dynamics on the attitude motion and the associated control effort to keep the attitude stable during the manipulator's operation. The dynamics analysis is performed in the close proximity phase of rendezvous docking/berthing operation. In such scenario the linear system equations for the translation and attitude relative motions are appropriate. The computer simulations are implemented for the relative translational and rotational motion. The equations of motion have been simulated through computer by using the MatLab software. The LQR and the PID control laws are used for linear and nonlinear control, respectively, aiming to keep the attitude stable while the robot is in and out of service. The gravity-gradient and the residual magnetic torque are considered as external disturbances. The control efforts are analyzed for the manipulator in and out of service. The control laws allow the system stabilization and good performance when the manipulator is in service.

Proper Motions of Dwarf Spheroidal Galaxies from Hubble Space Telescope Imaging. IV. Measurement for Sculptor

NASA Astrophysics Data System (ADS)

Piatek, Slawomir; Pryor, Carlton; Bristow, Paul; Olszewski, Edward W.; Harris, Hugh C.; Mateo, Mario; Minniti, Dante; Tinney, Christopher G.

2006-03-01

This article presents a measurement of the proper motion of the Sculptor dwarf spheroidal galaxy determined from images taken with the Hubble Space Telescope using the Space Telescope Imaging Spectrograph in the imaging mode. Each of two distinct fields contains a quasi-stellar object that serves as the ``reference point.'' The measured proper motion of Sculptor, expressed in the equatorial coordinate system, is (μα, μδ)=(9+/-13, 2+/-13) mas century-1. Removing the contributions from the motion of the Sun and the motion of the local standard of rest produces the proper motion in the Galactic rest frame: (μGrfα, μGrfδ)=(-23+/-13, 45+/-13) mas century-1. The implied space velocity with respect to the Galactic center has a radial component of Vr=79+/-6 km s-1 and a tangential component of Vt=198+/-50 km s-1. Integrating the motion of Sculptor in a realistic potential for the Milky Way produces orbital elements. The perigalacticon and apogalacticon are 68 (31, 83) and 122 (97, 313) kpc, respectively, where the values in the parentheses represent the 95% confidence interval derived from Monte Carlo experiments. The eccentricity of the orbit is 0.29 (0.26, 0.60), and the orbital period is 2.2 (1.5, 4.9) Gyr. Sculptor is on a polar orbit around the Milky Way: the angle of inclination is 86° (83°, 90°). Based on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555.

More surprises from the violent gamma-ray binary LS 2883 /B1259-63.

NASA Astrophysics Data System (ADS)

Kargaltsev, Oleg; Hare, Jeremy; Pavlov, George G.

2018-01-01

We report the results of a Chandra X-ray Observatory (CXO) monitoring campaign of the high-mass gamma-ray binary LS 2883, which hosts the young pulsar B1259-63. The monitoring now covers two binary cycles (6.8 years) and allows us to conclude that ejections of high-velocity X-ray emitting material are common for this binary. In the first cycle we observed an extended feature which detached and moved away from the binary. The observed changes in position were consistent with a steady motion with v=(0.07+/-0.01)c and a slight hint of acceleration. Tracing the motion back in time suggested that the X-ray emitting matter was ejected close to periastron passage. In the last orbital cycle, accelerated motion (reaching (0.13+/-0.02)c) is strongly preferred over a steady motion (the latter would imply that the ejected material was launched ~400 days after the periastron passage). The moving feature is also more luminous, compared to the previous binary cycle, larger in its apparent extent, and exhibits a puzzling morphology. We will show the CXO movies from both binary cycles and discuss physical interpretation of the resolved outflow dynamics in this remarkable system, which provides unique insight into the properties of the pulsar and stellar winds and their interaction.

Orientational dynamics of a triaxial ellipsoid in simple shear flow: Influence of inertia.

PubMed

Rosén, Tomas; Kotsubo, Yusuke; Aidun, Cyrus K; Do-Quang, Minh; Lundell, Fredrik

2017-07-01

The motion of a single ellipsoidal particle in simple shear flow can provide valuable insights toward understanding suspension flows with nonspherical particles. Previously, extensive studies have been performed on the ellipsoidal particle with rotational symmetry, a so-called spheroid. The nearly prolate ellipsoid (one major and two minor axes of almost equal size) is known to perform quasiperiodic or even chaotic orbits in the absence of inertia. With small particle inertia, the particle is also known to drift toward this irregular motion. However, it is not previously understood what effects from fluid inertia could be, which is of highest importance for particles close to neutral buoyancy. Here, we find that fluid inertia is acting strongly to suppress the chaotic motion and only very weak fluid inertia is sufficient to stabilize a rotation around the middle axis. The mechanism responsible for this transition is believed to be centrifugal forces acting on fluid, which is dragged along with the rotational motion of the particle. With moderate fluid inertia, it is found that nearly prolate triaxial particles behave similarly to the perfectly spheroidal particles. Finally, we also are able to provide predictions about the stable rotational states for the general triaxial ellipsoid in simple shear with weak inertia.

OTVE turbopump condition monitoring, task E.5

NASA Technical Reports Server (NTRS)

Coleman, Paul T.; Collins, J. J.

1989-01-01

Recent work has been carried out on development of isotope wear analysis and optical and eddy current technologies to provide bearing wear measurements and real time monitoring of shaft speed, shaft axial displacement and shaft orbit of the Orbit Transfer Vehicle hydrostatic bearing tester. Results show shaft axial displacement can be optically measured (at the same time as shaft orbital motion and speed) to within 0.3 mils by two fiberoptic deflectometers. Evaluation of eddy current probes showed that, in addition to measuring shaft orbital motion, they can be used to measure shaft speed without having to machine grooves on the shaft surface as is the usual practice for turbomachinery. The interim results of this condition monitoring effort are presented.

Spin-orbit splitted excited states using explicitly-correlated equation-of-motion coupled-cluster singles and doubles eigenvectors

NASA Astrophysics Data System (ADS)

Bokhan, Denis; Trubnikov, Dmitrii N.; Perera, Ajith; Bartlett, Rodney J.

2018-04-01

An explicitly-correlated method of calculation of excited states with spin-orbit couplings, has been formulated and implemented. Developed approach utilizes left and right eigenvectors of equation-of-motion coupled-cluster model, which is based on the linearly approximated explicitly correlated coupled-cluster singles and doubles [CCSD(F12)] method. The spin-orbit interactions are introduced by using the spin-orbit mean field (SOMF) approximation of the Breit-Pauli Hamiltonian. Numerical tests for several atoms and molecules show good agreement between explicitly-correlated results and the corresponding values, calculated in complete basis set limit (CBS); the highly-accurate excitation energies can be obtained already at triple- ζ level.

Development and evaluation of a hybrid averaged orbit generator

NASA Technical Reports Server (NTRS)

Mcclain, W. D.; Long, A. C.; Early, L. W.

1978-01-01

A rapid orbit generator based on a first-order application of the Generalized Method of Averaging has been developed for the Research and Development (R&D) version of the Goddard Trajectory Determination System (GTDS). The evaluation of the averaged equations of motion can use both numerically averaged and recursively evaluated, analytically averaged perturbation models. These equations are numerically integrated to obtain the secular and long-period motion. Factors affecting efficient orbit prediction are discussed and guidelines are presented for treatment of each major perturbation. Guidelines for obtaining initial mean elements compatible with the theory are presented. An overview of the orbit generator is presented and comparisons with high precision methods are given.

Subdaily alias and draconitic errors in the IGS orbits

NASA Astrophysics Data System (ADS)

Griffiths, J.; Ray, J.

2011-12-01

Harmonic signals with a fundamental period near the GPS draconitic year (351.2 d) and overtones up to the 8th multiple have been observed in the power spectra of nearly all products of the International GNSS Service (IGS), including station position time series [Ray et al., 2008; Collilieux et al., 2007; Santamaría-Gómez et al., 2011], apparent geocenter motions [Hugentobler et al., 2008], and orbit jumps between successive days and midnight discontinuities in Earth orientation parameter (EOP) rates [Ray and Griffiths, 2009]. Ray et al. [2008] suggested two mechanisms for the harmonics: mismodeling of orbit dynamics and aliasing of near-sidereal local station multipath effects. King and Watson [2010] have studied the propagation of local multipath errors into draconitic position variations, but orbit-related processes have been less well examined. Here we elaborate our earlier analysis of GPS orbit jumps [Griffiths and Ray, 2009; Gendt et al., 2010] where we observed some draconitic features as well as prominent spectral bands near 29, 14, 9, and 7 d periods. Finer structures within the sub-seasonal bands fall close to the expected alias frequencies of subdaily EOP tide lines but do not coincide precisely. While once-per-rev empirical orbit parameters should strongly absorb any subdaily EOP tide errors due to near-resonance of their respective periods, the observed differences require explanation. This has been done by simulating known EOP tidal errors and checking their impact on a long series of daily GPS orbits. Indeed, simulated tidal aliases are found to be very similar to the observed orbital features in the sub-seasonal bands. Moreover and unexpectedly, some low draconitic harmonics were also stimulated, potentially a source for the widespread errors in most IGS products.

The dynamics and control of large flexible space structures. Volume 3, part B: The modelling, dynamics, and stability of large Earth pointing orbiting structures

NASA Technical Reports Server (NTRS)

Bainum, P. M.; Kumar, V. K.

1980-01-01

The dynamics and stability of large orbiting flexible beams, and platforms and dish type structures oriented along the local horizontal are treated both analytically and numerically. It is assumed that such structures could be gravitationally stabilized by attaching a rigid light-weight dumbbell at the center of mass by a spring loaded hinge which also could provide viscous damping. For the beam, the small amplitude inplane pitch motion, dumbbell librational motion, and the anti-symmetric elastic modes are all coupled. The three dimensional equations of motion for a circular flat plate and shallow spherical shell in orbit with a two-degree-of freedom gimballed dumbbell are also developed and show that only those elastic modes described by a single nodal diameter line are influenced by the dumbbell motion. Stability criteria are developed for all the examples and a sensitivity study of the system response characteristics to the key system parameters is carried out.

An Efficient Method for Studying the Stability and Dynamics of the Rotational Motions of Celestial Bodies

NASA Astrophysics Data System (ADS)

Pavlov, A. I.; Maciejewski, A. J.

2003-08-01

We use the alternative MEGNO (Mean Exponential Growth of Nearby Orbits) technique developed by Cincotta and Simo to study the stability of orbital-rotational motions for plane oscillations and three-dimensional rotations. We present a detailed numerical-analytical study of a rigid body in the case where the proper rotation of the body is synchronized with its orbital motion as 3: 2 (Mercurian-type synchronism). For plane rotations, the loss of stability of the periodic solution that corresponds to a 3: 2 resonance is shown to be soft, which should be taken into account to estimate the upper limit for the ellipticity of Mercury. In studying stable and chaotic translational-rotational motions, we point out that the MEGNO criterion can be effectively used. This criterion gives a clear picture of the resonant structures and allows the calculations to be conveniently presented in the form of the corresponding MEGNO stability maps for multidimensional systems. We developed an appropriate software package.

On the stability of dust orbits in mean-motion resonances perturbed by from an interstellar wind

NASA Astrophysics Data System (ADS)

Pástor, Pavol

2014-09-01

Circumstellar dust particles can be captured in a mean-motion resonance (MMR) with a planet and simultaneously be affected by non-gravitational effects. It is possible to describe the secular variations of a particle orbit in the MMR analytically using averaged resonant equations. We derive the averaged resonant equations from the equations of motion in near-canonical form. The secular variations of the particle orbit depending on the orientation of the orbit in space are taken into account. The averaged resonant equations can be derived/confirmed also from Lagrange's planetary equations. We apply the derived theory to the case when the non-gravitational effects are the Poynting-Robertson effect, the radial stellar wind, and an interstellar wind. The analytical and numerical results obtained are in excellent agreement. We found that the types of orbits correspond to libration centers of the conservative problem. The averaged resonant equations can lead to a system of equations which holds for stationary points in a subset of resonant variables. Using this system we show analytically that for the considered non-gravitational effects, all stationary points should correspond to orbits which are stationary in interplanetary space after an averaging over a synodic period. In an exact resonance, the stationary orbits are stable. The stability is achieved by a periodic repetition of the evolution during the synodic period. Numerical solutions of this system show that there are no stationary orbits for either the exact or non-exact resonances.

An approach to ground based space surveillance of geostationary on-orbit servicing operations

NASA Astrophysics Data System (ADS)

Scott, Robert (Lauchie); Ellery, Alex

2015-07-01

On Orbit Servicing (OOS) is a class of dual-use robotic space missions that could potentially extend the life of orbiting satellites by fuel replenishment, repair, inspection, orbital maintenance or satellite repurposing, and possibly reduce the rate of space debris generation. OOS performed in geostationary orbit poses a unique challenge for the optical space surveillance community. Both satellites would be performing proximity operations in tight formation flight with separations less than 500 m making atmospheric seeing (turbulence) a challenge to resolving a geostationary satellite pair when viewed from the ground. The two objects would appear merged in an image as the resolving power of the telescope and detector, coupled with atmospheric seeing, limits the ability to resolve the two objects. This poses an issue for obtaining orbital data for conjunction flight safety or, in matters pertaining to space security, inferring the intent and trajectory of an unexpected object perched very close to one's satellite asset on orbit. In order to overcome this problem speckle interferometry using a cross spectrum approach is examined as a means to optically resolve the client and servicer's relative positions to enable a means to perform relative orbit determination of the two spacecraft. This paper explores cases where client and servicing satellites are in unforced relative motion flight and examines the observability of the objects. Tools are described that exploit cross-spectrum speckle interferometry to (1) determine the presence of a secondary in the vicinity of the client satellite and (2) estimate the servicing satellite's motion relative to the client. Experimental observations performed with the Mont Mégantic 1.6 m telescope on co-located geostationary satellites (acting as OOS proxy objects) are described. Apparent angular separations between Anik G1 and Anik F1R from 5 to 1 arcsec were observed as the two satellites appeared to graze one another. Data reduction using differential angular measurements derived from speckle images collected by the 1.6 m telescope produced relative orbit estimates with better than 90 m accuracy in the cross-track and in-track directions but exhibited highly variable behavior in the radial component from 50 to 1800 m. Simulations of synthetic tracking data indicated that the radial component requires approximately six hours of tracking data for an Extended Kalman Filter to converge on an relative orbit estimate with less than 100 m overall uncertainty. The cross-spectrum approach takes advantage of the Fast Fourier Transform (FFT) permitting near real-time estimation of the relative orbit of the two satellites. This also enables the use of relatively larger detector arrays (>106 pixels) helping to ease acquisition process to acquire optical angular data.

Application of the integral manifold method to the analysis of the spatial motion of a rigid body fixed to a cable

NASA Astrophysics Data System (ADS)

Zabolotnov, Yu. M.

2016-07-01

We analyze the spatial motion of a rigid body fixed to a cable about its center of mass when the orbital cable system is unrolling. The analysis is based on the integral manifold method, which permits separating the rigid body motion into the slow and fast components. The motion of the rigid body is studied in the case of slow variations in the cable tension force and under the action of various disturbances.We estimate the influence of the static and dynamic asymmetry of the rigid body on its spatial motion about the cable fixation point. An example of the analysis of the rigid body motion when the orbital cable system is unrolling is given for a special program of variations in the cable tension force. The conditions of applicability of the integral manifold method are analyzed.

Periodic orbit-attitude solutions along planar orbits in a perturbed circular restricted three-body problem for the Earth-Moon system

NASA Astrophysics Data System (ADS)

Bucci, Lorenzo; Lavagna, Michèle; Guzzetti, Davide; Howell, Kathleen C.

2018-06-01

Interest on Large Space Structures (LSS), orbiting in strategic and possibly long-term stable locations, is nowadays increasing in the space community. LSS can serve as strategic outpost to support a variety of manned and unmanned mission, or may carry scientific payloads for astronomical observations. The paper focuses on analysing LSS in the Earth-Moon system, exploring dynamical structures that are available within a multi-body gravitational environment. Coupling between attitude and orbital dynamics is investigated, with particular interest on the gravity gradient torque exerted by the two massive attractors. First, natural periodic orbit-attitude solutions are obtained; a LSS that exploits such solutions would benefit of a naturally periodic body rotation synchronous with the orbital motion, easing the effort of the attitude control system to satisfy pointing requirements. Then, the solar radiation pressure is introduced into the fully coupled dynamical model and its effects investigated, discovering novel periodic attitude solutions. Benefits of periodic behaviours that incorporate solar radiation pressure are discussed, and analysed via the variation of some parameters (e.g reflection/absorption coefficients, position of the centre of pressure). As a final step to refine the current perturbed orbit-attitude model, a structure flexibility is also superimposed to a reference orbit-attitude rigid body motion via a simple, yet effective model. The coupling of structural vibrations and attitude motion is preliminarily explored, and allows identification of possible challenges, that may be faced to position a LSS in a periodic orbit within the Earth-Moon system.

Turbulence generation by waves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kaftori, D.; Nan, X.S.; Banerjee, S.

The interaction between two-dimensional mechanically generated waves, and a turbulent stream was investigated experimentally in a horizontal channel, using a 3-D LDA synchronized with a surface position measuring device and a micro-bubble tracers flow visualization with high speed video. Results show that although the wave induced orbital motion reached all the way to the wall, the characteristics of the turbulence wall structures and the turbulence intensity close to the wall were not altered. Nor was the streaky nature of the wall layer. On the other hand, the mean velocity profile became more uniform and the mean friction velocity was increased.more » Close to the free surface, the turbulence intensity was substantially increased as well. Even in predominantly laminar flows, the introduction of 2-D waves causes three dimensional turbulence. The turbulence enhancement is found to be proportional to the wave strength.« less

Eclipsing binary stars as tests of gravity theories - The apsidal motion of AS Camelopardalis

NASA Technical Reports Server (NTRS)

Maloney, Frank P.; Guinan, Edward F.; Boyd, Patricia T.

1989-01-01

AS Camelopardalis is an 8th-magnitude eclipsing binary that consists of two main-sequence (B8 V and a B9.5 V) components in an eccentric orbit (e = 0.17) with an orbital period of 3.43 days. Like the eccentric eclipsing system DI Herculis, and a few other systems, AS Cam is an important test case for studying relativistic apsidal motion. In these systems, the theoretical general relativistic apsidal motion is comparable to that expected from classical effects arising from tidal and rotational deformation of the stellar components. Accurate determinations of the orbital and stellar properties of AS Cam have been made by Hilditch (1972) and Khalliulin and Kozyreva (1983) that permit the theoretical relativistic and classical contributions to the apsidal motion to be determined reasonably well. All the published timings of primary and secondary minima have been gathered and supplemented with eclipse timings from 1899 to 1920 obtained from the Harvard plate collection. Least-squares solutions of the eclipse timings extending over an 80 yr interval yield a smaller than expected apsidal motion, in agreement with that found by Khalliulin and Kozyreva from a smaller set of data. The observed apsidal motion for AS Cam is about one-third that expected from the combined relativistic and classical effects. Thus, AS Cam joins DI Her in having an observed apsidal motion significantly less than that predicted from theory.

Relative motion of orbiting particles under the influence of perturbing forces. Volume 1: Summary

NASA Technical Reports Server (NTRS)

Eades, J. B., Jr.

1974-01-01

The relative motion for orbiting vehicles, under the influence of various perturbing forces, has been studied to determine what influence these inputs, and others, can have. The analytical tasks are discribed in general terms; the force types considered, are outlined modelled and simulated, and the capabilities of the computer programs which have evolved in support of this work are denoted.

The orbital motion of the quintuplet cluster—a common origin for the arches and quintuplet clusters?

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stolte, A.; Hußmann, B.; Habibi, M.

2014-07-10

We investigate the orbital motion of the Quintuplet cluster near the Galactic center with the aim of constraining formation scenarios of young, massive star clusters in nuclear environments. Three epochs of adaptive optics high-angular resolution imaging with the Keck/NIRC2 and Very Large Telescope/NAOS-CONICA systems were obtained over a time baseline of 5.8 yr, delivering an astrometric accuracy of 0.5-1 mas yr{sup –1}. Proper motions were derived in the cluster reference frame and were used to distinguish cluster members from the majority of the dense field star population toward the inner bulge. Fitting the cluster and field proper motion distributions withmore » two-dimensional (2D) Gaussian models, we derive the orbital motion of the cluster for the first time. The Quintuplet is moving with a 2D velocity of 132 ± 15 km s{sup –1} with respect to the field along the Galactic plane, which yields a three-dimensional orbital velocity of 167 ± 15 km s{sup –1} when combined with the previously known radial velocity. From a sample of 119 stars measured in three epochs, we derive an upper limit to the velocity dispersion of σ{sub 1D} < 10 km s{sup –1} in the core of the Quintuplet cluster. Knowledge of the three velocity components of the Quintuplet allows us to model the cluster orbit in the potential of the inner Galaxy. Under the assumption that the Quintuplet is located in the central 200 pc at the present time, these simulations exclude the possibility that the cluster is moving on a circular orbit. Comparing the Quintuplet's orbit with our earlier measurements of the Arches' orbit, we discuss the possibility that both clusters originated in the same area of the central molecular zone (CMZ). According to the model of Binney et al., two families of stable cloud orbits are located along the major and minor axes of the Galactic bar, named x1 and x2 orbits, respectively. The formation locus of these clusters is consistent with the outermost x2 orbit and might hint at cloud collisions at the transition region between the x1 and x2 orbital families located at the tip of the minor axis of the Galactic bar. The formation of young, massive star clusters in circumnuclear rings is discussed in the framework of the channeling in of dense gas by the bar potential. We conclude that the existence of a large-scale bar plays a major role in supporting ongoing star and cluster formation, not only in nearby spiral galaxies with circumnuclear rings, but also in the Milky Way's CMZ.« less

Inverse-Square Orbits: A Geometric Approach.

ERIC Educational Resources Information Center

Rainwater, James C.; Weinstock, Robert

1979-01-01

Presents a derivation of Kepler's first law of planetary motion from Newtonian principles. Analogus derivations of the hyperbolic and parabolic orbits of nonreturning comets and the hyperbolic orbit for a particle in a repulsive inverse-square field are also presented. (HM)

Optimal spacecraft formation establishment and reconfiguration propelled by the geomagnetic Lorentz force

NASA Astrophysics Data System (ADS)

Huang, Xu; Yan, Ye; Zhou, Yang

2014-12-01

The Lorentz force acting on an electrostatically charged spacecraft as it moves through the planetary magnetic field could be utilized as propellantless electromagnetic propulsion for orbital maneuvering, such as spacecraft formation establishment and formation reconfiguration. By assuming that the Earth's magnetic field could be modeled as a tilted dipole located at the center of Earth that corotates with Earth, a dynamical model that describes the relative orbital motion of Lorentz spacecraft is developed. Based on the proposed dynamical model, the energy-optimal open-loop trajectories of control inputs, namely, the required specific charges of Lorentz spacecraft, for Lorentz-propelled spacecraft formation establishment or reconfiguration problems with both fixed and free final conditions constraints are derived via Gauss pseudospectral method. The effect of the magnetic dipole tilt angle on the optimal control inputs and the relative transfer trajectories for formation establishment or reconfiguration is also investigated by comparisons with the results derived from a nontilted dipole model. Furthermore, a closed-loop integral sliding mode controller is designed to guarantee the trajectory tracking in the presence of external disturbances and modeling errors. The stability of the closed-loop system is proved by a Lyapunov-based approach. Numerical simulations are presented to verify the validity of the proposed open-loop control methods and demonstrate the performance of the closed-loop controller. Also, the results indicate the dipole tilt angle should be considered when designing control strategies for Lorentz-propelled spacecraft formation establishment or reconfiguration.

Fragmentation hierarchy of bright sungrazing comets and the birth and orbital evolution of the Kreutz system. I. Two-superfragment model

NASA Technical Reports Server (NTRS)

Sekanina, Zdenek; Chodas, Paul W.

2004-01-01

A back-and-forth orbit integration technique, developed for our previous investigation of the splitting of the parent of the sungrazers C/1882 R1 and C/1965 S1, is now applied in an effort to understand the history and orbital evolution of the Kreutz sungrazer system, starting with the birth of two subgroups, which show prominently among the bright members and whose inception dates back to the progenitor's breakup into two superfragments. The integration technique is used to reproduce the motion of comet C/1843 D1 - the second brightest sungrazer known and presumably the most massive surviving piece of superfragment I - from the motion of C/1882 R1 - the brightest sungrazer on record and arguably the most massive surviving piece of superfragment II. Running the orbit of C/1882 R1 back to A.D. 326, the progenitor comet is found to have split at a heliocentric distance of 50 AU and nearly 30 yr before perihelion. The superfragments acquired separation velocities of similar to8 m s(-1) in opposite directions. Using the same technique, we show next that (1) the motions of two additional sungrazers, C/1880 C1 and C/1887 B1, are matched extremely well if these objects shared a common parent with C/1843 D1, and (2) C/1963 R1 (Pereyra), the second brightest subgroup I member on record, is more closely related to subgroup II objects (such as C/1882 R1 and C/1965 S1) than to C/1843 D1. This finding raises serious doubts about the major role of the subgroups in the system's orbital history and offers an incentive for considering an alternative dynamical scenario. The fragmentation models for C/1963 R1 and two additional bright sungrazers, C/1945 X1 and C/1970 K1, suggest that (1) these comets may have been the most massive pieces of the fragment populations formed from their respective disintegrating parents, and (2) the course of evolution of the Kreutz system at the upper end of the mass spectrum may be better ascertained from the distribution of the sungrazers' arrival times than from the sources of subgroups. If so, the fragment hierarchy should be determined primarily by the cascading nature of the fragmentation process, which was recently shown by Sekanina to control the evolution of minor fragments as well. The sungrazer system's estimated age is in any case very short, less than 1700 yr.

Estimates of Comet Fragment Masses from Impact Crater Chains on Callisto and Ganymede

NASA Technical Reports Server (NTRS)

McKinnon, William B.; Schenk, Paul M.

1995-01-01

Chains of impact craters, or catenae, have been identified in Voyager images of Callisto and Ganymede. Although these resemble in some respects secondary crater chains, the source craters and basins for the catenae cannot be identified. The best explanation is a phenomenon similar to that displayed by former comet Shoemaker-Levy 9; tidal (or other) breakup close to Jupiter followed by gradual orbital separation of the fragments and collision with a Galilean satellite on the outbound leg of the trajectory. Because the trajectories must pass close to Jupiter, this constrains the impact geometry (velocity and impact angle) of the individual fragments. For the dominant classes of impactors, short period Jupiter-family comets and asteroids, velocities at Callisto and Ganymede are dominated by Jovian gravity and a satellite's orbital motion, and are insensitive to the pre-fragmentation heliocentric velocity; velocities are insensitive to satellite gravity for all impactor classes. Complex crater shapes on Callisto and Ganymede are determined from Voyager images and Schmidt-Holsapple scaling is used to back out individual fragment masses. We find that comet fragment radii are generally less than about 500 m (for ice densities) but can be larger. These estimates can be compared with those for the Shoemaker-Levy 9 impactors.

Super-Sharp Radio "Vision" Measures Galaxy's Motion in Space

NASA Astrophysics Data System (ADS)

2005-03-01

Astronomers using the National Science Foundation's Very Long Baseline Array (VLBA) have measured the motion across the sky of a galaxy nearly 2.4 million light-years from Earth. While scientists have been measuring the motion of galaxies directly toward or away from Earth for decades, this is the first time that the transverse motion (called proper motion by astronomers) has been measured for a galaxy that is not a satellite of our own Milky Way Galaxy. M33 Radio/Optical Image of M33 CREDIT: NRAO/AUI/NSF, NOAO/AURA/NSF (Click on image for more files) An international scientific team analyzed VLBA observations made over two and a half years to detect minuscule shifts in the sky position of the spiral galaxy M33. Combined with previous measurements of the galaxy's motion toward Earth, the new data allowed the astronomers to calculate M33's movement in three dimensions for the first time. "A snail crawling on Mars would appear to be moving across the surface more than 100 times faster than the motion we measured for this galaxy," said Mark Reid, of the Harvard-Smithsonian Center for Astrophysics in Cambridge, MA. M33 is a satellite of the larger galaxy M31, the well-known Andromeda Galaxy that is the most distant object visible to the naked eye. Both are part of the Local Group of galaxies that includes the Milky Way. In addition to measuring the motion of M33 as a whole, the astronomers also were able to make a direct measurement of the spiral galaxy's rotation. Both measurements were made by observing the changes in position of giant clouds of molecules inside the galaxy. The water vapor in these clouds acts as a natural maser, strengthening, or amplifying, radio emission the same way that lasers amplify light emission. The natural masers acted as bright radio beacons whose movement could be tracked by the ultra-sharp radio "vision" of the VLBA. Reid and his colleagues plan to continue measuring M33's motion and also to make similar measurements of M31's motion. This will allow them to answer important questions about the composition, history and fates of the two galaxies as well as of the Milky Way. "We want to determine the orbits of M31 and M33. That will help us learn about their history, specifically, how close have they come in the past?" Reid explained. "If they have passed very closely, then maybe M33's small size is a result of having material pulled off it by M31 during the close encounter," he added. Accurate knowledge of the motions of both galaxies also will help determine if there's a collision in their future. In addition, orbital analysis can give astronomers valuable clues about the amount and distribution of dark matter in the galaxies. M33's motion in space M33's motion in space, relative to M31 and the Milky Way CREDIT: Bill Saxton, NRAO/AUI/NSF (Click on image for larger version) The direct measurement of M33's transverse angular spin is the first time such a measurement has been done accurately. In the 1920s, some astronomers thought they had measured the spin of spiral galaxies, but their results proved to be in error. More recently, radio astronomers have measured the Doppler shift of hydrogen gas in galaxies to determine the spin speed, which, when combined with the angular spin, gives a direct estimate of the distance of the galaxy. The astronomers' task was not simple. Not only did they have to detect an impressively tiny amount of motion across the sky, but they also had to separate the actual motion of M33 from the apparent motion caused by our Solar System's motion around the center of the Milky Way. The motion of the Solar System and the Earth around the Galactic center, some 26,000 light-years away, has been accurately measured using the VLBA over the last decade. "The VLBA is the only telescope system in the world that could do this work," Reid said. "Its extraordinary ability to resolve fine detail is unmatched and was the absolute prerequisite to making these measurements." Reid worked with Andreas Brunthaler of the Max Planck Institute for Radioastronomy in Bonn, Germany; Heino Falcke of ASTRON in the Netherlands; Lincoln Greenhill, also of the Harvard- Smithsonian Center for Astrophysics; and Christian Henkel, also of the Max Planck Institute in Bonn. The scientists reported their findings in the March 4 issue of the journal Science. The VLBA is a system of ten radio-telescope antennas, each with a dish 25 meters (82 feet) in diameter and weighing 240 tons. From Mauna Kea on the Big Island of Hawaii to St. Croix in the U.S. Virgin Islands, the VLBA spans more than 5,000 miles, providing astronomers with the sharpest vision of any telescope on Earth or in orbit. Dedicated in 1993, the VLBA has an ability to see fine detail equivalent to being able to stand in New York and read a newspaper in Los Angeles. The VLBA's scientific achievements include making the most accurate distance measurement ever made of an object beyond the Milky Way Galaxy; the first mapping of the magnetic field of a star other than the Sun; movies of motions in powerful cosmic jets and of distant supernova explosions; the first measurement of the propagation speed of gravity; and long-term measurements that have improved the reference frame used to map the Universe and detect tectonic motions of Earth's continents. The National Radio Astronomy Observatory is a facility of the National Science Foundation, operated under cooperative agreement by Associated Universities, Inc.

Physical Meaning of Virtual Kohn-Sham Orbitals and Orbital Energies: An Ideal Basis for the Description of Molecular Excitations.

PubMed

van Meer, R; Gritsenko, O V; Baerends, E J

2014-10-14

In recent years, several benchmark studies on the performance of large sets of functionals in time-dependent density functional theory (TDDFT) calculations of excitation energies have been performed. The tested functionals do not approximate exact Kohn-Sham orbitals and orbital energies closely. We highlight the advantages of (close to) exact Kohn-Sham orbitals and orbital energies for a simple description, very often as just a single orbital-to-orbital transition, of molecular excitations. Benchmark calculations are performed for the statistical average of orbital potentials (SAOP) functional for the potential [J. Chem. Phys. 2000, 112, 1344; 2001, 114, 652], which approximates the true Kohn-Sham potential much better than LDA, GGA, mGGA, and hybrid potentials do. An accurate Kohn-Sham potential does not only perform satisfactorily for calculated vertical excitation energies of both valence and Rydberg transitions but also exhibits appealing properties of the KS orbitals including occupied orbital energies close to ionization energies, virtual-occupied orbital energy gaps very close to excitation energies, realistic shapes of virtual orbitals, leading to straightforward interpretation of most excitations as single orbital transitions. We stress that such advantages are completely lost in time-dependent Hartree-Fock and partly in hybrid approaches. Many excitations and excitation energies calculated with local density, generalized gradient, and hybrid functionals are spurious. There is, with an accurate KS, or even the LDA or GGA potentials, nothing problematic about the "band gap" in molecules: the HOMO-LUMO gap is close to the first excitation energy (the optical gap).

Quantitative Measures of Chaotic Charged Particle Dynamics in the Magnetotail

NASA Astrophysics Data System (ADS)

Holland, D. L.; Martin, R. F., Jr.; Burris, C.

2017-12-01

It has long been noted that the motion of charged particles in magnetotail-like magnetic fields is chaotic, however, efforts to quantify the degree of chaos have had conflicting conclusions. In this paper we re-examine the question by focusing on quantitative measures of chaos. We first examine the percentage of orbits that enter the chaotic region of phase space and the average trapping time of those particles. We then examine the average exponential divergence rate (AEDR) of the chaotic particles between their first and last crossing of the mid-plane. We show that at resonant energies where the underlying phase space has a high degree of symmetry, only a small number of particle enter the chaotic region, but they are trapped for long periods of time and the time asymptotic value of the AEDR is very close to the average value of the AEDR. At the off-resonant energies where the phase space is highly asymmetric, the majority of the particle enter the chaotic region for fairly short periods of time and the time asymptotic value of the AEDR is much smaller than the average value. The root cause is that in the resonant case, the longest-lived orbits tend interact with the current many times and sample the entire chaotic region, whereas in the non-resonant case the longest-lived orbits only interact with the current sheet a small number of times but have very long mirrorings where the motion is nearly regular. Additionally we use an ad-hoc model where we model the current sheet as a Lorentz scattering system with each interaction with the current sheet being considered as a "collision". We find that the average kick per collision is greatest at off-resonant energies. Finally, we propose a chaos parameter as the product of the AEDR times the average chaotic particle trapping time times the percentage of orbits that are chaotic. We find that this takes on peak values at the resonant energies.

Time Dependence of Collision Probabilities During Satellite Conjunctions

NASA Technical Reports Server (NTRS)

Hall, Doyle T.; Hejduk, Matthew D.; Johnson, Lauren C.

2017-01-01

The NASA Conjunction Assessment Risk Analysis (CARA) team has recently implemented updated software to calculate the probability of collision (P (sub c)) for Earth-orbiting satellites. The algorithm can employ complex dynamical models for orbital motion, and account for the effects of non-linear trajectories as well as both position and velocity uncertainties. This “3D P (sub c)” method entails computing a 3-dimensional numerical integral for each estimated probability. Our analysis indicates that the 3D method provides several new insights over the traditional “2D P (sub c)” method, even when approximating the orbital motion using the relatively simple Keplerian two-body dynamical model. First, the formulation provides the means to estimate variations in the time derivative of the collision probability, or the probability rate, R (sub c). For close-proximity satellites, such as those orbiting in formations or clusters, R (sub c) variations can show multiple peaks that repeat or blend with one another, providing insight into the ongoing temporal distribution of risk. For single, isolated conjunctions, R (sub c) analysis provides the means to identify and bound the times of peak collision risk. Additionally, analysis of multiple actual archived conjunctions demonstrates that the commonly used “2D P (sub c)” approximation can occasionally provide inaccurate estimates. These include cases in which the 2D method yields negligibly small probabilities (e.g., P (sub c)) is greater than 10 (sup -10)), but the 3D estimates are sufficiently large to prompt increased monitoring or collision mitigation (e.g., P (sub c) is greater than or equal to 10 (sup -5)). Finally, the archive analysis indicates that a relatively efficient calculation can be used to identify which conjunctions will have negligibly small probabilities. This small-P (sub c) screening test can significantly speed the overall risk analysis computation for large numbers of conjunctions.

The Gemini NICI Planet-finding Campaign: Discovery of a Close Substellar Companion to the Young Debris Disk Star PZ Tel

NASA Astrophysics Data System (ADS)

Biller, Beth A.; Liu, Michael C.; Wahhaj, Zahed; Nielsen, Eric L.; Close, Laird M.; Dupuy, Trent J.; Hayward, Thomas L.; Burrows, Adam; Chun, Mark; Ftaclas, Christ; Clarke, Fraser; Hartung, Markus; Males, Jared; Reid, I. Neill; Shkolnik, Evgenya L.; Skemer, Andrew; Tecza, Matthias; Thatte, Niranjan; Alencar, Silvia H. P.; Artymowicz, Pawel; Boss, Alan; de Gouveia Dal Pino, Elisabete; Gregorio-Hetem, Jane; Ida, Shigeru; Kuchner, Marc J.; Lin, Douglas; Toomey, Douglas

2010-09-01

We report the discovery of a tight substellar companion to the young solar analog PZ Tel, a member of the β Pic moving group observed with high-contrast adaptive optics imaging as part of the Gemini Near-Infrared Coronagraphic Imager Planet-Finding Campaign. The companion was detected at a projected separation of 16.4 ± 1.0 AU (0farcs33 ± 0farcs01) in 2009 April. Second-epoch observations in 2010 May demonstrate that the companion is physically associated and shows significant orbital motion. Monte Carlo modeling constrains the orbit of PZ Tel B to eccentricities >0.6. The near-IR colors of PZ Tel B indicate a spectral type of M7 ± 2 and thus this object will be a new benchmark companion for studies of ultracool, low-gravity photospheres. Adopting an age of 12+8 -4 Myr for the system, we estimate a mass of 36 ± 6 M Jup based on the Lyon/DUSTY evolutionary models. PZ Tel B is one of the few young substellar companions directly imaged at orbital separations similar to those of giant planets in our own solar system. Additionally, the primary star PZ Tel A shows a 70 μm emission excess, evidence for a significant quantity of circumstellar dust that has not been disrupted by the orbital motion of the companion. Based on observations obtained at the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science Foundation (United States), the Science and Technology Facilities Council (United Kingdom), the National Research Council (Canada), CONICYT (Chile), the Australian Research Council (Australia), Ministério da Ciência e Tecnologia (Brazil), and Ministerio de Ciencia, Tecnología e Innovación Productiva (Argentina).

Coupled orbit-attitude dynamics and relative state estimation of spacecraft near small Solar System bodies

NASA Astrophysics Data System (ADS)

Misra, Gaurav; Izadi, Maziar; Sanyal, Amit; Scheeres, Daniel

2016-04-01

The effects of dynamical coupling between the rotational (attitude) and translational (orbital) motion of spacecraft near small Solar System bodies is investigated. This coupling arises due to the weak gravity of these bodies, as well as solar radiation pressure. The traditional approach assumes a point-mass spacecraft model to describe the translational motion of the spacecraft, while the attitude motion is considered to be completely decoupled from the translational motion. The model used here to describe the rigid-body spacecraft dynamics includes the non-uniform rotating gravity field of the small body up to second degree and order along with the attitude dependent terms, solar tide, and solar radiation pressure. This model shows that the second degree and order gravity terms due to the small body affect the dynamics of the spacecraft to the same extent as the orbit-attitude coupling due to the primary gravity (zeroth order) term. Variational integrators are used to simulate the dynamics of both the rigid spacecraft and the point mass. The small bodies considered here are modeled after Near-Earth Objects (NEO) 101955 Bennu, and 25143 Itokawa, and are assumed to be triaxial ellipsoids with uniform density. Differences in the numerically obtained trajectories of a rigid spacecraft and a point mass are then compared, to illustrate the impact of the orbit-attitude coupling on spacecraft dynamics in proximity of small bodies. Possible implications on the performance of model-based spacecraft control and on the station-keeping budget, if the orbit-attitude coupling is not accounted for in the model of the dynamics, are also discussed. An almost globally asymptotically stable motion estimation scheme based solely on visual/optical feedback that estimates the relative motion of the asteroid with respect to the spacecraft is also obtained. This estimation scheme does not require a model of the dynamics of the asteroid, which makes it perfectly suited for asteroids whose properties are not well known.

The Prediction of the Motion of Atens, Apollos and Amors over Long Intervals of Time

NASA Astrophysics Data System (ADS)

Wlodarczyk, I.

2002-01-01

Equations of motion of 930 Atens, Apollos and Amors (AAA) were integrated 300,000 years forward using RA15 Everhart method (Everhart, 1974). The Osterwinter model of Solar System was used (Osterwinter and Cohen, 1972). The differences in mean anomaly between unchanged and changed orbits were calculated. The changed orbits were constructed by adding or subtracting to the starting orbital elements one after the other errors of determination of orbital elements. When the differences in mean anomaly were greater than 360 deg. then computations were stopped. In almost all cases after about 1000 years in forwards or backwards integrations differences in mean anomaly between neighbors orbits growth rapidly. It denotes that it is impossible to predict behavior of asteroids outside this time. This time I have called time of stability.

Decomposition technique and optimal trajectories for the aeroassisted flight experiment

NASA Technical Reports Server (NTRS)

Miele, A.; Wang, T.; Deaton, A. W.

1990-01-01

An actual geosynchronous Earth orbit-to-low Earth orbit (GEO-to-LEO) transfer is considered with reference to the aeroassisted flight experiment (AFE) spacecraft, and optimal trajectories are determined by minimizing the total characteristic velocity. The optimization is performed with respect to the time history of the controls (angle of attack and angle of bank), the entry path inclination and the flight time being free. Two transfer maneuvers are considered: direct ascent (DA) to LEO and indirect ascent (IA) to LEO via parking Earth orbit (PEO). By taking into account certain assumptions, the complete system can be decoupled into two subsystems: one describing the longitudinal motion and one describing the lateral motion. The angle of attack history, the entry path inclination, and the flight time are determined via the longitudinal motion subsystem. In this subsystem, the difference between the instantaneous bank angle and a constant bank angle is minimized in the least square sense subject to the specified orbital inclination requirement. Both the angles of attack and the angle of bank are shown to be constant. This result has considerable importance in the design of nominal trajectories to be used in the guidance of AFE and aeroassisted orbital transfer (AOT) vehicles.

PHYSICAL CHARACTERISTICS AND NON-KEPLERIAN ORBITAL MOTION OF 'PROPELLER' MOONS EMBEDDED IN SATURN'S RINGS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tiscareno, Matthew S.; Burns, Joseph A.; Hedman, Matthew M.

2010-08-01

We report the discovery of several large 'propeller' moons in the outer part of Saturn's A ring, objects large enough to be followed over the 5 year duration of the Cassini mission. These are the first objects ever discovered that can be tracked as individual moons, but do not orbit in empty space. We infer sizes up to 1-2 km for the unseen moonlets at the center of the propeller-shaped structures, though many structural and photometric properties of propeller structures remain unclear. Finally, we demonstrate that some propellers undergo sustained non-Keplerian orbit motion.

Modelling of charged satellite motion in Earth's gravitational and magnetic fields

NASA Astrophysics Data System (ADS)

Abd El-Bar, S. E.; Abd El-Salam, F. A.

2018-05-01

In this work Lagrange's planetary equations for a charged satellite subjected to the Earth's gravitational and magnetic force fields are solved. The Earth's gravity, and magnetic and electric force components are obtained and expressed in terms of orbital elements. The variational equations of orbit with the considered model in Keplerian elements are derived. The solution of the problem in a fully analytical way is obtained. The temporal rate of changes of the orbital elements of the spacecraft are integrated via Lagrange's planetary equations and integrals of the normalized Keplerian motion obtained by Ahmed (Astron. J. 107(5):1900, 1994).

Colliding Stellar Wind Models with Orbital Motion

NASA Astrophysics Data System (ADS)

Wilkin, Francis P.; O'Connor, Brendan

2018-01-01

We present thin-shell models for the collision between two ballistic stellar winds, including orbital motion.The stellar orbits are assumed circular, so that steady-state solutions exist in the rotating frame, where we include centrifugal and Coriolis forces. Exact solutions for the pre-shock winds are incorporated. Here we discuss 2-D model results for equal wind momentum-loss rates, although we allow for the winds to have distinct speeds and mass loss rates. For these unequal wind conditions, we obtain a clear violation of skew-symmetry, despite equal momentum loss rates, due to the Coriolis force.

The classical Taub-Nut system: factorization, spectrum generating algebra and solution to the equations of motion

NASA Astrophysics Data System (ADS)

Latini, Danilo; Ragnisco, Orlando

2015-05-01

The formalism of SUperSYmmetric quantum mechanics (SUSYQM) is properly modified in such a way to be suitable for the description and the solution of a classical maximally superintegrable Hamiltonian system, the so-called Taub-Nut system, associated with the Hamiltonian: In full agreement with the results recently derived by Ballesteros et al for the quantum case, we show that the classical Taub-Nut system shares a number of essential features with the Kepler system, that is just its Euclidean version arising in the limit η \\to 0, and for which a ‘SUSYQM’ approach has been recently introduced by Kuru and Negro. In particular, for positive η and negative energy the motion is always periodic; it turns out that the period depends upon η and goes to the Euclidean value as η \\to 0. Moreover, the maximal superintegrability is preserved by the η-deformation, due to the existence of a larger symmetry group related to an η-deformed Runge-Lenz vector, which ensures that in {{{R}}3} closed orbits are again ellipses. In this context, a deformed version of the third Kepler’s law is also recovered. The closing section is devoted to a discussion of the η \\lt 0 case, where new and partly unexpected features arise.

Nonlinear dynamic phenomena in the space shuttle thermal protection system

NASA Technical Reports Server (NTRS)

Housner, J. M.; Edighoffer, H. H.; Park, K. C.

1981-01-01

The development of an analysis for examining the nonlinear dynamic phenomena arising in the space shuttle orbiter tile/pad thermal protection system is presented. The tile/pad system consists of ceramic tiles bonded to the aluminum skin of the orbiter through a thin nylon felt pad. The pads are a soft nonlinear material which permits large strains and displays both hysteretic and nonlinear viscous damping. Application of the analysis to a square tile subjected to transverse sinusoidal motion of the orbiter skin is presented and the following nonlinear dynamic phenomena are considered: highly distorted wave forms, amplitude-dependent resonant frequencies which initially decrease and then increase with increasing amplitude of motion, magnification of substrate motion which is higher than would be expected in a similarly highly damped linear system, and classical parametric resonance instability.

Fundamental limits on beam stability at the Advanced Photon Source.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Decker, G. A.

1998-06-18

Orbit correction is now routinely performed at the few-micron level in the Advanced Photon Source (APS) storage ring. Three diagnostics are presently in use to measure and control both AC and DC orbit motions: broad-band turn-by-turn rf beam position monitors (BPMs), narrow-band switched heterodyne receivers, and photoemission-style x-ray beam position monitors. Each type of diagnostic has its own set of systematic error effects that place limits on the ultimate pointing stability of x-ray beams supplied to users at the APS. Limiting sources of beam motion at present are magnet power supply noise, girder vibration, and thermal timescale vacuum chamber andmore » girder motion. This paper will investigate the present limitations on orbit correction, and will delve into the upgrades necessary to achieve true sub-micron beam stability.« less

Harnessing Orbital Debris to Sense the Space Environment

NASA Astrophysics Data System (ADS)

Mutschler, S.; Axelrad, P.; Matsuo, T.

A key requirement for accurate space situational awareness (SSA) is knowledge of the non-conservative forces that act on space objects. These effects vary temporally and spatially, driven by the dynamical behavior of space weather. Existing SSA algorithms adjust space weather models based on observations of calibration satellites. However, lack of sufficient data and mismodeling of non-conservative forces cause inaccuracies in space object motion prediction. The uncontrolled nature of debris makes it particularly sensitive to the variations in space weather. Our research takes advantage of this behavior by inverting observations of debris objects to infer the space environment parameters causing their motion. In addition, this research will produce more accurate predictions of the motion of debris objects. The hypothesis of this research is that it is possible to utilize a "cluster" of debris objects, objects within relatively close proximity of each other, to sense their local environment. We focus on deriving parameters of an atmospheric density model to more precisely predict the drag force on LEO objects. An Ensemble Kalman Filter (EnKF) is used for assimilation; the prior ensemble to the posterior ensemble is transformed during the measurement update in a manner that does not require inversion of large matrices. A prior ensemble is utilized to empirically determine the nonlinear relationship between measurements and density parameters. The filter estimates an extended state that includes position and velocity of the debris object, and atmospheric density parameters. The density is parameterized as a grid of values, distributed by latitude and local sidereal time over a spherical shell encompassing Earth. This research focuses on LEO object motion, but it can also be extended to additional orbital regimes for observation and refinement of magnetic field and solar radiation models. An observability analysis of the proposed approach is presented in terms of the measurement cadence necessary to estimate the local space environment.

NASA Educational Briefs for the Classroom. Orbits of Bodies in Space

NASA Technical Reports Server (NTRS)

1982-01-01

The difference between an orbit and a revolution is explained and it is shown why space shuttle Columbia's period of revolution was longer than its orbital period. Parameters of orbits examined include apoapsis, periapsis, apogee, perigee, aphelion, perihelion, orbital plane, and inclination. Orbit velocity and duration, Newton's law of gravitation, and Kepler's three laws of motion are considered. The principles involved in geostationary satellites are also explored.

Spin-Orbit Coupling and the Conservation of Angular Momentum

ERIC Educational Resources Information Center

Hnizdo, V.

2012-01-01

In nonrelativistic quantum mechanics, the total (i.e. orbital plus spin) angular momentum of a charged particle with spin that moves in a Coulomb plus spin-orbit-coupling potential is conserved. In a classical nonrelativistic treatment of this problem, in which the Lagrange equations determine the orbital motion and the Thomas equation yields the…

Effects of prolonged weightlessness on self-motion perception and eye movements evoked by roll and pitch

NASA Technical Reports Server (NTRS)

Reschke, Millard F.; Parker, Donald E.

1987-01-01

Seven astronauts reported translational self-motion during roll simulation 1-3 h after landing following 5-7 d of orbital flight. Two reported strong translational self-motion perception when they performed pitch head motions during entry and while the orbiter was stationary on the runway. One of two astronauts from whom adequate data were collected exhibited a 132-deg shift in the phase angle between roll stimulation and horizontal eye position 2 h after landing. Neither of two from whom adequate data were collected exhibited increased horizontal eye movement amplitude or disturbance of voluntary pitch or roll body motion immediately postflight. These results are generally consistent with an otolith tilt-translation reinterpretation model and are being applied to the development of apparatus and procedures intended to preadapt astronauts to the sensory rearrangement of weightlessness.

Regularization in Orbital Mechanics; Theory and Practice

NASA Astrophysics Data System (ADS)

Roa, Javier

2017-09-01

Regularized equations of motion can improve numerical integration for the propagation of orbits, and simplify the treatment of mission design problems. This monograph discusses standard techniques and recent research in the area. While each scheme is derived analytically, its accuracy is investigated numerically. Algebraic and topological aspects of the formulations are studied, as well as their application to practical scenarios such as spacecraft relative motion and new low-thrust trajectories.

Heartbeat Stars Artist Concept

NASA Image and Video Library

2016-10-21

This artist's concept depicts "heartbeat stars," which have been detected by NASA's Kepler Space Telescope and others. The illustration shows two heartbeat stars swerving close to one another in their closest approach along their highly elongated orbits around one another. The mutual gravitation of the two stars would cause the stars themselves to become slightly ellipsoidal in shape. A third, more distant star in the system is shown in the upper left. Astronomers speculate that such unseen companions may exist in some of these heartbeat star systems, and could be responsible for maintaining these oddly stretched-out orbits. The overlaid curve depicts the inferred cyclic change in velocities in one such system, called KIC 9965691, looking something like the graph of an electrocardiogram (hence the name "heartbeat stars"). The solid points represent measurements made by the HIRES instrument at the W.M. Keck Observatory, and the curve is the best fit model for the motions of this system. http://photojournal.jpl.nasa.gov/catalog/PIA21075

The Centaur--Jupiter Family Comet Link

NASA Astrophysics Data System (ADS)

Bailey, Brenae; Malhotra, R.

2008-09-01

The Centaurs’ orbital evolution is characterized by strong chaos and frequent planetary close encounters. We have investigated the transition between the Centaurs and the Jupiter family comets (JFCs), the latter defined as having Tisserand parameter with respect to Jupiter of 2 < TJ < 3. We find that 80% of the known sample of Centaurs spend part of their dynamical lifetimes as JFCs. The amount of time spent as a JFC is typically on the order of a few hundred thousand years, similar to the dynamical lifetimes of JFCs. We also find that the majority of these objects are "handed off” toward the inner solar system from one giant planet to the next before being ejected. In contrast, the orbital evolution of the Centaurs that spend little or no time as JFCs is either dominated by Saturn or consists largely of hopping among mean motion resonances with Uranus and Neptune. This suggests that the JFCs may originate from a dynamically distinct subset of Centaurs.

Absolute dimensions and masses of eclipsing binaries. V. IQ Persei

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lacy, C.H.; Frueh, M.L.

1985-08-01

New photometric and spectroscopic observations of the 1.7 day eclipsing binary IQ Persei (B8 + A6) have been analyzed to yield very accurate fundamental properties of the system. Reticon spectroscopic observations obtained at McDonald Observatory were used to determine accurate radial velocities of both stars in this slightly eccentric large light-ratio binary. A new set of VR light curves obtained at McDonald Observatory were analyzed by synthesis techniques, and previously published UBV light curves were reanalyzed to yield accurate photometric orbits. Orbital parameters derived from both sets of photometric observations are in excellent agreement. The absolute dimensions, masses, luminosities, andmore » apsidal motion period (140 yr) derived from these observations agree well with the predictions of theoretical stellar evolution models. The A6 secondary is still very close to the zero-age main sequence. The B8 primary is about one-third of the way through its main-sequence evolution. 27 references.« less

Bottom boundary layer spectral dissipation estimates in the presence of wave motions

NASA Astrophysics Data System (ADS)

Gross, T. F.; Williams, A. J.; Terray, E. A.

1994-08-01

Turbulence measurements are an essential element of the Sediment TRansport Events on Shelves and Slopes experiment (STRESS). Sediment transport under waves is initiated within the wave boundary layer at the seabed, at most a few tens of centimeters deep. The suspended load is carried by turbulent diffusion above the wave boundary layer. Quantification of the turbulent diffusion active above the wave boundary layer requires estimates of shear stress or energy dissipation in the presence of oscillating flows. Measurements by Benthic Acoustic Stress Sensors of velocity fluctuations were used to derive the dissipation rate from the energy level of the spectral inertial range (the -5/3 spectrum). When the wave orbital velocity is of similar magnitude to the mean flow, kinematic effects on the estimation techniques of stress and dissipation must be included. Throughout the STRESS experiment there was always significant wave energy affecting the turbulent bottom boundary layer. LUMLEY and TERRAY [(1983) Journal of Physical Oceanography, 13, 2000-2007] presented a theory describing the effect of orbital motions on kinetic energy spectra. Their model is used here with observations of spectra taken within a turbulent boundary layer which is affected by wave motion. While their method was an explicit solution for circular wave orbits aligned with mean current we extrapolated it to the case of near bed horizontal motions, not aligned with the current. The necessity of accounting for wave orbital motion is demonstrated, but variability within the field setting limited our certainty of the improvement in accuracy the corrections afforded.

Kepler-36: a pair of planets with neighboring orbits and dissimilar densities.

PubMed

Carter, Joshua A; Agol, Eric; Chaplin, William J; Basu, Sarbani; Bedding, Timothy R; Buchhave, Lars A; Christensen-Dalsgaard, Jørgen; Deck, Katherine M; Elsworth, Yvonne; Fabrycky, Daniel C; Ford, Eric B; Fortney, Jonathan J; Hale, Steven J; Handberg, Rasmus; Hekker, Saskia; Holman, Matthew J; Huber, Daniel; Karoff, Christopher; Kawaler, Steven D; Kjeldsen, Hans; Lissauer, Jack J; Lopez, Eric D; Lund, Mikkel N; Lundkvist, Mia; Metcalfe, Travis S; Miglio, Andrea; Rogers, Leslie A; Stello, Dennis; Borucki, William J; Bryson, Steve; Christiansen, Jessie L; Cochran, William D; Geary, John C; Gilliland, Ronald L; Haas, Michael R; Hall, Jennifer; Howard, Andrew W; Jenkins, Jon M; Klaus, Todd; Koch, David G; Latham, David W; MacQueen, Phillip J; Sasselov, Dimitar; Steffen, Jason H; Twicken, Joseph D; Winn, Joshua N

2012-08-03

In the solar system, the planets' compositions vary with orbital distance, with rocky planets in close orbits and lower-density gas giants in wider orbits. The detection of close-in giant planets around other stars was the first clue that this pattern is not universal and that planets' orbits can change substantially after their formation. Here, we report another violation of the orbit-composition pattern: two planets orbiting the same star with orbital distances differing by only 10% and densities differing by a factor of 8. One planet is likely a rocky "super-Earth," whereas the other is more akin to Neptune. These planets are 20 times more closely spaced and have a larger density contrast than any adjacent pair of planets in the solar system.

Quantum mechanics of hyperbolic orbits in the Kepler problem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rauh, Alexander; Parisi, Juergen

2011-04-15

The problem of deriving macroscopic properties from the Hamiltonian of the hydrogen atom is resumed by extending previous results in the literature, which predicted elliptic orbits, into the region of hyperbolic orbits. As a main tool, coherent states of the harmonic oscillator are used which are continued to imaginary frequencies. The Kustaanheimo-Stiefel (KS) map is applied to transform the original configuration space into the product space of four harmonic oscillators with a constraint. The relation derived between real time and oscillator (pseudo) time includes quantum corrections. In the limit ({h_bar}/2{pi}){yields}0, the time-dependent mean values of position and velocity describe themore » classical motion on a hyperbola and a circular hodograph, respectively. Moreover, the connection between pseudotime and real time comes out in analogy to Kepler's equation for elliptic orbits. The mean-square-root deviations of position and velocity components behave similarly in time to the corresponding ones of a spreading Gaussian wave packet in free space. To check the approximate treatment of the constraint, its contribution to the mean energy is determined with the result that it is negligible except for energy values close to the parabolic orbit with eccentricity equal to 1. It is inevitable to introduce a suitable scalar product in R{sup 4} which makes both the transformed Hamiltonian and the velocity operators Hermitian. An elementary necessary criterion is given for the energy interval where the constraint can be approximated by averaging.« less

Domain wall in a quantum anomalous Hall insulator as a magnetoelectric piston

NASA Astrophysics Data System (ADS)

Upadhyaya, Pramey; Tserkovnyak, Yaroslav

2016-07-01

We theoretically study the magnetoelectric coupling in a quantum anomalous Hall insulator state induced by interfacing a dynamic magnetization texture to a topological insulator. In particular, we propose that the quantum anomalous Hall insulator with a magnetic configuration of a domain wall, when contacted by electrical reservoirs, acts as a magnetoelectric piston. A moving domain wall pumps charge current between electrical leads in a closed circuit, while applying an electrical bias induces reciprocal domain-wall motion. This pistonlike action is enabled by a finite reflection of charge carriers via chiral modes imprinted by the domain wall. Moreover, we find that, when compared with the recently discovered spin-orbit torque-induced domain-wall motion in heavy metals, the reflection coefficient plays the role of an effective spin-Hall angle governing the efficiency of the proposed electrical control of domain walls. Quantitatively, this effective spin-Hall angle is found to approach a universal value of 2, providing an efficient scheme to reconfigure the domain-wall chiral interconnects for possible memory and logic applications.

A spectroscopic search for colliding stellar winds in O-type close binary systems. II - Plaskett's star (HD 47129)

NASA Technical Reports Server (NTRS)

Wiggs, Michael S.; Gies, Douglas R.

1992-01-01

New evidence for colliding winds in the massive O-type binary system Plaskett's star is reported. High S/N ratio spectra of the H-alpha and He I 6678 emission lines are presented, and their orbital phase-related variations are examined in order to derive the locations and motions of the high-density gas in the system. Radial velocity cures for several absorption and emission lines associated with the photosphere of the primary are also provided. The H-alpha emission profiles are complex, with very broad wings and a sharp spikelike feature that approximately follows the motion of the primary star. The radial velocity curve for this spike lags behind the photospheric velocity curve of the primary by 0.066 in phase. It is suggested that the high-velocity H-alpha emission is related to instabilities in the intershock region between the two component stars. The H-alpha phase-related variations are compared with those observed in the UV wind lines in IUE archival spectra.

Diabolical points in multi-scatterer optomechanical systems

PubMed Central

Chesi, Stefano; Wang, Ying-Dan; Twamley, Jason

2015-01-01

Diabolical points, which originate from parameter-dependent accidental degeneracies of a system's energy levels, have played a fundamental role in the discovery of the Berry phase as well as in photonics (conical refraction), in chemical dynamics, and more recently in novel materials such as graphene, whose electronic band structure possess Dirac points. Here we discuss diabolical points in an optomechanical system formed by multiple scatterers in an optical cavity with periodic boundary conditions. Such configuration is close to experimental setups using micro-toroidal rings with indentations or near-field scatterers. We find that the optomechanical coupling is no longer an analytic function near the diabolical point and demonstrate the topological phase arising through the mechanical motion. Similar to a Fabry-Perot resonator, the optomechanical coupling can grow with the number of scatterers. We also introduce a minimal quantum model of a diabolical point, which establishes a connection to the motion of an arbitrary-spin particle in a 2D parabolic quantum dot with spin-orbit coupling. PMID:25588627

Dynamics of a b-nut failure

NASA Astrophysics Data System (ADS)

Zarubin, Peter V.

1999-06-01

In August of 1989, the Galileo spacecraft, consisting of an orbiter and probe, was mounted to an Inertial Upper Stage (IUS) rocket stage being readied for flight aboard NASA's Space Shuttle, 'STS-34,' 'Atlantis.' During routine age testing of an IUS igniter fire line circuit, a 'b-nut' failure occurred. On board the Galileo/IUS first stage rocket motor was a b-nut from this failed lot. There was concern that the mission could be jeopardized if the b-nut failed because of the close proximity of the IUS second stage rocket motor nozzle. A fix had to be made to insure mission success. Chemical Systems Division was called upon to provide high- speed motion picture photography at 3000 frames per second to analyze the dynamics of a b-nut failure, and verify that the fix would prevent damage to the second stage nozzle, should a b-nut failure occur. This report will show how displacement and velocity measurements can be made from 16 mm motion picture film.

Nonlinear gyrotropic motion of skyrmion in a magnetic nanodisk

NASA Astrophysics Data System (ADS)

Chen, Yi-fu; Li, Zhi-xiong; Zhou, Zhen-wei; Xia, Qing-lin; Nie, Yao-zhuang; Guo, Guang-hua

2018-07-01

We study the nonlinear gyrotropic motion of a magnetic skyrmion in a nanodisk by means of micromagnetic simulations. The skyrmion is driven by a linearly polarized harmonic field with the frequency of counterclockwise gyrotropic mode. It is found that the motion of the skyrmion displays different patterns with increasing field amplitude. In the linear regime of weak driving field, the skyrmion performs a single counterclockwise gyrotropic motion. The guiding center of the skyrmion moves along a helical line from the centre of the nanodisk to a stable circular orbit. The stable orbital radius increases linearly with the field amplitude. When the driving field is larger than a critical value, the skyrmion exhibits complex nonlinear motion. With the advance of time, the motion trajectory of the skyrmion goes through a series of evolution process, from a single circular motion to a bird nest-like and a flower-like trajectory and finally, to a gear-like steady-state motion. The frequency spectra show that except the counterclockwise gyrotropic mode, the clockwise gyrotropic mode is also nonlinearly excited and its amplitude increases with time. The complex motion trajectory of the skyrmion is the result of superposition of the two gyrotropic motions with changing amplitude. Both the linear and nonlinear gyrotropic motions of the skyrmion can be well described by a generalized Thiele's equation of motion.

Optimal four-impulse rendezvous between coplanar elliptical orbits

NASA Astrophysics Data System (ADS)

Wang, JianXia; Baoyin, HeXi; Li, JunFeng; Sun, FuChun

2011-04-01

Rendezvous in circular or near circular orbits has been investigated in great detail, while rendezvous in arbitrary eccentricity elliptical orbits is not sufficiently explored. Among the various optimization methods proposed for fuel optimal orbital rendezvous, Lawden's primer vector theory is favored by many researchers with its clear physical concept and simplicity in solution. Prussing has applied the primer vector optimization theory to minimum-fuel, multiple-impulse, time-fixed orbital rendezvous in a near circular orbit and achieved great success. Extending Prussing's work, this paper will employ the primer vector theory to study trajectory optimization problems of arbitrary eccentricity elliptical orbit rendezvous. Based on linearized equations of relative motion on elliptical reference orbit (referred to as T-H equations), the primer vector theory is used to deal with time-fixed multiple-impulse optimal rendezvous between two coplanar, coaxial elliptical orbits with arbitrary large eccentricity. A parameter adjustment method is developed for the prime vector to satisfy the Lawden's necessary condition for the optimal solution. Finally, the optimal multiple-impulse rendezvous solution including the time, direction and magnitudes of the impulse is obtained by solving the two-point boundary value problem. The rendezvous error of the linearized equation is also analyzed. The simulation results confirmed the analyzed results that the rendezvous error is small for the small eccentricity case and is large for the higher eccentricity. For better rendezvous accuracy of high eccentricity orbits, a combined method of multiplier penalty function with the simplex search method is used for local optimization. The simplex search method is sensitive to the initial values of optimization variables, but the simulation results show that initial values with the primer vector theory, and the local optimization algorithm can improve the rendezvous accuracy effectively with fast convergence, because the optimal results obtained by the primer vector theory are already very close to the actual optimal solution. If the initial values are taken randomly, it is difficult to converge to the optimal solution.

Close up view of the Orbiter Discovery in the Orbiter ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

Close up view of the Orbiter Discovery in the Orbiter Processing Facility at Kennedy Space Center. The view is a detail of the aft, starboard landing gear and a general view of the Thermal Protection System tiles around the landing-gear housing. - Space Transportation System, Orbiter Discovery (OV-103), Lyndon B. Johnson Space Center, 2101 NASA Parkway, Houston, Harris County, TX

Relative attitude dynamics and control for a satellite inspection mission

NASA Astrophysics Data System (ADS)

Horri, Nadjim M.; Kristiansen, Kristian U.; Palmer, Phil; Roberts, Mark

2012-02-01

The problem of conducting an inspection mission from a chaser satellite orbiting a target spaceraft is considered. It is assumed that both satellites follow nearly circular orbits. The relative orbital motion is described by the Hill-Clohessy-Wiltshire equation. In the case of an elliptic relative orbit, it is shown that an inspection mission is feasible when the chaser is inertially pointing, provided that the camera mounted on the chaser satellite has sufficiently large field of view. The same possibility is shown when the optical axis of the chaser's camera points in, or opposite to, the tangential direction of the local vertical local horizontal frame. For an arbitrary relative orbit and arbitrary initial conditions, the concept of relative Euler angles is defined for this inspection mission. The expression of the desired relative angular velocity vector is derived as a function of Cartesian coordinates of the relative orbit. A quaternion feedback controller is then designed and shown to perform relative attitude control with admissible internal torques. Three different types of relative orbits are considered, namely the elliptic, Pogo and drifting relative orbits. Measurements of the relative orbital motion are assumed to be available from optical navigation.

Scientists Track Collision of Powerful Stellar Winds

NASA Astrophysics Data System (ADS)

2005-04-01

Astronomers using the National Science Foundation's Very Long Baseline Array (VLBA) radio telescope have tracked the motion of a violent region where the powerful winds of two giant stars slam into each other. The collision region moves as the stars, part of a binary pair, orbit each other, and the precise measurement of its motion was the key to unlocking vital new information about the stars and their winds. WR 140 Image Sequence Motion of Wind Collision Region Graphic superimposes VLBA images of wind collision region on diagram of orbit of Wolf-Rayet (WR) star and its giant (O) companion. Click on image for larger version (412K) CREDIT: Dougherty et al., NRAO/AUI/NSF In Motion: Shockwave File Animated Gif File AVI file Both stars are much more massive than the Sun -- one about 20 times the mass of the Sun and the other about 50 times the Sun's mass. The 20-solar-mass star is a type called a Wolf-Rayet star, characterized by a very strong wind of particles propelled outward from its surface. The more massive star also has a strong outward wind, but one less intense than that of the Wolf-Rayet star. The two stars, part of a system named WR 140, circle each other in an elliptical orbit roughly the size of our Solar System. "The spectacular feature of this system is the region where the stars' winds collide, producing bright radio emission. We have been able to track this collision region as it moves with the orbits of the stars," said Sean Dougherty, an astronomer at the Herzberg Institute for Astrophysics in Canada. Dougherty and his colleagues presented their findings in the April 10 edition of the Astrophysical Journal. The supersharp radio "vision" of the continent-wide VLBA allowed the scientists to measure the motion of the wind collision region and then to determine the details of the stars' orbits and an accurate distance to the system. "Our new calculations of the orbital details and the distance are vitally important to understanding the nature of these Wolf-Rayet stars and of the wind-collision region," Dougherty said. The stars in WR 140 complete an orbital cycle in 7.9 years. The astronomers tracked the system for a year and a half, noting dramatic changes in the wind collision region. "People have worked out theoretical models for these collision regions, but the models don't seem to fit what our observations have shown," said Mark Claussen, of the National Radio Astronomy Observatory in Socorro, New Mexico. "The new data on this system should provide the theorists with much better information for refining their models of how Wolf-Rayet stars evolve and how wind-collision regions work," Claussen added. The scientists watched the changes in the stellar system as the star's orbits carried them in paths that bring them nearly as close to each other as Mars is to the Sun and as far as Neptune is from the Sun. Their detailed analysis gave them new information on the Wolf-Rayet star's strong wind. At some points in the orbit, the wind collision region strongly emitted radio waves, and at other points, the scientists could not detect the collison region. Wolf-Rayet stars are giant stars nearing the time when they will explode as supernovae. "No other telescope in the world can see the details revealed by the VLBA," Claussen said. "This unmatched ability allowed us to determine the masses and other properties of the stars, and will help us answer some basic questions about the nature of Wolf-Rayet stars and how they develop." he added. The astronomers plan to continue observing WR 140 to follow the system's changes as the two massive stars continue to circle each other. Dougherty and Claussen worked with Anthony Beasley of the Atacama Large Millimeter Array office, Ashley Zauderer of the University of Maryland and Nick Bolingbroke of the University of Victoria, British Columbia. The National Radio Astronomy Observatory is a facility of the National Science Foundation, operated under cooperative agreement by Associated Universities, Inc.

OrbitMaster: An Online Tool for Investigating Solar System Dynamics and Visualizing Orbital Uncertainties in the Undergraduate Classroom

NASA Astrophysics Data System (ADS)

Puckett, Andrew W.; Rector, Travis A.; Baalke, Ron; Ajiki, Osamu

2016-01-01

OrbitMaster is a 3-D orbit visualization tool designed for the undergraduate astronomy classroom. It has been adapted from AstroArts' interactive OrbitViewer applet under the GNU General Public License, as part of the Research-Based Science Education for Undergraduates (RBSEU) curriculum. New features allow the user to alter an asteroid's orbital parameters using slider controls, and to monitor its changing position and speed relative to both Sun and Earth. It detects close approaches and collisions with Earth, and calculates revised distances and impact speeds due to Earth's gravitational attraction. It can also display many asteroid orbits at once, with direct application to visualizing the uncertainty in a single asteroid's orbital parameters. When paired with Project Pluto's Find_Orb orbit determination software and a source of asteroid astrometry, this enables monitoring of changes in orbital uncertainties with time and/or additional observational data. See http://facstaff.columbusstate.edu/puckett_andrew/orbitmaster.html.A series of undergraduate labs using the OrbitMaster applet are available as part of the RBSEU curriculum. In the first lab, students gain hands-on experience with the mechanics of asteroid orbits and confirm Kepler's laws of planetary motion. In the second, they study the orbits of Potentially Hazardous Asteroids as they build their own "Killer Asteroids" and investigate the minimum and maximum speed limits that apply to Earth-impacting objects. In the third and fourth labs, they discover the kinetic energy-crater size relationship, engage in their own Crater Scene Investigation (C.S.I.) to estimate impactor size, and understand the regional consequences of impacts. These labs may be used separately, or in support of a further seven-week sequence culminating in an authentic research project in which students submit measurements to the Minor Planet Center to refine a real asteroid's orbit. As with all RBSE projects, the overarching goal is for students to learn science by actually doing science, and to retain knowledge learned in-context. For more information, see http://rbseu.uaa.alaska.edu.

Periodic motion near non-principal-axis rotation asteroids

NASA Astrophysics Data System (ADS)

Shang, Haibin; Wu, Xiaoyu; Qin, Xiao; Qiao, Dong

2017-11-01

The periodic motion near non-principal-axis (NPA) rotation asteroids is proved to be markedly different from that near uniformly rotating bodies due to the complex spin state with precession, raising challenges in terms of the theoretical implications of dynamical systems. This paper investigates the various periodic motions near the typical NPA asteroid 4179 Toutatis, which will contribute to the understanding of the dynamical environments near the widespread asteroids in the Solar system. A novel method with the incorporation of the ellipsoid-mascon gravitational field model and global optimization is developed to efficiently locate periodic solutions in the system. The numerical results indicate that abundant periodic orbits appear near the NPA asteroids. These various orbits are theoretically classified into five topological types with special attention paid to the cycle stability. Although the concept of classical family disappears in our results, some orbits with the same topological structure constitute various generalized `families' as the period increases. Among these `families' a total of 4 kinds of relationships between orbits, including rotation, evolution, distortion and quasi-symmetry, are found to construct the global mapping of these types. To cover the rotation statuses of various NPA asteroids, this paper also discusses the variation of periodic orbits with diverse asteroid spin rates, showing that the scales of some orbits expand, shrink or almost annihilate as the system period changes; meanwhile, their morphology and topology remain unchanged.

Point vortex modelling of the wake dynamics behind asymmetric vortex generator arrays

NASA Astrophysics Data System (ADS)

Baldacchino, D.; Ferreira, C.; Ragni, D.; van Bussel, G. J. W.

2016-09-01

In this work, we present a simple inviscid point vortex model to study the dynamics of asymmetric vortex rows, as might appear behind misaligned vortex generator vanes. Starting from the existing solution of the infinite vortex cascade, a numerical model of four base-vortices is chosen to represent two primary counter-rotating vortex pairs and their mirror plane images, introducing the vortex strength ratio as a free parameter. The resulting system of equations is also defined in terms of the vortex row separation and the qualitative features of the ensuing motion are mapped. A translating and orbiting regime are identified for different cascade separations. The latter occurs for all unequal strength vortex pairs. Thus, the motion is further classified by studying the cyclic behaviour of the orbiting regime and it is shown that for small mismatches in vortex strength, the orbiting length and time scales are sufficiently large as to appear, in the near wake, as translational (non-orbiting). However, for larger mismatches in vortex strength, the orbiting motion approaches the order of the starting height of the vortex. Comparisons between experimental data and the potential flow model show qualitative agreement whilst viscous effects account for the major discrepancies. Despite this, the model captures the orbital mode observed in the measurements and provides an impetus for considering the impact of these complex interactions on vortex generator designs.

Instabilities in the Sun-Jupiter-Asteroid three body problem

NASA Astrophysics Data System (ADS)

Urschel, John C.; Galante, Joseph R.

2013-03-01

We consider dynamics of a Sun-Jupiter-Asteroid system, and, under some simplifying assumptions, show the existence of instabilities in the motions of an asteroid. In particular, we show that an asteroid whose initial orbit is far from the orbit of Mars can be gradually perturbed into one that crosses Mars' orbit. Properly formulated, the motion of the asteroid can be described as a Hamiltonian system with two degrees of freedom, with the dynamics restricted to a "large" open region of the phase space reduced to an exact area preserving map. Instabilities arise in regions where the map has no invariant curves. The method of MacKay and Percival is used to explicitly rule out the existence of these curves, and results of Mather abstractly guarantee the existence of diffusing orbits. We emphasize that finding such diffusing orbits numerically is quite difficult, and is outside the scope of this paper.

Star motion around rotating black hole in the Galactic Center in real time

NASA Astrophysics Data System (ADS)

Dokuchaev, Vyacheslav; Nazarova, Natalia

2017-12-01

The Event Horizon Telescope team intends by the 2020 to resolve the shadow of supermassive black hole SgrA* in the Galactic Center. It would be the first attempt for direct identification of the enigmatic black hole. In other words, it would be the first experimental verification of the General Relativity in the strong field limit. There is a chance to find a star moving on the relativistic orbit close to this black hole. We present the animated numerical model of the gravitational lensing of a star (or any other lighting probe), moving around rotating Kerr black hole in the Galactic Center and viewed by the distant observer.

STS-69 Flight Day 3 Highlights

NASA Technical Reports Server (NTRS)

1995-01-01

On the third day of the STS-69 mission, the flight crew (Cmdr. Dave Walker, Pilot Ken Cockrell, and Mission Specialists Jim Voss, Mike Gernhardt, and Jim Newman) test the Orbital Maneuvering System and prepare for the retrieval of the SPARTAN satellite with a checkout procedure of the space shuttle's robot arm. Physiological and chemical experiments on fluid dynamics are conducted as part of the Sea Lab project. Urine and blood samples from the crew are collected and studied under microgravity conditions, and a slime mold experiment is conducted to determine the properties of motion, growth, and chemistry in zero gravity conditions. Earth views include cloud cover, a hurricane, and a close-up of its eye.

Millisecond Oscillations in X-ray Binaries

NASA Astrophysics Data System (ADS)

van der Klis, M.

The first millisecond X-ray variability phenomena from accreting compact objects have recently been discovered with the Rossi X-ray Timing Explorer. Three new phenomena are observed from low-mass X-ray binaries containing low-magnetic-field neutron stars: millisecond pulsations, burst oscillations, and kilohertz quasi-periodic oscillations. Models for these new phenomena involve the neutron star spin and orbital motion close around the neutron star, and rely explicitly on our understanding of strong gravity and dense matter. I review the observations of these new neutron-star phenomena and some possibly related phenomena in black-hole candidates, and describe the attempts to use these observations to perform measurements of fundamental physical interest in these systems.

Near-optimal reconfiguration and maintenance of close spacecraft formations.

PubMed

Lovell, T A; Tragesser, S G

2004-05-01

This paper investigates orbit guidance algorithms for formation flying experiments. The relative motion of one satellite about a reference satellite is formulated in terms of a set of parameters that clearly describe the size, shape, and orientation of the formation. A nominal three-impulse burn maneuver algorithm is presented that is applicable for both reconfiguration and maintenance of spacecraft formations. Two methods of implementing the algorithm are discussed, one involving fixed times between each burn and one allowing the wait times to vary. The implications of employing four or more impulses for maneuvers are assessed. Examples applying the algorithm to various formation scenarios are presented, along with practical implications of each result.

Bloch equations applied to ion cyclotron resonance spectroscopy: Broadband interconversion between magnetron and cyclotron motion for ion axialization

NASA Astrophysics Data System (ADS)

Guan, Shenheng; Marshall, Alan G.

1993-03-01

Conversion of magnetron motion to cyclotron motion combined with collisional cooling of the cyclotron motion provides an efficient way to reduce the kinetic energy of trapped heavy ions and to reduce their magnetron radii in an ion cyclotron resonance (ICR) ion trap. The coupling of magnetron and cyclotron motion can be realized by azimuthal quadrupolar excitation. Theoretical understanding of the coupling process has until now been based on resonant single-frequency quadrupolar excitation at the combination frequency ωc=ω++ω-, in which ωc is the ion cyclotron orbital frequency in the absence of electrostatic field; and ω+ and ω- are the reduced cyclotron and magnetron frequencies in the presence of an electrostatic trapping potential. In this work, we prove that the magnetron/cyclotron coupling is closely related to a two energy level system whose behavior is described by the well-known Bloch equations. By means of a special transformation, the equations of motion for the coupling may be expressed in Bloch-type equations in spherical coordinates. We show that magnetron-to-cyclotron conversion by single-frequency quadrupolar excitation in ICR is analogous to a 180° pulse in nuclear magnetic resonance (NMR). We go on to show that simultaneous magnetron-to-cyclotron conversion of ions over a finite mass-to-charge ratio range may be produced by quadrupolar frequency-sweep excitation, by analogy to adiabatic rapid passage in magnetic resonance. Axialization by broadband magnetron-to-cyclotron conversion followed by cyclotron cooling is successfully demonstrated experimentally for a crude oil distillate sample.

Unbounded orbits of a swinging Atwood's machine

NASA Astrophysics Data System (ADS)

Tufillaro, N.; Nunes, A.; Casasayas, J.

1988-12-01

The motion of a swinging Atwood's machine is examined when the orbits are unbounded. Expressions for the asymptotic behavior of the orbits are derived that exhibit either an infinite number of oscillations or no oscillations, depending only on a critical value of the mass ratio.

Instantaneous Impulses.

ERIC Educational Resources Information Center

Erlichson, Herman

2000-01-01

Describes an experiment that extends Newton's instantaneous-impulse method of orbital analysis to a graphical method of orbit determination. Discusses the experiment's usefulness for teaching both horizontal projectile motion and instantaneous impulse. (WRM)

Relative dynamics and motion control of nanosatellite formation flying

NASA Astrophysics Data System (ADS)

Pimnoo, Ammarin; Hiraki, Koju

2016-04-01

Orbit selection is a necessary factor in nanosatellite formation mission design/meanwhile, to keep the formation, it is necessary to consume fuel. Therefore, the best orbit design for nanosatellite formation flying should be one that requires the minimum fuel consumption. The purpose of this paper is to analyse orbit selection with respect to the minimum fuel consumption, to provide a convenient way to estimate the fuel consumption for keeping nanosatellite formation flying and to present a simplified method of formation control. The formation structure is disturbed by J2 gravitational perturbation and other perturbing accelerations such as atmospheric drag. First, Gauss' Variation Equations (GVE) are used to estimate the essential ΔV due to the J2 perturbation and atmospheric drag. The essential ΔV presents information on which orbit is good with respect to the minimum fuel consumption. Then, the linear equations which account for J2 gravitational perturbation of Schweighart-Sedwick are presented and used to estimate the fuel consumption to maintain the formation structure. Finally, the relative dynamics motion is presented as well as a simplified motion control of formation structure by using GVE.

Application of the multireference equation of motion coupled cluster method, including spin-orbit coupling, to the atomic spectra of Cr, Mn, Fe and Co

NASA Astrophysics Data System (ADS)

Liu, Zhebing; Huntington, Lee M. J.; Nooijen, Marcel

2015-10-01

The recently introduced multireference equation of motion (MR-EOM) approach is combined with a simple treatment of spin-orbit coupling, as implemented in the ORCA program. The resulting multireference equation of motion spin-orbit coupling (MR-EOM-SOC) approach is applied to the first-row transition metal atoms Cr, Mn, Fe and Co, for which experimental data are readily available. Using the MR-EOM-SOC approach, the splittings in each L-S multiplet can be accurately assessed (root mean square (RMS) errors of about 70 cm-1). The RMS errors for J-specific excitation energies range from 414 to 783 cm-1 and are comparable to previously reported J-averaged MR-EOM results using the ACESII program. The MR-EOM approach is highly efficient. A typical MR-EOM calculation of a full spin-orbit spectrum takes about 2 CPU hours on a single processor of a 12-core node, consisting of Intel XEON 2.93 GHz CPUs with 12.3 MB of shared cache memory.

One-step methods for the prediction of orbital motion, taking its periodic components into account

NASA Astrophysics Data System (ADS)

Lavrov, K. N.

1988-03-01

The paper examines the design and analysis of the properties of implicit one-step integration methods which use the trigonometric approximation of ordinary differential equations containing periodic components. With reference to an orbital-motion prediction example, it is shown that the proposed schemes are more efficient in terms of computer memory than Everhart's (1974) approach. The results obtained make it possible to improve Everhart's method.

Analysis of Formation Flying in Eccentric Orbits Using Linearized Equations of Relative Motion

NASA Technical Reports Server (NTRS)

Lane, Christopher; Axelrad, Penina

2004-01-01

Geometrical methods for formation flying design based on the analytical solution to Hill's equations have been previously developed and used to specify desired relative motions in near circular orbits. By generating relationships between the vehicles that are intuitive, these approaches offer valuable insight into the relative motion and allow for the rapid design of satellite configurations to achieve mission specific requirements, such as vehicle separation at perigee or apogee, minimum separation, or a specific geometrical shape. Furthermore, the results obtained using geometrical approaches can be used to better constrain numerical optimization methods; allowing those methods to converge to optimal satellite configurations faster. This paper presents a set of geometrical relationships for formations in eccentric orbits, where Hill.s equations are not valid, and shows how these relationships can be used to investigate formation designs and how they evolve with time.

Bouncing ball problem: stability of the periodic modes.

PubMed

Barroso, Joaquim J; Carneiro, Marcus V; Macau, Elbert E N

2009-02-01

Exploring all its ramifications, we give an overview of the simple yet fundamental bouncing ball problem, which consists of a ball bouncing vertically on a sinusoidally vibrating table under the action of gravity. The dynamics is modeled on the basis of a discrete map of difference equations, which numerically solved fully reveals a rich variety of nonlinear behaviors, encompassing irregular nonperiodic orbits, subharmonic and chaotic motions, chattering mechanisms, and also unbounded nonperiodic orbits. For periodic motions, the corresponding conditions for stability and bifurcation are determined from analytical considerations of a reduced map. Through numerical examples, it is shown that a slight change in the initial conditions makes the ball motion switch from periodic to chaotic orbits bounded by a velocity strip v=+/-Gamma(1-epsilon) , where Gamma is the nondimensionalized shaking acceleration and epsilon the coefficient of restitution which quantifies the amount of energy lost in the ball-table collision.

Analytic theory of orbit contraction

NASA Technical Reports Server (NTRS)

Vinh, N. X.; Longuski, J. M.; Busemann, A.; Culp, R. D.

1977-01-01

The motion of a satellite in orbit, subject to atmospheric force and the motion of a reentry vehicle are governed by gravitational and aerodynamic forces. This suggests the derivation of a uniform set of equations applicable to both cases. For the case of satellite motion, by a proper transformation and by the method of averaging, a technique appropriate for long duration flight, the classical nonlinear differential equation describing the contraction of the major axis is derived. A rigorous analytic solution is used to integrate this equation with a high degree of accuracy, using Poincare's method of small parameters and Lagrange's expansion to explicitly express the major axis as a function of the eccentricity. The solution is uniformly valid for moderate and small eccentricities. For highly eccentric orbits, the asymptotic equation is derived directly from the general equation. Numerical solutions were generated to display the accuracy of the analytic theory.

The CAMEO barium release - E/parallel/ fields over the polar cap

NASA Technical Reports Server (NTRS)

Heppner, J. P.; Miller, M. L.; Pongratz, M. B.; Smith, G. M.; Smith, L. L.; Mende, S. B.; Nath, N. R.

1981-01-01

Four successive thermite barium releases at an altitude of 965 km over polar cap invariant latitudes 84 to 76 deg near magnetic midnight were conducted from the orbiting second stage of the vehicle that launched Nimbus 7; the releases were made as part of the CAMEO (Chemically Active Material Ejected in Orbit) program. This was the first opportunity to observe the behavior of conventional barium release when conducted at orbital velocity in the near-earth magnetic field. The principal unexpected characteristic in the release dynamics was the high, 1.4 to 2.6 km/s, initial Ba(+) expansion velocity relative to an expected velocity of 0.9 km/s. Attention is also given to neutral cloud expansion, initial ion cloud expansion, convective motion, and the characteristics of field-aligned motion. The possibility of measuring parallel electric fields over the polar cap by observing perturbations in the motion of the visible ions is assessed.

Particle motion around magnetized black holes: Preston-Poisson space-time

DOE Office of Scientific and Technical Information (OSTI.GOV)

Konoplya, R. A.

We analyze the motion of massless and massive particles around black holes immersed in an asymptotically uniform magnetic field and surrounded by some mechanical structure, which provides the magnetic field. The space-time is described by the Preston-Poisson metric, which is the generalization of the well-known Ernst metric with a new parameter, tidal force, characterizing the surrounding structure. The Hamilton-Jacobi equations allow the separation of variables in the equatorial plane. The presence of a tidal force from the surroundings considerably changes the parameters of the test particle motion: it increases the radius of circular orbits of particles and increases the bindingmore » energy of massive particles going from a given circular orbit to the innermost stable orbit near the black hole. In addition, it increases the distance of the minimal approach, time delay, and bending angle for a ray of light propagating near the black hole.« less

A search of impact orbits for near-Earth objects by means of minimization of two target functions product. (Russian Title: Поиск столкновительных орбит астероидов, сближающихся с Землей, с помощью минимизации произведения двух целевых функций)

NASA Astrophysics Data System (ADS)

Baturin, A. P.

2011-07-01

The method of NEO's impact orbits search based on two target functions product minimization is presented. These functions are: a square of asteroid-Earth distance at the moment of close approach and a sum of squares of angular residuals. Besides, the method includes a minimization of asteroid-Earth distance's square in function of time alone when initial motion parameters are fixed. Both minimizations are carrying out in turn each by another. The testing of method has been made on the problem of Apophis's impact orbit search. The results of the testing have depicted an effectivity of presented method in searching of impact orbits for the Apophis's Earth encounters in 2036 and 2037.

Secular dynamics of multiplanetary circumbinary systems: stationary solutions and binary-planet secular resonance

NASA Astrophysics Data System (ADS)

Andrade-Ines, Eduardo; Robutel, Philippe

2018-01-01

We present an analytical formalism to study the secular dynamics of a system consisting of N-2 planets orbiting a binary star in outer orbits. We introduce a canonical coordinate system and expand the disturbing function in terms of canonical elliptic elements, combining both Legendre polynomials and Laplace coefficients, to obtain a general formalism for the secular description of this type of configuration. With a quadratic approximation of the development, we present a simplified analytical solution for the planetary orbits for both the single planet and the two-planet cases. From the two-planet model, we show that the inner planet accelerates the precession rate of the binary pericenter, which, in turn, may enter in resonance with the secular frequency of the outer planet, characterizing a secular resonance. We calculate an analytical expression for the approximate location of this resonance and apply it to known circumbinary systems, where we show that it can occur at relatively close orbits, for example at 2.4 au for the Kepler-38 system. With a more refined model, we analyse the dynamics of this secular resonance and we show that a bifurcation of the corresponding fixed points can affect the long- term evolution and stability of planetary systems. By comparing our results with complete integrations of the exact equations of motion, we verified the accuracy of our analytical model.

Implementation of a Collision Probability Prediction Technique for Constellation Maneuver Planning

NASA Technical Reports Server (NTRS)

Concha, Marco a.

2007-01-01

On March 22, 2006, the Space Technology 5 (ST5) constellation spacecraft were successfully delivered to orbit by a Pegasus XI, launch vehicle. An unexpected relative motion experienced by the constellation after orbit insertion brought about a problem. Soon after launch the observed relative position of the inert rocket body was between the leading and the middle spacecraft within the constellation. The successful planning and execution of an orbit maneuver that would create a fly-by of the rocket body was required to establish the.formation. This maneuver would create a close approach that needed to conform to predefined collision probability requirements. On April 21, 2006, the ST5 "155" spacecraft performed a large orbit maneuver and successfully passed the inert Pegasus 3rd Stage Rocket Body on April 30, 2006 15:20 UTC at a distance of 2.55 km with a Probability of Collision of less than 1.0E-06. This paper will outline the technique that was implemented to establish the safe planning and execution of the fly-by maneuver. The method makes use of Gaussian distribution models of state covariance to determine underlying probabilities of collision that arise under low velocity encounters. Specific numerical examples used for this analysis are discussed in detail. The mechanics of this technique are explained to foster deeper understanding of the concepts presented and to improve existing processes for use in future constellation maneuver planning.

Prediction of stellar occultations by distant solar system bodies in the Gaia era

NASA Astrophysics Data System (ADS)

Desmars, Josselin; Camargo, Julio; Sicardy, Bruno; Braga-Ribas, Felipe; Vieira-Martins, Roberto; Assafin, Marcelo; Bérard, Diane; Benedetti-Rossi, Gustavo

2018-04-01

Stellar occultations are a unique technique to access physical characteristics of distant solar system objects from the ground. They allow the measure of the size and the shape at kilometric level, the detection of tenuous atmospheres (few nanobars), and the investigation of close vicinity (satellites, rings) of Transneptunian objects and Centaurs. This technique is made successful thanks to accurate predictions of occultations. Accuracy of the predictions depends on the uncertainty in the position of the occulted star and the object's orbit. The Gaia stellar catalogue (Gaia Collaboration (2017)) now allows to get accurate astrometric stellar positions (to the mas level). The main uncertainty remains on the orbit. In this context, we now take advantage of the NIMA method (Desmars et al.(2015)) for the orbit determination and of the Gaia DR1 catalogue for the astrometry. In this document, we show how the orbit determination is improved by reducing current and some past observations with Gaia DR1. Moreover, we also use more than 45 past positive occultations observed in the 2009-2017 period to derive very accurate astrometric positions only depending on the position of the occulted stars (about few mas with Gaia DR1). We use the case of (10199) Chariklo as an illustration. The main limitation lies in the imprecision of the proper motions which is going to be solved by the Gaia DR2 release.

Singular Optimal Controls of Rocket Motion (Survey)

NASA Astrophysics Data System (ADS)

Kiforenko, B. N.

2017-05-01

Survey of modern state and discussion of problems of the perfection of methods of investigation of variational problems with a focus on mechanics of space flight are presented. The main attention is paid to the enhancement of the methods of solving of variational problems of rocket motion in the gravitational fields, including rocket motion in the atmosphere. These problems are directly connected with the permanently actual problem of the practical astronautics to increase the payload that is orbited by the carrier rockets in the circumplanetary orbits. An analysis of modern approaches to solving the problems of control of rockets and spacecraft motion on the trajectories with singular arcs that are optimal for the motion of the variable mass body in the medium with resistance is given. The presented results for some maneuvers can serve as an information source for decision making on designing promising rocket and space technology

Chaotic dynamics of Comet 1P/Halley: Lyapunov exponent and survival time expectancy

NASA Astrophysics Data System (ADS)

Muñoz-Gutiérrez, M. A.; Reyes-Ruiz, M.; Pichardo, B.

2015-03-01

The orbital elements of Comet Halley are known to a very high precision, suggesting that the calculation of its future dynamical evolution is straightforward. In this paper we seek to characterize the chaotic nature of the present day orbit of Comet Halley and to quantify the time-scale over which its motion can be predicted confidently. In addition, we attempt to determine the time-scale over which its present day orbit will remain stable. Numerical simulations of the dynamics of test particles in orbits similar to that of Comet Halley are carried out with the MERCURY 6.2 code. On the basis of these we construct survival time maps to assess the absolute stability of Halley's orbit, frequency analysis maps to study the variability of the orbit, and we calculate the Lyapunov exponent for the orbit for variations in initial conditions at the level of the present day uncertainties in our knowledge of its orbital parameters. On the basis of our calculations of the Lyapunov exponent for Comet Halley, the chaotic nature of its motion is demonstrated. The e-folding time-scale for the divergence of initially very similar orbits is approximately 70 yr. The sensitivity of the dynamics on initial conditions is also evident in the self-similarity character of the survival time and frequency analysis maps in the vicinity of Halley's orbit, which indicates that, on average, it is unstable on a time-scale of hundreds of thousands of years. The chaotic nature of Halley's present day orbit implies that a precise determination of its motion, at the level of the present-day observational uncertainty, is difficult to predict on a time-scale of approximately 100 yr. Furthermore, we also find that the ejection of Halley from the Solar system or its collision with another body could occur on a time-scale as short as 10 000 yr.

Analytic theory of orbit contraction and ballistic entry into planetary atmospheres

NASA Technical Reports Server (NTRS)

Longuski, J. M.; Vinh, N. X.

1980-01-01

A space object traveling through an atmosphere is governed by two forces: aerodynamic and gravitational. On this premise, equations of motion are derived to provide a set of universal entry equations applicable to all regimes of atmospheric flight from orbital motion under the dissipate force of drag through the dynamic phase of reentry, and finally to the point of contact with the planetary surface. Rigorous mathematical techniques such as averaging, Poincare's method of small parameters, and Lagrange's expansion, applied to obtain a highly accurate, purely analytic theory for orbit contraction and ballistic entry into planetary atmospheres. The theory has a wide range of applications to modern problems including orbit decay of artificial satellites, atmospheric capture of planetary probes, atmospheric grazing, and ballistic reentry of manned and unmanned space vehicles.

High Fidelity Modeling of SRP and Its Effect on the Relative Motion of Starshade and WFIRST

NASA Technical Reports Server (NTRS)

Farres, Ariadna; Webster, Cassandra; Folta, Dave

2018-01-01

In this paper we perform a detailed analysis of how Solar Radiation Pressure (SRP) affects the relative motion of two spacecrafts, the Wide-Field Infrared Survey Telescope (WFIRST) and Starshade, orbiting in the vicinity of the Sun-Earth L2. While WFIRST orbits about its own Libration Point Orbit (LPO), Starshade will fly a specific trajectory to align with WFIRST and observe a Design Reference Mission of pre-determined target stars. In this analysis, we focus on the transfer orbit for Starshade from one observation to the other. We will describe how SRP affects the dynamics of the Starshade relative to WFIRSTand how relevant this effect is in order to get an accurate estimate of the total difference in velocity (delta v).

LETTER TO THE EDITOR: Quantum manifestations of closed orbits in the photoexcitation scaled spectrum of the hydrogen atom in crossed fields

NASA Astrophysics Data System (ADS)

Rao, Jianguo; Delande, D.; Taylor, K. T.

2001-06-01

The scaled photoexcitation spectrum of the hydrogen atom in crossed electric and magnetic fields has been obtained by means of accurate quantum mechanical calculation using a new algorithm. Closed orbits in the corresponding classical system have also been obtained, using a new, efficient and practical searching procedure. Two new classes of closed orbit have been identified. Fourier transforming each photoexcitation quantum spectrum to yield a plot against scaled action has allowed direct comparison between peaks in such plots and the scaled action values of closed orbits. Excellent agreement has been found with all peaks assigned.

Satellite orbit computation methods

NASA Technical Reports Server (NTRS)

1977-01-01

Mathematical and algorithmical techniques for solution of problems in satellite dynamics were developed, along with solutions to satellite orbit motion. Dynamical analysis of shuttle on-orbit operations were conducted. Computer software routines for use in shuttle mission planning were developed and analyzed, while mathematical models of atmospheric density were formulated.

Dynamics and control of tethered antennas/reflectors in orbit

NASA Astrophysics Data System (ADS)

Liu, Liangdong; Bainum, Peter M.

The system linear equations for the motion of a tethered shallow spherical shell in orbit with its symmetry axis nominally following the local vertical are developed. The shell roll, yaw, tether out-of-plane swing motion and elastic vibrations are decoupled from the shell and tether in-plane pitch motions and elastic vibrations. The neutral gravity stability conditions for the special case of a constant length rigid tether are given for in-plane motion and out-of-plant motion. It is proved that the in-plane motion of the system could be asymptotically stable based on Rupp's tension control law, for a variable length tether. However, the system simulation results indicate that the transient responses can be improved significantly, especially for the damping of the tether and shell pitch motion, by an optimal feedback control law for the rigid variable length tether model. It is also seen that the system could be unstable when the effect of tether flexibility is included if the control gains are not chosen carefully. The transient responses for three different tension control laws are compared during typical station keeping operations.

X-Ray Pulsar Studies With RXTE

NASA Technical Reports Server (NTRS)

Rappaport, Saul

2004-01-01

Our activities here at MIT have largely concentrated on four different binary X-ray pulsars: LMC X-4; 4UO352+3O/XPer; 4U0115+63; and X1908+075. We have also recently initiated a search for millisecond X-ray pulsations in RXTE archival data for several bright LMXBs using a new technique. Since this study is just getting under way, we will not report any results here. Using RXTE timing observations of LMC X-4 we have definitively measured, for the first time, the orbital decay of this high-mass X-ray binary. The e-folding decay time scale is very close to lo6 years, comparable to, but somewhat longer than, the corresponding orbital decay times for SMC X-1 and Cen X-3. We find that the orbital decay in LMC X-4 is likely driven by tidal interactions, where the asynchronism between the orbital motion and the rotation of the companion star is maintained by the evolutionary expansion of the companion. Under NASA grant NAGS7479 we carried out RXTE observations of X Per/4U0352+30 in order to track the pulse phase over a one year interval. This effort was successful in tentatively identifying a N 250-day orbital period. However, due to the fact that the observing interval was only somewhat longer than the orbital period, we asked for the observations of X Per to continue as public, or non-proprietary observations. Dr. Jean Swank kindly agreed to the continuation of the observations and they were carried out on a less frequent basis over the next year and a half. After 72 separate observations of X Per, we have the orbital period and semimajor axis firmly determined. In addition, we were able to measure the orbital eccentricity-which turns out to be remarkably small (e = 0.10) for such a wide binary orbit. This has led us establish the birth of a neutron star with a very small (or zero) natal kick.

Long-term observations of the pulsars in 47 Tucanae - II. Proper motions, accelerations and jerks

NASA Astrophysics Data System (ADS)

Freire, P. C. C.; Ridolfi, A.; Kramer, M.; Jordan, C.; Manchester, R. N.; Torne, P.; Sarkissian, J.; Heinke, C. O.; D'Amico, N.; Camilo, F.; Lorimer, D. R.; Lyne, A. G.

2017-10-01

This paper is the second in a series where we report the results of the long-term timing of the millisecond pulsars (MSPs) in 47 Tucanae with the Parkes 64-m radio telescope. We obtain improved timing parameters that provide additional information for studies of the cluster dynamics: (a) the pulsar proper motions yield an estimate of the proper motion of the cluster as a whole (μα = 5.00 ± 0.14 mas yr - 1, μδ = - 2.84 ± 0.12 mas yr - 1) and the motion of the pulsars relative to each other. (b) We measure the second spin-period derivatives caused by the change of the pulsar line-of-sight accelerations; 47 Tuc H, U and possibly J are being affected by nearby objects. (c) For 10 binary systems, we now measure changes in the orbital period caused by their acceleration in the gravitational field of the cluster. From all these measurements, we derive a cluster distance no smaller than ˜4.69 kpc and show that the characteristics of these MSPs are very similar to their counterparts in the Galactic disc. We find no evidence in favour of an intermediate mass black hole at the centre of the cluster. Finally, we describe the orbital behaviour of four 'black widow' systems. Two of them, 47 Tuc J and O, exhibit orbital variability similar to that observed in other such systems, while for 47 Tuc I and R the orbits seem to be remarkably stable. It appears therefore that not all 'black widows' have unpredictable orbital behaviour.

Spin-orbit-torque-induced magnetic domain wall motion in Ta/CoFe nanowires with sloped perpendicular magnetic anisotropy.

PubMed

Zhang, Yue; Luo, Shijiang; Yang, Xiaofei; Yang, Chang

2017-05-17

In materials with the gradient of magnetic anisotropy, spin-orbit-torque-induced magnetization behaviour has attracted attention because of its intriguing scientific principle and potential application. Most of the magnetization behaviours microscopically originate from magnetic domain wall motion, which can be precisely depicted using the standard cooperative coordinate method (CCM). However, the domain wall motion in materials with the gradient of magnetic anisotropy using the CCM remains lack of investigation. In this paper, by adopting CCM, we established a set of equations to quantitatively depict the spin-orbit-torque-induced motion of domain walls in a Ta/CoFe nanotrack with weak Dzyaloshinskii-Moriya interaction and magnetic anisotropy gradient. The equations were solved numerically, and the solutions are similar to those of a micromagnetic simulation. The results indicate that the enhanced anisotropy along the track acts as a barrier to inhibit the motion of the domain wall. In contrast, the domain wall can be pushed to move in a direction with reduced anisotropy, with the velocity being accelerated by more than twice compared with that for the constant anisotropy case. This substantial velocity manipulation by anisotropy engineering is important in designing novel magnetic information devices with high reading speeds.

Flyght Dynamics of Artificial Satellite of the Minor Asteroid

NASA Astrophysics Data System (ADS)

Zakharov, Alexander; Eismont, Natan; Ledkov, Anton; Simonov, Alexander; Pol, Vadim

During last years the scientific interest to the asteroid is constantly growing. It may be explained by different reasons. One of the most important from them is confirmation of the fact that the asteroids present the real hazard to the Earth. The Chelyabinsk event demonstrates strong in support of this statement. Besides, the asteroids exploration promises to supply new data for understanding of the solar system origin and evolution. And the projects aimed to reach this goal have begun from the NASA NEAR mission to Eros. It was the first one when the spacecraft was landed on the surface of the asteroid. The other successive mission was fulfilled by JAXA with Hayabusa spacecraft which has returned to the Earth soil samples of Itokawa asteroid. In the nearest future the mission to RQ 36 asteroid is planned supposing landing and soil samples return. Unavoidable phase of such missions is the spacecraft flight in vicinity of the target asteroid, for example on the asteroid satellite orbit. It should be mentioned that quite visible number of asteroids has geometric form which is far from being sphere. Accordingly the gravity field of such asteroid cannot be presented as the one close to sphere. The problem is that prior to the mission to the asteroid one cannot receive good enough knowledge of its gravity field and even its gravity field constant. In the paper the flight dynamics problem of spacecraft moving along asteroid satellite orbit is explored. It is supposed that the asteroid is comparatively small with diameter (maximum size) about 300 m, like Apophis asteroid has, or less. To approximate the gravity field of asteroid the last is considered as totality of mass points. We assume such approach as more simple and effective as compared with the commonly accepted use of Legendre polynomial expansion. Different orbits near asteroid are analyzed with the sets of orbital parameters determining the size of orbit, its shape and position with respect to the Sun. The goal of this analysis is to understand what initial orbital parameters deliver stability of the orbit in terms of avoiding the collision with the asteroid surface. The orbital heights are calculated which allow to consider the asteroid gravity field as close to the spherical one de-pending on the shape of asteroid. Also maneuvers are estimated necessary for keeping the spacecraft on asteroid satellite orbit and for changing orbital parameters. Taking into account that gravity field parameters of the target asteroids may have pure accuracy it is supposed that spacecraft starts its motion in vicinity of the asteroid from the high enough orbit and then after processing of the tracking data maneuvers are executed to decrease spacecraft altitude. Methods of this procedure optimization are explored.

Short- and Long-Term Propagation of Spacecraft Orbits

NASA Technical Reports Server (NTRS)

Smith, John C., Jr.; Sweetser, Theodore; Chung, Min-Kun; Yen, Chen-Wan L.; Roncoli, Ralph B.; Kwok, Johnny H.; Vincent, Mark A.

2008-01-01

The Planetary Observer Planning Software (POPS) comprises four computer programs for use in designing orbits of spacecraft about planets. These programs are the Planetary Observer High Precision Orbit Propagator (POHOP), the Planetary Observer Long-Term Orbit Predictor (POLOP), the Planetary Observer Post Processor (POPP), and the Planetary Observer Plotting (POPLOT) program. POHOP and POLOP integrate the equations of motion to propagate an initial set of classical orbit elements to a future epoch. POHOP models shortterm (one revolution) orbital motion; POLOP averages out the short-term behavior but requires far less processing time than do older programs that perform long-term orbit propagations. POPP postprocesses the spacecraft ephemeris created by POHOP or POLOP (or optionally can use a less accurate internal ephemeris) to search for trajectory-related geometric events including, for example, rising or setting of a spacecraft as observed from a ground site. For each such event, POPP puts out such user-specified data as the time, elevation, and azimuth. POPLOT is a graphics program that plots data generated by POPP. POPLOT can plot orbit ground tracks on a world map and can produce a variety of summaries and generic ordinate-vs.-abscissa plots of any POPP data.

Air-Breathing Ramjet Electric Propulsion for Controlling Low-Orbit Spacecraft Motion to Compensate for Aerodynamic Drag

NASA Astrophysics Data System (ADS)

Erofeev, A. I.; Nikiforov, A. P.; Popov, G. A.; Suvorov, M. O.; Syrin, S. A.; Khartov, S. A.

2017-12-01

Problems on designing the air-breathing ramjet electric propulsion thruster for controlling loworbit spacecraft motion are examined in the paper. Information for choosing orbits' altitudes for reasonable application of an air-breathing ramjet electric propulsion thruster and propellant exhaust velocity is presented. Estimates of the probable increase of gas concentration in the area of air-breathing ramjet ionization are presented. The test results of the thruster are also given.

Feasibility of Single and Dual Satellite Systems to Enable Continuous Communication Capability to a Manned Mars Mission

DTIC Science & Technology

2014-09-01

periodicity for many centuries but it was not until Johannes Kepler (1619), a German mathematician, developed his three laws of planetary motion in the early...ORBITS Johannes Kepler was a brilliant mathematician hired to map the orbit of Mars by the infamous elk owner, duelist, and astronomer Tycho Brahe...Dreyer & Brahe, 1890). Despite a difference in viewpoints ( Kepler supported Copernicus while Brahe developed his own model of planetary motion in

Orbital evolution and search for eccentricity and apsidal motion in the eclipsing HMXB 4U 1700-37

NASA Astrophysics Data System (ADS)

Islam, Nazma; Paul, Biswajit

2016-09-01

In the absence of detectable pulsations in the eclipsing high-mass X-ray binary 4U 1700-37, the orbital period decay is necessarily determined from the eclipse timing measurements. We have used the earlier reported mid-eclipse time measurements of 4U 1700-37 together with the new measurements from long-term light curves obtained with the all sky monitors RXTE-ASM, Swift-BAT and MAXI-GSC, as well as observations with RXTE-PCA, to measure the long-term orbital evolution of the binary. The orbital period decay rate of the system is estimated to be {dot{P}}/P = -(4.7 ± 1.9) × 10^{-7} yr-1, smaller compared to its previous estimates. We have also used the mid-eclipse times and the eclipse duration measurements obtained from 10-years-long X-ray light curve with Swift-BAT to separately put constraints on the eccentricity of the binary system and attempted to measure any apsidal motion. For an apsidal motion rate greater than 5 deg yr-1, the eccentricity is found to be less than 0.008, which limits our ability to determine the apsidal motion rate from the current data. We discuss the discrepancy of the current limit of eccentricity with the earlier reported values from radial velocity measurements of the companion star.

Modelling resonances and orbital chaos in disk galaxies. Application to a Milky Way spiral model

NASA Astrophysics Data System (ADS)

Michtchenko, T. A.; Vieira, R. S. S.; Barros, D. A.; Lépine, J. R. D.

2017-01-01

Context. Resonances in the stellar orbital motion under perturbations from the spiral arm structure can play an important role in the evolution of the disks of spiral galaxies. The epicyclic approximation allows the determination of the corresponding resonant radii on the equatorial plane (in the context of nearly circular orbits), but is not suitable in general. Aims: We expand the study of resonant orbits by analysing stellar motions perturbed by spiral arms with Gaussian-shaped groove profiles without any restriction on the stellar orbital configurations, and we expand the concept of Lindblad (epicyclic) resonances for orbits with large radial excursions. Methods: We define a representative plane of initial conditions, which covers the whole phase space of the system. Dynamical maps on representative planes of initial conditions are constructed numerically in order to characterize the phase-space structure and identify the precise location of the co-rotation and Lindblad resonances. The study is complemented by the construction of dynamical power spectra, which provide the identification of fundamental oscillatory patterns in the stellar motion. Results: Our approach allows a precise description of the resonance chains in the whole phase space, giving a broader view of the dynamics of the system when compared to the classical epicyclic approach. We generalize the concept of Lindblad resonances and extend it to cases of resonant orbits with large radial excursions, even for objects in retrograde motion. The analysis of the solar neighbourhood shows that, depending on the current azimuthal phase of the Sun with respect to the spiral arms, a star with solar kinematic parameters (SSP) may evolve in dynamically distinct regions, either inside the stable co-rotation resonance or in a chaotic zone. Conclusions: Our approach contributes to quantifying the domains of resonant orbits and the degree of chaos in the whole Galactic phase-space structure. It may serve as a starting point to apply these techniques to the investigation of clumps in the distribution of stars in the Galaxy, such as kinematic moving groups.

Project Physics Handbook 2, Motion in the Heavens.

ERIC Educational Resources Information Center

Harvard Univ., Cambridge, MA. Harvard Project Physics.

Nine experiments and 17 activities are presented in this handbook. The experiments are related to the earth's size and orbit, Piton height, telescope operations, Mars and Mercury orbits, stepwise approximation, and models of comet orbits. Further naked-eye observations in astronomy are designed in connection with the sun, moon, and planet…

Dance of the Planets

ERIC Educational Resources Information Center

Riddle, Bob

2005-01-01

As students continue their monthly plotting of the planets along the ecliptic they should start to notice differences between inner and outer planet orbital motions, and their relative position or separation from the Sun. Both inner and outer planets have direct eastward motion, as well as retrograde motion. Inner planets Mercury and Venus,…

Stability of Multi-Planet Systems Orbiting in the Alpha Centauri AB System

NASA Astrophysics Data System (ADS)

Lissauer, Jack

2018-04-01

We evaluate how closely-spaced planetary orbits in multiple planet systems can be and still survive for billion-year timescales within the alpha Centauri AB system. Although individual planets on nearly circular, coplanar orbits can survive throughout the habitable zones of both stars, perturbations from the companion star imply that the spacing of such planets in multi-planet systems must be significantly larger than the spacing of similar systems orbiting single stars in order to be long-lived. Because the binary companion induces a forced eccentricity upon circumstellar planets, stable orbits with small initial eccentricities aligned with the binary orbit are possible to slightly larger initial semimajor axes than are initially circular orbits. Initial eccentricities close to the appropriate forced eccentricity can have a much larger affect on how closely planetary orbits can be spaced, on how many planets may remain in the habitable zones, although the required spacing remains significantly higher than for planets orbiting single stars.

Analysis of orbit determination from Earth-based tracking for relay satellites in a perturbed areostationary orbit

NASA Astrophysics Data System (ADS)

Romero, P.; Pablos, B.; Barderas, G.

2017-07-01

Areostationary satellites are considered a high interest group of satellites to satisfy the telecommunications needs of the foreseen missions to Mars. An areostationary satellite, in an areoequatorial circular orbit with a period of 1 Martian sidereal day, would orbit Mars remaining at a fixed location over the Martian surface, analogous to a geostationary satellite around the Earth. This work addresses an analysis of the perturbed orbital motion of an areostationary satellite as well as a preliminary analysis of the aerostationary orbit estimation accuracy based on Earth tracking observations. First, the models for the perturbations due to the Mars gravitational field, the gravitational attraction of the Sun and the Martian moons, Phobos and Deimos, and solar radiation pressure are described. Then, the observability from Earth including possible occultations by Mars of an areostationary satellite in a perturbed areosynchronous motion is analyzed. The results show that continuous Earth-based tracking is achievable using observations from the three NASA Deep Space Network Complexes in Madrid, Goldstone and Canberra in an occultation-free scenario. Finally, an analysis of the orbit determination accuracy is addressed considering several scenarios including discontinuous tracking schedules for different epochs and different areoestationary satellites. Simulations also allow to quantify the aerostationary orbit estimation accuracy for various tracking series durations and observed orbit arc-lengths.

Study of an orbiting tethered dumbbell system having positive orbital energy

NASA Technical Reports Server (NTRS)

Arnold, David A.

1988-01-01

For very long tethered systems the sum of the kinetic and potential energy can be positive. The system remains in a circular orbit as long as the masses remain vertically aligned. The system is unstable without constant control of the alignment. If the upper mass rotates forward in the direction of the orbital motion, the system escapes out of orbit. If the upper mass rotates backward, the system falls out of orbit and the lower mass impacts the body around which the system is orbiting.

First Results from a Hardware-in-the-Loop Demonstration of Closed-Loop Autonomous Formation Flying

NASA Technical Reports Server (NTRS)

Gill, E.; Naasz, Bo; Ebinuma, T.

2003-01-01

A closed-loop system for the demonstration of autonomous satellite formation flying technologies using hardware-in-the-loop has been developed. Making use of a GPS signal simulator with a dual radio frequency outlet, the system includes two GPS space receivers as well as a powerful onboard navigation processor dedicated to the GPS-based guidance, navigation, and control of a satellite formation in real-time. The closed-loop system allows realistic simulations of autonomous formation flying scenarios, enabling research in the fields of tracking and orbit control strategies for a wide range of applications. The autonomous closed-loop formation acquisition and keeping strategy is based on Lyapunov's direct control method as applied to the standard set of Keplerian elements. This approach not only assures global and asymptotic stability of the control but also maintains valuable physical insight into the applied control vectors. Furthermore, the approach can account for system uncertainties and effectively avoids a computationally expensive solution of the two point boundary problem, which renders the concept particularly attractive for implementation in onboard processors. A guidance law has been developed which strictly separates the relative from the absolute motion, thus avoiding the numerical integration of a target trajectory in the onboard processor. Moreover, upon using precise kinematic relative GPS solutions, a dynamical modeling or filtering is avoided which provides for an efficient implementation of the process on an onboard processor. A sample formation flying scenario has been created aiming at the autonomous transition of a Low Earth Orbit satellite formation from an initial along-track separation of 800 m to a target distance of 100 m. Assuming a low-thrust actuator which may be accommodated on a small satellite, a typical control accuracy of less than 5 m has been achieved which proves the applicability of autonomous formation flying techniques to formations of satellites as close as 50 m.

The VMC survey. XXVIII. Improved measurements of the proper motion of the Galactic globular cluster 47 Tucanae

NASA Astrophysics Data System (ADS)

Niederhofer, Florian; Cioni, Maria-Rosa L.; Rubele, Stefano; Schmidt, Thomas; Bekki, Kenji; de Grijs, Richard; Emerson, Jim; Ivanov, Valentin D.; Oliveira, Joana M.; Petr-Gotzens, Monika G.; Ripepi, Vincenzo; Sun, Ning-Chen; van Loon, Jacco Th.

2018-05-01

We use deep multi-epoch point-spread function (PSF) photometry taken with the Visible and Infrared Survey Telescope for Astronomy (VISTA) to measure and analyze the proper motions of stars within the Galactic globular cluster 47 Tucanae (47 Tuc, NGC 104). The observations are part of the ongoing near-infrared VISTA survey of the Magellanic Cloud system (VMC). The data analyzed in this study correspond to one VMC tile, which covers a total sky area of 1.77 deg2. Absolute proper motions with respect to 9070 background galaxies are calculated from a linear regression model applied to the positions of stars in 11 epochs in the Ks filter. The data extend over a total time baseline of about 17 months. We found an overall median proper motion of the stars within 47 Tuc of (μαcos(δ), μδ) = (+5.89 ± 0.02 (statistical) ± 0.13 (systematic), -2.14 ± 0.02 (statistical) ± 0.08 (systematic)) mas yr-1, based on the measurements of 35 000 individual sources between 5' and 42' from the cluster center. We compared our result to the proper motions from the newest US Naval Observatory CCD Astrograph Catalog (UCAC5), which includes data from the Gaia data release 1. Selecting cluster members ( 2700 stars), we found a median proper motion of (μαcos(δ), μδ) = (+5.30 ± 0.03 (statistical) ± 0.70 (systematic), -2.70 ± 0.03 (statistical) ± 0.70 (systematic)) mas yr-1. Comparing the results with measurements in the literature, we found that the values derived from the VMC data are consistent with the UCAC5 result, and are close to measurements obtained using the Hubble Space Telescope. We combined our proper motion results with radial velocity measurements from the literature and reconstructed the orbit of 47 Tuc, finding that the cluster is on an orbit with a low ellipticity and is confined within the inner 7.5 kpc of the Galaxy. We show that the use of an increased time baseline in combination with PSF-determined stellar centroids in crowded regions significantly improves the accuracy of the method. In future works, we will apply the methods described here to more VMC tiles to study in detail the kinematics of the Magellanic Clouds. Based on observations made with VISTA at the Paranal Observatory under program ID 179.B-2003.

ORBITAL DISTRIBUTIONS OF CLOSE-IN PLANETS AND DISTANT PLANETS FORMED BY SCATTERING AND DYNAMICAL TIDES

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nagasawa, M.; Ida, S., E-mail: nagasawa.m.ad@m.titech.ac.jp

2011-12-01

We investigated the formation of close-in planets (hot Jupiters) by a combination of mutual scattering, Kozai effect, and tidal circularization, through N-body simulations of three gas giant planets, and compared the results with discovered close-in planets. We found that in about 350 cases out of 1200 runs ({approx}30%), the eccentricity of one of the planets is excited highly enough for tidal circularization by mutual close scatterings followed by secular effects due to outer planets, such as the Kozai mechanism, and the planet becomes a close-in planet through the damping of eccentricity and semimajor axis. The formation probability of close-in planetsmore » by such scattering is not affected significantly by the effect of the general relativity and inclusion of inertial modes in addition to fundamental modes in the tides. Detailed orbital distributions of the formed close-in planets and their counterpart distant planets in our simulations were compared with observational data. We focused on the possibility for close-in planets to retain non-negligible eccentricities ({approx}> 0.1) on timescales of {approx}10{sup 9} yr and have high inclinations, because close-in planets in eccentric or highly inclined orbits have recently been discovered. In our simulations we found that as many as 29% of the close-in planets have retrograde orbits, and the retrograde planets tend to have small eccentricities. On the other hand, eccentric close-in planets tend to have orbits of small inclinations.« less

Vibration properties of a rotating piezoelectric energy harvesting device that experiences gyroscopic effects

NASA Astrophysics Data System (ADS)

Lu, Haohui; Chai, Tan; Cooley, Christopher G.

2018-03-01

This study investigates the vibration of a rotating piezoelectric device that consists of a proof mass that is supported by elastic structures with piezoelectric layers. Vibration of the proof mass causes deformation in the piezoelectric structures and voltages to power the electrical loads. The coupled electromechanical equations of motion are derived using Newtonian mechanics and Kirchhoff's circuit laws. The free vibration behavior is investigated for devices with identical (tuned) and nonidentical (mistuned) piezoelectric support structures and electrical loads. These devices have complex-valued, speed-dependent eigenvalues and eigenvectors as a result of gyroscopic effects caused by their constant rotation. The characteristics of the complex-valued eigensolutions are related to physical behavior of the device's vibration. The free vibration behaviors differ significantly for tuned and mistuned devices. Due to gyroscopic effects, the proof mass in the tuned device vibrates in either forward or backward decaying circular orbits in single-mode free response. This is proven analytically for all tuned devices, regardless of the device's specific parameters or operating speed. For mistuned devices, the proof mass has decaying elliptical forward and backward orbits. The eigenvalues are shown to be sensitive to changes in the electrical load resistances. Closed-form solutions for the eigenvalues are derived for open and close circuits. At high rotation speeds these devices experience critical speeds and instability.

The Orbital Period of the SU Ursae Majoris Star EK Trianguli Australis and Evidence for Ring-Like Accretion Disks in Long-Supercycle Length SU Ursae Majoris Stars

NASA Astrophysics Data System (ADS)

Mennickent, Ronald E.; Arenas, Jose

1998-06-01

An orbital period of 0.06288(5) d has been found from a radial velocity study of the Hα emission line. In addition, we have detected an extra line emitting source located ~ 80(deg) apart from the vector joining the secondary--primary centers, as measured in the opposite sense to the binary rotational motion. This is not the expected location for the hotspot in dwarf novae. This anomaly could be removed by assuming a line emission lagging behind the white dwarf binary motion. In addition, we have estimated line emissivity (~ r(-alpha ) ) and disk radius (R equiv r_in/r_out) for 8 SU UMa stars. Most stars fit alpha = 1.8 +/- 0.1 but AK Cnc and WZ Sge strongly deviate from the mean; their emission line shapes can be explained assuming a post-outburst accretion disk mostly emitting close to the white dwarf (AK Cnc) and a ring-like disk (WZ Sge). In addition, we have found a tendency of long-supercycle length SU UMa stars to show very compact (large R; probably ring-like) accretion disks. If the supercycle length were basically controlled by the mass transfer rate (dot {M}), the inner disk radius would be a function of dot {M}. A white dwarf magnetic field ~ 5000 G is required to fit the truncation radius with the magnetosphere radius of SU UMa stars.

The system integration and verification testing of an orbital maneuvering vehicle for an air bearing floor

NASA Technical Reports Server (NTRS)

Shields, N. L., Jr.; Martin, M. F.; Paulukaitis, K. R.; Haslam, J. W., Jr.; Henderson, D. E.

1986-01-01

The teleoperator and Robotics Evaluation Facility (TOREF) is composed of a 4,000 square foot precision air bearing floor, the Teleoperator Motion Base, the Target Motion and Support Simulator, the mock-ups of the Hubble Space Telescope, Multi-mission Modular Spacecraft, and the Orbital Maneuvering Vehicle (OMV). The TOREF and its general capabilities to support the OMV and other remote system simulations; the facility operating procedures and requirements; and the results of generic OMV investigations are summarized.

Dynamics of planetary rings

NASA Technical Reports Server (NTRS)

Araki, Suguru

1991-01-01

The modeling of the dynamics of particle collisions within planetary rings is discussed. Particles in the rings collide with one another because they have small random motions in addition to their orbital velocity. The orbital speed is roughly 10 km/s, while the random motions have an average speed of about a tenth of a millimeter per second. As a result, the particle collisions are very gentle. Numerical analysis and simulation of the ring dynamics, performed with the aid of a supercomputer, is outlined.

Beyond Orbital-Motion-Limited theory effects for dust transport in tokamaks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Delzanno, Gian Luca; Tang, Xianzhu

Dust transport in tokamaks is very important for ITER. Can many kilograms of dust really accumulate in the device? Can the dust survive? The conventional dust transport model is based on Orbital-Motion-Limited theory (OML). But OML can break in the limit where the dust grain becomes positively charged due to electron emission processes because it overestimates the dust collected power. An OML + approximation of the emitted electrons trapped/passing boundary is shown to be in good agreement with PIC simulations.

The integration of the motion equations of low-orbiting earth satellites using Taylor's method

NASA Astrophysics Data System (ADS)

Krivov, A. V.; Chernysheva, N. A.

1990-04-01

A method for the numerical integration of the equations of motion for a satellite is proposed, taking the earth's oblateness and atmospheric drag into account. The method is based on Taylor's representation of the solution to the corresponding polynomial system. The algorithm for choosing the integration step and error estimation is constructed. The method is realized as a subrouting package. The method is applied to a low-orbiting earth satellite and the results are compared with those obtained using Everhart's method.

Dynamics in the vicinity of (101955) Bennu: solar radiation pressure effects in equatorial orbits

NASA Astrophysics Data System (ADS)

Chanut, T. G. G.; Aljbaae, S.; Prado, A. F. B. A.; Carruba, V.

2017-09-01

Here, we study the dynamical effects of the solar radiation pressure (SRP) on a spacecraft that will survey the near-Earth rotating asteroid (101955) Bennu when the projected shadow is accounted for. The spacecraft's motion near (101955) Bennu is modelled in the rotating frame fixed at the centre of the asteroid, neglecting the Sun gravity effects. We calculate the SRP at the perihelion, semimajor axis and aphelion distances of the asteroid from the Sun. The goals of this work are to analyse the stability for both homogeneous and inhomogeneous mass distribution and study the effects of the SRP in equatorial orbits close to the asteroid (101955) Bennu. As results, we find that the mascon model divided into 10 equal layers seems to be the most suitable for this problem. We can highlight that the centre point E8, which was linearly stable in the case of the homogeneous mass distribution, becomes unstable in this new model changing its topological structure. For a Sun initial longitude ψ0 = -180°, starting with the spacecraft longitude λ = 0, the orbits suffer fewer impacts and some (between 0.4 and 0.5 km), remaining unwavering even if the maximum solar radiation is considered. When we change the initial longitude of the Sun to ψ0 = -135°, the orbits with initial longitude λ = 90° appear to be more stable. Finally, when the passage of the spacecraft in the shadow is accounted for, the effects of SRP are softened, and we find more stable orbits.

Investigating the Relativistic Motion of the Stars Near the Supermassive Black Hole in the Galactic Center

NASA Astrophysics Data System (ADS)

Parsa, M.; Eckart, A.; Shahzamanian, B.; Karas, V.; Zajaček, M.; Zensus, J. A.; Straubmeier, C.

2017-08-01

The S-star cluster in the Galactic center allows us to study the physics close to a supermassive black hole, including distinctive dynamical tests of general relativity. Our best estimates for the mass of and the distance to Sgr A* using the three stars with the shortest period (S2, S38, and S55/S0-102) and Newtonian models are M BH = (4.15 ± 0.13 ± 0.57) × 106 M ⊙ and R 0 = 8.19 ± 0.11 ± 0.34 kpc. Additionally, we aim at a new and practical method to investigate the relativistic orbits of stars in the gravitational field near Sgr A*. We use a first-order post-Newtonian approximation to calculate the stellar orbits with a broad range of periapse distance r p . We present a method that employs the changes in orbital elements derived from elliptical fits to different sections of the orbit. These changes are correlated with the relativistic parameter defined as ϒ ≡ r s /r p (with r s being the Schwarzschild radius) and can be used to derive ϒ from observational data. For S2 we find a value of ϒ = 0.00088 ± 0.00080, which is consistent, within the uncertainty, with the expected value of ϒ = 0.00065 derived from M BH and the orbit of S2. We argue that the derived quantity is unlikely to be dominated by perturbing influences such as noise on the derived stellar positions, field rotation, and drifts in black hole mass.

Fast, Safe, Propellant-Efficient Spacecraft Motion Planning Under Clohessy-Wiltshire-Hill Dynamics

NASA Technical Reports Server (NTRS)

Starek, Joseph A.; Schmerling, Edward; Maher, Gabriel D.; Barbee, Brent W.; Pavone, Marco

2016-01-01

This paper presents a sampling-based motion planning algorithm for real-time and propellant-optimized autonomous spacecraft trajectory generation in near-circular orbits. Specifically, this paper leverages recent algorithmic advances in the field of robot motion planning to the problem of impulsively actuated, propellant- optimized rendezvous and proximity operations under the Clohessy-Wiltshire-Hill dynamics model. The approach calls upon a modified version of the FMT* algorithm to grow a set of feasible trajectories over a deterministic, low-dispersion set of sample points covering the free state space. To enforce safety, the tree is only grown over the subset of actively safe samples, from which there exists a feasible one-burn collision-avoidance maneuver that can safely circularize the spacecraft orbit along its coasting arc under a given set of potential thruster failures. Key features of the proposed algorithm include 1) theoretical guarantees in terms of trajectory safety and performance, 2) amenability to real-time implementation, and 3) generality, in the sense that a large class of constraints can be handled directly. As a result, the proposed algorithm offers the potential for widespread application, ranging from on-orbit satellite servicing to orbital debris removal and autonomous inspection missions.

The Actual Mass of the Object Orbiting Epsilon Eridani

NASA Astrophysics Data System (ADS)

Gatewood, G.

2000-10-01

We have tested our 112 Multichannel Astrometric Photometer (MAP) (Gatewood 1987, AJ 94, 213) observations (beginning in 1988) of Epsilon Eridani against the orbital elements provided to us by W. Cochran (private communication). The reduction algorithm is detailed most recently by Gatewood, Han, and Black (2000 ApJ Letters, in press). The seven year period is clearly shown in a variance vs trial periods plot. Although it is near the limit of the current instrument, the astrometric orbital motion is apparent in the residuals to a standard derivation of the star's proper motion and parallax. The astrometric orbital parameters derived by forcing the spectroscopic elements are: semimajor axis = 1.51 +/- 0.44 mas, node of the orbit on the sky = 120 +/- 28 deg, inclination out of the plane of the sky = 46 +/- 17 deg, actual mass = 1.2 +/- 0.33 times that of Jupiter. Our study confirms this object (this is not a minimum mass) as the nearest extrasolar Jupiter mass companion to our solar system. In view of its large orbital eccentricity, however, its exact nature remains unclear.

Planet Formation Instrument for the Thirty Meter Telescope

DOE Office of Scientific and Technical Information (OSTI.GOV)

Macintosh, B; Troy, M; Graham, J

2006-02-22

In the closing years of the 20th Century humankind began its exploration of the planetary systems in the solar neighborhood. Precision radial velocity measurements have now yielded the discovery of over 160 planets. Direct imaging of these planets, as opposed to detection of the effects of orbital motion on their parent star, is now feasible, and the first young planet in a wide orbit may have been detected using adaptive optics systems. Gemini and the VLT are building the first generation of high contrast adaptive optics systems, which deliver planet-imaging performance within few Airy rings of the host star. Thesemore » systems will make the first surveys of the outer regions of solar systems by detecting the self-luminous radiation of young planets. These instruments will establish whether Jovian planets form predominantly through 'top-down' (global gravitational instability) or 'bottom-up' (core accretion) processes. The 8-m 'extreme' AO systems cannot see close enough to the host stars to image Doppler planets, and they cannot reach the relatively distant, young clusters and associations where planets are forming. The Planet Formation Instrument will use the nearly four-fold improved angular resolution of TMT to peer into the inner solar systems of Doppler-planet bearing stars to yield a unified sample of planets with known Keplerian orbital elements and atmospheric properties. In star formation regions, where T Tauri stars (young solar type stars) are found in abundance, PFI can see into the snow line, where the icy cores of planets like Jupiter must have formed. Thus, TMT will be the first facility to witness the formation of new planets.« less

Correlated motion of electrons in the He atom irradiated with coherent light

NASA Astrophysics Data System (ADS)

Someda, Kiyohiko

2018-05-01

Correlated motion of electrons in the He atom irradiated with linearly polarised light is discussed. Mixing of the 2pz orbital into the 1s orbital is interpreted as motion of an electron along the z-axis. The transitions to the configurations (1s)(2pz) and (2pz)(2pz) from (1s)(1s) are described by using 1s-2pz hybridised orbitals with variable coefficients of hybridisation, in other words, by using the Thouless parameters. The quasi-eigenstates of the atom in stationary light are obtained on the basis of the Floquet formalism, and the behaviour of the Thouless parameters is analysed. Trajectories of time evolution of the Thouless parameters are found to be useful to grasp the motion of electrons. Shapes of the trajectories are classified into four modes: (1) two electrons try to stay away from each other due to Coulomb repulsion, (2) one of the electrons is solely driven to run, (3) two electrons are driven to travel together and (4) two electrons run anti-parallel with each other. The conditions of intensity and frequency of light causing these four modes are clarified and summarised in a kind of phase diagram.

Chaos in the Solar System

NASA Technical Reports Server (NTRS)

Lecar, Myron; Franklin, Fred A.; Holman, Matthew J.; Murray, Norman J.

2001-01-01

The physical basis of chaos in the solar system is now better understood: In all cases investigated so far, chaotic orbits result from overlapping resonances. Perhaps the clearest examples are found in the asteroid belt. Overlapping resonances account for its kirkwood gaps and were used to predict and find evidence for very narrow gaps in the outer belt. Further afield, about one new "short-peroid" comet is discovered each year. They are believed to come from the "Kuiper Belt" (at 40 AU or more) via chaotic orbits produced by mean-motion and secular resonances with Neptune. Finally, the planetary system itself is not immune from chaos. In the inner solar system, overlapping secular resonances have been identified as the possible source of chaos. For example, Mercury in 1012 years, may suffer a close encounter with Venus or plunge into the Sun. In the outer solar system, three-body resonances have been identified as a source of chaos, but on an even longer time scale of 109 times the age of the solar system. On the human time scale, the planets do follow their orbits in a stately procession, and we can predict their trajectories for hundreds of thousands of years. That is because the mavericks, with shorter instability times, have long since been ejected. The solar system is not stable; it is just old!

Evolution of the Quadrantid meteor stream

NASA Technical Reports Server (NTRS)

Jones, James; Jones, William

1992-01-01

According to previous orbital calculations, the last close approach of the Quadrantid stream with Jupiter occurred 3200 years ago at which time the parent comet of the stream may have been captured into its present short-period orbit. If this is the case the stream may only be a few thousand years old. We have modeled the evolution of the stream to determine if such a short time scale is consistent with the observed features of the Quadrantid/ delta- Aquarid/Arietid/Ursid complex. A detailed modeling of a stream consisting of 500 test particles released 4000 yr ago and which included the effects of the gravitational perturbations of 6 planets as well as the likely spread in the initial orbital elements resulting from the ejection of the grains from the comet was carried out. Our calculations indicate that an intense shower should be seen a few days before the Quadrantid shower, and that, 4000 yr is too short a period for the branch corresponding to the D-Arietid branch to appear. We have considered the quasi-constants of motion 1/a and J, the Tisserand quantity, and find that the Ursids and the D-Arietids are unlikely to be members of the complex, and that, the complex is probably be less than 4000 yr old.

Are we close to putting the anomalous perihelion precessions from Verlinde's emergent gravity to the test?

NASA Astrophysics Data System (ADS)

Iorio, Lorenzo

2017-03-01

In the framework of the emergent gravity scenario by Verlinde, it was recently observed by Liu and Prokopec that, among other things, an anomalous pericenter precession would affect the orbital motion of a test particle orbiting an isolated central body. Here, it is shown that, if it were real, its expected magnitude for the inner planets of the Solar System would be at the same level of the present-day accuracy in constraining any possible deviations from their standard perihelion precessions as inferred from long data records spanning about the last century. The most favorable situation for testing the Verlinde-type precession seems to occur for Mars. Indeed, according to recent versions of the EPM and INPOP planetary ephemerides, non-standard perihelion precessions, of whatsoever physical origin, which are larger than some ≈ 0.02-0.11 milliarcseconds per century are not admissible, while the putative precession predicted by Liu and Prokopec amounts to 0.09 milliarcseconds per century. Other potentially interesting astronomical and astrophysical scenarios like, e.g., the Earth's LAGEOS II artificial satellite, the double pulsar system PSR J0737-3039A/B and the S-stars orbiting the Supermassive Black Hole in Sgr A^* are, instead, not viable because of the excessive smallness of the predicted precessions for them.

Long-term evaluation of orbital dynamics in the Sun-planet system considering axial-tilt

NASA Astrophysics Data System (ADS)

Bakhtiari, Majid; Daneshjou, Kamran

2018-05-01

In this paper, the axial-tilt (obliquity) effect of planets on the motion of planets’ orbiter in prolonged space missions has been investigated in the presence of the Sun gravity. The proposed model is based on non-simplified perturbed dynamic equations of planetary orbiter motion. From a new point of view, in this work, the dynamic equations regarding a disturbing body in elliptic inclined three-dimensional orbit are derived. The accuracy of this non-simplified method is validated with dual-averaged method employed on a generalized Earth-Moon system. It is shown that the neglected short-time oscillations in dual-averaged technique can accumulate and propel to remarkable errors in the prolonged evolution. After validation, the effects of the planet’s axial-tilt on eccentricity, inclination and right ascension of the ascending node of the orbiter are investigated. Moreover, a generalized model is provided to study the effects of third-body inclination and eccentricity on orbit characteristics. It is shown that the planet’s axial-tilt is the key to facilitating some significant changes in orbital elements in long-term mission and short-time oscillations must be considered in accurate prolonged evaluation.

Multi-epoch observations with high spatial resolution of multiple T Tauri systems

NASA Astrophysics Data System (ADS)

Csépány, Gergely; van den Ancker, Mario; Ábrahám, Péter; Köhler, Rainer; Brandner, Wolfgang; Hormuth, Felix; Hiss, Hector

2017-07-01

Context. In multiple pre-main-sequence systems the lifetime of circumstellar discs appears to be shorter than around single stars, and the actual dissipation process may depend on the binary parameters of the systems. Aims: We report high spatial resolution observations of multiple T Tauri systems at optical and infrared wavelengths. We determine whether the components are gravitationally bound and orbital motion is visible, derive orbital parameters, and investigate possible correlations between the binary parameters and disc states. Methods: We selected 18 T Tau multiple systems (16 binary and two triple systems, yielding 16 + 2 × 2 = 20 binary pairs) in the Taurus-Auriga star-forming region from a previous survey, with spectral types from K1 to M5 and separations from 0.22″ (31 AU) to 5.8″ (814 AU). We analysed data acquired in 2006-07 at Calar Alto using the AstraLux lucky imaging system, along with data from SPHERE and NACO at the VLT, and from the literature. Results: We found ten pairs to orbit each other, five pairs that may show orbital motion, and five likely common proper motion pairs. We found no obvious correlation between the stellar parameters and binary configuration. The 10 μm infra-red excess varies between 0.1 and 7.2 mag (similar to the distribution in single stars, where it is between 1.7 and 9.1), implying that the presence of the binary star does not greatly influence the emission from the inner disc. Conclusions: We have detected orbital motion in young T Tauri systems over a timescale of ≈ 20 yr. Further observations with even longer temporal baseline will provide crucial information on the dynamics of these young stellar systems.

Explanation of relativistic phenomena on the basis of interactions of particle energy, applied energy, and field energy

NASA Astrophysics Data System (ADS)

Fernando, Viraj

2011-09-01

This paper formulates a coherent theory of occurrence of relativistic phenomena in their interconnection in a feedback loop, unlike other theories, by tracing back concepts that Newton held but suppressed, when he developed his mechanics in his Principia. Despite Newtonian mechanics being based on a closed system, Newton in the General Scholium has indicated that in reality thee is in an open system, where 'a certain most subtle spirit' participates and directs all interactions from motion of bodies, to motion of light, to how the human brain operates. We have identified this 'most subtle spirit' as the non-empirical 'universal governing field' and that no empirical interaction in this universe can occur without exchange of energy between the empirical interactants and the governing field. By analyzing the energy momentum equation, we have demonstrated that everything empirical has a non-empirical substratum, identified with Spinoza's primitive substance, which binds everything in the universe to the field and through it to one another. Algorithm of Motion is founded on the Pythagorean character of the energy-momentum equation, which is applicable to all velocities 0

Project Physics Tests 2, Motion in the Heavens.

ERIC Educational Resources Information Center

Harvard Univ., Cambridge, MA. Harvard Project Physics.

Test items relating to Project Physics Unit 2 are presented in this booklet. Included are 70 multiple-choice and 22 problem-and-essay questions. Concepts of motion in the heavens are examined for planetary motions, heliocentric theory, forces exerted on the planets, Kepler's laws, gravitational force, Galileo's work, satellite orbits, Jupiter's…

From Ancient Paradoxes to Modern Orbit Determination

NASA Astrophysics Data System (ADS)

Giorgini, Jon D.

2008-09-01

In the 5th century BC, Zeno advanced a set of paradoxes to show motion and time are impossible, hence an illusion. The problem of motion has since driven much scientific thought and discovery, extending to Einstein's insights and the quantum revolution. To determine and predict the motion of remote objects within the solar system, a methodology has been refined over centuries. It integrates ideas from astronomy, physics, mathematics, measurement, and probability theory, having motivated most of those developments. Recently generalized and made numerically efficient, statistical orbit determination has made it possible to remotely fly Magellan and other spacecraft through the turbulent atmospheres of Venus and other planets while estimating atmospheric structure and internal mass distributions of the planet. Over limited time-scales, the methodology can predict the position of the Moon within a meter and asteroids within tens of meters -- their velocities at the millimeter per second level -- while characterizing the probable correctness of the prediction. Current software and networks disseminate such ephemeris information in moments; over the last 12 years, 10 million ephemerides have been provided by the Horizons system, at the request of 300000 different users. Applications range from ground and space telescope pointing to correlation with observations recorded on Babylonian cuneiform tablets. Rapid orbit updates are particularly important for planetary radars integrating weak small-body echoes moving quickly through the frequency spectrum due to relative motion. A loop is established in which the predicted delay-Doppler measurement and uncertainties are used to configure the radar. Both predictions are then compared to actual results, the asteroid or comet orbit solution improved, and the radar system optimally adjusted. Still, after 2500 years and tremendous descriptive success, there remain substantial problems understanding and predicting motion.

Close up detail of the underside of the Orbiter Discovery ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

Close up detail of the underside of the Orbiter Discovery in the Vehicle Assembly Building at NASA's Kennedy Space Center. This view is from underneath the aft section looking forward. It is a close-up view of the High-temperature Reusable Surface Insulation tiles showing the wear patterns from the heat of reentry, consequential replacement of worn and damaged tiles. The wear and replacement patters are unique to each Orbiter which can serve as their particular "fingerprint". - Space Transportation System, Orbiter Discovery (OV-103), Lyndon B. Johnson Space Center, 2101 NASA Parkway, Houston, Harris County, TX

A large motion zero-gravity suspension system for experimental simulation of orbital construction and deployment. M.S. Thesis

NASA Technical Reports Server (NTRS)

Straube, Timothy Milton

1993-01-01

The design and implementation of a vertical degree of freedom suspension system is described which provides a constant force off-load condition to counter gravity over large displacements. By accommodating motions up to one meter for structures weighing up to 100 pounds, the system is useful for experiments which simulate orbital construction events such as docking, multiple component assembly, or structural deployment. A unique aspect of this device is the combination of a large stroke passive off-load device augmented by electromotive torque actuated force feedback. The active force feedback has the effect of reducing break-away friction by a factor of twenty over the passive system alone. The thesis describes the development of the suspension hardware and the control algorithm. Experiments were performed to verify the suspensions system's effectiveness in providing a gravity off-load and simulating the motion of a structure in orbit. Additionally, a three dimensional system concept is presented as an extension of the one dimensional suspension system which was implemented.

The Motion of a Satellite of the Moon

NASA Technical Reports Server (NTRS)

Lass, Harry

1960-01-01

The motion of a satellite of the Moon depends on the potential field due to the Moon as well as the gravitational effects of the Earth and Sun. If one chooses a frame of reference attached to the Moon, it can be shown that the force field resulting from the Sun can be neglected when compared with the perturbing field of the Moon resulting from its oblateness. The effect of the Earth's field on the satellite is of the some order of magnitude as the Moon's perturbing field and must be included in an analysis of the motion of a satellite of the Moon. We will assume that the distance between Earth and Moon remains constant, and we will consider satellite orbits of small eccentricity. It will be shown that a nearly circular polar orbit will digress less than 1 deg from a polar orbit and that the change in eccentricity is less than a factor of e in one year.

Influence of tides in viscoelastic bodies of planet and satellite on the satellite's orbital motion

NASA Astrophysics Data System (ADS)

Emelyanov, N. V.

2018-06-01

The problem of influence of tidal friction in both planetary and satellite bodies upon satellite's orbital motion is considered. Using the differential equations in satellite's rectangular planetocentric coordinates, the differential equations describing the changes in semimajor axis and eccentricity are derived. The equations in rectangular coordinates were taken from earlier works on the problem. The calcultations carried out for a number of test examples prove that the averaged solutions of equations in coordinates and precise solutions of averaged equations in the Keplerian elements are identical. For the problem of tides raised on planet's body, it was found that, if satellite's mean motion n is equal to 11/18 Ω, where Ω is the planet's angular rotation rate, the orbital eccentricity does not change. This conclusion is in agreement with the results of other authors. It was also found that there is essential discrepancy between the equations in the elements obtained in this paper and analogous equations published by earlier researchers.

Close up oblique view aft, port side of the Orbiter ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

Close up oblique view aft, port side of the Orbiter Discovery in the Vehicle Assembly Building at NASA's Kennedy Space Center. This view shows a close up of the elevons and underside of the port wing. On the aft fuselage in the approximate center rift of the image is the T-0 umbilical panels. - Space Transportation System, Orbiter Discovery (OV-103), Lyndon B. Johnson Space Center, 2101 NASA Parkway, Houston, Harris County, TX

A comparison of Lorentz, planetary gravitational, and satellite gravitational resonances

NASA Technical Reports Server (NTRS)

Hamilton, Douglas P.

1994-01-01

We consider a charged dust grain whose orbital motion is dominated by a planet's point-source gravity, but perturbed by higher-order terms in the planet's gravity field as well as by the Lorentz force arising from an asymmetric planetary magnetic field. Perturbations to Keplerian orbits due to a nonspherical gravity field are expressed in the traditional way: in terms of a disturbing function which can be expanded in a series of spherical harmonics (W. M. Kaula, 1966). In order to calculate the electromagnetic perturbation, we first write the Lorentz force in terms of the orbital elements and then substitute it into Gauss' perturbation equations. We use our result to derive strengths of Lorentz resonances and elucidate their properties. In particular, we compare Lorentz resonances to two types of gravitational resonances: those arising from periodic tugs of a satellite and those due to the attraction of an arbitrarily shaped planet. We find that Lorentz resonances share numerous properties with their gravitational counterparts and show, using simple physical arguments, that several of these patterns are fundamental, applying not only to our expansions, but to all quantities expressed in terms of orbital elements. Some of these patterns have been previously called 'd'Alembert rules' for satellite resonances. Other similarities arise because, to first-order in the perturbing force, the three problems share an integral of the motion. Yet there are also differences; for example, first-order inclination resonances exist for perturbations arising from planetary gravity and from the Lorentz force, but not for those due to an orbiting satellite. Finally, we provide a heuristic treatment of a particle's orbital evolution under the influence of drag and resonant forces. Particles brought into mean-motion resonances experience either trapping or resonant 'jumps,' depending on the direction from which the resonance is approached. We show that this behavior does not depend on the details of the perturbing force but rather is fundamental to all mean-motion resonances.

Generalized YORP evolution: Onset of tumbling and new asymptotic states

NASA Astrophysics Data System (ADS)

Vokrouhlický, D.; Breiter, S.; Nesvorný, D.; Bottke, W. F.

2007-11-01

Asteroids have a wide range of rotation states. While the majority spin a few times to several times each day in principal axis rotation, a small number spin so slowly that they have somehow managed to enter into a tumbling rotation state. Here we investigate whether the Yarkovsky-Radzievskii-O'Keefe-Paddack (YORP) thermal radiation effect could have produced these unusual spin states. To do this, we developed a Lie-Poisson integrator of the orbital and rotational motion of a model asteroid. Solar torques, YORP, and internal energy dissipation were included in our model. Using this code, we found that YORP can no longer drive the spin rates of bodies toward values infinitely close to zero. Instead, bodies losing too much rotation angular momentum fall into chaotic tumbling rotation states where the spin axis wanders randomly for some interval of time. Eventually, our model asteroids reach rotation states that approach regular motion of the spin axis in the body frame. An analytical model designed to describe this behavior does a good job of predicting how and when the onset of tumbling motion should take place. The question of whether a given asteroid will fall into a tumbling rotation state depends on the efficiency of its internal energy dissipation and on the precise way YORP modifies the spin rates of small bodies.

The envelope of ballistic trajectories and elliptic orbits

NASA Astrophysics Data System (ADS)

Butikov, Eugene I.

2015-11-01

Simple geometric derivations are given for the shape of the "safety domain" boundary for the family of Keplerian orbits of equal energy in a central gravitational field and for projectile trajectories in a uniform field. Examples of practical uses of the envelope of the family of orbits are discussed and illustrated by computer simulations. This material is appropriate for physics teachers and undergraduate students studying classical mechanics and orbital motions.

Sub-1% accuracy in fundamental stellar parameters from triply eclipsing systems

NASA Astrophysics Data System (ADS)

Prsa, Andrej

The current state-of-the-art level of accuracy in fundamental stellar parameters from eclipsing binary stars is 2-3%. Here we propose to use eclipsing triple stars to reduce the error bars by an entire order of magnitude, i.e. to 0.2-0.3%. This can be done because a presence of the third component breaks most of the degeneracy inherent in binary systems between the inclination and stellar sizes. We detail the feasibility arguments and foresee that these results will provide exceptional benchmark objects for stringent tests of stellar evolution and population models. The formation channel of close binary stars (with separations of several stellar radii) is a matter of debate. It is clear that close binaries cannot form in situ because (1) the physical radius of a star shrinks by a large factor between birth and the main sequence, yet many main-sequence stars have companions orbiting at a distance of only a few stellar radii, and (2) in current theories of planet formation, the region within 0.1 AU of a protostar is too hot and rarefied for a Jupiter-mass planet to form, yet many hot jupiters are observed at such distances. Current theories of dynamic orbital evolution attribute orbital shrinking to Kozai cycles and tidal friction, which are long-lasting, perturbative effects that take Gyrs to shrink orbits by 1-2 orders of magnitude. This implies that, if a binary star system has a tertiary companion, it will be in a hierarchical structure, and any disruptive orbital encounters should be exceedingly rare after a certain period. The Kepler satellite observed continuously over 2800 eclipsing binary stars over 4 years of its mission lifetime. The ultra-high precision photometry and essentially uninterrupted time coverage enables us to time the eclipses to a 6 second precision. Because of the well understood physics that governs the orbital motion of two bodies around the center of mass, the expected times of eclipses can be predicted to a fraction of a second. When other physical processes interplay, such as apsidal motion, mass transfer or third body interactions, the times of eclipses deviate from predictions: they either come early or late. These deviations are called eclipse timing variations (ETVs) and can range from a few seconds to a few hours. Our team measured ETVs for the entire Kepler data-set of eclipsing binaries and found 516 that demonstrate significant deviations. Of those, 16 show strong interactions between the binary system and the tertiary component that significantly affects the binary orbit within a single encounter. This observed rate of dynamical perturbation events is unexpectedly high and at odds with current theories. We propose to study these objects in great detail: (1) to apply a developed photodynamical code to model multiple body interactions; (2) to fully solve orbital dynamics of these interacting bodies using all available Kepler data, deriving masses of all objects to better than 1%; (3) to measure the occurrence rate of strong orbital interactions in multiple systems and compare it to the predicted rates; (4) to hypothesize and simulate additional evolution channels that could potentially lead to such a high occurrence rate of disruptive events; and (5) to integrate these systems over time and test whether this dynamic evolution can cause efficient orbital tightening and the creation of short period binaries. The team consists of a PI who has experience with Kepler satellite's idiosyncrasies, two postdoctoral fellows, one graduate student, and six undergraduate students that will invest their summer months to learn about multiple body interactions. The proposed study has far-reaching research goals in stellar and planetary science astrophysics, a strong educational/training component and is aligned with NASA's objectives as outlined in the NRA call. Kepler is the only instrument that can provide the accuracy and temporal coverage required for the execution of this project.

Contraction of high eccentricity satellite orbits using uniformly regular KS canonical elements with oblate diurnally varying atmosphere.

NASA Astrophysics Data System (ADS)

Raj, Xavier James

2016-07-01

Accurate orbit prediction of an artificial satellite under the influence of air drag is one of the most difficult and untraceable problem in orbital dynamics. The orbital decay of these satellites is mainly controlled by the atmospheric drag effects. The effects of the atmosphere are difficult to determine, since the atmospheric density undergoes large fluctuations. The classical Newtonian equations of motion, which is non linear is not suitable for long-term integration. Many transformations have emerged in the literature to stabilize the equations of motion either to reduce the accumulation of local numerical errors or allowing the use of large integration step sizes, or both in the transformed space. One such transformation is known as KS transformation by Kustaanheimo and Stiefel, who regularized the nonlinear Kepler equations of motion and reduced it into linear differential equations of a harmonic oscillator of constant frequency. The method of KS total energy element equations has been found to be a very powerful method for obtaining numerical as well as analytical solution with respect to any type of perturbing forces, as the equations are less sensitive to round off and truncation errors. The uniformly regular KS canonical equations are a particular canonical form of the KS differential equations, where all the ten KS Canonical elements αi and βi are constant for unperturbed motion. These equations permit the uniform formulation of the basic laws of elliptic, parabolic and hyperbolic motion. Using these equations, developed analytical solution for short term orbit predictions with respect to Earth's zonal harmonic terms J2, J3, J4. Further, these equations were utilized to include the canonical forces and analytical theories with air drag were developed for low eccentricity orbits (e < 0.2) with different atmospheric models. Using uniformly regular KS canonical elements developed analytical theory for high eccentricity (e > 0.2) orbits by assuming the atmosphere to be oblate only. In this paper a new non-singular analytical theory is developed for the motion of high eccentricity satellite orbits with oblate diurnally varying atmosphere in terms of the uniformly regular KS canonical elements. The analytical solutions are generated up to fourth-order terms using a new independent variable and c (a small parameter dependent on the flattening of the atmosphere). Due to symmetry, only two of the nine equations need to be solved analytically to compute the state vector and change in energy at the end of each revolution. The theory is developed on the assumption that density is constant on the surfaces of spheroids of fixed ellipticity ɛ (equal to the Earth's ellipticity, 0.00335) whose axes coincide with the Earth's axis. Numerical experimentation with the analytical solution for a wide range of perigee height, eccentricity, and orbital inclination has been carried out up to 100 revolutions. Comparisons are made with numerically integrated values and found that they match quite well. Effectiveness of the present analytical solutions will be demonstrated by comparing the results with other analytical solutions in the literature.

Precise Orbital and Geodetic Parameter Estimation using SLR Observations for ILRS AAC

NASA Astrophysics Data System (ADS)

Kim, Young-Rok; Park, Eunseo; Oh, Hyungjik Jay; Park, Sang-Young; Lim, Hyung-Chul; Park, Chandeok

2013-12-01

In this study, we present results of precise orbital geodetic parameter estimation using satellite laser ranging (SLR) observations for the International Laser Ranging Service (ILRS) associate analysis center (AAC). Using normal point observations of LAGEOS-1, LAGEOS-2, ETALON-1, and ETALON-2 in SLR consolidated laser ranging data format, the NASA/ GSFC GEODYN II and SOLVE software programs were utilized for precise orbit determination (POD) and finding solutions of a terrestrial reference frame (TRF) and Earth orientation parameters (EOPs). For POD, a weekly-based orbit determination strategy was employed to process SLR observations taken from 20 weeks in 2013. For solutions of TRF and EOPs, loosely constrained scheme was used to integrate POD results of four geodetic SLR satellites. The coordinates of 11 ILRS core sites were determined and daily polar motion and polar motion rates were estimated. The root mean square (RMS) value of post-fit residuals was used for orbit quality assessment, and both the stability of TRF and the precision of EOPs by external comparison were analyzed for verification of our solutions. Results of post-fit residuals show that the RMS of the orbits of LAGEOS-1 and LAGEOS-2 are 1.20 and 1.12 cm, and those of ETALON-1 and ETALON-2 are 1.02 and 1.11 cm, respectively. The stability analysis of TRF shows that the mean value of 3D stability of the coordinates of 11 ILRS core sites is 7.0 mm. An external comparison, with respect to International Earth rotation and Reference systems Service (IERS) 08 C04 results, shows that standard deviations of polar motion XP and YP are 0.754 milliarcseconds (mas) and 0.576 mas, respectively. Our results of precise orbital and geodetic parameter estimation are reasonable and help advance research at ILRS AAC.

Investigation of probabilistic orbital evolution of near-Earth asteroids moving in the vicinity of resonances with Mercury

NASA Astrophysics Data System (ADS)

Galushina, T. Yu.; Titarenko, E. Yu

2014-12-01

The purpose of this work is the investigation of probabilistic orbital evolution of near-Earth asteroids (NEA) moving in the vicinity of resonances with Mercury. In order to identify such objects the equations of all NEA motion have been integrated on the time interval (1000, 3000 years). The initial data has been taken from the E. Bowell catalog on February 2014. The motion equations have been integrated numerically by Everhart method. The resonance characteristics are critical argument that defines the connection longitude of the asteroid and the planet and its time derivative, called resonance "band". The study has identified 15 asteroids moving in the vicinity of different resonances with Mercury. Six of them (52381 1993 HA, 172034 2001 WR1, 2008 VB1, 2009 KT4, 2013 CQ35, 2013 TH) move in the vicinity of the resonance 1/6, five of them (142561 2002 TX68, 159608 2002 AC2, 241370 2008 LW8, 2006 UR216, 2009 XB2) move in the vicinity of the resonance 1/9 and one by one asteroid moves in the vicinity of resonances 1/3, 1/7, 1/8 and 2/7 (2006 SE6, 2002 CV46, 2013 CN35 and 2006 VY2 respectively). The orbits of all identified asteroids have been improved by least square method using the available optical observations and probabilistic orbital evolution has been investigated. Improvement have been carried out at the time of the best conditionality in accounting perturbations from the major planets, Pluto, Moon, Ceres, Pallas and Vesta, the relativistic effects from the Sun and the Solar oblateness. The estimation of the nonlinearity factor has showed that for all the considered NEA it does not exceed the critical value of 0.1, which makes it possible to use the linear method for constructing the initial probability domain. The domain has been built in the form of an ellipsoid in six-dimensional phase space of coordinates and velocity components on the base of the full covariance matrix, the center of ellipsoid is the nominal orbit obtained by improving. The 10 000 clones distributed according to the normal law has been chosen in the initial probability domain. The nonlinear method by numerical integration of the differential equations of each clone motion has been used for study of probabilistic orbital evolution. The force model has corresponded to the model used in the improvement. The time interval has been limited by ephemeris DE406 and accuracy of integration and has been amounted for different objects from two to six thousand years. As a result of the orbit improvement from the available optical positional observations it has been turned out that the orbits of NEA 2006 SE6, 2009 KT4, 2013 CQ35, 2013 TH, 2002 CV46, 2013 CN35 and 2006 VY2 are poorly defined, that does not allow to conclude about their resonance capture. The remaining objects can be divided into two classes. Asteroids 172034 2001 WR1, 2008 VB1, 159608 2002 AC2 and 2006 UR216 move in the vicinity of the resonance over the entire interval of the study. Probability domains of NEA 52381 1993 HA, 142561 2002 TX68, 241370 2008 LW8 и 2009 XB2 are increase significantly under the influence of close encounters, and part of clones are out of resonance. It should be noted that for all the considered objects the critical argument varies around the moving center of libration or circulates that suggests instability resonance.

Thermally induced vibrations of smart solar panel in a low-orbit satellite

NASA Astrophysics Data System (ADS)

Azadi, E.; Fazelzadeh, S. Ahmad; Azadi, M.

2017-03-01

In this paper, a smart flexible satellite moving in a circular orbit with two flexible panels are studied. The panels have been modeled as clamped-free-free-free rectangular plates with attached piezoelectric actuators. It is assumed that the satellite has a pitch angle rotation maneuver. Rapid temperature changes at day-night transitions in orbit generate time dependent bending moments. Satellite maneuver and temperature varying induce vibrations in the appendages. So, to simulate the system, heat radiation effects on the appendages have been considered. The nonlinear equations of motion and the heat transfer equations are coupled and solved simultaneously. So, the governing equations of motion are nonlinear and very complicated ones. Finally, the whole system is simulated and the effects of the heat radiation, radius of the orbit, piezoelectric voltages, and piezoelectric locations on the response of the system are studied.

Effect of passengers' active head tilt and opening/closure of eyes on motion sickness in lateral acceleration environment of cars.

PubMed

Wada, Takahiro; Yoshida, Keigo

2016-08-01

This study examined the effect of passengers' active head-tilt and eyes-open/eyes-closed conditions on the severity of motion sickness in the lateral acceleration environment of cars. In the centrifugal head-tilt condition, participants intentionally tilted their heads towards the centrifugal force, whereas in the centripetal head-tilt condition, the participants tilted their heads against the centrifugal acceleration. The eyes-open and eyes-closed cases were investigated for each head-tilt condition. In the experimental runs, the sickness rating in the centripetal head-tilt condition was significantly lower than that in the centrifugal head-tilt condition. Moreover, the sickness rating in the eyes-open condition was significantly lower than that in the eyes-closed condition. The results suggest that an active head-tilt motion against the centrifugal acceleration reduces the severity of motion sickness both in the eyes-open and eyes-closed conditions. They also demonstrate that the eyes-open condition significantly reduces the motion sickness even when the head-tilt strategy is used. Practitioner Summary: Little is known about the effect of head-tilt strategies on motion sickness. This study investigated the effects of head-tilt direction and eyes-open/eyes-closed conditions on motion sickness during slalom automobile driving. Passengers' active head tilt towards the centripetal direction and the eyes-open condition greatly reduce the severity of motion sickness.

The self-calibration method for multiple systems at the CHARA Array

NASA Astrophysics Data System (ADS)

O'Brien, David

The self-calibration method, a new interferometric technique at the CHARA Array, has been used to derive orbits for several spectroscopic binaries. This method uses the wide component of a hierarchical triple system to calibrate visibility measurements of the triple's close binary system. At certain baselines and separations, the calibrator in one of these systems can be observed quasi-simultaneously with the target. Depending on the orientation of the CHARA observation baseline relative to the orientation of the wide orbit of the triple system, separated fringe packets may be observed. A sophisticated observing scheme must be put in place to ensure the existence of separated fringe packets on nights of observation. Prior to the onset of this project, the reduction of separated fringe packet data had never included the goal of deriving visibilities for both fringe packets, so new data reduction software has been written. Visibilities obtained with separated fringe packet data for the target close binary are run through both Monte Carlo simulations and grid search programs in order to determine the best-fit orbital elements of the close binary. Several targets have been observed in this fashion, and orbits have been derived for seven targets, including three new orbits. Derivation of the orbit of the close pair in a triple system allows for the calculation of the mutual inclination, which is the angle between the planes of the wide and close orbit. Knowledge of this quantity may give insight into the formation processes that create multiple star systems. INDEX WORDS: Long-baseline interferometry, Self calibration, Separated fringe packets, Triple systems, Close binaries, Multiple systems, Orbital parameters, Near-infrared interferometry

Exciting an Initially Cold Asteroid Belt Through a Planetary Instability

NASA Astrophysics Data System (ADS)

Deienno, Rogerio; Izidoro, Andre; Morbidelli, Alessandro; Gomes, Rodney; Nesvorny, David; Raymond, Sean N.

2018-04-01

The main asteroid belt (MB) is low in mass but dynamically excited, with much larger eccentricities and inclinations than the planets. In recent years, the Grand Tack model has been the predominant model capable of reconciling the formation of the terrestrial planets with a depleted but excited MB. Despite this success, the Grand Tack is still not generally accepted because of uncertainties in orbital migration. It was recently proposed that chaotic early evolution of Jupiter and Saturn could excite the initially cold MB. However, hydrodynamical simulations predict that the giant planets should generally emerge from the gas disk phase on orbits characterized by resonant and regular motion. Here we propose a new mechanism to excite the MB during the giant planets' ('Nice model') instability, which is expected to have included repeated close encounters between Jupiter and one or more ice giants ('Jumping Jupiter' -- JJ). We show that when Jupiter temporarily reaches a high enough level of excitation, both in eccentricity and inclination, it induces strong forced vectors of eccentricity and inclination within the MB region. Because during the JJ instability Jupiter's orbit 'jumps' around, forced vectors keep changing both in magnitude and phase throughout the whole MB region. The entire cold primordial MB can thus be excited as a natural outcome of the JJ instability. Furthermore, we show that the subsequent evolution of the Solar System is capable of reshaping the resultant MB to its present day orbital state, and that a strong mass depletion is always associated to the JJ instability phase.

Closed almost-periodic orbits in semiclassical quantization of generic polygons

PubMed

Biswas

2000-05-01

Periodic orbits are the central ingredients of modern semiclassical theories and corrections to these are generally nonclassical in origin. We show here that, for the class of generic polygonal billiards, the corrections are predominantly classical in origin owing to the contributions from closed almost-periodic (CAP) orbit families. Furthermore, CAP orbit families outnumber periodic families but have comparable weights. They are hence indispensable for semiclassical quantization.

Software package for modeling spin-orbit motion in storage rings

NASA Astrophysics Data System (ADS)

Zyuzin, D. V.

2015-12-01

A software package providing a graphical user interface for computer experiments on the motion of charged particle beams in accelerators, as well as analysis of obtained data, is presented. The software package was tested in the framework of the international project on electric dipole moment measurement JEDI (Jülich Electric Dipole moment Investigations). The specific features of particle spin motion imply the requirement to use a cyclic accelerator (storage ring) consisting of electrostatic elements, which makes it possible to preserve horizontal polarization for a long time. Computer experiments study the dynamics of 106-109 particles in a beam during 109 turns in an accelerator (about 1012-1015 integration steps for the equations of motion). For designing an optimal accelerator structure, a large number of computer experiments on polarized beam dynamics are required. The numerical core of the package is COSY Infinity, a program for modeling spin-orbit dynamics.

Contact dynamics math model

NASA Technical Reports Server (NTRS)

Glaese, John R.; Tobbe, Patrick A.

1986-01-01

The Space Station Mechanism Test Bed consists of a hydraulically driven, computer controlled six degree of freedom (DOF) motion system with which docking, berthing, and other mechanisms can be evaluated. Measured contact forces and moments are provided to the simulation host computer to enable representation of orbital contact dynamics. This report describes the development of a generalized math model which represents the relative motion between two rigid orbiting vehicles. The model allows motion in six DOF for each body, with no vehicle size limitation. The rotational and translational equations of motion are derived. The method used to transform the forces and moments from the sensor location to the vehicles' centers of mass is also explained. Two math models of docking mechanisms, a simple translational spring and the Remote Manipulator System end effector, are presented along with simulation results. The translational spring model is used in an attempt to verify the simulation with compensated hardware in the loop results.

Chaotic motion of a harmonically bound charged particle in a magnetic field, in the presence of a half-plane barrier

NASA Astrophysics Data System (ADS)

Geurts, Bernard J.; Wiegel, Frederik W.; Creswick, Richard J.

1990-05-01

The motion in the plane of an harmonically bound charged particle interacting with a magnetic field and a half-plane barrier along the positive x-axis is studied. The magnetic field is perpendicular to the plane in which the particle moves. This motion is integrable in between collisions of the particle with the barrier. However, the overall motion of the particle is very complicated. Chaotic regions in phase space exist next to island structures associated with linearly stable periodic orbits. We study in detail periodic orbits of low period and in particular their bifurcation behavior. Independent sequences of period doubling bifurcations and resonant bifurcations are observed associated with independent fixed points in the Poincaré section. Due to the perpendicular magnetic field an orientation is induced on the plane and time-reversal symmetry is broken.

Utility of the CS and IOS approximations for calculating generalized phenomenological cross sections in atom-diatom systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fitz, D.E.; Kouri, D.J.; Liu, W.K.

1982-04-01

The calculation of shear viscosity and thermal conductivity coefficients in the presence of a magnetic field requires the accurate calculation of several types of generalized phenomenological cross sections in which velocity and angular momentum tensors are coupled with the orbital and rotational motion of the system. These cross sections are then averaged over energy in a fashion appropriate for the phenomenon of interest. The coupled states (CS) and/or infinite order sudden (IOS) approximations have been used to calculate several such cross sections for systems such as He-HCl, He-CO, He-H/sub 2/, HD-Ne, Ar-N/sub 2/, and Ne-H/sub 2/. Excellent results are obtainedmore » compared with close-coupled methods for cross sections which are symmetric in tensor index, especially in the CS approximation, and these results are not very sensitive to the choice of orbital wave parameter. On the other hand, the cross sections which are asymmetric in tensor index are much more sensitive to interference effects and are unsatisfactory in many cases.« less

Curves from Motion, Motion from Curves

DTIC Science & Technology

2000-01-01

De linearum curvarum cum lineis rectis comparatione dissertatio geometrica - an appendix to a treatise by de Lalouv~re (this was the only publication... correct solution to the problem of motion in the gravity of a permeable rotating Earth, considered by Torricelli (see §3). If the Earth is a homogeneous...in 1686, which contains the correct solution as part of a remarkably comprehensive theory of orbital motions under centripetal forces. It is a

Orbital Motion of Electrically Charged Spheres in Microgravity

ERIC Educational Resources Information Center

Banerjee, Shubho; Andring, Kevin; Campbell, Desmond; Janeski, John; Keedy, Daniel; Quinn, Sean; Hoffmeister, Brent

2008-01-01

The similar mathematical forms of Coulomb's law and Newton's law of gravitation suggest that two uniformly charged spheres should be able to orbit each other just as two uniform spheres of mass are known to do. In this paper we describe an experiment that we performed to demonstrate such an orbit. This is the first published account of a…

Late type close binary system CM Dra

NASA Astrophysics Data System (ADS)

Kalomeni, Belinda

2015-08-01

In this study, we present new observations of the close binary system CM Dra. We analyzed all the available data of the system and estimated the physical parameters of the system stars highly accurately. Using the newly obtained parameters the distance of the system is determined to be 11.6 pc. A possible giant planet orbiting the close binary system has been detected. This orbital period would likely make it one of the longest known orbital period planet.

Photometrical research geostationary satellite "SBIRS GEO-2"

NASA Astrophysics Data System (ADS)

Sukhov, P. P.; Epishev, V. P; Sukhov, K. P; Kudak, V. I.

The multicolor photometrical observations GSS "Sbirs Geo-2" were carried in B,V,R filters out during the autumn equinox 2014 and spring 2015 y. Periodic appearance of many light curves and dips of mirror reflections suggests that the GSS was not in orbit in a static position, predetermined three-axis orientation and in dynamic motion. On the basis of computer modeling suggests the following dynamics GSS "Sbirs Geo-2" in orbit. Helically scanning the visible Earth's surface infrared satellite sensors come with period P1 = 15.66 sec. and the rocking of the GSS about the direction of the motion vector of the satellite in orbit with P2 = 62.64 sec., most likely with the purpose to survey the greatest possible portion of the earth's surface.

Open quantum random walks: Bistability on pure states and ballistically induced diffusion

NASA Astrophysics Data System (ADS)

Bauer, Michel; Bernard, Denis; Tilloy, Antoine

2013-12-01

Open quantum random walks (OQRWs) deal with quantum random motions on a line for systems with internal and orbital degrees of freedom. The internal system behaves as a quantum random gyroscope coding for the direction of the orbital moves. We reveal the existence of a transition, depending on OQRW moduli, in the internal system behaviors from simple oscillations to random flips between two unstable pure states. This induces a transition in the orbital motions from the usual diffusion to ballistically induced diffusion with a large mean free path and large effective diffusion constant at large times. We also show that mixed states of the internal system are converted into random pure states during the process. We touch upon possible experimental realizations.

Accuracy of gravitational physics tests using ranges to the inner planets

NASA Technical Reports Server (NTRS)

Ashby, N.; Bender, P.

1981-01-01

A number of different types of deviations from Kepler's laws for planetary orbits can occur in nonNewtonian metric gravitational theories. These include secular changes in all of the orbital elements and in the mean motion, plus additional periodic perturbations in the coordinates. The first order corrections to the Keplerian motion of a single planet around the Sun due to the parameterized post Newtonian theory parameters were calculated as well as the corrections due to the solar quadrupole moment and a possible secular change in the gravitational constant. The results were applied to the case of proposed high accuracy ranging experiments from the Earth to a Mercury orbiting spacecraft in order to see how well the various parameters can be determined.

Long-term orbit prediction for the Venus Radar Mapper Mission using an averaging method

NASA Technical Reports Server (NTRS)

Kwok, J. H.

1984-01-01

A set of singly averaged equations of motion are presented and applied to long-term orbit prediction of an orbiting spacecraft around a slowly rotating planet, using the Venus Radar Mapper Mission as an example. The equations of motion used are valid for all eccentricities less than one. The disturbing potentials used include nonsphericity of the Venus gravity field and third-body effects due to the sun. Recursive relationships are used in the expansion and evaluation of these potentials and their respective partial derivatives. Special care is taken to optimize computational efficiency. The averaging method is compared with high precision Cowell's method using a desktop microcomputer and shows computational saving of about two orders of magnitude.

Indexing and retrieving motions of characters in close contact.

PubMed

Ho, Edmond S L; Komura, Taku

2009-01-01

Human motion indexing and retrieval are important for animators due to the need to search for motions in the database which can be blended and concatenated. Most of the previous researches of human motion indexing and retrieval compute the Euclidean distance of joint angles or joint positions. Such approaches are difficult to apply for cases in which multiple characters are closely interacting with each other, as the relationships of the characters are not encoded in the representation. In this research, we propose a topology-based approach to index the motions of two human characters in close contact. We compute and encode how the two bodies are tangled based on the concept of rational tangles. The encoded relationships, which we define as TangleList, are used to determine the similarity of the pairs of postures. Using our method, we can index and retrieve motions such as one person piggy-backing another, one person assisting another in walking, and two persons dancing / wrestling. Our method is useful to manage a motion database of multiple characters. We can also produce motion graph structures of two characters closely interacting with each other by interpolating and concatenating topologically similar postures and motion clips, which are applicable to 3D computer games and computer animation.

Spacecraft formation control using analytical finite-duration approaches

NASA Astrophysics Data System (ADS)

Ben Larbi, Mohamed Khalil; Stoll, Enrico

2018-03-01

This paper derives a control concept for formation flight (FF) applications assuming circular reference orbits. The paper focuses on a general impulsive control concept for FF which is then extended to the more realistic case of non-impulsive thrust maneuvers. The control concept uses a description of the FF in relative orbital elements (ROE) instead of the classical Cartesian description since the ROE provide a direct insight into key aspects of the relative motion and are particularly suitable for relative orbit control purposes and collision avoidance analysis. Although Gauss' variational equations have been first derived to offer a mathematical tool for processing orbit perturbations, they are suitable for several different applications. If the perturbation acceleration is due to a control thrust, Gauss' variational equations show the effect of such a control thrust on the Keplerian orbital elements. Integrating the Gauss' variational equations offers a direct relation between velocity increments in the local vertical local horizontal frame and the subsequent change of Keplerian orbital elements. For proximity operations, these equations can be generalized from describing the motion of single spacecraft to the description of the relative motion of two spacecraft. This will be shown for impulsive and finite-duration maneuvers. Based on that, an analytical tool to estimate the error induced through impulsive maneuver planning is presented. The resulting control schemes are simple and effective and thus also suitable for on-board implementation. Simulations show that the proposed concept improves the timing of the thrust maneuver executions and thus reduces the residual error of the formation control.

Orbital motion in T Tauri binary systems

NASA Astrophysics Data System (ADS)

Woitas, J.; Köhler, R.; Leinert, Ch.

2001-04-01

Using speckle-interferometry we have carried out repeated measurements of relative positions for the components of 34 T Tauri binary systems. The projected separation of these components is low enough that orbital motion is expected to be observable within a few years. In most cases orbital motion has indeed been detected. The observational data is discussed in a manner similar to Ghez et al. (\\cite{Ghez95}). However, we extend their study to a larger number of objects and a much longer timespan. The database presented in this paper is valuable for future visual orbit determinations. It will yield empirical masses for T Tauri stars that now are only poorly known. The available data is however not sufficient to do this at the present time. Instead, we use short series of orbital data and statistical distributions of orbital parameters to derive an average system mass that is independent of theoretical assumptions about the physics of PMS stars. For our sample this mass is 2.0 Msun and thus in the order of magnitude one expects for the mass sum of two T Tauri stars. It is also comparable to mass estimates obtained for the same systems using theoretical PMS evolutionary models. Based on observations collected at the German-Spanish Astronomical Center on Calar Alto, Spain, and at the European Southern Observatory, La Silla, Chile. Table A.1 is only available in electronic form at the CDS, via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5), or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/369/249

Group theoretical formulation of free fall and projectile motion

NASA Astrophysics Data System (ADS)

Düztaş, Koray

2018-07-01

In this work we formulate the group theoretical description of free fall and projectile motion. We show that the kinematic equations for constant acceleration form a one parameter group acting on a phase space. We define the group elements ϕ t by their action on the points in the phase space. We also generalize this approach to projectile motion. We evaluate the group orbits regarding their relations to the physical orbits of particles and unphysical solutions. We note that the group theoretical formulation does not apply to more general cases involving a time-dependent acceleration. This method improves our understanding of the constant acceleration problem with its global approach. It is especially beneficial for students who want to pursue a career in theoretical physics.

Parabolic flight - Loss of sense of orientation

NASA Technical Reports Server (NTRS)

Lackner, J. R.; Graybiel, A.

1979-01-01

On the earth, or in level flight, a blindfolded subject being rotated at constant velocity about his recumbent long body axis experiences illusory orbital motion of his body in the opposite direction. By contrast, during comparable rotation in the free-fall phase of parabolic flight, no body motion is perceived and all sense of external orientation may be lost; when touch and pressure stimulation is applied to the body surface, a sense of orientation is reestablished immediately. The increased gravitoinertial force period of a parabola produces an exaggeration of the orbital motion experienced in level flight. These observations reveal an important influence of touch, pressure, and kinesthetic information on spatial orientation and provide a basis for understanding many of the postural illusions reported by astronauts in space flight.

Spontaneous mode-selection in the self-propelled motion of a solid/liquid composite driven by interfacial instability

NASA Astrophysics Data System (ADS)

Takabatake, Fumi; Magome, Nobuyuki; Ichikawa, Masatoshi; Yoshikawa, Kenichi

2011-03-01

Spontaneous motion of a solid/liquid composite induced by a chemical Marangoni effect, where an oil droplet attached to a solid soap is placed on a water phase, was investigated. The composite exhibits various characteristic motions, such as revolution (orbital motion) and translational motion. The results showed that the mode of this spontaneous motion switches with a change in the size of the solid scrap. The essential features of this mode-switching were reproduced by ordinary differential equations by considering nonlinear friction with proper symmetry.

Model-independent and fast determination of optical functions in storage rings via multiturn and closed-orbit data

NASA Astrophysics Data System (ADS)

Riemann, Bernard; Grete, Patrick; Weis, Thomas

2011-06-01

Multiturn (or turn-by-turn) data acquisition has proven to be a new source of direct measurements for Twiss parameters in storage rings. On the other hand, closed-orbit measurements are a long-known tool for analyzing closed-orbit perturbations with conventional beam position monitor (BPM) systems and are necessarily available at every storage ring. This paper aims at combining the advantages of multiturn measurements and closed-orbit data. We show that only two multiturn BPMs and four correctors in one localized drift space in the storage ring (diagnostic drift) are sufficient for model-independent and absolute measuring of β and φ functions at all BPMs, including the conventional ones, instead of requiring all BPMs being equipped with multiturn electronics.

Stability of Multi-Planet Systems in the Alpha Centauri System

NASA Technical Reports Server (NTRS)

Lissauer, Jack J.

2017-01-01

We evaluate the extent of the regions within the alpha Centauri AB star system where small planets are able to orbit for billion-year timescales (Quarles & Lissauer 2016, Astron. J. 151, 111), as well as how closely-spaced planetary orbits can be within those regions in which individual planets can survive. Although individual planets on low inclination, low eccentricity, orbits can survive throughout the habitable zones of both stars, perturbations from the companion star imply that the spacing of planets in multi-planet systems within the habitable zones of each star must be significantly larger than the spacing of similar multi-planet systems orbiting single stars in order to be long-lived. Because the binary companion induces a forced eccentricity upon the orbits of planets in orbit around either star, appropriately-aligned circumstellar orbits with small initial eccentricities are stable to slightly larger initial semimajor axes than are initially circular orbits. Initial eccentricities close to forced eccentricities can have a much larger affect on how closely planetary orbits can be spaced, and therefore on how many planets may remain in the habitable zones, although the required spacing remains significantly higher than for planets orbiting single stars.

Illusory visual motion stimulus elicits postural sway in migraine patients

PubMed Central

Imaizumi, Shu; Honma, Motoyasu; Hibino, Haruo; Koyama, Shinichi

2015-01-01

Although the perception of visual motion modulates postural control, it is unknown whether illusory visual motion elicits postural sway. The present study examined the effect of illusory motion on postural sway in patients with migraine, who tend to be sensitive to it. We measured postural sway for both migraine patients and controls while they viewed static visual stimuli with and without illusory motion. The participants’ postural sway was measured when they closed their eyes either immediately after (Experiment 1), or 30 s after (Experiment 2), viewing the stimuli. The patients swayed more than the controls when they closed their eyes immediately after viewing the illusory motion (Experiment 1), and they swayed less than the controls when they closed their eyes 30 s after viewing it (Experiment 2). These results suggest that static visual stimuli with illusory motion can induce postural sway that may last for at least 30 s in patients with migraine. PMID:25972832

SODA In Train Swarm Example

NASA Image and Video Library

2017-07-13

SODA, Swarm Orbital Dynamics Advisor, a tool that provides the orbital maneuvers required to achieve a desired type of relative swarm motion for satellite missions. For the in-train swarm type, the objective is to phase the satellites ahead and behind one another to achieve a string-of-pearls relative position configuration. SODA maneuvers each satellite by performing a two-impulse elliptical transfer orbit from and back to the same orbit, known as a phasing maneuver.

A Survey of Uncontrolled Satellite reentry and Impact Prediction

DTIC Science & Technology

1993-09-23

NORAD produces " element sets " which are mean values of the orbital elements that have been obtained by removing the periodic orbital variations in a...Final Element Set --a listing of the final orbit parameters. The eccentricity and mean motion data from the listing were used in the investigation...yielded altitude and orbital elements as a function of time. Computer run results for these simulations were extremely long and therefore the decision was

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schäfer, Gerhard

The current knowledge in the post-Newtonian (PN) dynamics and motion of non-spinning and spinning compact binaries will be presented based on the Arnowitt-Deser-Misner Hamiltonian approach to general relativity. The presentation will cover the binary dynamics with non-spinning components up to the 4PN order and for spinning binaries up to the next-to-next-to-leading order in the spin-orbit and spin-spin couplings. Radiation reaction will be treated for both non-spinning and spinning binaries. Explicit analytic expressions for the motion will be given, innermost stable circular orbits will be discussed.

Bound Motion of Bodies and Paticles in the Rotating Systems

NASA Astrophysics Data System (ADS)

Pardy, Miroslav

2007-04-01

The Lagrange theory of particle motion in the noninertial systems is applied to the Foucault pendulum, isosceles triangle pendulum and the general triangle pendulum swinging on the rotating Earth. As an analogue, planet orbiting in the rotating galaxy is considered as the giant galactic gyroscope. The Lorentz equation and the Bargmann-Michel-Telegdi equations are generalized for the rotation system. The knowledge of these equations is inevitable for the construction of LHC where each orbital proton “feels” the Coriolis force caused by the rotation of the Earth.

How I Learned to Stop Worrying and Love Eclipsing Binaries

NASA Astrophysics Data System (ADS)

Moe, Maxwell Cassady

Relatively massive B-type stars with closely orbiting stellar companions can evolve to produce Type Ia supernovae, X-ray binaries, millisecond pulsars, mergers of neutron stars, gamma ray bursts, and sources of gravitational waves. However, the formation mechanism, intrinsic frequency, and evolutionary processes of B-type binaries are poorly understood. As of 2012, the binary statistics of massive stars had not been measured at low metallicities, extreme mass ratios, or intermediate orbital periods. This thesis utilizes large data sets of eclipsing binaries to measure the physical properties of B-type binaries in these previously unexplored portions of the parameter space. The updated binary statistics provide invaluable insight into the formation of massive stars and binaries as well as reliable initial conditions for population synthesis studies of binary star evolution. We first compare the properties of B-type eclipsing binaries in our Milky Way Galaxy and the nearby Magellanic Cloud Galaxies. We model the eclipsing binary light curves and perform detailed Monte Carlo simulations to recover the intrinsic properties and distributions of the close binary population. We find the frequency, period distribution, and mass-ratio distribution of close B-type binaries do not significantly depend on metallicity or environment. These results indicate the formation of massive binaries are relatively insensitive to their chemical abundances or immediate surroundings. Second, we search for low-mass eclipsing companions to massive B-type stars in the Large Magellanic Cloud Galaxy. In addition to finding such extreme mass-ratio binaries, we serendipitously discover a new class of eclipsing binaries. Each system comprises a massive B-type star that is fully formed and a nascent low-mass companion that is still contracting toward its normal phase of evolution. The large low-mass secondaries discernibly reflect much of the light they intercept from the hot B-type stars, thereby producing sinusoidal variations in perceived brightness as they orbit. These nascent eclipsing binaries are embedded in the hearts of star-forming emission nebulae, and therefore provide a unique snapshot into the formation and evolution of massive binaries and stellar nurseries. We next examine a large sample of B-type eclipsing binaries with intermediate orbital periods. To achieve such a task, we develop an automated pipeline to classify the eclipsing binaries, measure their physical properties from the observed light curves, and recover the intrinsic binary statistics by correcting for selection effects. We find the population of massive binaries at intermediate separations differ from those orbiting in close proximity. Close massive binaries favor small eccentricities and have correlated component masses, demonstrating they coevolved via competitive accretion during their formation in the circumbinary disk. Meanwhile, B-type binaries at slightly wider separations are born with large eccentricities and are weighted toward extreme mass ratios, indicating the components formed relatively independently and subsequently evolved to their current configurations via dynamical interactions. By using eclipsing binaries as accurate age indicators, we also reveal that the binary orbital eccentricities and the line-of-sight dust extinctions are anticorrelated with respect to time. These empirical relations provide robust constraints for tidal evolution in massive binaries and the evolution of the dust content in their surrounding environments. Finally, we compile observations of early-type binaries identified via spectroscopy, eclipses, long-baseline interferometry, adaptive optics, lucky imaging, high-contrast photometry, and common proper motion. We combine the samples from the various surveys and correct for their respective selection effects to determine a comprehensive nature of the intrinsic binary statistics of massive stars. We find the probability distributions of primary mass, secondary mass, orbital period, and orbital eccentricity are all interrelated. These updated multiplicity statistics imply a greater frequency of low-mass X-ray binaries, millisecond pulsars, and Type Ia supernovae than previously predicted.

Input profile for satellite orbit transfer by tether mechanism; Part I: Tether length profile using feed-forward procedure

NASA Astrophysics Data System (ADS)

Hokamoto, Shinji

This study deals with orbital transfer of a satellite using a tether extension / retrieval mechanism. Instead of using propellant for the orbital transfer, the present concept uses electrical energy. By controlling the pitch motion of the tether system, we can achieve a prescribed velocity of the satellite at a prescribed position. By cutting the tether at that instant, we can inject the satellite into a designed new orbit. This paper considers co-planar motion and proposes a technique to achieve the desired tether length, pitch angle, and pitch angular rate at a designated position in orbit by using only tether length control. These three state variables are adjusted to their target values in three consecutive sections in the orbit; 1) control for the angular momentum of the pitching motion, which implies to adjust the tether length, 2) control for the pitch angle, and 3) control for the pitch angular rate. In each section, a pitch acceleration profile can be formed by using Fourier series as an alternative input for tether length profile. Their coefficients can be obtained without numerical iterations by using the simple initial / final relationships for the pitch angle and pitch angular rate. Therefore, this proposed procedure requires less computational cost than a numerical search, is easily applicable for different models and orbits, and can cope with physical restrictions of the system, such as tether tension or maximum tether length. Furthermore, the resulting final states precisely coincide with the target values. To demonstrate that the proposed procedure can successfully generate proper input profiles, this paper presents an orbital transfer problem as an example, and verifies its effectiveness. The simulation results show that the maximum tether length is less than 5km, and that the tether tension is kept positive during the mission.

The motion of an Earth satellite after imposition of a non-holonomic third-order constraint

NASA Astrophysics Data System (ADS)

Dodonov, V. V.; Soltakhanov, Sh. Kh.; Yushkov, M. P.

2018-05-01

We consider the motion of an Earth satellite in the case when, starting from a certain instant of time, the magnitude of its acceleration remains unchanged. This requirement is equivalent to a second-order nonlinear non-holonomic constraint imposed to the satellite motion. The results of calculations are given for the motion of three Soviet satellites, two of which are located on highly elliptical orbits.

V342 Andromedae B is an eccentric-orbit eclipsing binary

NASA Astrophysics Data System (ADS)

Dimitrov, W.; Kamiński, K.; Lehmann, H.; Ligęza, P.; Fagas, M.; Bagińska, P.; Kwiatkowski, T.; Bąkowska, K.; Kowalczyk, A.; Polińska, M.; Bartczak, P.; Przybyszewska, A.; Kruszewski, A.; Kurzawa, K.; Schwarzenberg-Czerny, A.

2015-03-01

We present a photometric and spectroscopic study of the visual binary V342 Andromedae. Visual components of the system have angular separations of 3 arcseconds. We obtained two spectroscopic data sets. An examination of both the A and B component spectra reveals that the B component is a spectroscopic binary with an eccentric orbit. The orbital period, taken from the Hipparcos Catalog, agrees with the orbital period of the B component measured spectroscopically. We also collected a new set of photometric measurements. The argument of periastron is close to 270° and the orbit eccentricity is not seen in our photometric data. About five years after the first spectroscopic observations, a new set of spectroscopic data was obtained. We analysed the apsidal motion, but we did not find any significant changes in the orbital orientation. A Wilson-Devinney model was calculated based on the photometric and the radial velocity curves. The result shows two very similar stars with masses M1 = 1.27 ± 0.01 M⊙, M2 = 1.28 ± 0.01 M⊙, respectively. The radii are R1 = 1.21 ± 0.01 R⊙, R2 = 1.25 ± 0.01 R⊙, respectively. Radial velocity measurements of component A, the most luminous star in the system, reveal no significant periodic variations. We calculated the time of the eclipsing binary orbit's circularization, which is about two orders of magnitude shorter than the estimated age of the system. The discrepancies in the age estimation can be explained by the Kozai effect induced by the visual component A. The atmospheric parameters and the chemical abundances for the eclipsing pair, as well as the LSD profiles for both visual components, were calculated from two high-resolution, well-exposed spectra obtained on the 2-m class telescope. Based on spectroscopy obtained at the David Dunlap Observatory, University of Toronto, Canada, Poznań Spectroscopic Telescope 1, Poland and Thüringer Landessternwarte, Tautenburg, Germany.

Analysis of Probabilistic Orbital Evolution of the Asteroids 2011 CQ1 and 2011 MD

NASA Astrophysics Data System (ADS)

Sambarov, G. E.; Syusina, O. M.

2018-06-01

The orbital evolution of asteroids 2011 CQ1 and 2011 MD approaching to the Earth is investigated. The influence of perturbing forces on the accuracy of constructing the regions of their possible motions is investigated.

Two activities with a simple model of the solar system: discovering Kepler’s 3rd law and investigating apparent motion of Venus

NASA Astrophysics Data System (ADS)

Rovšek, Barbara; Guštin, Andrej

2018-01-01

An astronomy ‘experiment’ composed of three parts is described in the article. Being given necessary data a simple model of inner planets of the solar system is made in the first part with planets’ circular orbits using appropriate scale. In the second part revolution of the figurines used as model representations of the planets along their orbits is observed. In the third part of activity apparent motion of Venus with respect to the observer on the Earth is studied. In the second part of the paper problems are given, which relate to experimental activities and are designed to test if learning outcomes of the experiment have been achieved: if correlation between orbital radius and orbital velocity has been perceived, concepts related to motion of Venus as observed from the Earth have been acquired and periodicity recognized. Described astronomy ‘experiment’ was one of the three science experiments given to 11 and 12 years old students prior to Slovene science competition in 2017 (the call for competition is at www.dmfa.si, guidelines for the experiment (in Slovene) can be found at www.kresnickadmfa.si/files/2016/07/poskus_1617_r67p1_S.pdf). At the end of the paper the results obtained at competition are presented.

Conceptual design of an orbital debris collector

NASA Technical Reports Server (NTRS)

Odonoghue, Peter (Editor); Brenton, Brian; Chambers, Ernest; Schwind, Thomas; Swanhart, Christopher; Williams, Thomas

1991-01-01

The current Lower Earth Orbit (LEO) environment has become overly crowded with space debris. An evaluation of types of debris is presented in order to determine which debris poses the greatest threat to operation in space, and would therefore provide a feasible target for removal. A target meeting these functional requirements was found in the Cosmos C-1B Rocket Body. These launchers are spent space transporters which constitute a very grave risk of collision and fragmentation in LEO. The motion and physical characteristics of these rocket bodies have determined the most feasible method of removal. The proposed Orbital Debris Collector (ODC) device is designed to attach to the Orbital Maneuvering Vehicle (OMV), which provides all propulsion, tracking, and power systems. The OMV/ODC combination, the Rocket Body Retrieval Vehicle (RBRV), will match orbits with the rocket body, use a spin table to match the rotational motion of the debris, capture it, despin it, and remove it from orbit by allowing it to fall into the Earth's atmosphere. A disposal analysis is presented to show how the debris will be deorbited into the Earth's atmosphere. The conceptual means of operation of a sample mission is described.

About the possibility of magnetic and gravitational capture of the technogenic nanoparticles injected in the near-Earth space in high circular orbits

NASA Astrophysics Data System (ADS)

Kolesnikov, E. K.; Chernov, S. V.

2018-05-01

A detailed study of the conditions for the realization of the phenomena of magnetic and gravity capture (MGC) of nanoparticles (NP) injected into the near-Earth space in circular orbits with altitudes and inclinations characteristic for orbits of satellites of navigation systems (GLONASS, GPS, etc.) is carried out. Spherical aluminum oxide particles with radii from 4 to 100 nm were considered as injected particles. It was assumed that injection of NP is performed at various points of circular orbits with a height of 19130 km, an inclination angle to the equatorial plane equal to 64.8 degrees and a longitude of the ascending node of 0, 120 and 240 degrees. Calculations of the motion of nanoparticles in near-Earth space were performed for conditions of low level solar and geomagnetic activity. The results of numerical experiments show that for all the considered spatial orientations of the orbit of the parent body (PB) of the NP motion in the magnetic and gravitational capture mode with extremely long orbital existence times (more than two years) can be realized only for nanoparticles with radii in the narrow gap from 8.6 to 10.2 nm.

Sea ice motion measurements from Seasat SAR images

NASA Technical Reports Server (NTRS)

Leberl, F.; Raggam, J.; Elachi, C.; Campbell, W. J.

1983-01-01

Data from the Seasat synthetic aperture radar (SAR) experiment are analyzed in order to determine the accuracy of this information for mapping the distribution of sea ice and its motion. Data from observations of sea ice in the Beaufort Sea from seven sequential orbits of the satellite were selected to study the capabilities and limitations of spaceborne radar application to sea-ice mapping. Results show that there is no difficulty in identifying homologue ice features on sequential radar images and the accuracy is entirely controlled by the accuracy of the orbit data and the geometric calibration of the sensor. Conventional radargrammetric methods are found to serve well for satellite radar ice mapping, while ground control points can be used to calibrate the ice location and motion measurements in the cases where orbit data and sensor calibration are lacking. The ice motion was determined to be approximately 6.4 + or - 0.5 km/day. In addition, the accuracy of pixel location was found over land areas. The use of one control point in 10,000 sq km produced an accuracy of about + or 150 m, while with a higher density of control points (7 in 1000 sq km) the location accuracy improves to the image resolution of + or - 25 m. This is found to be applicable for both optical and digital data.

Time-resolved photometry of the nova remnants DM Gem, CP Lac, GI Mon, V400 Per, CT Ser and XX Tau

NASA Astrophysics Data System (ADS)

Rodríguez-Gil, P.; Torres, M. A. P.

2005-02-01

We present the first results of a photometric survey of poorly studied nova remnants in the Northern Hemisphere. The main results are as follows: DM Gem shows a modulation at 0.123 d (probably linked to the orbit) and rapid variations at ˜ 22 min. A moderate resolution spectrum taken at the time of the photometric observations shows intense He II 4686 and Bowen emission, characteristic of an intermediate polar or a SW Sex star. Variability at 0.127 d and intense flickering (or quasi-periodic oscillations) are the main features of the light curve of CP Lac. A 0.1-mag dip lasting for ˜ 45 min is observed in GI Mon, which could be an eclipse. A clear modulation (probably related to the orbital motion) either at 0.179 d or 0.152 d is observed in the B-band light curve of V400 Per. The results for CT Ser point to an orbital period close to 0.16 d. Intense flickering is also characteristic of this old nova. Finally, XX Tau shows a possible periodic signal near 0.14 d and displays fast variability at ˜ 24 min. Its brightness seems to be modulated at ˜ 5 d. We relate this long periodicity to the motion of an eccentric/tilted accretion disc in the binary. Based in part on observations made with the Jacobus Kapteyn Telescope, which was operated on the island of La Palma by the Isaac Newton Group in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias (IAC), and on observations made with the IAC80 telescope, operated on the island of Tenerife by the IAC in the Spanish Observatorio del Teide of the IAC. Observations were also obtained at the FLWO Observatory, a facility of the Smithsonian Institution.

Analysis of close encounters with Ganymede and Callisto using a genetic n-body algorithm

NASA Astrophysics Data System (ADS)

Winter, Philip M.; Galiazzo, Mattia A.; Maindl, Thomas I.

2018-05-01

In this work we describe a genetic algorithm which is used in order to study orbits of minor bodies in the frames of close encounters. We find that the algorithm in combination with standard orbital numerical integrators can be used as a good proxy for finding typical orbits of minor bodies in close encounters with planets and even their moons, saving a lot of computational time compared t0 long-term orbital numerical integrations. Here, we study close encounters of Centaurs with Callisto and Ganymede in particular. We also perform n-body numerical simulations for comparison. We find typical impact velocities to be between v rel = 20[v esc ] and v rel = 30[v esc ] for Ganymede and between v rel = 25[v esc ] and v rel = 35[v esc ] for Callisto.

Orbit period modulation for relative motion using continuous low thrust in the two-body and restricted three-body problems

NASA Astrophysics Data System (ADS)

Arnot, C. S.; McInnes, C. R.; McKay, R. J.; Macdonald, M.; Biggs, J.

2018-02-01

This paper presents rich new families of relative orbits for spacecraft formation flight generated through the application of continuous thrust with only minimal intervention into the dynamics of the problem. Such simplicity facilitates implementation for small, low-cost spacecraft with only position state feedback, and yet permits interesting and novel relative orbits in both two- and three-body systems with potential future applications in space-based interferometry, hyperspectral sensing, and on-orbit inspection. Position feedback is used to modify the natural frequencies of the linearised relative dynamics through direct manipulation of the system eigenvalues, producing new families of stable relative orbits. Specifically, in the Hill-Clohessy-Wiltshire frame, simple adaptations of the linearised dynamics are used to produce a circular relative orbit, frequency-modulated out-of-plane motion, and a novel doubly periodic cylindrical relative trajectory for the purposes of on-orbit inspection. Within the circular restricted three-body problem, a similar minimal approach with position feedback is used to generate new families of stable, frequency-modulated relative orbits in the vicinity of a Lagrange point, culminating in the derivation of the gain requirements for synchronisation of the in-plane and out-of-plane frequencies to yield a singly periodic tilted elliptical relative orbit with potential use as a Lunar far-side communications relay. The Δ v requirements for the cylindrical relative orbit and singly periodic Lagrange point orbit are analysed, and it is shown that these requirements are modest and feasible for existing low-thrust propulsion technology.

Astrometric and photometric measurements of binary stars with adaptive optics: observations from 2001 to 2006

NASA Astrophysics Data System (ADS)

Roberts, Lewis C.; Mason, Brian D.

2018-02-01

The adaptive optics system at the 3.6 m Advanced Electro-Optical System telescope was used to measure the astrometry and differential magnitude in I band of binary star systems between 2002 and 2006. We report 413 astrometric and photometric measurements of 373 stellar pairs. The astrometric measurements will be of use for future orbital determination, and the photometric measurements will be of use in estimating the spectral types of the component stars. For 21 binaries that had not been observed in decades, we are able to confirm that the systems share common proper motion. Candidate new companions were detected in 24 systems; for these we show the discovery images. Follow-up observations should be able to determine if these systems share common proper motion and are gravitationally bound objects. We computed orbits for nine binaries. Of these, the orbits of five systems are improved compared to prior orbits and four systems have their orbits computed for the first time. In addition, 315 stars were unresolved and the full-width half maxima of the images are presented.

Analysis of some types of intermediate orbits used in the theory of artificial Earth satellite motion for the purposes of geodesy.

NASA Astrophysics Data System (ADS)

Kotseva, V. I.

Survey, analysis and comparison of 15 types of intermediate orbits used in the satellite movement theories for the purposes both of the geodesy and geodynamics have been made. The paper is a continuation of the investigations directed to practical realization both of analytical and semi-analytical methods for satellite orbit determination. It is indicated that the intermediate orbit proposed and elaborated by Aksenov, Grebenikov and Demin has got some good qualities and priorities over all the rest intermediate orbits.

Investigating the Relativistic Motion of the Stars Near the Supermassive Black Hole in the Galactic Center

DOE Office of Scientific and Technical Information (OSTI.GOV)

Parsa, M.; Eckart, A.; Shahzamanian, B.

The S-star cluster in the Galactic center allows us to study the physics close to a supermassive black hole, including distinctive dynamical tests of general relativity. Our best estimates for the mass of and the distance to Sgr A* using the three stars with the shortest period (S2, S38, and S55/S0-102) and Newtonian models are M {sub BH} = (4.15 ± 0.13 ± 0.57) × 10{sup 6} M {sub ⊙} and R {sub 0} = 8.19 ± 0.11 ± 0.34 kpc. Additionally, we aim at a new and practical method to investigate the relativistic orbits of stars in the gravitationalmore » field near Sgr A*. We use a first-order post-Newtonian approximation to calculate the stellar orbits with a broad range of periapse distance r {sub p} . We present a method that employs the changes in orbital elements derived from elliptical fits to different sections of the orbit. These changes are correlated with the relativistic parameter defined as ϒ ≡ r {sub s} / r {sub p} (with r {sub s} being the Schwarzschild radius) and can be used to derive ϒ from observational data. For S2 we find a value of ϒ = 0.00088 ± 0.00080, which is consistent, within the uncertainty, with the expected value of ϒ = 0.00065 derived from M {sub BH} and the orbit of S2. We argue that the derived quantity is unlikely to be dominated by perturbing influences such as noise on the derived stellar positions, field rotation, and drifts in black hole mass.« less

Rotation state of 495 Eulalia and its implication

NASA Astrophysics Data System (ADS)

Vokrouhlický, D.; Ďurech, J.; Pravec, P.; Oey, J.; Vraštil, J.; Hornoch, K.; Kušnirák, P.; Groom, R.; Warner, B. D.; Bottke, W. F.

2016-01-01

Context. The low-albedo part of the Nysa-Polana-Hertha asteroid complex has recently been found to consist of at least two families. The larger of them has been associated with asteroid 495 Eulalia, hereafter named the Eulalia family. The unstable location of this body very close to Jupiter's 3:1 mean motion resonance (J3/1 resonance) at the periphery of the associated family in the space of proper orbital elements makes this case peculiar. Aims: We consider the possibility that 495 Eulalia was originally positioned farther from the J3/1 resonance when the family formed via a catastrophic impact than it is today. It was then transported to its current orbit by the Yarkovsky thermal forces over hundreds of millions of years. This requires that 495 Eulalia had a prograde rotation state. Methods: We use photometric observations and lightcurve inversion methods to determine the rotation pole of 495 Eulalia. Numerical simulation accounting for perturbations from the Yarkovsky effect then reveals the possible pathways of Eulalia orbital evolution. Results: We find that both of the possible pole solutions are prograde, in accordance with our initial hypothesis. In studying the long-term evolution of Eulalia's spin state, we show that the obliquity can oscillate over a large interval of values yet always remain <90°. We estimate that Eulalia could have migrated by as much as ~0.007 au toward the J3/1 resonance within the past 1 Gyr. Our numerical runs show that it could have originated in the orbital zone well aligned with other family members in proper eccentricity, whichafter it gained its current orbit by chaotic evolution along the J3/1 resonance.

Variational and symplectic integrators for satellite relative orbit propagation including drag

NASA Astrophysics Data System (ADS)

Palacios, Leonel; Gurfil, Pini

2018-04-01

Orbit propagation algorithms for satellite relative motion relying on Runge-Kutta integrators are non-symplectic—a situation that leads to incorrect global behavior and degraded accuracy. Thus, attempts have been made to apply symplectic methods to integrate satellite relative motion. However, so far all these symplectic propagation schemes have not taken into account the effect of atmospheric drag. In this paper, drag-generalized symplectic and variational algorithms for satellite relative orbit propagation are developed in different reference frames, and numerical simulations with and without the effect of atmospheric drag are presented. It is also shown that high-order versions of the newly-developed variational and symplectic propagators are more accurate and are significantly faster than Runge-Kutta-based integrators, even in the presence of atmospheric drag.

Motion and collision of particles in a rotating linear dilaton black hole

NASA Astrophysics Data System (ADS)

González, P. A.; Olivares, Marco; Papantonopoulos, Eleftherios; Vásquez, Yerko

2018-03-01

We study the motion of particles in the background of a four-dimensional linear dilaton black hole. We solve analytically the equations of motion of the test particles, and we describe their motion. We show that the dilaton black hole acts as a particle accelerator by analyzing the energy in the center of mass frame of two colliding particles in the vicinity of its horizon. In particular, we find that there is a critical value of the angular momentum, which depends on the string coupling, and a particle with this critical angular momentum can reach the inner horizon with an arbitrarily high c.m. energy. This is known as the Bañados, Silk, and West process. We also show that the motion and collisions of particles have behavior similar to the three-dimensional Bañados-Teitelboim-Zanelli black hole. In fact, the photons can plunge into the horizon or escape to infinity, and they cannot be deflected, while for massive particles there are no confined orbits of the first kind, like planetary or circular orbits.

Null Angular Momentum and Weak KAM Solutions of the Newtonian N-Body Problem

NASA Astrophysics Data System (ADS)

Percino-Figueroa, Boris A.

2017-08-01

In [Arch. Ration. Mech. Anal. 213 (2014), 981-991] it has been proved that in the Newtonian N-body problem, given a minimal central configuration a and an arbitrary configuration x, there exists a completely parabolic orbit starting on x and asymptotic to the homothetic parabolic motion of a, furthermore such an orbit is a free time minimizer of the action functional. In this article we extend this result in abundance of completely parabolic motions by proving that under the same hypothesis it is possible to get that the completely parabolic motion starting at x has zero angular momentum. We achieve this by characterizing the rotation invariant weak KAM solutions as those defining a lamination on the configuration space by free time minimizers with zero angular momentum.

Tidal-cycle changes in oscillation ripples on the inner part of an estuarine sand flat

USGS Publications Warehouse

Dingler, J.R.; Clifton, H.E.

1984-01-01

Oscillation ripples form on subaqueous sand beds when wave-generated, near-bottom water motions are strong enough to move sand grains. The threshold of grain motion is the lower bound of the regime of oscillation ripples and the onset of sheet flow is the upper bound. Based on the relation between ripple spacing and orbital diameter, three types of symmetrical ripples occur within the ripple regime. In the lower part of the ripple regime (orbital ripples), spacing is proportional to orbital diameter; in the upper part (anorbital ripples) spacing is independent of orbital diameter. Between these regions occurs a transitional region (suborbital ripples). Oscillation ripples develop on a sandy tidal flat in Willapa Bay, Washington, as a result of waves traversing the area when it is submerged. Because wave energy is usually low within the bay, the ripples are primarily orbital in type. This means that their spacing should respond in a systematic way to changes in wave conditions. During the high-water parts of some tidal cycles, ripples near the beach decrease in spacing during the latter stage of the ebb tide while ripples farther offshore do not change. Observations made over several tidal cycles show that the zone of active ripples shifts on- or offshore in response to different wave conditions. Detailed bed profiles and current measurements taken during the high-water part of spring tides show the manner in which the oscillation ripples change with changes in orbital diameter. Changes in ripple spacing at the study site could be correlated with changes in orbital diameter in the manner suggested by the criterion for orbital ripples. However, there appeared to be a lag time between a decrease in orbital diameter and the corresponding decrease in ripple spacing. Absence of change during a tidal cycle could be attributed to orbital velocities below the threshold for grain motion that negated the effects of changes in orbital diameter. Because changes in sand-flat ripples depend both upon changes in orbital diameter and upon the magnitude of the orbital velocity, exposed ripples were not necessarily produced during the preceding high tide. In fact, some ripples may have been just produced, while others, farther offshore, may have been produced an unknown number of tides earlier. Therefore, when interpreting past wave conditions over tidal flats from low-tide ripples, one must remember that wave periods have to be short enough to produce velocities greater than the threshold velocity for the orbital diameters calculated from the observed ripple spacings. ?? 1984.

A satellite orbital testbed for SATCOM using mobile robots

NASA Astrophysics Data System (ADS)

Shen, Dan; Lu, Wenjie; Wang, Zhonghai; Jia, Bin; Wang, Gang; Wang, Tao; Chen, Genshe; Blasch, Erik; Pham, Khanh

2016-05-01

This paper develops and evaluates a satellite orbital testbed (SOT) for satellite communications (SATCOM). SOT can emulate the 3D satellite orbit using the omni-wheeled robots and a robotic arm. The 3D motion of satellite is partitioned into the movements in the equatorial plane and the up-down motions in the vertical plane. The former actions are emulated by omni-wheeled robots while the up-down motions are performed by a stepped-motor-controlled-ball along a rod (robotic arm), which is attached to the robot. The emulated satellite positions will go to the measure model, whose results will be used to perform multiple space object tracking. Then the tracking results will go to the maneuver detection and collision alert. The satellite maneuver commands will be translated to robots commands and robotic arm commands. In SATCOM, the effects of jamming depend on the range and angles of the positions of satellite transponder relative to the jamming satellite. We extend the SOT to include USRP transceivers. In the extended SOT, the relative ranges and angles are implemented using omni-wheeled robots and robotic arms.

Analyzing the Proper Motion of Two Double Star Systems from Astrometric Measurements

NASA Astrophysics Data System (ADS)

Falatoun, Alex; Barrera, Janet; de Neef, Anna; Gonzalez, Aura; Calanog, Jae; Boyce, Pat; Boyce, Grady

2018-04-01

The iTelescope network was used to obtain astrometric measurements of double star systems WDS 12202-1408 (STF 1631) and WDS 12339+5522 (STI 2286). Through astrometric measurement softwares SAOImage DS9 and Mira Pro x64, a mean position angle for STF 1631 of 304.8° ± 0.9° and a mean separation 14.7" ± 0.2" was measured. For STI 2286, a newly measured mean position angle of 85.9° ± 0.9° and mean separation 11.5" ± 0.3" were obtained. The relative proper motion of 1631 shows that the system could be demonstrating a linear path or an approximately circular orbit with a period of 1400 years. Parallax measurements of the secondary star will aid in classifying if this system is a physical or a visual pair. The proper motion of STI 2286 indicates that it could be a physical pair, featuring an orbit nearing a turning point. Follow-up observations in three to four year intervals will further validate or refute this claim and constrain the shape of a possible orbit.

Vision-based localization for on-orbit servicing of a partially cooperative satellite

NASA Astrophysics Data System (ADS)

Oumer, Nassir W.; Panin, Giorgio; Mülbauer, Quirin; Tseneklidou, Anastasia

2015-12-01

This paper proposes ground-in-the-loop, model-based visual localization system based on transmitted images to ground, to aid rendezvous and docking maneuvers between a servicer and a target satellite. In particular, we assume to deal with a partially cooperative target, i.e. passive and without fiducial markers, but supposed at least to keep a controlled attitude, up to small fluctuations, so that the approach mainly involves translational motion. For the purpose of localization, video cameras provide an effective and relatively inexpensive solution, working at a wide range of distances with an increasing accuracy and robustness during the approach. However, illumination conditions in space are especially challenging, due to the direct sunlight exposure and to the glossy surface of a satellite, that creates strong reflections and saturations and therefore a high level of background clutter and missing detections. We employ a monocular camera for mid-range tracking (20 - 5 m) and stereo camera at close-range (5 - 0.5 m), with the respective detection and tracking methods, both using intensity edges and robustly dealing with the above issues. Our tracking system has been extensively verified at the facility of the European Proximity Operations Simulator (EPOS) of DLR, which is a very realistic ground simulation able to reproduce sunlight conditions through a high power floodlight source, satellite surface properties using multilayer insulation foils, as well as orbital motion trajectories with ground-truth data, by means of two 6 DOF industrial robots. Results from this large dataset show the effectiveness and robustness of our method against the above difficulties.

On the origin of the Monoceros Ring - I. Kinematics, proper motions, and the nature of the progenitor

NASA Astrophysics Data System (ADS)

Guglielmo, Magda; Lane, Richard R.; Conn, Blair C.; Ho, Anna Y. Q.; Ibata, Rodrigo A.; Lewis, Geraint F.

2018-03-01

The Monoceros Ring (MRi) structure is an apparent stellar overdensity that has been postulated to entirely encircle the Galactic plane and has been variously described as being due to line-of-sight effects of the Galactic warp and flare or of extragalactic origin (via accretion). Despite being intensely scrutinized in the literature for more than a decade, no studies to date have been able to definitively uncover its origins. Here we use N-body simulations and a genetic algorithm to explore the parameter space for the initial position, orbital parameters, and, for the first time, the final location of a satellite progenitor. We fit our models to the latest Pan-STARRS data to determine whether an accretion scenario is capable of producing an in-plane ring-like structure matching the known parameters of the MRi. Our simulations produce streams that closely match the location, proper motion, and kinematics of the MRi structure. However, we are not able to reproduce the mass estimates from earlier studies based on Pan-STARRS data. Furthermore, in contrast to earlier studies, our best-fitting models are those for progenitors on retrograde orbits. If the MRi was produced by satellite accretion, we find that its progenitor has an initial mass upper limit of ˜1010 M⊙ and the remnant is likely located behind the Galactic bulge, making it difficult to locate observationally. While our models produce realistic MRi-like structures, we cannot definitively conclude that the MRi was produced by the accretion of a satellite galaxy.

How does the Structure of Spherical Dark Matter Halos Affect the Types of Orbits in Disk Galaxies?

NASA Astrophysics Data System (ADS)

Zotos, Euaggelos E.

The main objective of this work is to determine the character of orbits of stars moving in the meridional (R,z) plane of an axially symmetric time-independent disk galaxy model with a central massive nucleus and an additional spherical dark matter halo component. In particular, we try to reveal the influence of the scale length of the dark matter halo on the different families of orbits of stars, by monitoring how the percentage of chaotic orbits, as well as the percentages of orbits of the main regular resonant families evolve when this parameter varies. The smaller alignment index (SALI) was computed by numerically integrating the equations of motion as well as the variational equations to extensive samples of orbits in order to distinguish safely bet ween ordered and chaotic motion. In addition, a method based on the concept of spectral dynamics that utilizes the Fourier transform of the time series of each coordinate is used to identify the various families of regular orbits and also to recognize the secondary resonances that bifurcate from them. Our numerical computations reveal that when the dark matter halo is highly concentrated, that is when the scale length has low values the vast majority of star orbits move in regular orbits, while on the oth er hand in less concentrated dark matter halos the percentage of chaos increases significantly. We also compared our results with early related work.

Classifying orbits in galaxy models with a prolate or an oblate dark matter halo component

NASA Astrophysics Data System (ADS)

Zotos, Euaggelos E.

2014-03-01

Aims: The distinction between regular and chaotic motion in galaxies is undoubtedly an issue of paramount importance. We explore the nature of orbits of stars moving in the meridional plane (R,z) of an axially symmetric galactic model with a disk, a spherical nucleus, and a flat biaxial dark matter halo component. In particular, we study the influence of all the involved parameters of the dynamical system by computing both the percentage of chaotic orbits and the percentages of orbits of the main regular resonant families in each case. Methods: To distinguish between ordered and chaotic motion, we use the smaller alignment index (SALI) method to extensive samples of orbits by numerically integrating the equations of motion as well as the variational equations. Moreover, a method based on the concept of spectral dynamics that utilizes the Fourier transform of the time series of each coordinate is used to identify the various families of regular orbits and also to recognize the secondary resonances that bifurcate from them. Two cases are studied for every parameter: (i) the case where the halo component is prolate and (ii) the case where an oblate dark halo is present. Results: Our numerical investigation indicates that all the dynamical quantities affect, more or less, the overall orbital structure. It was observed that the mass of the nucleus, the halo flattening parameter, the scale length of the halo, the angular momentum, and the orbital energy are the most influential quantities, while the effect of all the other parameters is much weaker. It was also found that all the parameters corresponding to the disk only have a minor influence on the nature of orbits. Furthermore, some other quantities, such as the minimum distance to the origin, the horizontal, and the vertical force, were tested as potential chaos detectors. Our analysis revealed that only general information can be obtained from these quantities. We also compared our results with early related work. Appendix A is available in electronic form at http://www.aanda.org

The rotation of Titan and Ganymede

NASA Astrophysics Data System (ADS)

Van Hoolst, Tim; Coyette, Alexis; Baland, Rose-Marie; Trinh, Antony

2016-10-01

The rotation rates of Titan and Ganymede, the largest satellites of Saturn and Jupiter, are on average equal to their orbital mean motion. Here we discuss small deviations from the average rotation for both satellites and evaluate the polar motion of Titan induced by its surface fluid layers. We examine different causes at various time scales and assess possible consequences and the potential of using librations and polar motion as probes of the interior structure of the satellites.The rotation rate of Titan and Ganymede cannot be constant on the orbital time scale as a result of the gravitational torque of the central planet acting on the satellites. Titan is moreover expected to show significant polar motion and additional variations in the rotation rate due to angular momentum exchange with the atmosphere, mainly at seasonal periods. Observational evidence for deviations from the synchronous state has been reported several times for Titan but is unfortunately inconclusive. The measurements of the rotation variations are based on determinations of the shift in position of Cassini radar images taken during different flybys. The ESA JUICE (JUpiter ICy moons Explorer) mission will measure the rotation variations of Ganymede during its orbital phase around the satellite starting in 2032.We report on different theoretical aspects of the librations and polar motion. We consider the influence of the rheology of the ice shell and take into account Cassini measurements of the external gravitational field and of the topography of Titan and similar Galileo data about Ganymede. We also evaluate the librations and polar motion induced by Titan's hydrocarbon seas and use the most recent results of Titan's atmosphere dynamics. We finally evaluate the potential of rotation variations to constrain the satellite's interior structure, in particular its ice shell and ocean.

The Chaotic Long-term X-ray Variability of 4U 1705-44

NASA Astrophysics Data System (ADS)

Phillipson, R. A.; Boyd, P. T.; Smale, A. P.

2018-04-01

The low-mass X-ray binary 4U1705-44 exhibits dramatic long-term X-ray time variability with a timescale of several hundred days. The All-Sky Monitor (ASM) aboard the Rossi X-ray Timing Explorer (RXTE) and the Japanese Monitor of All-sky X-ray Image (MAXI) aboard the International Space Station together have continuously observed the source from December 1995 through May 2014. The combined ASM-MAXI data provide a continuous time series over fifty times the length of the timescale of interest. Topological analysis can help us identify 'fingerprints' in the phase-space of a system unique to its equations of motion. The Birman-Williams theorem postulates that if such fingerprints are the same between two systems, then their equations of motion must be closely related. The phase-space embedding of the source light curve shows a strong resemblance to the double-welled nonlinear Duffing oscillator. We explore a range of parameters for which the Duffing oscillator closely mirrors the time evolution of 4U1705-44. We extract low period, unstable periodic orbits from the 4U1705-44 and Duffing time series and compare their topological information. The Duffing and 4U1705-44 topological properties are identical, providing strong evidence that they share the same underlying template. This suggests that we can look to the Duffing equation to help guide the development of a physical model to describe the long-term X-ray variability of this and other similarly behaved X-ray binary systems.

Jupiter: Giant of the solar system. [its solar orbits

NASA Technical Reports Server (NTRS)

1975-01-01

Jupiter, its relationship to the other planets in the solar system, its twelve natural satellites, solar orbit and the appearance of Jupiter in the sky, and the sightings and motions of Jupiter in 1973 are discussed. Educational study projects for students are also included.

Operational factors affecting microgravity levels in orbit

NASA Technical Reports Server (NTRS)

Olsen, R. E.; Mockovciak, J., Jr.

1980-01-01

Microgravity levels desired for proposed materials processing payloads are fundamental considerations in the design of future space platforms. Disturbance sources, such as aerodynamic drag, attitude control torques, crew motion and orbital dynamics, influence the microgravity levels attainable in orbit. The nature of these effects are assessed relative to platform design parameters such as orbital altitude and configuration geometry, and examples are presented for a representative spacecraft configuration. The possible applications of control techniques to provide extremely low acceleration levels are also discussed.

Gravitational waveforms from unequal-mass binaries with arbitrary spins under leading order spin-orbit coupling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tessmer, Manuel

This paper generalizes the structure of gravitational waves from orbiting spinning binaries under leading order spin-orbit coupling, as given in the work by Koenigsdoerffer and Gopakumar [Phys. Rev. D 71, 024039 (2005)] for single-spin and equal-mass binaries, to unequal-mass binaries and arbitrary spin configurations. The orbital motion is taken to be quasicircular and the fractional mass difference is assumed to be small against one. The emitted gravitational waveforms are given in analytic form.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hammeschlag, S.B.; Hughes, S.; O'Reilly, G.V.

Orbital blow-out fractures were experimentally created in eight human cadavers. Each orbit underwent conventional radiographic studies, complex motion tomography, and computed tomographic examinations. A comparison of the three modalities was made. Anatomical correlation was obtained by dissecting the orbits. The significance of medial-wall fractures and enophthalmos is discussed. Limitation of inferior rectus muscle mobility is thought to be a result of muscle kinking associated with orbital fat-pad prolapse at the fracture site, rather than muscle incarceration. Blow-out fractures should be evaluated by computed tomographic computer reformations in the oblique sagittal plane.

Perturbative treatment of spin-orbit-coupling within spin-free exact two-component theory using equation-of-motion coupled-cluster methods

NASA Astrophysics Data System (ADS)

Cheng, Lan; Wang, Fan; Stanton, John F.; Gauss, Jürgen

2018-01-01

A scheme is reported for the perturbative calculation of spin-orbit coupling (SOC) within the spin-free exact two-component theory in its one-electron variant (SFX2C-1e) in combination with the equation-of-motion coupled-cluster singles and doubles method. Benchmark calculations of the spin-orbit splittings in 2Π and 2P radicals show that the accurate inclusion of scalar-relativistic effects using the SFX2C-1e scheme extends the applicability of the perturbative treatment of SOC to molecules that contain heavy elements. The contributions from relaxation of the coupled-cluster amplitudes are shown to be relatively small; significant contributions from correlating the inner-core orbitals are observed in calculations involving third-row and heavier elements. The calculation of term energies for the low-lying electronic states of the PtH radical, which serves to exemplify heavy transition-metal containing systems, further demonstrates the quality that can be achieved with the pragmatic approach presented here.

Structurally adaptive space crane concept for assembling space systems on orbit

NASA Technical Reports Server (NTRS)

Dorsey, John T.; Sutter, Thomas R.; Wu, K. Chauncey

1992-01-01

Many future human space exploration missions will probably require large vehicles that must be assembled on orbit. Thus, a device that can move, position, and assemble large and massive spacecraft components on orbit becomes essential for these missions. A concept is described for such a device: a space crane concept that uses erectable truss hardware to achieve high-stiffness and low-mass booms and uses articulating truss joints that can be assembled on orbit. The hardware has been tested and shown to have linear load-deflection response and to be structurally predictable. The hardware also permits the crane to be reconfigured into different geometries to satisfy future assembly requirements. A number of articulating and rotary joint concepts have been sized and analyzed, and the results are discussed. Two strategies were proposed to suppress motion-induced vibration: placing viscous dampers in selected truss struts and preshaping motion commands. Preliminary analyses indicate that these techniques have the potential to greatly enhance structural damping.