Introducing Earth's Orbital Eccentricity
ERIC Educational Resources Information Center
Oostra, Benjamin
2015-01-01
Most students know that planetary orbits, including Earth's, are elliptical; that is Kepler's first law, and it is found in many science textbooks. But quite a few are mistaken about the details, thinking that the orbit is very eccentric, or that this effect is somehow responsible for the seasons. In fact, the Earth's orbital eccentricity is…
Introducing Earth's Orbital Eccentricity
NASA Astrophysics Data System (ADS)
Oostra, Benjamin
2015-12-01
Most students know that planetary orbits, including Earth's, are elliptical; that is Kepler's first law, and it is found in many science textbooks. But quite a few are mistaken about the details, thinking that the orbit is very eccentric, or that this effect is somehow responsible for the seasons. In fact, the Earth's orbital eccentricity is small, and its only effect on the seasons is their unequal durations. Here I show a pleasant way to guide students to the actual value of Earth's orbital eccentricity, starting from the durations of the four seasons. The date of perihelion is also found.
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.
Introducing the Moon's Orbital Eccentricity
NASA Astrophysics Data System (ADS)
Oostra, Benjamin
2014-11-01
I present a novel way to introduce the lunar orbital eccentricity in introductory astronomy courses. The Moon is perhaps the clearest illustration of the general orbital elements such as inclination, ascending node, eccentricity, perigee, and so on. Furthermore, I like the students to discover astronomical phenomena for themselves, by means of a guided exercise, rather than just telling them the facts.1 The inclination and nodes may be found by direct observation, monitoring carefully the position of the Moon among the stars. Even the regression of the nodes may be discovered in this way2 To find the eccentricity from students' observations is also possible,3 but that requires considerable time and effort. if a whole class should discover it in a short time, here is a method more suitable for a one-day class or home assignment. The level I aim at is, more or less, advanced high school or first-year college students. I assume them to be acquainted with celestial coordinates and the lunar phases, and to be able to use algebra and trigonometry.
Orbital Evolution and Impact Hazard of Asteroids on Retrograde Orbits
NASA Astrophysics Data System (ADS)
Kankiewicz, P.; Włodarczyk, I.
2014-07-01
We present the past evolutional scenarios of known group of asteroids in retrograde orbits. Applying the latest observational data, we determined their nominal and averaged orbital elements. Next, we studied the behaviour of their orbital motion 1~My in the past (100~My in the future for two NEAs) taking into account the limitations of observational errors. It has been shown that the influence of outer planets perturbations in many cases can import small bodies on high inclination or retrograde orbits into the inner Solar System.
Asteroids in Retrograde Orbits: Interesting Cases
NASA Astrophysics Data System (ADS)
Kankiewicz, Paweł; Włodarczyk, Ireneusz
2014-12-01
We present the most interesting examples of the orbital evolution of asteroids in retrograde orbits (i > 90°). First, we used the latest observational data to determine nominal and averaged orbital elements of these objects. Next, the equations of motion of these asteroids were integrated backward 1 My, taking into account the propagation of observational errors. We used so-called 'cloning' procedure to reproduce the reliability of initial data. We obtained some possible scenarios of the orbit inversion in the past, what is often caused by the long-term influence of outer planets. For two most interesting cases (Apollo and Amor type) we did additional calculations: 100 My in the future. Additionally, we investigated the potential influence of Yarkovski/YORP effects on the long-time orbital evolution.
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
Orbital eccentricities in primordial black hole binaries
NASA Astrophysics Data System (ADS)
Cholis, Ilias; Kovetz, Ely D.; Ali-Haïmoud, Yacine; Bird, Simeon; Kamionkowski, Marc; Muñoz, Julian B.; Raccanelli, Alvise
2016-10-01
It was recently suggested that the merger of ˜30 M⊙ primordial black holes (PBHs) may provide a significant number of events in gravitational-wave observatories over the next decade, if they make up an appreciable fraction of the dark matter. Here we show that measurement of the eccentricities of the inspiralling binary black holes can be used to distinguish these binaries from those produced by more traditional astrophysical mechanisms. These PBH binaries are formed on highly eccentric orbits and can then merge on time scales that in some cases are years or less, retaining some eccentricity in the last seconds before the merger. This is to be contrasted with massive-stellar-binary, globular-cluster, or other astrophysical origins for binary black holes (BBHs) in which the orbits have very effectively circularized by the time the BBH enters the observable LIGO window. Here we discuss the features of the gravitational-wave signals that indicate this eccentricity and forecast the sensitivity of LIGO and the Einstein Telescope to such effects. We show that if PBHs make up the dark matter, then roughly one event should have a detectable eccentricity given LIGO's expected sensitivity and observing time of six years. The Einstein Telescope should see O (10 ) such events after ten years.
On eccentricities of globular cluster galactocentric orbits
NASA Astrophysics Data System (ADS)
Ninkovic, S.
The orbital eccentricities of 55 globular clusters are calculated and discussed. The data are taken from the study of Woltjer (1975), but include only those clusters for which reliable chemical compositions, positions, and line-of-sight velocities are given. The clusters are divided into six groups according to chemical composition and galactocentric distance, and the formulas of House and Wiegandt (1977) are employed in the calculations. The results are presented in tables and characterized individually. An LSR velocity of 225 km/sec is assumed, but some calculations using 275 km/sec are included for comparison. A general lower limit of eccentricity of 0.3 and upper limits (depending on cluster type) as high as 0.9 are estimated, with perigalactic distances not less than 1 kpc and apogalactic distances generally less than 25 but sometimes as high as 50-100 kpc. The mean orbital eccentricity of the groups is found to be better correlated to galactocentric distance than to chemical composition. The evolutionary contraction of the Galaxy is estimated to have lasted about 2-3 Gyr.
PRODUCTION OF NEAR-EARTH ASTEROIDS ON RETROGRADE ORBITS
Greenstreet, S.; Gladman, B.; Ngo, H.; Granvik, M.; Larson, S.
2012-04-20
While computing an improved near-Earth object (NEO) steady-state orbital distribution model, we discovered in the numerical integrations the unexpected production of retrograde orbits for asteroids that had originally exited from the accepted main-belt source regions. Our model indicates that {approx}0.1% (a factor of two uncertainty) of the steady-state NEO population (perihelion q < 1.3 AU) is on retrograde orbits. These rare outcomes typically happen when asteroid orbits flip to a retrograde configuration while in the 3:1 mean-motion resonance with Jupiter and then live for {approx}0.001 to 100 Myr. The model predicts, given the estimated near-Earth asteroid (NEA) population, that a few retrograde 0.1-1 km NEAs should exist. Currently, there are two known MPC NEOs with asteroidal designations on retrograde orbits which we therefore claim could be escaped asteroids instead of devolatilized comets. This retrograde NEA population may also answer a long-standing question in the meteoritical literature regarding the origin of high-strength, high-velocity meteoroids on retrograde orbits.
Production of Near-Earth Asteroids on Retrograde Orbits
NASA Astrophysics Data System (ADS)
Greenstreet, S.; Gladman, B.; Ngo, H.; Granvik, M.; Larson, S.
2012-04-01
While computing an improved near-Earth object (NEO) steady-state orbital distribution model, we discovered in the numerical integrations the unexpected production of retrograde orbits for asteroids that had originally exited from the accepted main-belt source regions. Our model indicates that ~0.1% (a factor of two uncertainty) of the steady-state NEO population (perihelion q < 1.3 AU) is on retrograde orbits. These rare outcomes typically happen when asteroid orbits flip to a retrograde configuration while in the 3:1 mean-motion resonance with Jupiter and then live for ~0.001 to 100 Myr. The model predicts, given the estimated near-Earth asteroid (NEA) population, that a few retrograde 0.1-1 km NEAs should exist. Currently, there are two known MPC NEOs with asteroidal designations on retrograde orbits which we therefore claim could be escaped asteroids instead of devolatilized comets. This retrograde NEA population may also answer a long-standing question in the meteoritical literature regarding the origin of high-strength, high-velocity meteoroids on retrograde orbits.
Introducing the Moon's Orbital Eccentricity
ERIC Educational Resources Information Center
Oostra, Benjamin
2014-01-01
I present a novel way to introduce the lunar orbital eccentricity in introductory astronomy courses. The Moon is perhaps the clearest illustration of the general orbital elements such as inclination, ascending node, eccentricity, perigee, and so on. Furthermore, I like the students to discover astronomical phenomena for themselves, by means of a…
Yarkovsky effect in the motion of asteroids in retrograde orbits
NASA Astrophysics Data System (ADS)
Kankiewicz, Paweł; Włodarczyk, Ireneusz
2016-06-01
Since the last few years, many small bodies in retrograde orbits was discovered, classified as asteroids. %Most of these orbits are located in peripherals of the Solar System. Main aim of our work is the analysis of their dynamical past and future. For 56 asteroids in retrograde orbits (i > 90) we studied the orbital evolution and calculated median dynamical lifetimes. Due to important role of the Yarkovsky effect in the motion of small bodies, we decided to apply the model with the Yarkovsky forces. Because the physical properties of these objects are still not well determined, we collected thermal parameters from literature or calculated from available formulas. The complete set of 'thermal' properties of each body is still not available from observational data, so our approach is a kind of approximation. Results obtained with these parameters allowed us to estimate the influence of the Yarkovsky effect on the stability of retrograde orbits.
WASP-17b: AN ULTRA-LOW DENSITY PLANET IN A PROBABLE RETROGRADE ORBIT
Anderson, D. R.; Hellier, C.; Smalley, B.; Maxted, P. F. L.; Bentley, S. J.; Gillon, M.; Triaud, A. H. M. J.; Queloz, D.; Mayor, M.; Pepe, F.; Segransan, D.; Udry, S.; Hebb, L.; Cameron, A. Collier; Enoch, B.; Horne, K.; Parley, N. R.; West, R. G.; Lister, T. A.; Pollacco, D.
2010-01-20
We report the discovery of the transiting giant planet WASP-17b, the least-dense planet currently known. It is 1.6 Saturn masses, but 1.5-2 Jupiter radii, giving a density of 6%-14% that of Jupiter. WASP-17b is in a 3.7 day orbit around a sub-solar metallicity, V = 11.6, F6 star. Preliminary detection of the Rossiter-McLaughlin effect suggests that WASP-17b is in a retrograde orbit (lambda approx -150{sup 0}), indicative of a violent history involving planet-planet or star-planet scattering. WASP-17b's bloated radius could be due to tidal heating resulting from recent or ongoing tidal circularization of an eccentric orbit, such as the highly eccentric orbits that typically result from scattering interactions. It will thus be important to determine more precisely the current orbital eccentricity by further high-precision radial velocity measurements or by timing the secondary eclipse, both to reduce the uncertainty on the planet's radius and to test tidal-heating models. Owing to its low surface gravity, WASP-17b's atmosphere has the largest scale height of any known planet, making it a good target for transmission spectroscopy.
Pervasive orbital eccentricities dictate the habitability of extrasolar earths.
Kita, Ryosuke; Rasio, Frederic; Takeda, Genya
2010-09-01
The long-term habitability of Earth-like planets requires low orbital eccentricities. A secular perturbation from a distant stellar companion is a very important mechanism in exciting planetary eccentricities, as many of the extrasolar planetary systems are associated with stellar companions. Although the orbital evolution of an Earth-like planet in a stellar binary system is well understood, the effect of a binary perturbation on a more realistic system containing additional gas-giant planets has been very little studied. Here, we provide analytic criteria confirmed by a large ensemble of numerical integrations that identify the initial orbital parameters leading to eccentric orbits. We show that an extrasolar earth is likely to experience a broad range of orbital evolution dictated by the location of a gas-giant planet, which necessitates more focused studies on the effect of eccentricity on the potential for life.
First law of mechanics for compact binaries on eccentric orbits
NASA Astrophysics Data System (ADS)
Le Tiec, Alexandre
2015-10-01
Using the canonical Arnowitt-Deser-Misner Hamiltonian formalism, a "first law of mechanics" is established for binary systems of point masses moving along generic stable bound (eccentric) orbits. This relationship is checked to hold within the post-Newtonian approximation to general relativity, up to third order. Several applications are discussed, including the use of gravitational self-force results to inform post-Newtonian theory and the effective one-body model for eccentric-orbit compact binaries.
Exoplanet orbital eccentricities derived from LAMOST-Kepler analysis.
Xie, Ji-Wei; Dong, Subo; Zhu, Zhaohuan; Huber, Daniel; Zheng, Zheng; De Cat, Peter; Fu, Jianning; Liu, Hui-Gen; Luo, Ali; Wu, Yue; Zhang, Haotong; Zhang, Hui; Zhou, Ji-Lin; Cao, Zihuang; Hou, Yonghui; Wang, Yuefei; Zhang, Yong
2016-10-11
The nearly circular (mean eccentricity [Formula: see text]) and coplanar (mean mutual inclination [Formula: see text]) orbits of the solar system planets motivated Kant and Laplace to hypothesize that planets are formed in disks, which has developed into the widely accepted theory of planet formation. The first several hundred extrasolar planets (mostly Jovian) discovered using the radial velocity (RV) technique are commonly on eccentric orbits ([Formula: see text]). This raises a fundamental question: Are the solar system and its formation special? The Kepler mission has found thousands of transiting planets dominated by sub-Neptunes, but most of their orbital eccentricities remain unknown. By using the precise spectroscopic host star parameters from the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) observations, we measure the eccentricity distributions for a large (698) and homogeneous Kepler planet sample with transit duration statistics. Nearly half of the planets are in systems with single transiting planets (singles), whereas the other half are multiple transiting planets (multiples). We find an eccentricity dichotomy: on average, Kepler singles are on eccentric orbits with [Formula: see text] 0.3, whereas the multiples are on nearly circular [Formula: see text] and coplanar [Formula: see text] degree) orbits similar to those of the solar system planets. Our results are consistent with previous studies of smaller samples and individual systems. We also show that Kepler multiples and solar system objects follow a common relation [[Formula: see text](1-2)[Formula: see text
Orbital dynamics of multi-planet systems with eccentricity diversity
Kane, Stephen R.; Raymond, Sean N.
2014-04-01
Since exoplanets were detected using the radial velocity method, they have revealed a diverse distribution of orbital configurations. Among these are planets in highly eccentric orbits (e > 0.5). Most of these systems consist of a single planet but several have been found to also contain a longer period planet in a near-circular orbit. Here we use the latest Keplerian orbital solutions to investigate four known systems which exhibit this extreme eccentricity diversity; HD 37605, HD 74156, HD 163607, and HD 168443. We place limits on the presence of additional planets in these systems based on the radial velocity residuals. We show that the two known planets in each system exchange angular momentum through secular oscillations of their eccentricities. We calculate the amplitude and timescale for these eccentricity oscillations and associated periastron precession. We further demonstrate the effect of mutual orbital inclinations on the amplitude of high-frequency eccentricity oscillations. Finally, we discuss the implications of these oscillations in the context of possible origin scenarios for unequal eccentricities.
Reducing orbital eccentricity in initial data of binary neutron stars
NASA Astrophysics Data System (ADS)
Kyutoku, Koutarou; Shibata, Masaru; Taniguchi, Keisuke
2014-09-01
We develop a method to compute low-eccentricity initial data of binary neutron stars required to perform realistic simulations in numerical relativity. The orbital eccentricity is controlled by adjusting the orbital angular velocity of a binary and incorporating an approaching relative velocity of the neutron stars. These modifications improve the solution primarily through the hydrostatic equilibrium equation for the binary initial data. The orbital angular velocity and approaching velocity of initial data are updated iteratively by performing time evolutions over ˜3 orbits. We find that the eccentricity can be reduced by an order of magnitude compared to standard quasicircular initial data, specifically from ˜0.01 to ≲0.001, by three successive iterations for equal-mass binaries leaving ˜10 orbits before the merger.
A retrograde co-orbital asteroid of Jupiter
NASA Astrophysics Data System (ADS)
Wiegert, Paul; Connors, Martin; Veillet, Christian
2017-03-01
Recent theoretical work in celestial mechanics has revealed that an asteroid may orbit stably in the same region as a planet, despite revolving around the Sun in the sense opposite to that of the planet itself. Asteroid 2015 BZ509 was discovered in 2015, but with too much uncertainty in its measured orbit to establish whether it was such a retrograde co-orbital body. Here we report observations and analysis that demonstrates that asteroid 2015 BZ509 is indeed a retrograde co-orbital asteroid of the planet Jupiter. We find that 2015 BZ509 has long-term stability, having been in its current, resonant state for around a million years. This is long enough to preclude precise calculation of the time or mechanism of its injection to its present state, but it may be a Halley-family comet that entered the resonance through an interaction with Saturn. Retrograde co-orbital asteroids of Jupiter and other planets may be more common than previously expected.
A retrograde co-orbital asteroid of Jupiter.
Wiegert, Paul; Connors, Martin; Veillet, Christian
2017-03-29
Recent theoretical work in celestial mechanics has revealed that an asteroid may orbit stably in the same region as a planet, despite revolving around the Sun in the sense opposite to that of the planet itself. Asteroid 2015 BZ509 was discovered in 2015, but with too much uncertainty in its measured orbit to establish whether it was such a retrograde co-orbital body. Here we report observations and analysis that demonstrates that asteroid 2015 BZ509 is indeed a retrograde co-orbital asteroid of the planet Jupiter. We find that 2015 BZ509 has long-term stability, having been in its current, resonant state for around a million years. This is long enough to preclude precise calculation of the time or mechanism of its injection to its present state, but it may be a Halley-family comet that entered the resonance through an interaction with Saturn. Retrograde co-orbital asteroids of Jupiter and other planets may be more common than previously expected.
Evidence for a Past High-Eccentricity Lunar Orbit
NASA Technical Reports Server (NTRS)
Garrick-Betthell, Ian; Wisdom, Jack; Zuber, Maria T.
2007-01-01
The large differences between the Moon's three principal moments of inertia have been mystery since Laplace considered them in 1799. Here we present calculations that show how past high eccentricity orbits can account for the moment differences, represented by the low-order lunar gravity field and libration parameters. One of our solutions is that the Moon may have once been in a 3:2 resonance of the orbit period to spin-period, similar to Mercury's present state. The possibility of past high-eccentricity orbits suggests a rich dynamical history and may influence our understanding of the early thermal evolution of the Moon.
Exoplanet orbital eccentricities derived from LAMOST–Kepler analysis
Xie, Ji-Wei; Dong, Subo; Zhu, Zhaohuan; Huber, Daniel; Zheng, Zheng; De Cat, Peter; Fu, Jianning; Liu, Hui-Gen; Luo, Ali; Wu, Yue; Zhang, Haotong; Zhang, Hui; Zhou, Ji-Lin; Cao, Zihuang; Hou, Yonghui; Wang, Yuefei; Zhang, Yong
2016-01-01
The nearly circular (mean eccentricity e¯≈0.06) and coplanar (mean mutual inclination i¯≈3°) orbits of the solar system planets motivated Kant and Laplace to hypothesize that planets are formed in disks, which has developed into the widely accepted theory of planet formation. The first several hundred extrasolar planets (mostly Jovian) discovered using the radial velocity (RV) technique are commonly on eccentric orbits (e¯≈0.3). This raises a fundamental question: Are the solar system and its formation special? The Kepler mission has found thousands of transiting planets dominated by sub-Neptunes, but most of their orbital eccentricities remain unknown. By using the precise spectroscopic host star parameters from the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) observations, we measure the eccentricity distributions for a large (698) and homogeneous Kepler planet sample with transit duration statistics. Nearly half of the planets are in systems with single transiting planets (singles), whereas the other half are multiple transiting planets (multiples). We find an eccentricity dichotomy: on average, Kepler singles are on eccentric orbits with e¯≈ 0.3, whereas the multiples are on nearly circular (e¯=0.04−0.04+0.03) and coplanar (i¯=1.4−1.1+0.8 degree) orbits similar to those of the solar system planets. Our results are consistent with previous studies of smaller samples and individual systems. We also show that Kepler multiples and solar system objects follow a common relation [e¯≈(1–2)×i¯] between mean eccentricities and mutual inclinations. The prevalence of circular orbits and the common relation may imply that the solar system is not so atypical in the galaxy after all. PMID:27671635
Exoplanet orbital eccentricities derived from LAMOST-Kepler analysis
NASA Astrophysics Data System (ADS)
Xie, Ji-Wei; Dong, Subo; Zhu, Zhaohuan; Huber, Daniel; Zheng, Zheng; De Cat, Peter; Fu, Jianning; Liu, Hui-Gen; Luo, Ali; Wu, Yue; Zhang, Haotong; Zhang, Hui; Zhou, Ji-Lin; Cao, Zihuang; Hou, Yonghui; Wang, Yuefei; Zhang, Yong
2016-10-01
The nearly circular (mean eccentricity e¯≈0.06) and coplanar (mean mutual inclination i¯≈3°) orbits of the solar system planets motivated Kant and Laplace to hypothesize that planets are formed in disks, which has developed into the widely accepted theory of planet formation. The first several hundred extrasolar planets (mostly Jovian) discovered using the radial velocity (RV) technique are commonly on eccentric orbits (e¯≈0.3). This raises a fundamental question: Are the solar system and its formation special? The Kepler mission has found thousands of transiting planets dominated by sub-Neptunes, but most of their orbital eccentricities remain unknown. By using the precise spectroscopic host star parameters from the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) observations, we measure the eccentricity distributions for a large (698) and homogeneous Kepler planet sample with transit duration statistics. Nearly half of the planets are in systems with single transiting planets (singles), whereas the other half are multiple transiting planets (multiples). We find an eccentricity dichotomy: on average, Kepler singles are on eccentric orbits with e¯≈0.3, whereas the multiples are on nearly circular (e¯=0.04-0.04+0.03) and coplanar (i¯=1.4-1.1+0.8 degree) orbits similar to those of the solar system planets. Our results are consistent with previous studies of smaller samples and individual systems. We also show that Kepler multiples and solar system objects follow a common relation [×i¯] between mean eccentricities and mutual inclinations. The prevalence of circular orbits and the common relation may imply that the solar system is not so atypical in the galaxy after all.
The orbital eccentricities of binary millisecond pulsars in globular clusters
NASA Technical Reports Server (NTRS)
Rasio, Frederic A.; Heggie, Douglas C.
1995-01-01
Low-mass binary millisecond pulsars (LMBPs) are born with very small orbital eccentricities, typically of order e(sub i) approximately 10(exp -6) to 10(exp -3). In globular clusters, however, higher eccentricities e(sub f) much greater than e(sub i) can be induced by dynamical interactions with passing stars. Here we show that the cross section for this process is much larger than previously estimated. This is becuse, even for initially circular binaries, the induced eccentricity e(sub f) for an encounter with pericenter separation r(sub p) beyond a few times the binary semimajor axis a declines only as a power law (e(sub f) varies as (r(sub p)/a)(exp -5/2), and not as an exponential. We find that all currently known LMBPs in clusters were probably affected by interactions, with their current eccentricities typically greater than at birth by an order of magnitude or more.
Exoplanet orbital eccentricity: multiplicity relation and the Solar System.
Limbach, Mary Anne; Turner, Edwin L
2015-01-06
The known population of exoplanets exhibits a much wider range of orbital eccentricities than Solar System planets and has a much higher average eccentricity. These facts have been widely interpreted to indicate that the Solar System is an atypical member of the overall population of planetary systems. We report here on a strong anticorrelation of orbital eccentricity with multiplicity (number of planets in the system) among cataloged radial velocity (RV) systems. The mean, median, and rough distribution of eccentricities of Solar System planets fits an extrapolation of this anticorrelation to the eight-planet case rather precisely despite the fact that no more than two Solar System planets would be detectable with RV data comparable to that in the exoplanet sample. Moreover, even if regarded as a single or double planetary system, the Solar System lies in a reasonably heavily populated region of eccentricity-multiplicity space. Thus, the Solar System is not anomalous among known exoplanetary systems with respect to eccentricities when its multiplicity is taken into account. Specifically, as the multiplicity of a system increases, the eccentricity decreases roughly as a power law of index -1.20. A simple and plausible but ad hoc and model-dependent interpretation of this relationship implies that ∼ 80% of the one-planet and 25% of the two-planet systems in our sample have additional, as yet undiscovered, members but that systems of higher observed multiplicity are largely complete (i.e., relatively rarely contain additional undiscovered planets). If low eccentricities indeed favor high multiplicities, habitability may be more common in systems with a larger number of planets.
The Orbital Evolution of 2007 VA85, an Amor-type Asteroid on a Retrograde Orbit.
NASA Astrophysics Data System (ADS)
Kankiewicz, P.; Włodarczyk, I.
2010-06-01
Among the known population of asteroids on retrograde orbits (i > 90°) we found an object classified as an Amor-type asteroid. During the analysis of the first results of astrometry, we found some possible Earth-impact solutions for this asteroid. After taking into account the latest observations, we excluded any significant impact solution. However, this asteroid is the first known example of potentially hazardous object on a retrograde orbit. We also investigated the orbital evolution of 2007 VA85 (1 My in the past), obtaining possible scenarios of its dynamical origin.
HEARTBEAT STARS: SPECTROSCOPIC ORBITAL SOLUTIONS FOR SIX ECCENTRIC BINARY SYSTEMS
Smullen, Rachel A.; Kobulnicky, Henry A.
2015-08-01
We present multi-epoch spectroscopy of “heartbeat stars,” eccentric binaries with dynamic tidal distortions and tidally induced pulsations originally discovered with the Kepler satellite. Optical spectra of six known heartbeat stars using the Wyoming Infrared Observatory 2.3 m telescope allow measurement of stellar effective temperatures and radial velocities from which we determine orbital parameters including the periods, eccentricities, approximate mass ratios, and component masses. These spectroscopic solutions confirm that the stars are members of eccentric binary systems with eccentricities e > 0.34 and periods P = 7–20 days, strengthening conclusions from prior works that utilized purely photometric methods. Heartbeat stars in this sample have A- or F-type primary components. Constraints on orbital inclinations indicate that four of the six systems have minimum mass ratios q = 0.3–0.5, implying that most secondaries are probable M dwarfs or earlier. One system is an eclipsing, double-lined spectroscopic binary with roughly equal-mass mid-A components (q = 0.95), while another shows double-lined behavior only near periastron, indicating that the F0V primary has a G1V secondary (q = 0.65). This work constitutes the first measurements of the masses of secondaries in a statistical sample of heartbeat stars. The good agreement between our spectroscopic orbital elements and those derived using a photometric model support the idea that photometric data are sufficient to derive reliable orbital parameters for heartbeat stars.
Exoplanet orbital eccentricity: Multiplicity relation and the Solar System
Limbach, Mary Anne; Turner, Edwin L.
2015-01-01
The known population of exoplanets exhibits a much wider range of orbital eccentricities than Solar System planets and has a much higher average eccentricity. These facts have been widely interpreted to indicate that the Solar System is an atypical member of the overall population of planetary systems. We report here on a strong anticorrelation of orbital eccentricity with multiplicity (number of planets in the system) among cataloged radial velocity (RV) systems. The mean, median, and rough distribution of eccentricities of Solar System planets fits an extrapolation of this anticorrelation to the eight-planet case rather precisely despite the fact that no more than two Solar System planets would be detectable with RV data comparable to that in the exoplanet sample. Moreover, even if regarded as a single or double planetary system, the Solar System lies in a reasonably heavily populated region of eccentricity−multiplicity space. Thus, the Solar System is not anomalous among known exoplanetary systems with respect to eccentricities when its multiplicity is taken into account. Specifically, as the multiplicity of a system increases, the eccentricity decreases roughly as a power law of index –1.20. A simple and plausible but ad hoc and model-dependent interpretation of this relationship implies that ∼80% of the one-planet and 25% of the two-planet systems in our sample have additional, as yet undiscovered, members but that systems of higher observed multiplicity are largely complete (i.e., relatively rarely contain additional undiscovered planets). If low eccentricities indeed favor high multiplicities, habitability may be more common in systems with a larger number of planets. PMID:25512527
A complete waveform model for compact binaries on eccentric orbits
NASA Astrophysics Data System (ADS)
George, Daniel; Huerta, Eliu; Kumar, Prayush; Agarwal, Bhanu; Schive, Hsi-Yu; Pfeiffer, Harald; Chu, Tony; Boyle, Michael; Hemberger, Daniel; Kidder, Lawrence; Scheel, Mark; Szilagyi, Bela
2017-01-01
We present a time domain waveform model that describes the inspiral, merger and ringdown of compact binary systems whose components are non-spinning, and which evolve on orbits with low to moderate eccentricity. We show that this inspiral-merger-ringdown waveform model reproduces the effective-one-body model for black hole binaries with mass-ratios between 1 to 15 in the zero eccentricity limit over a wide range of the parameter space under consideration. We use this model to show that the gravitational wave transients GW150914 and GW151226 can be effectively recovered with template banks of quasicircular, spin-aligned waveforms if the eccentricity e0 of these systems when they enter the aLIGO band at a gravitational wave frequency of 14 Hz satisfies e0GW 150914 <= 0 . 15 and e0GW 151226 <= 0 . 1 .
NASA Astrophysics Data System (ADS)
Svoren, J.; Neslusan, L.; Porubcan, V.
1994-08-01
All known parent bodies of meteor showers belong to bodies moving in high-eccentricity orbits (e => 0.5). Recently, asteroids in low-eccentricity orbits (e < 0.5) approaching the Earth's orbit, were suggested as another population of possible parent bodies of meteor streams. This paper deals with the problem of calculation of meteor radiants connected with the bodies in low-eccentricity orbits from the point of view of optimal results depending on the method applied. The paper is a continuation of our previous analysis of high-eccentricity orbits (Svoren, J., Neslusan, L., Porubcan, V.: 1993, Contrib. Astron. Obs. Skalnate Pleso 23, 23). Some additional methods resulting from mathematical modelling are presented and discussed together with Porter's, Steel-Baggaley's and Hasegawa's methods. In order to be able to compare how suitable the application of the individual radiant determination methods is, it is necessary to determine the accuracy with which they approximate real meteor orbits. To verify the accuracy with which the orbit of a meteoroid with at least one node at 1 AU fits the original orbit of the parent body, the Southworth-Hawkins D-criterion (Southworth, R.B., Hawkins, G.S.: 1963, Smithson. Contr. Astrophys. 7, 261) was applied. D <= 0.1 indicates a very good fit of orbits, 0.1 < D <= 0.2 is considered for a good fit and D > 0.2 means that the fit is rather poor and the change of orbit unrealistic. The optimal method, i.e. the one which results in the smallest D values for the population of low-eccentricity orbits, is that of adjusting the orbit by varying both the eccentricity and perihelion distance. A comparison of theoretical radiants obtained by various methods was made for typical representatives from each group of the NEA (near-Earth asteroids) objects.
Applying KAM Theory to Highly Eccentric Orbits
2014-03-27
period of a planet is proportional to the cube of the semi- major axis of its orbit. In 1687, Isaac Newton would prove Kepler’s discoveries after...solving the n-body problem) gave way for more exhaustive research efforts of Newton , Euler, Lagrange, Jacobi, Poincaré, and many others. The King...coordinates, H(I, θ) = H ′(I′), (2.5) 3. Solving the Hamilton-Jacobi equation for the following generating function (Equa- tion (2.6) using a Newton
CONFIRMATION OF A RETROGRADE ORBIT FOR EXOPLANET WASP-17b
Bayliss, Daniel D. R.; Sackett, Penny D.; Winn, Joshua N.; Mardling, Rosemary A.
2010-10-20
We present high-precision radial velocity observations of WASP-17 throughout the transit of its close-in giant planet, using the MIKE spectrograph on the 6.5 m Magellan Telescope at Las Campanas Observatory. By modeling the Rossiter-McLaughlin effect, we find the sky-projected spin-orbit angle to be {lambda} = 167.4 {+-} 11.2 deg. This independently confirms the previous finding that WASP-17b is on a retrograde orbit, suggesting it underwent migration via a mechanism other than just the gravitational interaction between the planet and the disk. Interestingly, our result for {lambda} differs by 45 {+-} 13 deg from the previously announced value, and we also find that the spectroscopic transit occurs 15 {+-} 5 minutes earlier than expected, based on the published ephemeris. The discrepancy in the ephemeris highlights the need for contemporaneous spectroscopic and photometric transit observations whenever possible.
Orbital Eccentricity and the Stability of Planets in the Alpha Centauri System
NASA Technical Reports Server (NTRS)
Lissauer, Jack
2016-01-01
Planets on initially circular orbits are typically more dynamically stable than planets initially having nonzero eccentricities. However, the presence of a major perturber that forces periodic oscillations of planetary eccentricity can alter this situation. We investigate the dependance of system lifetime on initial eccentricity for planets orbiting one star within the alpha Centauri system. Our results show that initial conditions chosen to minimize free eccentricity can substantially increase stability compared to planets on circular orbits.
Spectrum of 100-kyr glacial cycle: orbital inclination, not eccentricity.
Muller, R A; MacDonald, G J
1997-08-05
Spectral analysis of climate data shows a strong narrow peak with period approximately 100 kyr, attributed by the Milankovitch theory to changes in the eccentricity of the earth's orbit. The narrowness of the peak does suggest an astronomical origin; however the shape of the peak is incompatible with both linear and nonlinear models that attribute the cycle to eccentricity or (equivalently) to the envelope of the precession. In contrast, the orbital inclination parameter gives a good match to both the spectrum and bispectrum of the climate data. Extraterrestrial accretion from meteoroids or interplanetary dust is proposed as a mechanism that could link inclination to climate, and experimental tests are described that could prove or disprove this hypothesis.
HOW ECCENTRIC ORBITAL SOLUTIONS CAN HIDE PLANETARY SYSTEMS IN 2:1 RESONANT ORBITS
Anglada-Escude, Guillem; Chambers, John E.; Lopez-Morales, Mercedes E-mail: mercedes@dtm.ciw.ed
2010-01-20
The Doppler technique measures the reflex radial motion of a star induced by the presence of companions and is the most successful method to detect exoplanets. If several planets are present, their signals will appear combined in the radial motion of the star, leading to potential misinterpretations of the data. Specifically, two planets in 2:1 resonant orbits can mimic the signal of a single planet in an eccentric orbit. We quantify the implications of this statistical degeneracy for a representative sample of the reported single exoplanets with available data sets, finding that (1) around 35% of the published eccentric one-planet solutions are statistically indistinguishable from planetary systems in 2:1 orbital resonance, (2) another 40% cannot be statistically distinguished from a circular orbital solution, and (3) planets with masses comparable to Earth could be hidden in known orbital solutions of eccentric super-Earths and Neptune mass planets.
A general time element using Cartesian coordinates: Eccentric orbit integration
NASA Technical Reports Server (NTRS)
Janin, G.
1980-01-01
A general time element, valid with any arbitrary independent variables, and used with Cartesian coordinates for the integration of the elliptic motion in orbits, is examined. The derivation of the time element from a set of canonical elements of the Delaunay type, developed in the extended phase space, is presented. The application of the method using an example of a transfer orbit for a geosynchronous mission is presented. The eccentric and elliptic anomaly are utilized as the independent variable. The reduction of the in track error resulting from using Cartesian coordinates with the time element is reported.
The enigma of the Uranian satellites' orbital eccentricities
NASA Technical Reports Server (NTRS)
Squyres, S. W.; Reynolds, R. T.; Lissauer, J. J.
1985-01-01
The eccentricity decay times for the Uranian satellites are calculated using recent observations (Brown et al., 1982) of the diameters and orbital elements of the satellites and assuming reasonable dissipation functions and rigidities for icy satellites. For the outer two satellites, Titania and Oberon, the decay times are found to be very long, whereas the inner three satellites, Miranda, Ariel, and Umbriel, have decay times on the order of 10 to the 7th to 10 to the 8th years and have a near-commensurability in their mean motions that cannot force their eccentricities. There are several possible solutions for the lack of resonant forcing: (1) the reported eccentricities are incorrect, and are very nearly zero, (2) the reported mean motions are incorrect, and an exact commensurability exists, (3) the physical properties assumed for the satellites are grossly in error, and (4) the system is evolving rapidly, perhaps from a previous state of higher eccentricity. A new lower bound of about 17,000 on the dissipation function of Uranus is calculated from the mass of Ariel and its proximity to Uranus.
Complete waveform model for compact binaries on eccentric orbits
NASA Astrophysics Data System (ADS)
Huerta, E. A.; Kumar, Prayush; Agarwal, Bhanu; George, Daniel; Schive, Hsi-Yu; Pfeiffer, Harald P.; Haas, Roland; Ren, Wei; Chu, Tony; Boyle, Michael; Hemberger, Daniel A.; Kidder, Lawrence E.; Scheel, Mark A.; Szilagyi, Bela
2017-01-01
We present a time domain waveform model that describes the inspiral, merger and ringdown of compact binary systems whose components are nonspinning, and which evolve on orbits with low to moderate eccentricity. The inspiral evolution is described using third-order post-Newtonian equations both for the equations of motion of the binary, and its far-zone radiation field. This latter component also includes instantaneous, tails and tails-of-tails contributions, and a contribution due to nonlinear memory. This framework reduces to the post-Newtonian approximant TaylorT4 at third post-Newtonian order in the zero-eccentricity limit. To improve phase accuracy, we also incorporate higher-order post-Newtonian corrections for the energy flux of quasicircular binaries and gravitational self-force corrections to the binding energy of compact binaries. This enhanced prescription for the inspiral evolution is combined with a fully analytical prescription for the merger-ringdown evolution constructed using a catalog of numerical relativity simulations. We show that this inspiral-merger-ringdown waveform model reproduces the effective-one-body model of Ref. [Y. Pan et al., Phys. Rev. D 89, 061501 (2014)., 10.1103/PhysRevD.89.061501] for quasicircular black hole binaries with mass ratios between 1 to 15 in the zero-eccentricity limit over a wide range of the parameter space under consideration. Using a set of eccentric numerical relativity simulations, not used during calibration, we show that our new eccentric model reproduces the true features of eccentric compact binary coalescence throughout merger. We use this model to show that the gravitational-wave transients GW150914 and GW151226 can be effectively recovered with template banks of quasicircular, spin-aligned waveforms if the eccentricity e0 of these systems when they enter the aLIGO band at a gravitational-wave frequency of 14 Hz satisfies e0GW 150914≤0.15 and e0GW 151226≤0.1 . We also find that varying the spin
On the effect of eccentricity of a planetary orbit on the stability of satellite orbits
NASA Astrophysics Data System (ADS)
Ichtiaroglou, S.; Voyatzis, G.
1990-03-01
The effect of the eccentricity of a planet's orbit on the stability of the orbits of its satellites is studied. The model used is the elliptic Hill case of the planar restricted three-body problem. The linear stability of all the known families of periodic orbits is computed. No stable orbits are found, the majority of them possessing one or two pairs of real eigenvalues of the monodromy matrix, while some with complex instability are found. Two families of periodic orbits, bifurcating from the Lagrangian points of the corresponding circular case are found analytically. These orbits are very unstable and the determination of their stability coefficients is not accurate.
Long-term orbital stability of exosolar planetary systems with highly eccentric orbits
NASA Astrophysics Data System (ADS)
Antoniadou, Kyriaki I.; Voyatzis, George
2016-10-01
Nowadays, many extrasolar planetary systems possessing at least one planet on a highly eccentric orbit have been discovered. In this work, we study the possible long-term stability of such systems. We consider the general three body problem as our model. Highly eccentric orbits are out of the Hill stability regions. However, mean motion resonances can provide phase protection and orbits with long-term stability exist. We construct maps of dynamical stability based on the computation of chaotic indicators and we figure out regions in phase space, where the long-term stability is guaranteed. We focus on regions where at least one planet is highly eccentric and attempt to associate them with the existence of stable periodic orbits. The values of the orbital elements, which are derived from observational data, are often given with very large deviations. Generally, phase space regions of high eccentricities are narrow and thus, our dynamical analysis may restrict considerably the valid domain of the system's location.
Wakes Induced by a Moonlet on an Eccentric Orbit
NASA Astrophysics Data System (ADS)
Seiss, Martin; Salo, H.; Spahn, F.; Schmidt, J.
2008-09-01
Large moonlets embedded in a planetary ring can create gaps going around the whole circumference almost void of material. Two examples have been identified in Saturn's A-ring to date: Pan in the Encke gap and Daphnis in the Keeler gap. The gravity of the moons induces wavy-like structures (wakes) at the gap edges. Observations by the ISS imaging team revealed deviations of the edge form from the basic sinusoidal model. Gap edges perturbed by resonances, and alternatively, a moonlet on an eccentric orbit are suitable to explain the observations. Here we present results of N-particle box simulations of a gap edge including collisions where the edge is perturbed by a moonlet on an eccentric orbit. We especially compare the results with analytical predictions and non-collisional streamline kinematics. Further, the resulting streamlines are compared with the corresponding density isolines, showing that both can deviate significantly from each other. Additionally, based on these numerical experiments we investigate the damping behavior at the gap edge and draw conclusions for the analytical modeling of the wakes and for interpretation of Cassini data.
GBT Reveals Satellite of Milky Way in Retrograde Orbit
NASA Astrophysics Data System (ADS)
2003-05-01
New observations with National Science Foundation's Robert C. Byrd Green Bank Telescope (GBT) suggest that what was once believed to be an intergalactic cloud of unknown distance and significance, is actually a previously unrecognized satellite galaxy of the Milky Way orbiting backward around the Galactic center. Path of Complex H Artist's rendition of the path of satellite galaxy Complex H (in red) in relation to the orbit of the Sun (in yellow) about the center of the Milky Way Galaxy. The outer layers of Complex H are being stripped away by its interaction with the Milky Way. The hydrogen atmosphere (in blue) is shown surrounding the visible portion (in white) of the Galaxy. CREDIT: Lockman, Smiley, Saxton; NRAO/AUI Jay Lockman of the National Radio Astronomy Observatory (NRAO) in Green Bank, West Virginia, discovered that this object, known as "Complex H," is crashing through the outermost parts of the Milky Way from an inclined, retrograde orbit. Lockman's findings will be published in the July 1 issue of the Astrophysical Journal, Letters. "Many astronomers assumed that Complex H was probably a distant neighbor of the Milky Way with some unusual velocity that defied explanation," said Lockman. "Since its motion appeared completely unrelated to Galactic rotation, astronomers simply lumped it in with other high velocity clouds that had strange and unpredictable trajectories." High velocity clouds are essentially what their name implies, fast-moving clouds of predominately neutral atomic hydrogen. They are often found at great distances from the disk of the Milky Way, and may be left over material from the formation of our Galaxy and other galaxies in our Local Group. Over time, these objects can become incorporated into larger galaxies, just as small asteroids left over from the formation of the solar system sometimes collide with the Earth. Earlier studies of Complex H were hindered because the cloud currently is passing almost exactly behind the outer disk of
NASA Astrophysics Data System (ADS)
Hamilton, Douglas P.; Burns, Joseph A.
1992-03-01
Recently, Hamilton and Burns (1991) characterized the size and shape of a stability zone around an asteroid on a circular heliocentric orbit within which asteroid material could remain bound for an extended period of time. The present paper considers two additional effects: the asteroid's nonzero heliocentric eccentricity and solar radiation pressure. Results of numerical analyses show that, for an asteroid on an eccentric orbit, the stability zone scales roughly as the size of the Hill sphere calculated at the asteroid's pericenter. It was also found that solar radiation pressure is a very efficient mechanism for removing small (on the order of 0.1 mm) particles from circular asteroidal zone. Particles larger than a few centimeters are only slightly affected by radiation pressure. The results are applied to the Gaspra 951 asteroid.
The Dynamics of Orbit-Clearing for Planets on Eccentric Orbits
NASA Astrophysics Data System (ADS)
Hastings, Danielle; Margot, Jean-Luc
2016-10-01
The third requirement in the 2006 International Astronomical Union (IAU) definition of a planet is that the object has cleared the neighborhood around its orbit. Margot (2015) proposed a metric that quantitatively determines if an object has enough mass to clear an orbital zone of a specific extent within a defined time interval. In this metric, the size of the zone to be cleared is given by CRH, where C is a constant and RH is the Hill Radius. Margot (2015) adopts C=2*31/2 to describe the minimum extent of orbital clearing on the basis of the planet's feeding zone. However, this value of C may only apply for eccentricities up to about 0.3 (Quillen & Faber 2006). Here, we explore the timescales and boundaries of orbital clearing for planets over a range of orbital eccentricities and planet-star mass ratios using the MERCURY integration package (Chambers 1999). The basic setup for the integrations includes a single planet orbiting a star and a uniform distribution of massless particles extending beyond CRH. The system is integrated for at least 106 revolutions and the massless particles are tracked in order to quantify the timescale and extent of the clearing.
Habitability of planets on eccentric orbits: Limits of the mean flux approximation
NASA Astrophysics Data System (ADS)
Bolmont, Emeline; Libert, Anne-Sophie; Leconte, Jeremy; Selsis, Franck
2016-06-01
Unlike the Earth, which has a small orbital eccentricity, some exoplanets discovered in the insolation habitable zone (HZ) have high orbital eccentricities (e.g., up to an eccentricity of ~0.97 for HD 20782 b). This raises the question of whether these planets have surface conditions favorable to liquid water. In order to assess the habitability of an eccentric planet, the mean flux approximation is often used. It states that a planet on an eccentric orbit is called habitable if it receives on average a flux compatible with the presence of surface liquid water. However, because the planets experience important insolation variations over one orbit and even spend some time outside the HZ for high eccentricities, the question of their habitability might not be as straightforward. We performed a set of simulations using the global climate model LMDZ to explore the limits of the mean flux approximation when varying the luminosity of the host star and the eccentricity of the planet. We computed the climate of tidally locked ocean covered planets with orbital eccentricity from 0 to 0.9 receiving a mean flux equal to Earth's. These planets are found around stars of luminosity ranging from 1 L⊙ to 10-4L⊙. We use a definition of habitability based on the presence of surface liquid water, and find that most of the planets considered can sustain surface liquid water on the dayside with an ice cap on the nightside. However, for high eccentricity and high luminosity, planets cannot sustain surface liquid water during the whole orbital period. They completely freeze at apoastron and when approaching periastron an ocean appears around the substellar point. We conclude that the higher the eccentricity and the higher the luminosity of the star, the less reliable the mean flux approximation.
Launch window analysis of satellites in high eccentricity or large circular orbits
NASA Technical Reports Server (NTRS)
Renard, M. L.; Bhate, S. K.; Sridharan, R.
1973-01-01
Numerical methods and computer programs for studying the stability and evolution of orbits of large eccentricity are presented. Methods for determining launch windows and target dates are developed. Mathematical models are prepared to analyze the characteristics of specific missions.
Nebular gas drag and planetary accretion. II. Planet on an eccentric orbit.
NASA Astrophysics Data System (ADS)
Kary, David M.; Lissauer, Jack J.
1995-09-01
We study the trajectories of planetesimals whose orbits decay starward as a result of gas drag and are perturbed by the gravity of a massive planet on an eccentric orbit. Each planetesimal ultimately suffers one of three possible fates: (1) trapping in a mean motion resonance with the planet, (2) accretion by the planet, or (3) passage by the planet and continued orbital decay. At moderate to large planetary eccentricity, numerical 3-body integrations of the motion of a planetesimal in the solar nebula demonstrate that migrating planetesimals can become trapped in the 1/1 resonance. These bodies initially have large libration amplitudes (approaching 2π) which decay down to 0 at the trailing Lagrange point. With some combinations of drag rate and planetary eccentricity, over 15% of the planetesimals which encounter the planet are trapped in the 1/1 resonance. Bodies trapped in the this way could be the precursors of the Trojan asteroids. Migrating planetesimals can be caught in both pure Lindblad and combined Lindblad/corotation resonances exterior to the planet's orbit. Trapping has been found in several j/( j + k) resonances with k's ranging from 1 to 4. As one considers larger planetary eccentricities, corotation resonances become more important than Lindblad resonances, and (for a given drag rate) trapping can occur at higher k's and farther from the planet. At large planetary eccentricities, planetesimals can also be caught in ( j + 1)/ j Lindblad/corotation resonances interior to the planet. Interior trapping, which is dynamically forbidden in the case of a planet on a circular orbit, requires planetary eccentricity to increase both the planetesimal's semimajor axis and its eccentricity near conjunction to counter gas drag. Provided the planetesimal's and planet's apoapses are roughly aligned, and conjunction occurs while both bodies are approaching apoapse, then the planetesimal can become trapped in an interior resonance. The probability of a planetesimal
Low Lunar Orbit Design via Graphical Manipulation of Eccentricity Vector Evolution
NASA Technical Reports Server (NTRS)
Wallace, Mark S.; Sweetser, Theodore H.; Roncoli, Ralph B.
2012-01-01
Low lunar orbits, such as those used by GRAIL and LRO, experience predictable variations in the evolution of their eccentricity vectors. These variations are nearly invariant with respect to the initial eccentricity and argument of periapse and change only in the details with respect to the initial semi-major axis. These properties suggest that manipulating the eccentricity vector evolution directly can give insight into orbit maintenance designs and can reduce the number of propagations required. A trio of techniques for determining the desired maneuvers is presented in the context of the GRAIL extended mission.
Determining the Eccentricity of the Moon's Orbit without a Telescope
NASA Astrophysics Data System (ADS)
Krisciunas, Kevin
2010-01-01
Ancient Greek astronomers knew that Moon's distance from the Earth was not constant. Ptolemy's model of the Moon's motion implied that the Moon ranged in distance from 33 to 64 Earth radii. This implied that its angular size ranged nearly a factor of two. Tycho Brahe's model of the Moon's motion implied a smaller distance range, some ±3 percent at syzygy. However, the ancient and Renaissance astronomers are notably silent on the subject of measuring the angular size of the Moon as a check on the implied range of distance from their models of the position of the Moon. Using a quarter-inch hole in a piece of cardboard that slides along a yardstick, we show that pre-telescopic astronomers could have measured an accurate mean value of the angular size of the Moon, and that they could have determined a reasonably accurate value of the eccentricity of the Moon's orbit. The principal calibration for each observer is to measure the apparent angular diameter of a 91 mm disk viewed at a distance of 10 meters, giving a true angular size of 31.3 arcmin (the Moon's mean angular size). Because the sighting hole is not much bigger than the size of one's pupil, each observer obtains a personal correction factor with which to scale the raw measures. If one takes data over the course of 7 lunations (7.5 anomalistic months), any systematic errors which are a function of phase should even out over the course of the observations. We find that the random error of an individual observation of ±0.8 arcmin can be achieved.
Eccentricity pumping of a planet on an inclined orbit by a disc
NASA Astrophysics Data System (ADS)
Terquem, Caroline; Ajmia, Aikel
2010-05-01
In this paper, we show that the eccentricity of a planet on an inclined orbit with respect to a disc can be pumped up to high values by the gravitational potential of the disc, even when the orbit of the planet crosses the disc plane. This process is an extension of the Kozai effect. If the orbit of the planet is well inside the disc inner cavity, the process is formally identical to the classical Kozai effect. If the planet's orbit crosses the disc but most of the disc mass is beyond the orbit, the eccentricity of the planet grows when the initial angle between the orbit and the disc is larger than some critical value which may be significantly smaller than the classical value of 39°. Both the eccentricity and the inclination angle then vary periodically with time. When the period of the oscillations of the eccentricity is smaller than the disc lifetime, the planet may be left on an eccentric orbit as the disc dissipates.
Orbit Control of Fly-around Satellite with Highly Eccentric Orbit Using Solar Radiation Pressure
NASA Astrophysics Data System (ADS)
Yong-gang, Hou; Chang-yin, Zhao; Ming-jiang, Zhang; Rong-yu, Sun
2017-01-01
The method of controlling highly eccentric accompanying flight orbit using the solar wing is proposed in this paper. The formation is maintained by controlling the orbit of the accompanying satellite (follower). The accompanying satellite rotates around its inertial principal axis with a constant angular velocity. The control on the accompanying satellite is divided into the in-plane control and out-of-plane control. The in-plane control is superior to the out-of-plane control. The out-of-plane control force is applied when the in-plane error is eliminated or the in-plane control force can not be supplied due to some geometrical factors. By the sliding mode control method, the magnitude and direction of the control force required by the in-plane orbit control are calculated. Then accordingly, the expression of the solar wing orientation with respect to the satellite body in the control process is derived, so that by adjusting the orientation of the solar wing, the required control force can be obtained. Finally, the verification on this method is performed by numerical simulations, including the orbit adjustment, error elimination, and the orbit maintenance. It is shown that this method can keep the error less than 5 m, and it is feasible for the space formation flight.
Eccentricity growth and orbit flip in near-coplanar hierarchical three-body systems
Li, Gongjie; Naoz, Smadar; Kocsis, Bence; Loeb, Abraham
2014-04-20
The secular dynamical evolution of a hierarchical three-body system in which a distant third object orbits around a binary has been studied extensively, demonstrating that the inner orbit can undergo large eccentricity and inclination oscillations. It was shown before that starting with a circular inner orbit, large mutual inclination (40°-140°) can produce long timescale modulations that drive the eccentricity to extremely large values and can flip the orbit. Here, we demonstrate that starting with an almost coplanar configuration, for eccentric inner and outer orbits, the eccentricity of the inner orbit can still be excited to high values, and the orbit can flip by ∼180°, rolling over its major axis. The ∼180° flip criterion and the flip timescale are described by simple analytic expressions that depend on the initial orbital parameters. With tidal dissipation, this mechanism can produce counter-orbiting exoplanetary systems. In addition, we also show that this mechanism has the potential to enhance the tidal disruption or collision rates for different systems. Furthermore, we explore the entire e {sub 1} and i {sub 0} parameter space that can produce flips.
A Class of Selenocentric Retrograde Orbits With Innovative Applications to Human Lunar Operations
NASA Technical Reports Server (NTRS)
Adamo, Daniel R.; Lester, Daniel F.; Thronson, Harley A.; Barbee, Brent
2014-01-01
Selenocentric distant retrograde orbits with radii from approx. 12,500 km to approx. 25,000 km are assessed for stability and for suitability as crewed command and control infrastructure locations in support of telerobotic lunar surface operations and interplanetary human transport. Such orbits enable consistent transits to and from Earth at virtually any time if they are coplanar with the Moon's geocentric orbit. They possess multiple attributes and applications distinct from NASA's proposed destination orbit for a redirected asteroid about 70,000 km from the Moon.
The Transit Ingress and the Tilted Orbit of the Extraordinarily Eccentric Exoplanet HD 80606b
NASA Technical Reports Server (NTRS)
Winn, Joshua N.; Howard, Andrew W.; Johnson, John A.; Marcy, Geoffrey W.; Gazak, J. Zachary; Starkey, Donn; Ford, Eric B.; Colon, Knicole D.; Reyes, Francisco; Nortmann, Lisa; Dreizler, Stefan; Odewahn, Stephen; Welsh, William F.; Kadakia, Shimonee; Vanderbei, Robert J.; Adams, Elisabeth R.; Lockhart, Matthew; Crossfield, Ian J.; Valenti, Jeff A.; Dantowitz, Ronald; Carter, Joshua A.
2009-01-01
We reported the first detection of the transit ingress, revealing the transit duration to be 11.64 plus or minus 0.25 hr and allowing more robust determinations of the system parameters. Keck spectra obtained at midtransit exhibited an anomalous blueshift, giving definitive evidence that the stellar spin axis and planetary orbital axis are misaligned. Thus, the orbit of this planet is not only highly eccentric but is also tilted away from the equatorial plane of its parent star. A large tilt had been predicted, based on the idea that the planet's eccentric orbit was caused by the Kozai mechanism.
Moorhead, Althea V.; Ford, Eric B.; Morehead, Robert C.; Rowe, Jason; Caldwell, Douglas A.; Jenkins, Jon M.; Li Jie; Quintana, Elisa; Borucki, William J.; Bryson, Stephen T.; Koch, David G.; Lissauer, Jack J.; Batalha, Natalie M.; Fabrycky, Daniel C.; Lucas, Philip; Marcy, Geoffrey W.
2011-11-01
Doppler planet searches have discovered that giant planets follow orbits with a wide range of orbital eccentricities, revolutionizing theories of planet formation. The discovery of hundreds of exoplanet candidates by NASA's Kepler mission enables astronomers to characterize the eccentricity distribution of small exoplanets. Measuring the eccentricity of individual planets is only practical in favorable cases that are amenable to complementary techniques (e.g., radial velocities, transit timing variations, occultation photometry). Yet even in the absence of individual eccentricities, it is possible to study the distribution of eccentricities based on the distribution of transit durations (relative to the maximum transit duration for a circular orbit). We analyze the transit duration distribution of Kepler planet candidates. We find that for host stars with T{sub eff} > 5100 K we cannot invert this to infer the eccentricity distribution at this time due to uncertainties and possible systematics in the host star densities. With this limitation in mind, we compare the observed transit duration distribution with models to rule out extreme distributions. If we assume a Rayleigh eccentricity distribution for Kepler planet candidates, then we find best fits with a mean eccentricity of 0.1-0.25 for host stars with T{sub eff} {<=} 5100 K. We compare the transit duration distribution for different subsets of Kepler planet candidates and discuss tentative trends with planetary radius and multiplicity. High-precision spectroscopic follow-up observations for a large sample of host stars will be required to confirm which trends are real and which are the results of systematic errors in stellar radii. Finally, we identify planet candidates that must be eccentric or have a significantly underestimated stellar radius.
THREE-DIMENSIONAL ATMOSPHERIC CIRCULATION OF HOT JUPITERS ON HIGHLY ECCENTRIC ORBITS
Kataria, T.; Showman, A. P.; Lewis, N. K.; Fortney, J. J.; Marley, M. S.; Freedman, R. S.
2013-04-10
Of the over 800 exoplanets detected to date, over half are on non-circular orbits, with eccentricities as high as 0.93. Such orbits lead to time-variable stellar heating, which has major implications for the planet's atmospheric dynamical regime. However, little is known about the fundamental dynamical regime of such planetary atmospheres, and how it may influence the observations of these planets. Therefore, we present a systematic study of hot Jupiters on highly eccentric orbits using the SPARC/MITgcm, a model which couples a three-dimensional general circulation model (the MITgcm) with a plane-parallel, two-stream, non-gray radiative transfer model. In our study, we vary the eccentricity and orbit-average stellar flux over a wide range. We demonstrate that the eccentric hot Jupiter regime is qualitatively similar to that of planets on circular orbits; the planets possess a superrotating equatorial jet and exhibit large day-night temperature variations. As in Showman and Polvani, we show that the day-night heating variations induce momentum fluxes equatorward to maintain the superrotating jet throughout its orbit. We find that as the eccentricity and/or stellar flux is increased (corresponding to shorter orbital periods), the superrotating jet strengthens and narrows, due to a smaller Rossby deformation radius. For a select number of model integrations, we generate full-orbit light curves and find that the timing of transit and secondary eclipse viewed from Earth with respect to periapse and apoapse can greatly affect what we see in infrared (IR) light curves; the peak in IR flux can lead or lag secondary eclipse depending on the geometry. For those planets that have large temperature differences from dayside to nightside and rapid rotation rates, we find that the light curves can exhibit 'ringing' as the planet's hottest region rotates in and out of view from Earth. These results can be used to explain future observations of eccentric transiting exoplanets.
NASA Astrophysics Data System (ADS)
Mikóczi, Balázs; Forgács, Péter; Vasúth, Mátyás
2015-08-01
The inspiral and merger of supermassive black hole binary systems with high orbital eccentricity are among the promising sources of the advanced gravitational wave observatories. In this paper we compute gravitational waveforms in the frequency domain to the first post-Newtonian order, emitted by compact binary systems with arbitrary eccentricity. Our results are fully analytic, ready-to-use expressions of the waveforms in terms of a suitable generalization of Hansen coefficients known from celestial mechanics. Secular terms induced by the eccentricity are eliminated by introducing a suitable phase shift. The obtained waveforms have a rather simple structure, greatly facilitating their use in applications.
Contraction of high eccentricity satellite orbits using K-S elements with air drag.
NASA Astrophysics Data System (ADS)
Sharma, R. K.
1998-06-01
A new non-singular analytical theory for the contraction of high eccentricity satellite orbits under the influence of air drag is developed in terms of the K-S elements, using a spherically symmetrical atmospheric model. The series expansions include up to sixth power in terms of an independent variable λ, used by King-Hele in his theory. Numerical experimentation establishes a supremacy of the present theory over that of King-Hele over a wide range of the involved orbital parameters. The theory can be used effectively for the orbital decay of geostationary transfer orbits and during the mission planning of aeroassisted orbital transfer orbits.
Stripping of satellites on prograde and retrograde orbits
NASA Astrophysics Data System (ADS)
Gajda, Grzegorz; Łokas, Ewa L.
2017-03-01
We derived a revised expression for the tidal radius, which is a theoretical boundary of a satellite orbiting a host. Our expression properly takes into account possible rotation of the satellite. We verified our predictions against simulations and obtained satisfactory agreement.
Contraction of high eccentricity satellite orbits using KS elements in an oblate atmosphere
NASA Astrophysics Data System (ADS)
Sharma, Ram Krishan
1999-01-01
A non-singular analytical theory for the contraction of high eccentricity orbits (eccentricity e > 0.5) under the influence of air drag is developed in terms of the KS elements, using an oblate exponential atmospheric model. With the help of MACSYMA software, the series expansions include up to the sixth power in terms of an independent variable λ, introduced by Sterne as cos E = 1 - H λ2 / a e, where E and a are the eccentric anomaly and semi-major axis of the orbit and H, the density scale height, is assumed constant. The solution is tested numerically over a wide range of orbital parameters: perigee height (Hp), e and inclination (i) up to 100 revolutions and is found to be quite accurate. The % error in the semi-major axis computation when compared with numerically integrated values, for test cases whose perigee heights vary from 150 to 300 km and eccentricities increase from 0.6 to 0.8, is found to be less than one. The decay rates of a and e are found to be lower than those obtained with spherically symmetrical atmospheric models and increasing with increase in inclination. The theory can be effectively used for the orbital decay of Molniya type of communication satellites, decay of geostationary transfer orbits and during mission planning of aeroassisted orbital transfer orbits.
Non-numeric computation for high eccentricity orbits. [Earth satellite orbit perturbation
NASA Technical Reports Server (NTRS)
Sridharan, R.; Renard, M. L.
1975-01-01
Geocentric orbits of large eccentricity (e = 0.9 to 0.95) are significantly perturbed in cislunar space by the sun and moon. The time-history of the height of perigee, subsequent to launch, is particularly critical. The determination of 'launch windows' is mostly concerned with preventing the height of perigee from falling below its low initial value before the mission lifetime has elapsed. Between the extremes of high accuracy digital integration of the equations of motion and of using an approximate, but very fast, stability criteria method, this paper is concerned with the developement of a method of intermediate complexity using non-numeric computation. The computer is used as the theory generator to generalize Lidov's theory using six osculating elements. Symbolic integration is completely automatized and the output is a set of condensed formulae well suited for repeated applications in launch window analysis. Examples of applications are given.
Habitability of planets on eccentric orbits: limits of the mean flux approximation??
NASA Astrophysics Data System (ADS)
Bolmont, Emeline; Libert, Anne-Sophie; Leconte, Jeremy; Selsis, Franck
2015-07-01
A few of the planets found in the insolation habitable zone (as defined by Kasting et al. 1993) are on eccentric orbits, such as HD 136118 b (eccentricity of ˜0.3, Wittenmyer et al. 2009). This raises the question of the potential habitability of planets that only spend a fraction of their orbit in the habitable zone. Usually for a planet of semi-major axis a and eccentricity e, the averaged flux over one orbit received by the planet is considered. This averaged flux corresponds to the flux received by a planet on a circular orbit of radius r = a(1-eˆ2)ˆ1/4. If this orbital distance is within the habitable zone, the planet is considered "habitable". However, for a hot star, for which the habitable zone is far from the star, the climate can be degraded when the planet is temporarily outside the habitable zone. The influence of the orbital eccentricity of a planet on its climate has already been studied for Earth-like conditions (same star, same rotation period), with Global Climate Models (GCM) such as in Williams & Pollard 2002 and Linsenmeier et al. 2014. Spiegel 2010 and Dressing et al. 2010 have also studied the effect of eccentricity for more diverse conditions with energy-balanced models. We performed a set of simulations using the Global Climate Model LMDz (Wordsworth et al. 2011, Forget et al. 2013, Leconte et al. 2013). We computed the climate of aqua planets receiving a mean flux equal to Earth's, around stars of luminosity ranging from 1 Lsun to 10-4 Lsun and of orbital eccentricity from 0 to 0.9. We show the limits of the mean flux approximation, depending on the previous parameters and also the thermal inertia of oceans.
Analytical approach using KS elements to high eccentricity orbit predictions including drag
NASA Astrophysics Data System (ADS)
Sharma, Ram Krishan; Raj, M. Xavier James
2010-03-01
A new non-singular analytical theory for the contraction of high eccentricity satellite orbits under the influence of air drag is developed in terms of the KS elements using an oblate atmosphere with variation of density scale height with altitude. The series expansions include up to fourth power in terms of an independent variable Λ (function of the eccentric anomaly) and c (a small parameter dependent on the flattening of the atmosphere). Only two of the nine equations are solved analytically to compute the state vector and change in energy at the end of each revolution, due to symmetry in the equations of motion. It is observed that the analytically computed values of the semi-major axis (a) and eccentricity (e) match very well with the numerically integrated values up to 1000 revolutions over a wide range of the drag perturbed orbital parameters. Inclusion of the density scale height variation with altitude is found to increase the decay of the high eccentricity orbits up to eight percent. The theory can be used effectively for the orbital decay of aero-assisted orbital transfer orbits during mission planning.
Continuous, Low Thrust Coplanar Orbit Transfers with Varying Eccentricity
1988-12-01
velocity change and time for the constrained radii transfer. The program incorporates an ordinary differential equations integrator equipped with a...addition, other approaches to optimizing the eccentric transfer problem should be consid- ered in hopes of achieving better performance. For example...Form . . . . . 2-13 Planar Thrust Angle Optimal Control Law 2-14 Unconstrained Problem . . . . 2-14 Constrained Problem . . . . 2-17 Resulting
Effect of the orbit eccentricity on remote sensing micro-satellite attitude Kalman filtering
NASA Astrophysics Data System (ADS)
Roubache, Rima
Remote sensing satellites are required to meet stringent pointing and drift rate requirements for imaging operations. For achieving these pointing and stability requirements, continuous and accurate three-axis attitude information is required. This paper investigates the influence of the orbit eccentricity on the performance of the attitude determination and control subsystem pointing of passive Low Earth Orbit imaging satellites stabilized by a gravity gradient boom. Any non-symmetrical object of finite dimensions in orbit is subject to a gravitational torque because of the variation in earth’s gravitational force on the object. The gravity gradient torque results from the inverse square gravitational force field. For most applications, it is sufficient to assume a spherical mass distribution for the earth. The gravity gradient torque in the case of a non-circular orbit is used in this paper. The Quaternion-based Extended Kalman Filter is analyzed when the orbit eccentricity is considered in order to determine the influence of this disturbance on the convergence and stability of the filter. The simulations in this work are based on the true parameters of ALSAT-1 which is a typical LEO satellite stabilized by a gravity gradient boom. The results show that the orbit eccentricity has a big influence on the pointing system accuracy causing micro-vibrations that affect the geocentric pointing particularly after the de-orbiting phase. In this case, satellites have no orbital correction option. The Quaternion-based Extended Kalman Filter analyzed in this paper, achieved satisfactory results for eccentricity values less than 0.4 with respect to pointing system accuracy. However, singularities were observed for eccentricity values greater than 0.4.
CLIMATE PATTERNS OF HABITABLE EXOPLANETS IN ECCENTRIC ORBITS AROUND M DWARFS
Wang, Yuwei; Hu, Yongyun; Tian, Feng
2014-08-10
Previous studies show that synchronous rotating habitable exoplanets around M dwarfs should have an ''eyeball'' climate pattern—a limited region of open water on the day side and ice on the rest of the planet. However, exoplanets with nonzero eccentricities could have spin-orbit resonance states different from the synchronous rotation state. Here, we show that a striped-ball climate pattern, with a global belt of open water at low and middle latitudes and ice over both polar regions, should be common on habitable exoplanets in eccentric orbits around M dwarfs. We further show that these different climate patterns can be observed by future exoplanet detection missions.
A semi-empirical stability criterion for real planetary systems with eccentric orbits
NASA Astrophysics Data System (ADS)
Giuppone, C. A.; Morais, M. H. M.; Correia, A. C. M.
2013-12-01
We test a crossing orbit stability criterion for eccentric planetary systems, based on Wisdom's criterion of first-order mean motion resonance overlap. We show that this criterion fits the stability regions in real exoplanet systems quite well. In addition, we show that elliptical orbits can remain stable even for regions where the apocentre distance of the inner orbit is larger than the pericentre distance of the outer orbit, as long as the initial orbits are aligned. The analytical expressions provided here can be used to put rapid constraints on the stability zones of multiplanetary systems. As a byproduct of this research, we further show that the amplitude variations of the eccentricity can be used as a fast-computing stability indicator.
THE INFLUENCE OF ORBITAL ECCENTRICITY ON TIDAL RADII OF STAR CLUSTERS
Webb, Jeremy J.; Harris, William E.; Sills, Alison; Hurley, Jarrod R.
2013-02-20
We have performed N-body simulations of star clusters orbiting in a spherically symmetric smooth galactic potential. The model clusters cover a range of initial half-mass radii and orbital eccentricities in order to test the historical assumption that the tidal radius of a cluster is imposed at perigalacticon. The traditional assumption for globular clusters is that since the internal relaxation time is larger than its orbital period, the cluster is tidally stripped at perigalacticon. Instead, our simulations show that a cluster with an eccentric orbit does not need to fully relax in order to expand. After a perigalactic pass, a cluster recaptures previously unbound stars, and the tidal shock at perigalacticon has the effect of energizing inner region stars to larger orbits. Therefore, instead of the limiting radius being imposed at perigalacticon, it more nearly traces the instantaneous tidal radius of the cluster at any point in the orbit. We present a numerical correction factor to theoretical tidal radii calculated at perigalacticon which takes into consideration both the orbital eccentricity and current orbital phase of the cluster.
Eccentric orbit E/IMRI gravitational wave fluxes to 7PN order
NASA Astrophysics Data System (ADS)
Forseth, Erik; Evans, Charles R.; Hopper, Seth
2016-03-01
Knowledge of gravitational wave fluxes (energy and angular momentum, at both infinity and the horizon) from eccentric-orbit inspirals is extended from 3PN to 7PN order at lowest order in small mass ratio. Previous post-Newtonian eccentric-orbit results up to 3PN relative order are confirmed by our new black hole perturbation calculations. The calculations are based on Mano, Suzuki, and Takasugi (MST) analytic function expansions, and results are computed to 200 decimal places of accuracy using Mathematica. Over 1,700 distinct orbits were computed, each with as many as 7,000 Fourier-harmonic modes. A large number of PN coefficients between 3.5PN and 7PN orders were determined, either in exact analytic form or with accurate numerical values, in expansions in powers of a PN compactness parameter and its logarithm, and powers of eccentricity. We show a parametrization that removes singularities in the fluxes as the eccentricity approaches unity, thus making the expansions more convergent at high eccentricity. We also found (nearly) arbitrarily accurate expansions for the previously discussed 1.5PN, 2.5PN, and 3PN hereditary terms.
Stellar encounters as the origin of distant Solar System objects in highly eccentric orbits.
Kenyon, Scott J; Bromley, Benjamin C
2004-12-02
The Kuiper belt extends from the orbit of Neptune at 30 au to an abrupt outer edge about 50 au from the Sun. Beyond the edge is a sparse population of objects with large orbital eccentricities. Neptune shapes the dynamics of most Kuiper belt objects, but the recently discovered planet 2003 VB12 (Sedna) has an eccentric orbit with a perihelion distance of 70 au, far beyond Neptune's gravitational influence. Although influences from passing stars could have created the Kuiper belt's outer edge and could have scattered objects into large, eccentric orbits, no model currently explains the properties of Sedna. Here we show that a passing star probably scattered Sedna from the Kuiper belt into its observed orbit. The likelihood that a planet at 60-80 au can be scattered into Sedna's orbit is about 50 per cent; this estimate depends critically on the geometry of the fly-by. Even more interesting is the approximately 10 per cent chance that Sedna was captured from the outer disk of the passing star. Most captures have very high inclination orbits; detection of such objects would confirm the presence of extrasolar planets in our own Solar System.
Secular evolution of very eccentric, inclined orbits around a supermassive rotating black hole
NASA Astrophysics Data System (ADS)
Will, Clifford; Maitra, Matthew
2017-01-01
We analyze the secular evolution of the highly eccentric, inclined orbit of a star or black hole in the field of a rotating massive Kerr black hole. Such orbits, with 1 - e ranging from 10-2 to 10-6 may be the end result of a process of stellar interactions in a dense nuclear star cluster surrounding the black hole, leading to extreme-mass ratio inspirals (EMRIs). The calculations are done in post-Newtonian (PN) theory, through 3PN order in the conservative sector, including spin-orbit, quadrupolar and (spin)2 terms from the Kerr geometry, and through 4.5PN order, including 4PN spin-orbit contributions, in the radiation reaction sector. We also incorporate an accurate criterion for capture of the body by the rotating black hole for arbitrary inclinations. For a range of initial values of the body's semi-major axis, eccentricity and inclination, we determine the time and number of orbits until plunge and the final orbital eccentricity. We also estimate the gravitational-wave frequency and energy flux at the final plunge, as a function of the orbital inclination. Supported in part by the National Science Foundation PHY 13-06069 & PHY 16-00188.
Orbital stability of coplanar two-planet exosystems with high eccentricities
NASA Astrophysics Data System (ADS)
Antoniadou, Kyriaki I.; Voyatzis, George
2016-10-01
The long-term stability of the evolution of two-planet systems is considered by using the general three body problem (GTBP). Our study is focused on the stability of systems with adjacent orbits when at least one of them is highly eccentric. In these cases, in order for close encounters, which destabilize the planetary systems, to be avoided, phase protection mechanisms should be considered. Additionally, since the GTBP is a non-integrable system, chaos may also cause the destabilization of the system after a long time interval. By computing dynamical maps, based on Fast Lyapunov Indicator, we reveal regions in phase space with stable orbits even for very high eccentricities (e > 0.5). Such regions are present in mean motion resonances (MMRs). We can determine the position of the exact MMR through the computation of families of periodic orbits in a rotating frame. Elliptic periodic orbits are associated with the presence of apsidal corotation resonances (ACRs). When such solutions are stable, they are associated with neighbouring domains of initial conditions that provide long-term stability. We apply our methodology so that the evolution of planetary systems of highly eccentric orbits is assigned to the existence of such stable domains. Particularly, we study the orbital evolution of the extrasolar systems HD 82943, HD 3651, HD 7449, HD 89744 and HD 102272 and discuss the consistency between the orbital elements provided by the observations and the dynamical stability.
RADIO PULSAR BINARIES IN GLOBULAR CLUSTERS: THEIR ORBITAL ECCENTRICITIES AND STELLAR INTERACTIONS
Bagchi, Manjari; Ray, Alak
2009-08-20
High sensitivity searches of globular clusters (GCs) for radio pulsars by improved pulsar search algorithms and sustained pulsar timing observations have so far yielded some 140 pulsars in more than two dozen GCs. The observed distribution of orbital eccentricity and period of binary radio pulsars in GCs have imprints of the past interaction between single pulsars and binary systems or of binary pulsars and single passing noncompact stars. It is seen that GCs have different groups of pulsars. These may have arisen out of exchange or merger of a component of the binary with the incoming star or a 'fly-by' in which the original binary remains intact but undergoes a change of eccentricity and orbital period. We consider the genesis of the distribution of pulsars using analytical and computational tools such as STARLAB, which performs numerical scattering experiments with direct N-body integration. Cluster pulsars with intermediate eccentricities can mostly be accounted for by fly-bys, whereas those with high eccentricities are likely to be the result of exchanges and/or mergers of single stars with the binary companion of the pulsar, although there are a few objects which do not easily fit into this description. The corresponding distribution for galactic field pulsars shows notable differences from the GC pulsar orbital period and eccentricity distribution. The long orbital period pulsars in the galactic field with frozen out low eccentricities are largely missing from the GCs, and we show that the ionization of these systems in GCs cannot alone account for the peculiarities.
Distant Retrograde Orbits for space-based Near Earth Objects detection
NASA Astrophysics Data System (ADS)
Stramacchia, Michele; Colombo, Camilla; Bernelli-Zazzera, Franco
2016-09-01
We analyse a concept for the detection of Potentially Hazardous Asteroids (PHAs) from a space-based network of telescopes on retrograde Distant Periodic Orbits. Planar periodic orbits are designed in the Sun-Earth circular restricted three-body problem, starting from initial conditions in the Hill's problem available from the literature. A family of retrograde orbits centred at the Earth is selected as baseline, based on their maximum distance from Earth, larger than the Earth-L2 distance. Indeed, spacecraft on such orbits can detect PHAs incoming from the Sun direction, which could not otherwise be monitored from current Earth-based systems. A trade-off on the orbit amplitude, asteroid diameter to be detected, and the constellation size is performed considering current visible sensor telescope technology. The Chelyabinsk meteor scenario is studied and the potential warning time that could be gained with a space-based survey system with respect to an Earth based-survey system is shown.
Measuring the Eccentricity of the Earth's Orbit with a Nail and a Piece of Plywood
ERIC Educational Resources Information Center
Lahaye, Thierry
2012-01-01
I describe how to obtain a rather good experimental determination of the eccentricity of the Earth's orbit, as well as the obliquity of the Earth's rotation axis, by measuring, over the course of a year, the elevation of the Sun as a function of time during a day. With a very simple "instrument" consisting of an elementary sundial, first-year…
Low-Thrust Transfers from Distant Retrograde Orbits to L2 Halo Orbits in the Earth-Moon System
NASA Technical Reports Server (NTRS)
Parrish, Nathan L.; Parker, Jeffrey S.; Hughes, Steven P.; Heiligers, Jeannette
2016-01-01
This paper presents a study of transfers between distant retrograde orbits (DROs) and L2 halo orbits in the Earth-Moon system that could be flown by a spacecraft with solar electric propulsion (SEP). Two collocation-based optimal control methods are used to optimize these highly-nonlinear transfers: Legendre pseudospectral and Hermite-Simpson. Transfers between DROs and halo orbits using low-thrust propulsion have not been studied previously. This paper offers a study of several families of trajectories, parameterized by the number of orbital revolutions in a synodic frame. Even with a poor initial guess, a method is described to reliably generate families of solutions. The circular restricted 3-body problem (CRTBP) is used throughout the paper so that the results are autonomous and simpler to understand.
Habitability of planets on eccentric orbits: limits of the mean flux approximation
NASA Astrophysics Data System (ADS)
Bolmont, Emeline; Libert, Anne-Sophie; Leconte, Jérémy; Selsis, Franck; Turbet, Martin; Forget, François
2016-04-01
A few of the planets found in the insolation habitable zone (region in which a planet with an atmosphere can sustain surface liquid water, Kasting et al. 1993) are on eccentric orbits, such as GJ 667Cc (eccentricity of < 0.3, Anglada-Escude et al. 2012) or HD 16175 b (eccentricity of 0.6, Peek et al. 2009). This raises the question of the potential habitability of planets that only spend a fraction of their orbit in the habitable zone. Usually for a planet of semi-major axis a and eccentricity e, the averaged flux over one orbit received by the planet is considered. This averaged flux corresponds to the flux received by a planet on a circular orbit of radius r = a(1 -e2)1/4. If this orbital distance is within the habitable zone, the planet is said "habitable". However, for a hot star, for which the habitable zone is far from the star, the climate can be degraded when the planet is temporarily outside the habitable zone. We investigate here the limits of validity of the mean flux approximation used to assess the potential habitability of eccentric planets. For this study, we consider ocean planets in synchronized rotation and planets with a rotation period of 24 hr. We investigate the influence of the type of host star and the eccentricity of the orbit on the climate of a planet. We do so by scaling the duration of its orbital period and its apastron and periastron distance to ensure that it receives in average the same incoming flux as Earth's. We performed sets of 3D simulations using the Global Climate Model LMDz (Wordsworth et al. 2011, Forget et al. 2013, Leconte et al. 2013). The atmosphere is composed of N2, CO2 and H2O (gas, liquid, solid) in Earth-like proportions. First, we do not take into account the spectral difference between a low luminosity star and a Sun-like star. Second, the dependence of the albedo of ice and snow on the spectra of the host star is taken into account. This influences the positive ice-albedo feedback and can lead to a different
Orbital Evolution of Mass-transferring Eccentric Binary Systems. II. Secular Evolution
NASA Astrophysics Data System (ADS)
Dosopoulou, Fani; Kalogera, Vicky
2016-07-01
Finite eccentricities in mass-transferring eccentric binary systems can be explained by taking into account the mass loss and mass transfer processes that often occur in these systems. These processes can be treated as perturbations of the general two-body problem. The time-evolution equations for the semimajor axis and the eccentricity derived from perturbative methods are generally phase-dependent. The osculating semimajor axis and eccentricity change over the orbital timescale and are not easy to implement in binary evolution codes like MESA. However, the secular orbital element evolution equations can be simplified by averaging over the rapidly varying true anomalies. In this paper, we derive the secular time-evolution equations for the semimajor axis and the eccentricity for various mass loss/transfer processes using either the adiabatic approximation or the assumption of delta-function mass loss/transfer at periastron. We begin with the cases of isotropic and anisotropic wind mass loss. We continue with conservative and non-conservative non-isotropic mass ejection/accretion (including Roche-Lobe-Overflow) for both point-masses and extended bodies. We conclude with the case of phase-dependent mass accretion. Comparison of the derived equations with similar work in the literature is included and an explanation of the existing discrepancies is provided.
NASA Technical Reports Server (NTRS)
Sawyer, J. W.
1981-01-01
The effect of load eccentricity and substructure deformation on the ultimate strength and stress displacement properties of the shuttle orbiter thermal protection system (TPS) was determined. The LI-900 Reusable Surface Insulation (RSI) tiles mounted on the .41 cm thick Strain Isolator Pad (SIP) were investigated. Substructure deformations reduce the ultimate strength of the SIP/tile TPS and increase the scatter in the ultimate strength data. Substructure deformations that occur unsymmetric to the tile can cause the tile to rotate when subjected to a uniform applied load. Load eccentricity reduces SIP/tile TPS ultimate strength and causes tile rotation.
Scalar self-force for eccentric orbits around a Schwarzschild black hole
NASA Astrophysics Data System (ADS)
Vega, Ian; Wardell, Barry; Diener, Peter; Cupp, Samuel; Haas, Roland
2013-10-01
We revisit the problem of computing the self-force on a scalar charge moving along an eccentric geodesic orbit around a Schwarzschild black hole. This work extends previous scalar self-force calculations for circular orbits, which were based on a regular “effective” point-particle source and a full 3D evolution code. We find good agreement between our results and previous calculations based on a (1+1) time-domain code. Finally, our data visualization is unconventional: we plot the self-force through full radial cycles to create “self-force loops,” which reveal many interesting features that are less apparent in standard presentations of eccentric-orbit self-force data.
Orbital Evolution of Mass-transferring Eccentric Binary Systems. I. Phase-dependent Evolution
NASA Astrophysics Data System (ADS)
Dosopoulou, Fani; Kalogera, Vicky
2016-07-01
Observations reveal that mass-transferring binary systems may have non-zero orbital eccentricities. The time evolution of the orbital semimajor axis and eccentricity of mass-transferring eccentric binary systems is an important part of binary evolution theory and has been widely studied. However, various different approaches to and assumptions on the subject have made the literature difficult to comprehend and comparisons between different orbital element time evolution equations not easy to make. Consequently, no self-consistent treatment of this phase has ever been included in binary population synthesis codes. In this paper, we present a general formalism to derive the time evolution equations of the binary orbital elements, treating mass loss and mass transfer as perturbations of the general two-body problem. We present the self-consistent form of the perturbing acceleration and phase-dependent time evolution equations for the orbital elements under different mass loss/transfer processes. First, we study the cases of isotropic and anisotropic wind mass loss. Then, we proceed with non-isotropic ejection and accretion in a conservative as well as a non-conservative manner for both point masses and extended bodies. We compare the derived equations with similar work in the literature and explain the existing discrepancies.
HAT-P-7: A Retrograde or Polar Orbit, and a Third Body
NASA Technical Reports Server (NTRS)
Winn, Joshua N.; Johnson, John Asher; Albrecht, Simon; Howard, Andrew W.; Marcy, Geoffrey W.; Crossfield, Ian J.; Holman, Matthew J.
2009-01-01
We showed that the exoplanet HAT-P-7b has an extremely tilted orbit, with a true angle of at least 86 degrees 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 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 of the usual pattern, implying that the angle between the sky-projected orbital and stellar angular momentum vectors is 182.5 plus or minus 9.4 degrees. 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.
NASA Technical Reports Server (NTRS)
Murphy, J. P.
1972-01-01
Analytical prediction of expected eccentricity perturbations for the RAE 2 lunar orbit shows that the eccentricity will grow linearly in time. Parametric inclination studies and analysis of perturbation equations establish a critical retrograde inclination of 116.565 at which the positive perturbation slope vanishes for a circular orbit about 1100 m above the lunar surface with an eccentricity constraint of less than 0.005 during a period of about one year.
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.
Gravitational self-force on eccentric equatorial orbits around a Kerr black hole
NASA Astrophysics Data System (ADS)
van de Meent, Maarten
2016-08-01
This paper presents the first calculation of the gravitational self-force on a small compact object on an eccentric equatorial orbit around a Kerr black hole to first order in the mass ratio. That is the pointwise correction to the object's equations of motion (both conservative and dissipative) due to its own gravitational field, which is treated as a linear perturbation to the background Kerr spacetime generated by the much larger spinning black hole. The calculation builds on recent advances on constructing the local metric and self-force from solutions of the Teukolsky equation, which led to the calculation of the Detweiler-Barack-Sago redshift invariant on eccentric equatorial orbits around a Kerr black hole in a previous paper. After deriving the necessary expression to obtain the self-force from the Weyl scalar ψ4, we perform several consistency checks of the method and numerical implementation, including a check of the balance law relating the orbital average of the self-force to the average flux of energy and angular momentum out of the system. Particular attention is paid to the pointwise convergence properties of the sum over frequency modes in our method, identifying a systematic inherent loss of precision that any frequency domain calculation of the self-force on eccentric orbits must overcome.
Lewis, Karen M.; Fujii, Yuka
2014-08-20
We survey the methods proposed in the literature for detecting moons of extrasolar planets in terms of their ability to distinguish between prograde and retrograde moon orbits, an important tracer of the moon formation channel. We find that most moon detection methods, in particular, sensitive methods for detecting moons of transiting planets, cannot observationally distinguishing prograde and retrograde moon orbits. The prograde and retrograde cases can only be distinguished where the dynamical evolution of the orbit due to, e.g., three body effects is detectable, where one of the two cases is dynamically unstable, or where new observational facilities, which can implement a technique capable of differentiating the two cases, come online. In particular, directly imaged planets are promising targets because repeated spectral and photometric measurements, which are required to determine moon orbit direction, could also be conducted with the primary interest of characterizing the planet itself.
The 2D surfaces that generate Newtonian and general relativistic orbits with small eccentricities
NASA Astrophysics Data System (ADS)
Middleton, Chad A.
2015-07-01
Embedding diagrams prove to be quite useful when learning general relativity as they offer a way of visualizing spacetime curvature through warped two dimensional (2D) surfaces. In this manuscript, we present a different 2D construct that also serves as a useful conceptual tool for gaining insight into gravitation: orbital dynamics—namely, the cylindrically symmetric surfaces that generate Newtonian and general relativistic orbits with small eccentricities. Although we first show that no such surface exists that can exactly reproduce the arbitrary bound orbits of Newtonian gravitation or of general relativity (or, more generally, of any spherically symmetric potential), surfaces do exist that closely approximate the resulting orbital motion for small eccentricities (exactly the regime that describes the motion of the solar system planets). These surfaces help to illustrate the similarities and differences between the two theories of gravitation (i.e., stationary elliptical orbits in Newtonian gravitation and precessing elliptical-like orbits in general relativity) and offer, in this age of 3D printing, an opportunity for students and instructors to experimentally explore the predictions made by each.
Einstein@Home DISCOVERY OF A PALFA MILLISECOND PULSAR IN AN ECCENTRIC BINARY ORBIT
Knispel, B.; Allen, B.; Lyne, A. G.; Stappers, B. W.; Freire, P. C. C.; Lazarus, P.; Aulbert, C.; Bock, O.; Eggenstein, H.-B.; Fehrmann, H.; Bogdanov, S.; Camilo, F.; Brazier, A.; Chatterjee, S.; Cordes, J. M.; Cardoso, F.; Crawford, F.; Deneva, J. S.; Ferdman, R.; Hessels, J. W. T.; and others
2015-06-10
We report the discovery of the millisecond pulsar (MSP) PSR J1950+2414 (P = 4.3 ms) in a binary system with an eccentric (e = 0.08) 22 day orbit in Pulsar Arecibo L-band Feed Array survey observations with the Arecibo telescope. Its companion star has a median mass of 0.3 M{sub ⊙} and is most likely a white dwarf (WD). Fully recycled MSPs like this one are thought to be old neutron stars spun-up by mass transfer from a companion star. This process should circularize the orbit, as is observed for the vast majority of binary MSPs, which predominantly have orbital eccentricities e < 0.001. However, four recently discovered binary MSPs have orbits with 0. 027 < e < 0.44; PSR J1950+2414 is the fifth such system to be discovered. The upper limits for its intrinsic spin period derivative and inferred surface magnetic field strength are comparable to those of the general MSP population. The large eccentricities are incompatible with the predictions of the standard recycling scenario: something unusual happened during their evolution. Proposed scenarios are (a) initial evolution of the pulsar in a triple system which became dynamically unstable, (b) origin in an exchange encounter in an environment with high stellar density, (c) rotationally delayed accretion-induced collapse of a super-Chandrasekhar WD, and (d) dynamical interaction of the binary with a circumbinary disk. We compare the properties of all five known eccentric MSPs with the predictions of these formation channels. Future measurements of the masses and proper motion might allow us to firmly exclude some of the proposed formation scenarios.
The retrograde orbit of the HAT-P-6b exoplanet
NASA Astrophysics Data System (ADS)
Hébrard, G.; Ehrenreich, D.; Bouchy, F.; Delfosse, X.; Moutou, C.; Arnold, L.; Boisse, I.; Bonfils, X.; Díaz, R. F.; Eggenberger, A.; Forveille, T.; Lagrange, A.-M.; Lovis, C.; Pepe, F.; Perrier, C.; Queloz, D.; Santerne, A.; Santos, N. C.; Ségransan, D.; Udry, S.; Vidal-Madjar, A.
2011-03-01
We observed the transit of the HAT-P-6b exoplanet across its host star with the SOPHIE spectrograph (OHP, France). The resulting stellar radial velocities display the Rossiter-McLaughlin anomaly and reveal a retrograde orbit: the planetary orbital spin and the stellar rotational spin point in approximately opposite directions. A fit to the anomaly measures a sky-projected angle λ = 166° ± 10° between these two spin axes. All seven known retrograde planets are hot Jupiters with masses Mp < 3 MJup. About two thirds of the planets in this mass range, however, are prograde and aligned (λ ≃ 0°). In contrast, most of the more massive planets (Mp > 4 MJup) are prograde but misaligned. Different mechanisms may therefore be responsible for planetary obliquities above and below ~3.5 MJup. Based on observations collected with the SOPHIE spectrograph on the 1.93-m telescope at Observatoire de Haute-Provence (CNRS), France, by the SOPHIE Consortium (program 10A.PNP.CONS).SOPHIE radial velocities are only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/527/L11
An optical survey for space debris on highly eccentric and inclined MEO orbits
NASA Astrophysics Data System (ADS)
Silha, J.; Schildknecht, T.; Hinze, A.; Flohrer, T.; Vananti, A.
2017-01-01
Optical surveys for space debris in high-altitude orbits have been conducted since more than ten years. Originally these efforts concentrated mainly on the geostationary region (GEO). Corresponding observation strategies, processing techniques and cataloguing approaches have been developed and successfully applied. The ESA GEO surveys, e.g., resulted in the detection of a significant population of small-size debris and later in the discovery of high area-to-mass ratio objects in GEO-like orbits. Comparably less experience (both, in terms of practical observation and strategy definition) is available for eccentric orbits that (at least partly) are in the MEO region, in particular for the Molniya-type orbits. Different survey and follow-up strategies for searching space debris objects in highly-eccentric MEO orbits, and to acquire orbits which are sufficiently accurate to catalog such objects and to maintain their orbits over longer time spans were developed. Simulations were performed to compare the performance of different survey and cataloguing strategies. Eventually, optical observations were conducted in the framework of an ESA study using ESA's Space Debris Telescope (ESASDT) the 1-m Zeiss telescope located at the Optical Ground Station (OGS) at the Teide Observatory at Tenerife, Spain. Thirteen nights of surveys of Molniya-type orbits were performed between January and August 2013. Eventually 255 surveys were performed during these thirteen nights corresponding to about 47 h of observations. In total 30 uncorrelated faint objects were discovered. On average one uncorrelated object was found every 100 min of observations. Some of these objects show a considerable brightness variation and have a high area-to-mass ratio as determined in the orbit estimation process.
Spin–orbit precession for eccentric black hole binaries at first order in the mass ratio
NASA Astrophysics Data System (ADS)
Akcay, Sarp; Dempsey, David; Dolan, Sam R.
2017-04-01
We consider spin–orbit (‘geodetic’) precession for a compact binary in strong-field gravity. Specifically, we compute ψ, the ratio of the accumulated spin-precession and orbital angles over one radial period, for a spinning compact body of mass m 1 and spin s 1, with {{s}1}\\ll Gm12/c , orbiting a non-rotating black hole. We show that ψ can be computed for eccentric orbits in both the gravitational self-force and post-Newtonian frameworks, and that the results appear to be consistent. We present a post-Newtonian expansion for ψ at next-to-next-to-leading order, and a Lorenz-gauge gravitational self-force calculation for ψ at first order in the mass ratio. The latter provides new numerical data in the strong-field regime to inform the effective one-body model of the gravitational two-body problem. We conclude that ψ complements the Detweiler redshift z as a key invariant quantity characterizing eccentric orbits in the gravitational two-body problem.
V474 Car: A RARE HALO RS CVn BINARY IN RETROGRADE GALACTIC ORBIT
Bubar, Eric J.; Mamajek, Eric E.; Jensen, Eric L. N.; Walter, Frederick M.
2011-04-15
We report the discovery that the star V474 Car is an extremely active, high velocity halo RS CVn system. The star was originally identified as a possible pre-main-sequence star in Carina, given its enhanced stellar activity, rapid rotation (10.3 days), enhanced Li, and absolute magnitude which places it above the main sequence (MS). However, its extreme radial velocity (264 km s{sup -1}) suggested that this system was unlike any previously known pre-MS system. Our detailed spectroscopic analysis of echelle spectra taken with the CTIO 4 m finds that V474 Car is both a spectroscopic binary with an orbital period similar to the photometric rotation period and metal-poor ([Fe/H] {approx_equal}-0.99). The star's Galactic orbit is extremely eccentric (e {approx_equal} 0.93) with a perigalacticon of only {approx}0.3 kpc of the Galactic center-and the eccentricity and smallness of its perigalacticon are surpassed by only {approx}0.05% of local F/G-type field stars. The observed characteristics are consistent with V474 Car being a high-velocity, metal-poor, tidally locked, chromospherically active binary, i.e., a halo RS CVn binary, and one of only a few such specimens known.
An optical survey for space debris on highly eccentric and inclined MEO orbits
NASA Astrophysics Data System (ADS)
Schildknecht, Thomas; Flohrer, Tim; Hinze, Andreas; Vananti, Alessandro; Silha, Jiri
Optical surveys for space debris in high-altitude orbits have been conducted since more than fifteen years. Originally these efforts concentrated mainly on the geostationary ring (GEO) and its close region. Corresponding observation strategies, processing techniques and cataloguing approaches have been developed and successfully applied. The ESA GEO surveys, e.g., resulted in the detection of a significant population of small-size debris and later in the discovery of high area-to-mass ratio objects in GEO-like orbits. The observation scenarios were successively adapted to survey the geostationary transfer orbit (GTO) region; and surveys to search for debris in the medium Earth orbit (MEO) region of the global navigation satellite constellations were successfully conducted. Comparably less experience (both, in terms of practical observation and strategy definition) is available for eccentric orbits that (at least partly) are in the MEO region, in particular for the Molniya-type orbits. Several breakup events and deliberate fragmentations are known to have taken place in such orbits. Survey and follow-up strategies for searching space debris objects in highly-eccentric MEO orbits, and to acquire orbits which are sufficiently accurate to catalogue such objects and to maintain their orbits over longer time spans were developed and, eventually, optical observations were conducted in the framework of an ESA study using ESA' Space Debris Telescope (ESASDT) the 1-m Zeiss telescope located at the Optical Ground Station (OGS) at the Teide Observatory at Tenerife, Spain. Thirteen nights of surveys of Molniya-type orbits was performed between January and August 2013. A basic survey consisted of observing a single geocentric field for 10 minutes. If a faint object was found, follow-up observations were performed during the same night to ensure a save rediscovery of the object during the next nights. Additional follow-up observations to maintain the orbits of these newly
The aphelion distribution of the Near Earth meteoroid orbits with larger eccentricities
NASA Astrophysics Data System (ADS)
Kolomiyets, Svitlana; Voloshchuk, Yury
2015-08-01
The question of the stability of the Solar System has always sparked urgency to research. In some cases, larger values of eccentricity and/or inclination can be a sign of the instability. The time has now come to extend this question to a larger number of planetary systems. The discovery of extrasolar planets systems has raised many similar questions on their formation and dynamical evolution. The origin of the surprisingly large eccentricities and/or inclinations (relative to the stellar equator) of many extrasolar planets remains elusive: planet instabilities, planet-disk interactions, external perturbations from eccentric or inclined stars remain viable options. The understanding of our own planetary system and extrasolar planets systems can leap forward only with the combination of mutual research. The time has now come to the golden years of the space exploration on the distant Solar System bodies. At the same time every day the meteoric matter penetrates in the Earth atmosphere and carries information about the various locations of the Solar system. The meteoroid orbits with large eccentricities and large aphelion distances associated with the distant locations of the Solar system. We used the data of the ground-based radar observations in Kharkiv (Ukraine) to obtain the distribution of aphelion distances for the near Earth meteoroid orbits (100341) with large eccentricities (e>0.5). We analyzed the orbital inclinations too. We obtained the complicated structure of the sporadic meteoroid complex. It is the consequence of the plurality of parent bodies and origin mechanisms of meteoroids. In addition the perturbing action of the planets, non-gravitational forces affect on the stracture of meteoroid complex. Our experimental results in 1972-1978 demonstrated meteoroid masses 10^-3 -10^-6 g. The aphelion distance of orbits for these investigated meteoroids has the range from near 1 till 2 000 AU. Undoubtedly, the meteoric matter contains key information about
Mass and eccentricity constraints on the planetary debris orbiting the white dwarf WD 1145+017
NASA Astrophysics Data System (ADS)
Gurri, Pol; Veras, Dimitri; Gänsicke, Boris T.
2017-01-01
Being the first of its kind, the white dwarf WD 1145+017 exhibits a complex system of disintegrating debris which offers a unique opportunity to study its disruption process in real time. Even with plenty of transit observations there are no clear constraints on the masses or eccentricities of such debris. Using N-body simulations, we show that masses greater than ≃1020 kg (a tenth of the mass of Ceres) or orbits that are not nearly circular (eccentricity > 10-3) dramatically increase the chances of the system becoming unstable within 2 yr, which would contrast with the observational data over this timespan. We also provide a direct comparison between transit phase shifts detected in the observations and by our numerical simulations.
Pacemaking the ice ages by frequency modulation of Earth's orbital eccentricity
Rial
1999-07-23
Evidence from power spectra of deep-sea oxygen isotope time series suggests that the climate system of Earth responds nonlinearly to astronomical forcing by frequency modulating eccentricity-related variations in insolation. With the help of a simple model, it is shown that frequency modulation of the approximate 100,000-year eccentricity cycles by the 413,000-year component accounts for the variable duration of the ice ages, the multiple-peak character of the time series spectra, and the notorious absence of significant spectral amplitude at the 413,000-year period. The observed spectra are consistent with the classic Milankovitch theories of insolation, so that climate forcing by 100,000-year variations in orbital inclination that cause periodic dust accretion appear unnecessary.
Direct N-body simulations of globular clusters - III. Palomar 4 on an eccentric orbit
NASA Astrophysics Data System (ADS)
Zonoozi, Akram Hasani; Haghi, Hosein; Kroupa, Pavel; Küpper, Andreas H. W.; Baumgardt, Holger
2017-01-01
Palomar 4 is a low-density globular cluster with a current mass ≈30000 M⊙in the outer halo of the Milky Way with a two-body relaxation time of the order of a Hubble time. Yet, it is strongly mass segregated and contains a stellar mass function depleted of low-mass stars. Pal 4 was either born this way or it is a result of extraordinary dynamical evolution. Since two-body relaxation cannot explain these signatures alone, enhanced mass loss through tidal shocking may have had a strong influence on Pal 4. Here, we compute a grid of direct N-body simulations to model Pal 4 on various eccentric orbits within the Milky Way potential to find likely initial conditions that reproduce its observed mass, half-light radius, stellar MF-slope and line-of-sight velocity dispersion. We find that Pal 4 is most likely orbiting on an eccentric orbit with an eccentricity of e ≈ 0.9 and pericentric distance of Rp ≈ 5 kpc. In this scenario, the required 3D half-mass radius at birth is similar to the average sizes of typical GCs (Rh ≈ 4 - 5 pc), while its birth mass is about M0 ≈ 105 M⊙. We also find a high degree of primordial mass segregation among the cluster stars, which seems to be necessary in every scenario we considered. Thus, using the tidal effect to constrain the perigalactic distance of the orbit of Pal 4, we predict that the proper motion of Pal 4 should be in the range -0.52 ≤ μδ ≤ -0.38 mas yr-1 and -0.30 ≤ μαcos δ ≤ -0.15 mas yr-1.
NASA Astrophysics Data System (ADS)
Jones, S. L.
Solar radiation pressure alters satellites' eccentricity by accelerating and decelerating them during each orbit. The accumulated perturbation cancels yearly for geostationary satellites, but meanwhile the perigee radius changes. Disposed satellites must be reorbited higher to compensate, using more fuel. The examined disposal orbit points toward the Sun and uses the satellite's natural eccentricity. This causes the eccentricity vector to only change direction, keeping the perigee radius constant. This thesis verifies this behavior over one year with an analytical derivation and MATLAB simulation, gaining useful insights into its cause. The traditional and proposed disposal orbits are then modeled using NASA's GMAT for more realistic simulations. The proposed orbit's sensitivity to satellite and initialization errors is also examined. Relationships are developed to show these errors' effect on the perigee radius. In conclusion, while this orbit can be used in the short term, margins are necessary to guarantee protection of the geostationary belt.
The dynamics of Neptune Trojans - II. Eccentric orbits and observed objects
NASA Astrophysics Data System (ADS)
Zhou, Li-Yong; Dvorak, Rudolf; Sun, Yi-Sui
2011-01-01
In a previous paper, we presented a global view of the stability of Neptune Trojans (NTs hereafter) on inclined orbits. As the continuation of the investigation, we discuss in this paper the dependence of the stability of NT orbits on the eccentricity. For this task, high-resolution dynamical maps are constructed using the results of extensive numerical integrations of orbits initialized on fine grids of initial semimajor axis (a0) versus eccentricity (e0). The extensions of regions of stable orbits on the (a0, e0) plane at different inclinations are shown. The maximum eccentricities of stable orbits in the three most stable regions at low (0°, 12°), medium (22°, 36°) and high (51°, 59°) inclination are found to be 0.10, 0.12 and 0.04, respectively. The fine structures in the dynamical maps are described. Via the frequency-analysis method, the mechanisms that portray the dynamical maps are revealed. The secondary resonances, at the frequency of the librating resonant angle λ-λ8 and the frequency of the quasi 2:1 mean-motion resonance (MMR hereafter) between Neptune and Uranus, are found to be deeply involved in the motion of NTs. Secular resonances are detected and they also contribute significantly to the triggering of chaos in the motion. In particular, the effects of the secular resonance ν8, ν18 are clarified. We also investigate the orbital stabilities of six observed NTs by checking the orbits of hundreds of clones generated within the observing error bars. We conclude that four of them are deeply inside the stable region, with 2001 QR322 and 2005 TO74 being the exceptions. 2001 QR322 is in the close vicinity of the most significant secondary resonance. 2005 TO74 is located close to the boundary separating stable orbits from unstable ones, and it may be influenced by a secular resonance. This article was published online on 2010 October 25. Some errors were subsequently identified. This notice is included in the online and print versions to indicate
Results of Space Debris Survey Observations on Highly-Eccentric MEO Orbits
NASA Astrophysics Data System (ADS)
Hinze, Andreas; Schildknecht, T.; Flohrer, T.; Krag, H.
2013-08-01
Optical surveys for space debris in high-altitude orbits have been conducted since more than ten years. First observation strategies and processing techniques were successfully developed for the geostationary ring (GEO). The observations scenarios were adjusted for observations in the geostationary transfer orbit (GTO) and in the medium Earth orbit (MEO). After the already investigated circular MEO orbits of the GPS and GLONASS constellations the Astronomical Institute of the University of Bern (AIUB) developed survey and follow-up strategies for the systematically search of space debris in highly-eccentric orbits in the MEO region, in particular in Molniya-type orbits. Several breakup events and deliberate fragmentations are known to have taken place in such orbits. The AIUB performed several survey campaigns between January 2013 and April 2013 to search for debris objects in this MEO region. The optical observations were conducted in the framework of an ESA study using ESA's Space Debris Telescope (ESASDT) the 1-m Zeiss telescope located at the Optical Ground Station (OGS) at the Teide Observatory at Tenerife, Spain. The results from the different observation campaigns will be presented.
NASA Astrophysics Data System (ADS)
King-Hele, D. G.; Walker, Doreen M. C.
1986-02-01
Part 3 of this series of papers developed the theory of high-eccentricity orbits (e greater than 0.2) in an atmosphere having an exponential variation of air density with height, that is, with the density scale height H taken as constant. Part 4 derived the appropriate theory for low-eccentricity orbits (e less than 0.2) in a more realistic atmosphere where H varies linearly with height y (and mu = dH/dy less than 0.2). The present report treats the orbits of Part 3 when they meet the air drag specified by the atmospheric model of Part 4. Equations are derived showing how the perigee height varies with eccentricity, and the eccentricity varies with time, over the major part of the satellite's life. It is shown that the theory of Part 3 remains valid, to order mu sq, if H is evaluated at a specific height above perigee.
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.
Orbital pacing of carbon fluxes by a ∼9-My eccentricity cycle during the Mesozoic.
Martinez, Mathieu; Dera, Guillaume
2015-10-13
Eccentricity, obliquity, and precession are cyclic parameters of the Earth's orbit whose climatic implications have been widely demonstrated on recent and short time intervals. Amplitude modulations of these parameters on million-year time scales induce "grand orbital cycles," but the behavior and the paleoenvironmental consequences of these cycles remain debated for the Mesozoic owing to the chaotic diffusion of the solar system in the past. Here, we test for these cycles from the Jurassic to the Early Cretaceous by analyzing new stable isotope datasets reflecting fluctuations in the carbon cycle and seawater temperatures. Our results document a prominent cyclicity of ∼9 My in the carbon cycle paced by changes in the seasonal dynamics of hydrological processes and long-term sea level fluctuations. These paleoenvironmental changes are linked to a great eccentricity cycle consistent with astronomical solutions. The orbital forcing signal was mainly amplified by cumulative sequestration of organic matter in the boreal wetlands under greenhouse conditions. Finally, we show that the ∼9-My cycle faded during the Pliensbachian, which could either reflect major paleoenvironmental disturbances or a chaotic transition affecting this cycle.
Orbital pacing of carbon fluxes by a ∼9-My eccentricity cycle during the Mesozoic
Martinez, Mathieu; Dera, Guillaume
2015-01-01
Eccentricity, obliquity, and precession are cyclic parameters of the Earth’s orbit whose climatic implications have been widely demonstrated on recent and short time intervals. Amplitude modulations of these parameters on million-year time scales induce ‟grand orbital cycles,” but the behavior and the paleoenvironmental consequences of these cycles remain debated for the Mesozoic owing to the chaotic diffusion of the solar system in the past. Here, we test for these cycles from the Jurassic to the Early Cretaceous by analyzing new stable isotope datasets reflecting fluctuations in the carbon cycle and seawater temperatures. Our results document a prominent cyclicity of ∼9 My in the carbon cycle paced by changes in the seasonal dynamics of hydrological processes and long-term sea level fluctuations. These paleoenvironmental changes are linked to a great eccentricity cycle consistent with astronomical solutions. The orbital forcing signal was mainly amplified by cumulative sequestration of organic matter in the boreal wetlands under greenhouse conditions. Finally, we show that the ∼9-My cycle faded during the Pliensbachian, which could either reflect major paleoenvironmental disturbances or a chaotic transition affecting this cycle. PMID:26417080
NASA Astrophysics Data System (ADS)
Jontof-Hutter, Daniel; Lissauer, Jack J.; Rowe, Jason; Fabrycky, Daniel C.
2014-05-01
Outside our solar system, there is a small sample of planets with known masses and radii, mostly hot jupiters whose radii are known from transit depths, and whose masses are determined from radial velocity spectroscopy (RV). In the absence of mass determinations via RV observations, transit timing variations (TTVs) offer a chance to probe perturbations between planets that pass close to one another or are near resonance, and hence dynamical fits to observed transit times can measure planetary masses and orbital parameters. Such modeling can probe planetary masses at longer orbital periods than RV targets, although not without some challenges. For example, in modeling pairwise planetary perturbations near first order mean motion resonances, a degeneracy between eccentricity and mass exists that limits the accuracy of mass determinations. Nevertheless, in several compact multiplanet systems, fitting complex TTV signals can break the degeneracy, permitting useful mass constraints, and precise measures of small but non-zero eccentricity.The precision in measuring the radius of a transiting planet rests on the uncertainty in the stellar radius, which is typically ~10% for targets with spectral follow-up. With dynamical fits, however, solutions for the orbital parameters including the eccentricity vectors can, alongside the transit light curves, tightly constrain the stellar density and radius. Alongside spectroscopic data, our dynamical fits to TTVs reduced the stellar and hence planetary radius uncertainties at Kepler-11 and Kepler-79 to just 2%, permitting useful planetary density determinations. In the case of Kepler-79, planetary bulk densities are remarkably low given the planetary masses. Indeed, several multiplanet systems characterized by TTV show much lower planetary densities than typical RV determinations in the same mass range. While this reflects the detection biases of both techniques, it also represents a growing sample of characterized systems of
Muto, Takayuki; Takeuchi, Taku; Ida, Shigeru
2011-08-10
We present a new analytic approach to the disk-planet interaction that is especially useful for planets with eccentricity larger than the disk aspect ratio. We make use of the dynamical friction formula to calculate the force exerted on the planet by the disk, and the force is averaged over the period of the planet. The resulting migration and eccentricity damping timescale agree very well with previous works in which the planet eccentricity is moderately larger than the disk aspect ratio. The advantage of this approach is that it is possible to apply this formulation to arbitrary large eccentricity. We have found that the timescale of the orbital evolution depends largely on the adopted disk model in the case of highly eccentric planets. We discuss the possible implication of our results for the theory of planet formation.
The large-scale nebular pattern of a superwind binary in an eccentric orbit
NASA Astrophysics Data System (ADS)
Kim, Hyosun; Trejo, Alfonso; Liu, Sheng-Yuan; Sahai, Raghvendra; Taam, Ronald E.; Morris, Mark R.; Hirano, Naomi; Hsieh, I.-Ta
2017-03-01
Preplanetary nebulae and planetary nebulae are evolved, mass-losing stellar objects that show a wide variety of morphologies. Many of these nebulae consist of outer structures that are nearly spherical (spiral/shell/arc/halo) and inner structures that are highly asymmetric (bipolar/multipolar) 1,2 . The coexistence of such geometrically distinct structures is enigmatic because it hints at the simultaneous presence of both wide and close binary interactions, a phenomenon that has been attributed to stellar binary systems with eccentric orbits 3 . Here, we report high-resolution molecular line observations of the circumstellar spiral-shell pattern of AFGL 3068, an asymptotic giant branch star transitioning to the preplanetary nebula phase. The observations clearly reveal that the dynamics of the mass loss is influenced by the presence of an eccentric-orbit binary. This quintessential object opens a window on the nature of deeply embedded binary stars through the circumstellar spiral-shell patterns that reside at distances of several thousand au from the stars.
NASA Astrophysics Data System (ADS)
Svoren, J.; Neslusan, L.; Porubcan, V.
1993-07-01
It is evident that there is no uniform method of calculating meteor radiants which would yield reliable results for all types of cometary orbits. In the present paper an analysis of this problem is presented, together with recommended methods for various types of orbits. Some additional methods resulting from mathematical modelling are presented and discussed together with Porter's, Steel-Baggaley's and Hasegawa's methods. In order to be able to compare how suitable the application of the individual radiant determination methods is, it is necessary to determine the accuracy with which they approximate real meteor orbits. To verify the accuracy with which the orbit of a meteoroid with at least one node at 1 AU fits the original orbit of the parent body, we applied the Southworth-Hawkins D-criterion (Southworth, R.B., Hawkins, G.S.: 1963, Smithson. Contr. Astrophys 7, 261). D<=0.1 indicates a very good fit of orbits, 0.1
NASA Astrophysics Data System (ADS)
Xue, Yuxin; Masuda, Kento; Suto, Yasushi
2017-02-01
We investigate the formation of close-in planets in near-coplanar eccentric hierarchical triple systems via the secular interaction between an inner planet and an outer perturber (Coplanar High-eccentricity Migration; CHEM). We generalize the previous work on the analytical condition for successful CHEM for point masses interacting only through gravity by taking into account the finite mass effect of the inner planet. We find that efficient CHEM requires that the systems should have m1 ≪ m0 and m1 ≪ m2. In addition to the gravity for point masses, we examine the importance of the short-range forces, and provide an analytical estimate of the migration timescale. We perform a series of numerical simulations in CHEM for systems consisting of a Sun-like central star, giant gas inner planet, and planetary outer perturber, including the short-range forces and stellar and planetary dissipative tides. We find that most of such systems end up with a tidal disruption; a small fraction of the systems produce prograde hot Jupiters (HJs), but no retrograde HJ. In addition, we extend CHEM to super-Earth mass range, and show that the formation of close-in super-Earths in prograde orbits is also possible. Finally, we carry out CHEM simulation for the observed hierarchical triple and counter-orbiting HJ systems. We find that CHEM can explain a part of the former systems, but it is generally very difficult to reproduce counter-orbiting HJ systems.
NASA Astrophysics Data System (ADS)
Laurin, Jiří; Meyers, Stephen R.; Galeotti, Simone; Lanci, Luca
2016-05-01
Major advances in our understanding of paleoclimate change derive from a precise reconstruction of the periods, amplitudes and phases of the 'Milankovitch cycles' of precession, obliquity and eccentricity. While numerous quantitative approaches exist for the identification of these astronomical cycles in stratigraphic data, limitations in radioisotopic dating, and instability of the theoretical astronomical solutions beyond ∼50 Myr ago, can challenge identification of the phase relationships needed to constrain climate response and anchor floating astrochronologies. Here we demonstrate that interference patterns accompanying frequency modulation (FM) of short eccentricity provide a robust basis for identifying the phase of long eccentricity forcing in stratigraphic data. One- and two-dimensional models of sedimentary distortion of the astronomical signal are used to evaluate the veracity of the FM method, and indicate that pristine eccentricity FM can be readily distinguished in paleo-records. Apart from paleoclimatic implications, the FM approach provides a quantitative technique for testing and calibrating theoretical astronomical solutions, and for refining chronologies for the deep past. We present two case studies that use the FM approach to evaluate major carbon-cycle perturbations of the Eocene and Late Cretaceous. Interference patterns in the short-eccentricity band reveal that Eocene hyperthermals ETM2 ('Elmo'), H2, I1 and ETM3 (X; ∼52-54 Myr ago) were associated with maxima in the 405-kyr cycle of orbital eccentricity. The same eccentricity configuration favored regional anoxic episodes in the Mediterranean during the Middle and Late Cenomanian (∼94.5-97 Myr ago). The initial phase of the global Oceanic Anoxic Event II (OAE II; ∼93.9-94.5 Myr ago) coincides with maximum and falling 405-kyr eccentricity, and the recovery phase occurs during minimum and rising 405-kyr eccentricity. On a Myr scale, the event overlaps with a node in eccentricity
Optical observations of space debris in GEO and in highly-eccentric orbits
NASA Astrophysics Data System (ADS)
Schildknecht, T.; Musci, R.; Ploner, M.; Beutler, G.; Flury, W.; Kuusela, J.; de Leon Cruz, J.; de Fatima Dominguez Palmero, L.
2004-01-01
The space debris population in low Earth orbits (LEO) has been extensively studied during the last decade and reasonable models covering all size ranges were produced. Information on the distribution of objects in the geostationary ring (GEO), however, is still comparatively sparse. Until quite recently the population of man-made objects in GEO had to be inferred solely from the about 900 continuously tracked objects and the modeling of the two explosions known to have occurred in GEO. Optical observations from the last two years performed with ESA's 1-m telescope at the Teide observatory in Tenerife changed the situation substantially. A hitherto unknown but significant population of small-size objects with diameters as small as ten centimeters has been detected in GEO. Objects in highly-eccentric orbits crossing the GEO region, in particular objects in geostationary transfer orbits (GTO), also contribute to the density of space debris in GEO. This family is even less well known than the GEO population, although many explosion events were reported in this orbital region. The paper will summarize recent results from the ESA GEO survey and describe the techniques and first results of a trial GTO survey.
ORBITAL PHASE VARIATIONS OF THE ECCENTRIC GIANT PLANET HAT-P-2b
Lewis, Nikole K.; Showman, Adam P.; Knutson, Heather A.; Desert, Jean-Michel; Kao, Melodie; Cowan, Nicolas B.; Laughlin, Gregory; Fortney, Jonathan J.; Burrows, Adam; Bakos, Gaspar A.; Hartman, Joel D.; Deming, Drake; Crepp, Justin R.; Mighell, Kenneth J.; Agol, Eric; Charbonneau, David; Fischer, Debra A.; Hinkley, Sasha; Johnson, John Asher; Howard, Andrew W.; and others
2013-04-01
We present the first secondary eclipse and phase curve observations for the highly eccentric hot Jupiter HAT-P-2b in the 3.6, 4.5, 5.8, and 8.0 {mu}m bands of the Spitzer Space Telescope. The 3.6 and 4.5 {mu}m data sets span an entire orbital period of HAT-P-2b (P = 5.6334729 d), making them the longest continuous phase curve observations obtained to date and the first full-orbit observations of a planet with an eccentricity exceeding 0.2. We present an improved non-parametric method for removing the intrapixel sensitivity variations in Spitzer data at 3.6 and 4.5 {mu}m that robustly maps position-dependent flux variations. We find that the peak in planetary flux occurs at 4.39 {+-} 0.28, 5.84 {+-} 0.39, and 4.68 {+-} 0.37 hr after periapse passage with corresponding maxima in the planet/star flux ratio of 0.1138% {+-} 0.0089%, 0.1162% {+-} 0.0080%, and 0.1888% {+-} 0.0072% in the 3.6, 4.5, and 8.0 {mu}m bands, respectively. Our measured secondary eclipse depths of 0.0996% {+-} 0.0072%, 0.1031% {+-} 0.0061%, 0.071%{sub -0.013%}{sup +0.029,} and 0.1392% {+-} 0.0095% in the 3.6, 4.5, 5.8, and 8.0 {mu}m bands, respectively, indicate that the planet cools significantly from its peak temperature before we measure the dayside flux during secondary eclipse. We compare our measured secondary eclipse depths to the predictions from a one-dimensional radiative transfer model, which suggests the possible presence of a transient day side inversion in HAT-P-2b's atmosphere near periapse. We also derive improved estimates for the system parameters, including its mass, radius, and orbital ephemeris. Our simultaneous fit to the transit, secondary eclipse, and radial velocity data allows us to determine the eccentricity (e = 0.50910 {+-} 0.00048) and argument of periapse ({omega} = 188. Degree-Sign 09 {+-} 0. Degree-Sign 39) of HAT-P-2b's orbit with a greater precision than has been achieved for any other eccentric extrasolar planet. We also find evidence for a long-term linear
Orbital Phase Variations of the Eccentric Giant Planet HAT-P-2b
NASA Astrophysics Data System (ADS)
Lewis, Nikole K.; Knutson, Heather A.; Showman, Adam P.; Cowan, Nicolas B.; Laughlin, Gregory; Burrows, Adam; Deming, Drake; Crepp, Justin R.; Mighell, Kenneth J.; Agol, Eric; Bakos, Gáspár Á.; Charbonneau, David; Désert, Jean-Michel; Fischer, Debra A.; Fortney, Jonathan J.; Hartman, Joel D.; Hinkley, Sasha; Howard, Andrew W.; Johnson, John Asher; Kao, Melodie; Langton, Jonathan; Marcy, Geoffrey W.
2013-04-01
We present the first secondary eclipse and phase curve observations for the highly eccentric hot Jupiter HAT-P-2b in the 3.6, 4.5, 5.8, and 8.0 μm bands of the Spitzer Space Telescope. The 3.6 and 4.5 μm data sets span an entire orbital period of HAT-P-2b (P = 5.6334729 d), making them the longest continuous phase curve observations obtained to date and the first full-orbit observations of a planet with an eccentricity exceeding 0.2. We present an improved non-parametric method for removing the intrapixel sensitivity variations in Spitzer data at 3.6 and 4.5 μm that robustly maps position-dependent flux variations. We find that the peak in planetary flux occurs at 4.39 ± 0.28, 5.84 ± 0.39, and 4.68 ± 0.37 hr after periapse passage with corresponding maxima in the planet/star flux ratio of 0.1138% ± 0.0089%, 0.1162% ± 0.0080%, and 0.1888% ± 0.0072% in the 3.6, 4.5, and 8.0 μm bands, respectively. Our measured secondary eclipse depths of 0.0996% ± 0.0072%, 0.1031% ± 0.0061%, 0.071%^{+0.029%}_{-0.013%}, and 0.1392% ± 0.0095% in the 3.6, 4.5, 5.8, and 8.0 μm bands, respectively, indicate that the planet cools significantly from its peak temperature before we measure the dayside flux during secondary eclipse. We compare our measured secondary eclipse depths to the predictions from a one-dimensional radiative transfer model, which suggests the possible presence of a transient day side inversion in HAT-P-2b's atmosphere near periapse. We also derive improved estimates for the system parameters, including its mass, radius, and orbital ephemeris. Our simultaneous fit to the transit, secondary eclipse, and radial velocity data allows us to determine the eccentricity (e = 0.50910 ± 0.00048) and argument of periapse (ω = 188.°09 ± 0.°39) of HAT-P-2b's orbit with a greater precision than has been achieved for any other eccentric extrasolar planet. We also find evidence for a long-term linear trend in the radial velocity data. This trend suggests the presence
Kepler-432 b: a massive planet in a highly eccentric orbit transiting a red giant
NASA Astrophysics Data System (ADS)
Ciceri, S.; Lillo-Box, J.; Southworth, J.; Mancini, L.; Henning, Th.; Barrado, D.
2015-01-01
We report the first disclosure of the planetary nature of Kepler-432 b (aka Kepler object of interest KOI-1299.01). We accurately constrained its mass and eccentricity by high-precision radial velocity measurements obtained with the CAFE spectrograph at the CAHA 2.2-m telescope. By simultaneously fitting these new data and Kepler photometry, we found that Kepler-432 b is a dense transiting exoplanet with a mass of Mp = 4.87 ± 0.48MJup and radius of Rp = 1.120 ± 0.036RJup. The planet revolves every 52.5 d around a K giant star that ascends the red giant branch, and it moves on a highly eccentric orbit with e = 0.535 ± 0.030. By analysing two near-IR high-resolution images, we found that a star is located at 1.1'' from Kepler-432, but it is too faint to cause significant effects on the transit depth. Together with Kepler-56 and Kepler-91, Kepler-432 occupies an almost-desert region of parameter space, which is important for constraining the evolutionary processes of planetary systems. RV data (Table A.1) are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/573/L5
WASP-117b: a 10-day-period Saturn in an eccentric and misaligned orbit
NASA Astrophysics Data System (ADS)
Lendl, M.; Triaud, A. H. M. J.; Anderson, D. R.; Collier Cameron, A.; Delrez, L.; Doyle, A. P.; Gillon, M.; Hellier, C.; Jehin, E.; Maxted, P. F. L.; Neveu-VanMalle, M.; Pepe, F.; Pollacco, D.; Queloz, D.; Ségransan, D.; Smalley, B.; Smith, A. M. S.; Udry, S.; Van Grootel, V.; West, R. G.
2014-08-01
We report the discovery of WASP-117b, the first planet with a period beyond 10 days found by the WASP survey. The planet has a mass of Mp = 0.2755 ± 0.0089 MJ, a radius of Rp= 1.021_{-0.065+0.076 Rjup} and is in an eccentric (e = 0.302 ± 0.023), 10.02165 ± 0.00055 d orbit around a main-sequence F9 star. The host star's brightness (V = 10.15 mag) makes WASP-117 a good target for follow-up observations, and with a periastron planetary equilibrium temperature of Teq= 1225_{-39+36} K and a low planetary mean density (ρp= 0.259_{-0.048+0.054 ρjup}) it is one of the best targets for transmission spectroscopy among planets with periods around 10 days. From a measurement of the Rossiter-McLaughlin effect, we infer a projected angle between the planetary orbit and stellar spin axes of β = -44 ± 11 deg, and we further derive an orbital obliquity of ψ = 69.6 +4.7-4.1 deg. Owing to the large orbital separation, tidal forces causing orbital circularization and realignment of the planetary orbit with the stellar plane are weak, having had little impact on the planetary orbit over the system lifetime. WASP-117b joins a small sample of transiting giant planets with well characterized orbits at periods above 8 days. Based on data obtained with WASP-South, CORALIE and EulerCam at the Euler-Swiss telescope, TRAPPIST, and HARPS at the ESO 3.6 m telescope (Prog. IDs 087.C-0649, 089.C-0151, 090.C-0540)Photometric and radial velocities are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/568/A81
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
NASA Astrophysics Data System (ADS)
King-Hele, D. G.; Walker, Doreen M. C.
1987-05-01
Part III (King-Hele, 1962) of this series of papers developed the theory of high-eccentricity orbits (e greater than 0.2) in an atmosphere having an exponential variation of air density with height; that is, with the density scale height H taken as constant. Part IV (Cook and King-Hele, 1963) derived the appropriate theory for low-eccentricity orbits (e less than 0.2) in a more realistic atmosphere where H varies linearly with height y (and mu = dH/dy less than 0.2). The present paper treats the orbits of part III when they meet the air drag specified by the atmospheric model of part IV. Equations are derived showing how the perigee height varies with eccentricity, and the eccentricity varies with time, over the major part of the satellite's life. It is shown that the theory of part III remains valid, to order mu-squared, if H is evaluated at a specific height above perigee.
ORBITAL ORIENTATIONS OF EXOPLANETS: HAT-P-4b IS PROGRADE AND HAT-P-14b IS RETROGRADE
Winn, Joshua N.; Albrecht, Simon; Howard, Andrew W.; Marcy, Geoffrey W.; Isaacson, Howard; Johnson, John Asher; Crepp, Justin R.; Morton, Timothy D.; Shporer, Avi; Bakos, Gaspar A.; Hartman, Joel D.; Holman, Matthew J.
2011-02-15
We present observations of the Rossiter-McLaughlin effect for two exoplanetary systems, revealing the orientations of their orbits relative to the rotation axes of their parent stars. HAT-P-4b is prograde, with a sky-projected spin-orbit angle of {lambda} = -4.9 {+-} 11.9 deg. In contrast, HAT-P-14b is retrograde, with {lambda} = 189.1 {+-} 5.1 deg. These results conform with a previously noted pattern among the stellar hosts of close-in giant planets: hotter stars have a wide range of obliquities and cooler stars have low obliquities. This, in turn, suggests that three-body dynamics and tidal dissipation are responsible for the short-period orbits of many exoplanets. In addition, our data revealed a third body in the HAT-P-4 system, which could be a second planet or a companion star.
NASA Astrophysics Data System (ADS)
Staff, Jan E.; De Marco, Orsola; Macdonald, Daniel; Galaviz, Pablo; Passy, Jean-Claude; Iaconi, Roberto; Low, Mordecai-Mark Mac
2016-02-01
The Rotten Egg Nebula has at its core a binary composed of a Mira star and an A-type companion at a separation >10 au. It has been hypothesized to have formed by strong binary interactions between the Mira and a companion in an eccentric orbit during periastron passage ˜800 yr ago. We have performed hydrodynamic simulations of an asymptotic giant branch (AGB) star interacting with companions with a range of masses in orbits with a range of initial eccentricities and periastron separations. For reasonable values of the eccentricity, we find that Roche lobe overflow can take place only if the periods are ≪100 yr. Moreover, mass transfer causes the system to enter a common envelope phase within several orbits. Since the central star of the Rotten Egg nebula is an AGB star, we conclude that such a common envelope phase must have lead to a merger, so the observed companion must have been a tertiary companion of a binary that merged at the time of nebula ejection. Based on the mass and time-scale of the simulated disc formed around the companion before the common envelope phase, we analytically estimate the properties of jets that could be launched. Allowing for super-Eddington accretion rates, we find that jets similar to those observed are plausible, provided that the putative lost companion was relatively massive.
NASA Astrophysics Data System (ADS)
Misconi, Nebil Y.
2004-08-01
Model calculations were carried out to determine the extent of the effects on the rotational bursting of F-coronal dust in eccentric orbits due to their interaction with the flow of coronal mass ejections (CMEs). The model included an initial limiting perihelion distance of 8 solar radii ( RS) for all particles used. The parameters of the CMEs (velocity and proton number density) along with the various parameters of the dust particles (size and median density) were taken into consideration. By keeping these parameters the same and varying one of them, it was found that the velocity of the CMEs protons plays a major role in determining at which heliocentric distance the particle bursts. To a lesser degree, the median density of the particle also had a similar effect. Depending on the values of the dust particles orbital eccentricity, limiting sizes of the dust particles were found beyond which the particles do not burst. More particles bursted in regions close to their perihelion passage, however very few particles bursted near 8 RS from which we conclude that the majority of the fragmented particles were outside the F-corona region. The results show that rotational bursting of the dust in eccentric orbits inside the F-corona forces the particles to fragment outside 8 RS.
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.
NASA Astrophysics Data System (ADS)
Roscoe, Christopher William Thomas
Several methods are presented for the design of satellite formations for science missions in high-eccentricity reference orbits with quantifiable performance criteria specified throughout only a portion the orbit, called the Region of Interest (RoI). A modified form of the traditional average along-track drift minimization condition is introduced to account for the fact that performance criteria are only specified within the RoI, and a robust formation design algorithm (FDA) is defined to improve performance in the presence of formation initialization errors. Initial differential mean orbital elements are taken as the design variables and the Gim-Alfriend state transition matrix (G-A STM) is used for relative motion propagation. Using mean elements and the G-A STM allows for explicit inclusion of J2 perturbation effects in the design process. The methods are applied to the complete formation design problem of the NASA Magnetospheric Multiscale (MMS) mission and results are verified using the NASA General Mission Analysis Tool (GMAT). Since satellite formations in high-eccentricity orbits will spend long times at high altitude, third-body perturbations are an important design consideration as well. A detailed analytical analysis of third-body perturbation effects on satellite formations is also performed and averaged dynamics are derived for the particular case of the lunar perturbation. Numerical results of the lunar perturbation analysis are obtained for the example application of the MMS mission and verified in GMAT.
NASA Astrophysics Data System (ADS)
Seiß, M.; Spahn, F.; Schmidt, Jürgen
2010-11-01
Saturn's rings host two known moons, Pan and Daphnis, which are massive enough to clear circumferential gaps in the ring around their orbits. Both moons create wake patterns at the gap edges by gravitational deflection of the ring material (Cuzzi, J.N., Scargle, J.D. [1985]. Astrophys. J. 292, 276-290; Showalter, M.R., Cuzzi, J.N., Marouf, E.A., Esposito, L.W. [1986]. Icarus 66, 297-323). New Cassini observations revealed that these wavy edges deviate from the sinusoidal waveform, which one would expect from a theory that assumes a circular orbit of the perturbing moon and neglects particle interactions. Resonant perturbations of the edges by moons outside the ring system, as well as an eccentric orbit of the embedded moon, may partly explain this behavior (Porco, C.C., and 34 colleagues [2005]. Science 307, 1226-1236; Tiscareno, M.S., Burns, J.A., Hedman, M.M., Spitale, J.N., Porco, C.C., Murray, C.D., and the Cassini Imaging team [2005]. Bull. Am. Astron. Soc. 37, 767; Weiss, J.W., Porco, C.C., Tiscareno, M.S., Burns, J.A., Dones, L. [2005]. Bull. Am. Astron. Soc. 37, 767; Weiss, J.W., Porco, C.C., Tiscareno, M.S. [2009]. Astron. J. 138, 272-286). Here we present an extended non-collisional streamline model which accounts for both effects. We describe the resulting variations of the density structure and the modification of the nonlinearity parameter q. Furthermore, an estimate is given for the applicability of the model. We use the streamwire model introduced by Stewart (Stewart, G.R. [1991]. Icarus 94, 436-450) to plot the perturbed ring density at the gap edges. We apply our model to the Keeler gap edges undulated by Daphnis and to a faint ringlet in the Encke gap close to the orbit of Pan. The modulations of the latter ringlet, induced by the perturbations of Pan (Burns, J.A., Hedman, M.M., Tiscareno, M.S., Nicholson, P.D., Streetman, B.J., Colwell, J.E., Showalter, M.R., Murray, C.D., Cuzzi, J.N., Porco, C.C., and the Cassini ISS team [2005]. Bull. Am
Spiral-shells and nascent bipolar outflow in CIT 6: hints for an eccentric-orbit binary?
NASA Astrophysics Data System (ADS)
Kim, Hyosun; Liu, Sheng-Yuan; Hirano, Naomi; Zhao-Geisler, Ronny; Trejo, Alfonso; Yen, Hsi-Wei; Taam, Ronald E.; Kemper, Francisca; Kim, Jongsoo; Byun, Do-Young; Liu, Tie
2016-07-01
We present the essential results pointed out in a recently published paper, Kim et al. 2015, Astrophys. J., 814, 61. The carbon star CIT 6 reveals evidences for a binary in a high-resolution CO line emission map of its circumstellar envelope taken with the Submillimeter Array. The morphology of the outflow described by the spiral-shell pattern, bipolar (or possibly multipolar) outflow, one-sided interarm gaps, and double spiral feature point to a plausible scenario that CIT 6 is a binary system in an eccentric orbit with the mass losing star evolving from the AGB.
Measuring the eccentricity of the Earth’s orbit with a nail and a piece of plywood
NASA Astrophysics Data System (ADS)
Lahaye, Thierry
2012-09-01
I describe how to obtain a rather good experimental determination of the eccentricity of the Earth’s orbit, as well as the obliquity of the Earth’s rotation axis, by measuring, over the course of a year, the elevation of the Sun as a function of time during a day. With a very simple ‘instrument’ consisting of an elementary sundial, first-year students can carry out an appealing measurement programme, learn important concepts in experimental physics, see concrete applications of kinematics and changes of reference frames, and benefit from a hands-on introduction to astronomy.
NASA Astrophysics Data System (ADS)
Di Matteo, P.; Lehnert, M. D.; Qu, Y.; van Driel, W.
2011-01-01
We study the distribution of orbital eccentricities of stars in thick disks generated by the heating of a pre-existing thin stellar disk through a minor merger (mass ratio 1:10), using N-body/SPH numerical simulations of interactions that span a range of gas fractions in the primary disk and initial orbital configurations. The resulting eccentricity distributions have an approximately triangular shape, with a peak at 0.2-0.35, and a relatively smooth decline towards higher values. Stars originally in the satellite galaxy tend to have higher eccentricities (on average from e = 0.45 to e = 0.75), which is in general agreement with the models of Sales and collaborators, although in detail we find fewer stars with extreme values and no evidence of their secondary peak around e = 0.8. The absence of this high-eccentricity feature results in a distribution that qualitatively matches the observations. Moreover, the increase in the orbital eccentricities of stars in the solar neighborhood with vertical distance from the Galactic mid-plane found by Dierickx and collaborators can be qualitatively reproduced by our models, but only if the satellite is accreted onto a direct orbit. We thus speculate that if minor mergers were the dominant means of forming the Milky Way thick disk, the primary mechanism should be merging with satellite(s) on direct orbits.
Eccentric-orbit extreme-mass-ratio inspiral gravitational wave energy fluxes to 7PN order
NASA Astrophysics Data System (ADS)
Forseth, Erik; Evans, Charles R.; Hopper, Seth
2016-03-01
We present new results through 7PN order on the energy flux from eccentric extreme-mass-ratio binaries. The black hole perturbation calculations are made at very high accuracy (200 decimal places) using a Mathematica code based on the Mano-Suzuki-Takasugi analytic function expansion formalism. All published coefficients in the expansion through 3PN order at lowest order in the mass ratio are confirmed and new analytic and numeric terms are found to high order in powers of e2 at post-Newtonian orders between 3.5PN and 7PN. We also show original work in finding (nearly) arbitrarily accurate expansions for hereditary terms at 1.5PN, 2.5PN, and 3PN orders. An asymptotic analysis is developed that guides an understanding of eccentricity singular factors, which diverge at unit eccentricity and which appear at each PN order. We fit to a model at each PN order that includes these eccentricity singular factors, which allows the flux to be accurately determined out to e →1 .
NASA Astrophysics Data System (ADS)
Guzzo, Massimiliano
2001-07-01
I have improved the precision of the leap-frog symplectic integrators for perturbed Kepler problems at small eccentricities, without significant loss of CPU time. The integration scheme proposed is competitive, in some situations, with the so-called mixed variable integrators.
NASA Astrophysics Data System (ADS)
Matsuyama, I.; Nimmo, F.
2009-01-01
We consider the effect of spin-orbit resonance, nonzero eccentricity, despinning, and reorientation on Mercury's gravity and tectonic pattern. Large variations of the gravity and shape coefficients from the synchronous rotation and zero eccentricity values, J 2/C 22 = 10/3 and (b - c)/(a - c) = 1/4, arise because of nonsynchronous rotation and nonzero eccentricity even in the absence of reorientation or despinning. Reorientation or despinning induces additional variations. The large gravity coefficients J 2 = (6 +/- 2) × 10-5 and C 22 = (1 +/- 0.5) × 10-5 estimated from the Mariner 10 flybys cannot be attributed to Caloris alone since the required mass excess in this case would have caused Caloris to migrate to one of Mercury's hot poles. Similarly, a large remnant bulge due to a smaller semimajor axis and spin-orbit resonance can be dismissed since the required semimajor axis is unphysically small (<0.1 AU). Reorientation of a large remnant bulge recording an epoch of faster rotation (without significant semimajor axis variations) can explain the large gravity coefficients. This requires initial rotation rates $\\gtrsim$20 times the present value and a positive gravity anomaly associated with Caloris capable of driving ~10°-45° equatorward reorientation. The required gravity anomaly can be explained by infilling of the basin with material of thicknesses $\\gtrsim$7 km or an annulus of volcanic plains emplaced around the basin with an annulus width ~1200 km and fill thicknesses $\\gtrsim$2 km. The predicted tectonic pattern due to these despinning and reorientation scenarios, including some radial contraction, is in good agreement with the lobate scarp pattern observed by Mariner 10. We also predict that lobate scarps will follow a NE-SW orientation in the eastern hemisphere and a positive gravity anomaly (of a few hundred mGal) associated with Caloris.
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
Low-Thrust Transfers from Distant Retrograde Orbits to L2 Halo Orbits in the Earth-Moon System
NASA Technical Reports Server (NTRS)
Parrish, Nathan L.; Parker, Jeffrey S.; Hughes, Steven P.; Heiligers, Jennette
2016-01-01
Enable future missions Any mission to a DRO or halo orbit could benefit from the capability to transfer between these orbits Chemical propulsion could be used for these transfers, but at high propellant cost Fill gaps in knowledge A variety of transfers using SEP or solar sails have been studied for the Earth-Moon system Most results in literature study a single transfer This is a step toward understanding the wide array of types of transfers available in an N-body force model.
NASA Astrophysics Data System (ADS)
Linsenmeier, Manuel; Pascale, Salvatore; Lucarini, Valerio
2014-05-01
We explore the implications of seasonal variability for the habitability of idealized Earth-like planets as determined by the two parameters polar obliquity and orbital eccentricity. Commonly, the outer boundary of the habitable zone (HZ) is set by a completely frozen planet, or snowball state. Using a general circulation model coupled to a thermodynamic sea-ice model, we show that seasonal variability can extend this outer limit of the habitable zone (HZ) from 1.03 AU (no seasonal variability) to a maximum of 1.69 AU in our experiments. Moreover, our results show that also the multistability property of planets close to the outer edge of the HZ is influenced by seasonal variability. Cold states extend farest into the HZ for non-oblique planets. On highly oblique planets, cold states can also allow for habitable regions, which highlights the sufficient but not necessary condition of a warm climate state for habitability. Further, the range of distances that allow for two stable climate states decreases with eccentricity, possibly leading to monostability for planets with very large seasonal variations. Sensitivity experiments exploring the role of azimuthal obliquity, surface heat capacity, and maximal sea-ice thickness show the robustness of our results. An uneven distribution of annual mean irradiation among the two hemispheres extends the HZ outwards, whereas a reduction of heat capacity has only a negligible effect on the extent of the HZ. On circular orbits, our results are in good agreement with previous studies that use a one-dimensional energy balance model. Yet large differences on eccentric orbits hint to limitations of these simpler models. To our knowledge, this study provides for the first time a qualitative assessment of the effects of seasonal variability on the habitability of Earth-like planets that is based on a three-dimensional climate model. Differences found in the comparison with previous work underline the importance of using climate models
Orbital pacing of carbon fluxes by a ~9-Myr eccentricity cycle during the Mesozoic
NASA Astrophysics Data System (ADS)
Martinez, M.; Dera, G.
2015-12-01
A 73.6-Myr long signal of d18O and d13C from the Sinemurian (Early Jurassic) to the Aptian (Early Cretaceous) measured on belemnite rostra from NW Tethys has been compiled and analyzed for measuring the trends and Myr-cycles in the Jurassic and the Early Cretaceous. The resulting series have more than 3500 points and an average sample step of 0.04 Myr, which currently constitutes the highest-resolution series for this time interval. The long-term trend in the d18O series shows three warming events in the Jurassic linked to the activity of three major volcanic provinces, but no significant cycle has been observed in the series. Unlikely, the d13C series shows a prominent cycle of 9.1 Myr, having an amplitude of 1-2‰ on the d13C throughout the whole time interval. This cycle is attributed to a Myr-eccentricity forcing, already identified in the Cenozoic, the late Cretaceous and the Triassic. In addition, the d13C series also displays a minor-amplitude cycle at 1.9 Myr, which can be related to the 2.4-Myr eccentricity. The fluctuations of the d13C at the 9.1-Myr time scale follows the 2nd-order eustatic changes and we suggest that Myr-eccentricity cycles, by controlling humid-arid cycles in the tropical realms and sea-level changes, modulated the continental and oceanic primary productivity, storage of organic matter, carbonate platform production which triggered the observed fluctuations in the d13C.
NASA Astrophysics Data System (ADS)
Dawson, Rebekah I.; Murray-Clay, Ruth A.; Johnson, John Asher
2015-01-01
Gas giant planets orbiting within 0.1 AU of their host stars are unlikely to have formed in situ and are evidence for planetary migration. It is debated whether the typical hot Jupiter smoothly migrated inward from its formation location through the proto-planetary disk, or was perturbed by another body onto a highly eccentric orbit, which tidal dissipation subsequently shrank and circularized during close stellar passages. Socrates and collaborators predicted that the latter model should produce a population of super-eccentric proto-hot Jupiters readily observable by Kepler. We find a paucity of such planets in the Kepler sample, which is inconsistent with the theoretical prediction with 96.9% confidence. Observational effects are unlikely to explain this discrepancy. We find that the fraction of hot Jupiters with an orbital period P > 3 days produced by the star-planet Kozai mechanism does not exceed (at two-sigma) 44%. Our results may indicate that disk migration is the dominant channel for producing hot Jupiters with P > 3 days. Alternatively, the typical hot Jupiter may have been perturbed to a high eccentricity by interactions with a planetary rather than stellar companion, and began tidal circularization much interior to 1 AU after multiple scatterings. A final alternative is that early in the tidal circularization process at high eccentricities tidal circularization occurs much more rapidly than later in the process at low eccentricities, although this is contrary to current tidal theories.
Dawson, Rebekah I.; Murray-Clay, Ruth A.; Johnson, John Asher
2015-01-10
Gas giant planets orbiting within 0.1 AU of their host stars are unlikely to have formed in situ and are evidence for planetary migration. It is debated whether the typical hot Jupiter smoothly migrated inward from its formation location through the proto-planetary disk, or was perturbed by another body onto a highly eccentric orbit, which tidal dissipation subsequently shrank and circularized during close stellar passages. Socrates and collaborators predicted that the latter model should produce a population of super-eccentric proto-hot Jupiters readily observable by Kepler. We find a paucity of such planets in the Kepler sample, which is inconsistent with the theoretical prediction with 96.9% confidence. Observational effects are unlikely to explain this discrepancy. We find that the fraction of hot Jupiters with an orbital period P > 3 days produced by the star-planet Kozai mechanism does not exceed (at two-sigma) 44%. Our results may indicate that disk migration is the dominant channel for producing hot Jupiters with P > 3 days. Alternatively, the typical hot Jupiter may have been perturbed to a high eccentricity by interactions with a planetary rather than stellar companion, and began tidal circularization much interior to 1 AU after multiple scatterings. A final alternative is that early in the tidal circularization process at high eccentricities tidal circularization occurs much more rapidly than later in the process at low eccentricities, although this is contrary to current tidal theories.
NASA Astrophysics Data System (ADS)
Hopper, Seth; Kavanagh, Chris; Ottewill, Adrian C.
2016-02-01
We present a method for solving the first-order Einstein field equations in a post-Newtonian (PN) expansion. Our calculations generalize the work of Bini and Damour and subsequently Kavanagh et al. to consider eccentric orbits on a Schwarzschild background. We derive expressions for the retarded metric perturbation at the location of the particle for all ℓ-modes. We find that, despite first appearances, the Regge-Wheeler gauge metric perturbation is C0 at the particle for all ℓ. As a first use of our solutions, we compute the gauge-invariant quantity ⟨U ⟩ through 4PN while simultaneously expanding in eccentricity through e10. By anticipating the e →1 singular behavior at each PN order, we greatly improve the accuracy of our results for large e . We use ⟨U ⟩ to find 4PN contributions to the effective one body potential Q ^ through e10 and at linear order in the mass ratio.
NASA Astrophysics Data System (ADS)
De Becker, M.; Sana, H.; Absil, O.; Le Bouquin, J.-B.; Blomme, R.
2012-07-01
Using optical long baseline interferometry, we resolved for the first time the two wide components of HD 167971, a candidate hierarchical triple system known to efficiently accelerate particles. Our multi-epoch Very Large Telescope Interferometer observations provide direct evidence for a gravitational link between the O8 supergiant and the close eclipsing O + O binary. The separation varies from 8 to 15 mas over the 3-year baseline of our observations, suggesting that the components evolve on a wide and very eccentric orbit (most probably e > 0.5). These results provide evidence that the wide orbit revealed by our study is not coplanar with the orbit of the inner eclipsing binary. From our measurements of the near-infrared luminosity ratio, we constrain the spectral classification of the components in the close binary to be O6-O7, and confirm that these stars are likely main-sequence objects. Our results are discussed in the context of the bright non-thermal radio emission already reported for this system, and we provide arguments in favour of a maximum radio emission coincident with periastron passage. HD 167971 turns out to be an efficient O-type particle accelerator that constitutes a valuable target for future high angular resolution radio imaging using Very Long Baseline Interferometry facilities. Based on observations collected at the European Southern Observatory, Paranal, Chile, under the programme IDs 381.D-0095, 086.D-0586 and 087.D-0264.
A high-fidelity satellite ephemeris program for Earth satellites in eccentric orbits
NASA Technical Reports Server (NTRS)
Simmons, David R.
1990-01-01
A program for mission planning called the Analytic Satellite Ephemeris Program (ASEP), produces projected data for orbits that remain fairly close to the Earth. ASEP does not take into account lunar and solar perturbations. These perturbations are accounted for in another program called GRAVE, which incorporates more flexible means of input for initial data, provides additional kinds of output information, and makes use of structural programming techniques to make the program more understandable and reliable. GRAVE was revised, and a new program called ORBIT was developed. It is divided into three major phases: initialization, integration, and output. Results of the program development are presented.
NASA Astrophysics Data System (ADS)
Bini, Donato; Damour, Thibault; Geralico, Andrea
2016-03-01
We analytically compute, through the six-and-a-half post-Newtonian order, the second-order-in-eccentricity piece of the Detweiler-Barack-Sago gauge-invariant redshift function for a small mass in eccentric orbit around a Schwarzschild black hole. Using the first law of mechanics for eccentric orbits [A. Le Tiec, First law of mechanics for compact binaries on eccentric orbits, Phys. Rev. D 92, 084021 (2015).] we transcribe our result into a correspondingly accurate knowledge of the second radial potential of the effective-one-body formalism [A. Buonanno and T. Damour, Effective one-body approach to general relativistic two-body dynamics, Phys. Rev. D 59, 084006 (1999).]. We compare our newly acquired analytical information to several different numerical self-force data and find good agreement, within estimated error bars. We also obtain, for the first time, independent analytical checks of the recently derived, comparable-mass fourth-post-Newtonian order dynamics [T. Damour, P. Jaranowski, and G. Schaefer, Nonlocal-in-time action for the fourth post-Newtonian conservative dynamics of two-body systems, Phys. Rev. D 89, 064058 (2014).].
The Eccentric-Orbit Eclipsing Double-Lined System HP Draconis
NASA Astrophysics Data System (ADS)
Milone, Eugene F.; Kurpinska-Winiarska, M.; Oblak, E.
2009-01-01
The 10.76-d period EA system HP Dra was discovered through the HIPPARCOS mission (albeit with an incorrect period). Radial velocities from the Asiago and Haute Provence Observatories (HPO), and light curve data from Cracow Observatory (CO) and HIPPARCOS have been analyzed now with the most recent version of the Wilson-Devinney program. The Cracow photometry covers both eclipses completely, unlike the HIPPARCOS data in which only 3 and 7 points fall within the primary and secondary minima, respectively. Initial and unadjusted values came from our separate preliminary analyses. Color and spectral type suggest 6000 K as the temperature of Star 1, the hotter component. The analysis involved the simultaneous adjustment of 13 non-curve dependent parameters and 2 curve-dependent parameters, 19 parameters in total. The adjusted parameters were the semi-major axis, eccentricity, and its derivative, argument of periastron and its derivative, systemic radial velocity, secondary temperature, modified Kopal potentials of both components, period and its derivative, epoch, mass ratio (M2/M1), passband luminosity, and third light. From this analysis, there is no significant period variation, but a marginally significant apsidal motion and significant third light in each of the B, V, and hp passbands. This solution indicates that components 1 and 2 have masses of 1.15 and 1.11 Msun, radii of 1.38 and 1.06 Rsun, and have absolute bolometric magnitudes of 3.93 and 4.59, respectively. Work is continuing to verify the apsidal motion and to characterize better the 3rd light in the system, through new visual and infrared observations. This work was supported in part by grants from Canadian NSERC to EFM, and data acquisition at the HPO and CO was partly funded by the European program "Actions Integrees" POLONIUM and carried out within the framework of the European Associated Laboratory "Astrophysics Poland-France."
NASA Astrophysics Data System (ADS)
Chen, Ying-Tung; Lin, Hsing-Wen; Holman, Matthew J.; Payne, Matthew John; Fraser, Wesley Cristopher; Lacerda, Pedro; Ip, Wing-Huen; Pan-STARRS 1 Builders
2016-10-01
The origin of high inclination objects beyond Jupiter, including trans-Neptunian objects (TNOs) and Centaurs, remains uncertain. We report the discovery of a retrograde TNO, which we nickname "Niku", detected by the Pan-STARRS 1 Outer Solar System Survey. The numerical integrations show that the orbital dynamics of Niku are very similar to those of 2008 KV42 (Drac), with a half-life of ~ 500 Myr and analogous orbital evolution. Comparing similar high inclination members announced by the Minor-Planet Center (q > 10 AU, a < 100 AU and i > 60), we find these objects exhibit a surprising clustering of ascending node, populating a common orbital plane. The statistical significance of 3.8-sigma suggests it is unlikely to be coincidental. An unknown mechanism is required to explain the observed clustering. This discovery may provide a pathway to investigating a possible reservoir of high-inclination objects.
NASA Astrophysics Data System (ADS)
Caudal, Gérard
2017-04-01
Saturn's moon Mimas is a triaxial body orbiting close to the planet on an eccentric orbit, and as a consequence it is librating significantly. Libration is usually believed to enhance dissipation within a planetary satellite. In this paper Mimas' poorly understood strong inward migration obtained by Lainey et al. (2012a) is interpreted as an effect of dissipation within the librating moon. Tajeddine et al. (2014) performed observations of the phase and amplitude of libration and proposed several interior models, from which they retained only two models compatible with observations: a solid body with nonhydrostatic core, or a 3-layer body including an inner dense core, surrounded by a water ocean and an icy solid shell. In this paper I combined three major observations: libration amplitude and libration phase observed by Tajeddine et al. (2014), and inward migration da/dt obtained by Lainey et al. (2012a). A further study by Lainey et al. (2015) however tends to indicate that the Mimas' strong inward motion might be questioned, and therefore this paper also explores situations with smaller da/dt. Within the assumption that inward migration is mainly due to librational dissipation, the solid model with nonhydrostatic core is found to be inconsistent with the observations. In contrast, a 3-layer model including core, ocean and shell is compatible. The observations permit to determine the icy shell depth h, core equatorial flattening βi and core pendulum quality factor QPei, provided that an assumption is made concerning the core density. Due to the uncertainty of da/dt inferred from observations, the value of QPei is however rather uncertain. Dissipation within the oceanic boundary layers is found to contribute significantly to the total dissipated power.
Fast numerics for the spin orbit equation with realistic tidal dissipation and constant eccentricity
NASA Astrophysics Data System (ADS)
Bartuccelli, Michele; Deane, Jonathan; Gentile, Guido
2017-03-01
We present an algorithm for the rapid numerical integration of a time-periodic ODE with a small dissipation term that is C^1 in the velocity. Such an ODE arises as a model of spin-orbit coupling in a star/planet system, and the motivation for devising a fast algorithm for its solution comes from the desire to estimate probability of capture in various solutions, via Monte Carlo simulation: the integration times are very long, since we are interested in phenomena occurring on timescales of the order of 10^6 -10^7 years. The proposed algorithm is based on the high-order Euler method which was described in Bartuccelli et al. (Celest Mech Dyn Astron 121(3):233-260, 2015), and it requires computer algebra to set up the code for its implementation. The payoff is an overall increase in speed by a factor of about 7.5 compared to standard numerical methods. Means for accelerating the purely numerical computation are also discussed.
Eccentricity of small exoplanets
NASA Astrophysics Data System (ADS)
Van Eylen, Vincent; Albrecht, Simon
2015-12-01
Solar system planets move on almost circular orbits. In strong contrast, many massive gas giant exoplanets travel on highly elliptical orbits, whereas the shape of the orbits of smaller, more terrestrial, exoplanets remained largely elusive. This is because the stellar radial velocity caused by these small planets is extremely challenging to measure. Knowing the eccentricity distribution in systems of small planets would be important as it holds information about the planet's formation and evolution. Furthermore the location of the habitable zone depends on eccentricity, and eccentricity also influences occurrence rates inferred for these planets because planets on circular orbits are less likely to transit. We make these eccentricity measurements of small planets using photometry from the Kepler satellite and utilizing a method relying on Kepler's second law, which relates the duration of a planetary transit to its orbital eccentricity, if the stellar density is known.I present a sample of 28 multi-planet systems with precise asteroseismic density measurements, which host 74 planets with an average radius of 2.6 R_earth. We find that the eccentricity of planets in these systems is low and can be described by a Rayleigh distribution with sigma = 0.049 +- 0.013. This is in full agreement with solar system eccentricities, but in contrast to the eccentricity distributions previously derived for exoplanets from radial velocity studies. I further report the first results on the eccentricities of over 50 Kepler single-planet systems, and compare them with the multi-planet systems. I close the talk by showing how transit durations help distinguish between false positives and true planets, and present six new planets.
HAT-P-16b: A 4 M J Planet Transiting a Bright Star on an Eccentric Orbit
NASA Astrophysics Data System (ADS)
Buchhave, L. A.; Bakos, G. Á.; Hartman, J. D.; Torres, G.; Kovács, G.; Latham, D. W.; Noyes, R. W.; Esquerdo, G. A.; Everett, M.; Howard, A. W.; Marcy, G. W.; Fischer, D. A.; Johnson, J. A.; Andersen, J.; Fűrész, G.; Perumpilly, G.; Sasselov, D. D.; Stefanik, R. P.; Béky, B.; Lázár, J.; Papp, I.; Sári, P.
2010-09-01
We report the discovery of HAT-P-16b, a transiting extrasolar planet orbiting the V = 10.8 mag F8 dwarf GSC 2792-01700, with a period P = 2.775960 ± 0.000003 days, transit epoch Tc = 2455027.59293 ± 0.00031 (BJD10), and transit duration 0.1276 ± 0.0013 days. The host star has a mass of 1.22 ± 0.04 M sun, radius of 1.24 ± 0.05 R sun, effective temperature 6158 ± 80 K, and metallicity [Fe/H] = +0.17 ± 0.08. The planetary companion has a mass of 4.193 ± 0.094 M J and radius of 1.289 ± 0.066 R J, yielding a mean density of 2.42 ± 0.35 g cm-3. Comparing these observed characteristics with recent theoretical models, we find that HAT-P-16b is consistent with a 1 Gyr H/He-dominated gas giant planet. HAT-P-16b resides in a sparsely populated region of the mass-radius diagram and has a non-zero eccentricity of e = 0.036 with a significance of 10σ. Based in part on observations made with the Nordic Optical Telescope, operated on the island of La Palma jointly by Denmark, Finland, Iceland, Norway, and Sweden, in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias. Based in part on observations obtained at the W. M. Keck Observatory, which is operated by the University of California and the California Institute of Technology. Keck time has been granted by NASA (N018Hr).
NASA Astrophysics Data System (ADS)
Chen, Yuan-Yuan; Ma, Yuehua; Zheng, Jiaqing
2016-06-01
We explore planetary migration scenarios for the formation of high-inclination Neptunian Trojans (NTs) and how they are affected by the planetary migration of Neptune and Uranus. If Neptune's and Uranus's eccentricity and inclination were damped during planetary migration, then their eccentricities and inclinations were higher prior and during the migration than their current values. Using test particle integrations, we study the stability of primordial NTs, objects that were initially Trojans with Neptune prior to migration. We also study trans-Neptunian objects captured into resonance with Neptune and becoming NTs during planet migration. We find that most primordial NTs were unstable and lost if eccentricity and inclination damping took place during planetary migration. With damping, secular resonances with Neptune can increase a low eccentricity and inclination population of trans-Neptunian objects increasing the probability that they are captured into 1: 1 resonance with Neptune, becoming high-inclination NTs. We suggest that the resonant trapping scenario is a promising and more effective mechanism to explain the origin of NTs, which is particularly effective if Uranus and Neptune experienced eccentricity and inclination damping during planetary migration.
NASA Astrophysics Data System (ADS)
Da Silva Fernandes, Sandro; Das Chagas Carvalho, Francisco; Vilhena de Moraes, Rodolpho
The purpose of this work is to present a complete first order analytical solution, which includes short periodic terms, for the problem of optimal low-thrust limited power trajectories with large amplitude transfers (no rendezvous) between coplanar orbits with small eccentricities in Newtonian central gravity field. The study of these transfers is particularly interesting because the orbits found in practice often have a small eccentricity and the problem of transferring a vehicle from a low earth orbit to a high earth orbit is frequently found. Besides, the analysis has been motivated by the renewed interest in the use of low-thrust propulsion systems in space missions verified in the last two decades. Several researchers have obtained numerical and sometimes analytical solutions for a number of specific initial orbits and specific thrust profiles. Averaging methods are also used in such researches. Firstly, the optimization problem associated to the space transfer problem is formulated as a Mayer problem of optimal control with Cartesian elements - position and velocity vectors - as state variables. After applying the Pontryagin Maximum Principle, successive Mathieu transformations are performed and suitable sets of orbital elements are introduced. The short periodic terms are eliminated from the maximum Hamiltonian function through an infinitesimal canonical transformation built through Hori method - a perturbation canonical method based on Lie series. The new Hamiltonian function, which results from the infinitesimal canonical transformation, describes the extremal trajectories for long duration maneuvers. Closed-form analytical solutions are obtained for the new canonical system by solving the Hamilton-Jacobi equation through the separation of variables technique. By applying the transformation equations of the algorithm of Hori method, a first order analytical solution for the problem is obtained in non-singular orbital elements. For long duration maneuvers
NASA Astrophysics Data System (ADS)
Chen, Ying-Tung; Lin, Hsing Wen; Holman, Matthew J.; Payne, Matthew J.; Fraser, Wesley C.; Lacerda, Pedro; Ip, Wing-Huen; Chen, Wen-Ping; Kudritzki, Rolf-Peter; Jedicke, Robert; Wainscoat, Richard J.; Tonry, John L.; Magnier, Eugene A.; Waters, Christopher; Kaiser, Nick; Wang, Shiang-Yu; Lehner, Matthew
2016-08-01
Although the majority of Centaurs are thought to have originated in the scattered disk, with the high-inclination members coming from the Oort cloud, the origin of the high-inclination component of trans-Neptunian objects (TNOs) remains uncertain. We report the discovery of a retrograde TNO, which we nickname “Niku,” detected by the Pan-STARRS 1 Outer Solar System Survey. Our numerical integrations show that the orbital dynamics of Niku are very similar to that of 2008 KV42 (Drac), with a half-life of ˜500 Myr. Comparing similar high-inclination TNOs and Centaurs (q > 10 au, a < 100 au, and i > 60°), we find that these objects exhibit a surprising clustering of ascending node, and occupy a common orbital plane. This orbital configuration has high statistical significance: 3.8-σ. An unknown mechanism is required to explain the observed clustering. This discovery may provide a pathway to investigating a possible reservoir of high-inclination objects.
NASA Astrophysics Data System (ADS)
van der Helm, Edwin; Portegies Zwart, Simon; Pols, Onno
2016-01-01
The X-ray source HLX-1 near the spiral galaxy ESO 243-49 is currently the best intermediate-mass black hole candidate. It has a peak bolometric luminosity of 1042 erg s-1, which implies a mass inflow rate of ˜10-4 M⊙ yr-1, but the origin of this mass is unknown. It has been proposed that there is a star on an eccentric orbit around the black hole which transfers mass at pericentre. To investigate the orbital evolution of this system, we perform stellar evolution simulations using MESA and smoothed particle hydrodynamics simulations of a stellar orbit around an intermediate-mass black hole using FI. We run and couple these simulations using the AMUSE framework. We find that mass is lost through both the first and second Lagrange points and that there is a delay of up to 10 d between the pericentre passage and the peak mass-loss event. The orbital evolution time-scales we find in our simulations are larger than what is predicted by analytical models, but these models fall within the errors of our results. Despite the fast orbital evolution, we are unable to reproduce the observed change in outburst period. We conclude that the change in the stellar orbit, with the system parameters investigated here, is unable to account for all observed features of HLX-1.
NASA Astrophysics Data System (ADS)
Ma, Hongliang; Xu, Shijie
2016-11-01
By defining two open-time impulse points, the optimization of a two-impulse, open-time terminal rendezvous and docking with target spacecraft on large-eccentricity elliptical orbit is proposed in this paper. The purpose of optimization is to minimize the velocity increment for a terminal elliptic-reference-orbit rendezvous and docking. Current methods for solving this type of optimization problem include for example genetic algorithms and gradient based optimization. Unlike these methods, interval methods can guarantee that the globally best solution is found for a given parameterization of the input. The non-linear Tschauner- Hempel(TH) equations of the state transitions for a terminal elliptic target orbit are transformed form time domain to target orbital true anomaly domain. Their homogenous solutions and approximate state transition matrix for the control with a short true anomaly interval can be used to avoid interval integration. The interval branch and bound optimization algorithm is introduced for solving the presented rendezvous and docking optimization problem and optimizing two open-time impulse points and thruster pulse amplitudes, which systematically eliminates parts of the control and open-time input spaces that do not satisfy the path and final time state constraints. Several numerical examples are undertaken to validate the interval optimization algorithm. The results indicate that the sufficiently narrow spaces containing the global optimization solution for the open-time two-impulse terminal rendezvous and docking with target spacecraft on large-eccentricity elliptical orbit can be obtained by the interval algorithm (IA). Combining the gradient-based method, the global optimization solution for the discontinuous nonconvex optimization problem in the specifically remained search space can be found. Interval analysis is shown to be a useful tool and preponderant in the discontinuous nonconvex optimization problem of the terminal rendezvous and
Nagasawa, M.; Ida, S.
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 planets 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.
NASA Astrophysics Data System (ADS)
Smith, A. M. S.; Gandolfi, D.; Barragán, O.; Bowler, B.; Csizmadia, Sz.; Endl, M.; Fridlund, M. C. V.; Grziwa, S.; Guenther, E.; Hatzes, A. P.; Nowak, G.; Albrecht, S.; Alonso, R.; Cabrera, J.; Cochran, W. D.; Deeg, H. J.; Cusano, F.; Eigmüller, Ph.; Erikson, A.; Hidalgo, D.; Hirano, T.; Johnson, M. C.; Korth, J.; Mann, A.; Narita, N.; Nespral, D.; Palle, E.; Pätzold, M.; Prieto-Arranz, J.; Rauer, H.; Ribas, I.; Tingley, B.; Wolthoff, V.
2017-01-01
We report the discovery from K2 of a transiting planet in an 18.25-d, eccentric (0.19 ± 0.04) orbit around K2-99, an 11th magnitude subgiant in Virgo. We confirm the planetary nature of the companion with radial velocities, and determine that the star is a metal-rich ([Fe/H] = 0.20 ± 0.05) subgiant, with mass 1.60^{+0.14}_{-0.10} M⊙ and radius 3.1 ± 0.1 R⊙. The planet has a mass of 0.97 ± 0.09 MJup and a radius 1.29 ± 0.05 RJup. A measured systemic radial acceleration of -2.12 ± 0.04 ms-1 d-1 offers compelling evidence for the existence of a third body in the system, perhaps a brown dwarf orbiting with a period of several hundred days.
ECCENTRICITY EVOLUTION THROUGH ACCRETION OF PROTOPLANETS
Matsumoto, Yuji; Nagasawa, Makiko; Ida, Shigeru E-mail: nagasawa.m.ad@m.titech.ac.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. We 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.
Van Eylen, V.; Lund, M. N.; Aguirre, V. Silva; Arentoft, T.; Kjeldsen, H.; Pedersen, M. G.; Jessen-Hansen, J.; Tingley, B.; Christensen-Dalsgaard, J.; Albrecht, S.; Chaplin, W. J.; Campante, T. L.; Isaacson, H.; Aerts, C.; Bryson, S. T.
2014-02-10
We confirm the Kepler planet candidate Kepler-410A b (KOI-42b) as a Neptune-sized exoplanet on a 17.8 day, eccentric orbit around the bright (K {sub p} = 9.4) star Kepler-410A (KOI-42A). This is the third brightest confirmed planet host star in the Kepler field and one of the brightest hosts of all currently known transiting exoplanets. Kepler-410 consists of a blend between the fast rotating planet host star (Kepler-410A) and a fainter star (Kepler-410B), which has complicated the confirmation of the planetary candidate. Employing asteroseismology, using constraints from the transit light curve, adaptive optics and speckle images, and Spitzer transit observations, we demonstrate that the candidate can only be an exoplanet orbiting Kepler-410A. We determine via asteroseismology the following stellar and planetary parameters with high precision; M {sub *} = 1.214 ± 0.033 M {sub ☉}, R {sub *} = 1.352 ± 0.010 R {sub ☉}, age =2.76 ± 0.54 Gyr, planetary radius (2.838 ± 0.054 R {sub ⊕}), and orbital eccentricity (0.17{sub −0.06}{sup +0.07}). In addition, rotational splitting of the pulsation modes allows for a measurement of Kepler-410A's inclination and rotation rate. Our measurement of an inclination of 82.5{sub −2.5}{sup +7.5} [°] indicates a low obliquity in this system. Transit timing variations indicate the presence of at least one additional (non-transiting) planet (Kepler-410A c) in the system.
... problem. Alternative Names Ejaculation retrograde; Dry climax Images Male reproductive system References Bhasin S, Basson R. Sexual dysfunction in men and women. In: Kronenberg HM, Melmed S, Polonsky KS, Larsen PR, eds. Williams ... management of male infertility. In: Wein AJ, ed. Campbell-Walsh Urology . ...
NASA Astrophysics Data System (ADS)
Rouan, D.; Parviainen, H.; Moutou, C.; Deleuil, M.; Fridlund, M.; Ofir, A.; Havel, M.; Aigrain, S.; Alonso, R.; Auvergne, M.; Baglin, A.; Barge, P.; Bonomo, A. S.; Bordé, P.; Bouchy, F.; Cabrera, J.; Cavarroc, C.; Csizmadia, Sz.; Deeg, H. J.; Diaz, R. F.; Dvorak, R.; Erikson, A.; Ferraz-Mello, S.; Gandolfi, D.; Gillon, M.; Guillot, T.; Hatzes, A.; Hébrard, G.; Jorda, L.; Léger, A.; Llebaria, A.; Lammer, H.; Lovis, C.; Mazeh, T.; Ollivier, M.; Pätzold, M.; Queloz, D.; Rauer, H.; Samuel, B.; Santerne, A.; Schneider, J.; Tingley, B.; Wuchterl, G.
2012-01-01
We report the detection of CoRoT-23b, a hot Jupiter transiting in front of its host star with a period of 3.6314 ± 0.0001 days. This planet was discovered thanks to photometric data secured with the CoRoT satellite, combined with spectroscopic radial velocity (RV) measurements. A photometric search for possible background eclipsing binaries conducted at CFHT and OGS concluded with a very low risk of false positives. The usual techniques of combining RV and transit data simultaneously were used to derive stellar and planetary parameters. The planet has a mass of Mp = 2.8 ± 0.3 MJup, a radius of Rpl= 1.05 ± 0.13RJup, a density of ≈ 3 g cm-3. RV data also clearly reveal a nonzero eccentricity of e = 0.16 ± 0.02. The planet orbits a mature G0 main sequence star of V = 15.5 mag, with a mass M⋆ = 1.14 ± 0.08 M⊙, a radius R ⋆ = 1. 61 ± 0.18 R⊙ and quasi-solarabundances. The age of the system is evaluated to be 7 Gyr, not far from the transition to subgiant, in agreement with the rather large stellar radius. The two features of a significant eccentricity of the orbit and of a fairly high density are fairly uncommon for a hot Jupiter. The high density is, however, consistent with a model of contraction of a planet at this mass, given the age of the system. On the other hand, at such an age, circularization is expected to be completed. In fact, we show that for this planetary mass and orbital distance, any initial eccentricity should not totally vanish after 7 Gyr, as long as the tidal quality factor Qp is more than a few 105, a value that is the lower bound of the usually expected range. Even if CoRoT-23b features a density and an eccentricity that are atypical of a hot Jupiter, it is thus not an enigmatic object. The CoRoT space mission, launched on 27 December 2006, has been developed and is operated by CNES, with the contribution of Austria, Belgium, Brazil, ESA, Germany, and Spain. First CoRoT data are available to the public from the CoRoT archive: http
ECCENTRIC JUPITERS VIA DISK–PLANET INTERACTIONS
Duffell, Paul C.; Chiang, Eugene E-mail: echiang@astro.berkeley.edu
2015-10-20
Numerical hydrodynamics calculations are performed to determine the conditions under which giant planet eccentricities can be excited by parent gas disks. Unlike in other studies, Jupiter-mass planets are found to have their eccentricities amplified—provided their orbits start off as eccentric. We disentangle the web of co-rotation, co-orbital, and external resonances to show that this finite-amplitude instability is consistent with that predicted analytically. Ellipticities can grow until they reach of order of the disk's aspect ratio, beyond which the external Lindblad resonances that excite eccentricity are weakened by the planet's increasingly supersonic epicyclic motion. Forcing the planet to still larger eccentricities causes catastrophic eccentricity damping as the planet collides into gap walls. For standard parameters, the range of eccentricities for instability is modest; the threshold eccentricity for growth (∼0.04) is not much smaller than the final eccentricity to which orbits grow (∼0.07). If this threshold eccentricity can be lowered (perhaps by non-barotropic effects), and if the eccentricity driving documented here survives in 3D, it may robustly explain the low-to-moderate eccentricities ≲0.1 exhibited by many giant planets (including Jupiter and Saturn), especially those without planetary or stellar companions.
Kepler-432 b: a massive warm Jupiter in a 52-day eccentric orbit transiting a giant star
NASA Astrophysics Data System (ADS)
Ortiz, Mauricio; Gandolfi, Davide; Reffert, Sabine; Quirrenbach, Andreas; Deeg, Hans J.; Karjalainen, Raine; Montañés-Rodríguez, Pilar; Nespral, David; Nowak, Grzegorz; Osorio, Yeisson; Palle, Enric
2015-01-01
We study the Kepler object Kepler-432, an evolved star ascending the red giant branch. By deriving precise radial velocities from multi-epoch high-resolution spectra of Kepler-432 taken with the CAFE spectrograph at the 2.2 m telescope of Calar Alto Observatory and the FIES spectrograph at the Nordic Optical Telescope of Roque de Los Muchachos Observatory, we confirm the planetary nature of the object Kepler-432 b, which has a transit period of 52 days. We find a planetary mass of Mp = 5.84 ± 0.05MJup and a high eccentricity of e = 0.478 ± 0.004. With a semi-major axis of a = 0.303 ± 0.007 AU, Kepler-432 b is the first bona fide warm Jupiter detected to transit a giant star. We also find a radial velocity linear trend of γ˙ = 0.44 ± 0.04 m s-1 d-1, which suggests the presence of a third object in the system. Current models of planetary evolution in the post-main-sequence phase predict that Kepler-432 b will be most likely engulfed by its host star before the latter reaches the tip of the red giant branch. Based on observations collected at the German-Spanish Astronomical Center, Calar Alto, jointly operated by the Max-Planck-Institut für Astronomie (Heidelberg) and the Instituto de Astrofísica de Andalucía (IAA-CSIC, Granada).Based on observations obtained with the Nordic Optical Telescope, operated on the island of La Palma jointly by Denmark, Finland, Iceland, Norway, and Sweden, in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias.Table 3 is available in electronic form at http://www.aanda.org
NASA Astrophysics Data System (ADS)
Ortiz, Mauricio; Reffert, Sabine; Trifonov, Trifon; Quirrenbach, Andreas; Mitchell, David S.; Nowak, Grzegorz; Buenzli, Esther; Zimmerman, Neil; Bonnefoy, Mickaël; Skemer, Andy; Defrère, Denis; Lee, Man Hoi; Fischer, Debra A.; Hinz, Philip M.
2016-10-01
Context. For over 12 yr, we have carried out a precise radial velocity (RV) survey of a sample of 373 G- and K-giant stars using the Hamilton Échelle Spectrograph at the Lick Observatory. There are, among others, a number of multiple planetary systems in our sample as well as several planetary candidates in stellar binaries. Aims: We aim at detecting and characterizing substellar and stellar companions to the giant star HD 59686 A (HR 2877, HIP 36616). Methods: We obtained high-precision RV measurements of the star HD 59686 A. By fitting a Keplerian model to the periodic changes in the RVs, we can assess the nature of companions in the system. To distinguish between RV variations that are due to non-radial pulsation or stellar spots, we used infrared RVs taken with the CRIRES spectrograph at the Very Large Telescope. Additionally, to characterize the system in more detail, we obtained high-resolution images with LMIRCam at the Large Binocular Telescope. Results: We report the probable discovery of a giant planet with a mass of mp sin i = 6.92-0.24+0.18 MJup orbiting at ap = 1.0860-0.0007+0.0006 au from the giant star HD 59686 A. In addition to the planetary signal, we discovered an eccentric (eB = 0.729-0.003+0.004) binary companion with a mass of mB sin i = 0.5296-0.0008+0.0011 M⊙ orbiting at a close separation from the giant primary with a semi-major axis of aB = 13.56-0.14+0.18 au. Conclusions: The existence of the planet HD 59686 Ab in a tight eccentric binary system severely challenges standard giant planet formation theories and requires substantial improvements to such theories in tight binaries. Otherwise, alternative planet formation scenarios such as second-generation planets or dynamical interactions in an early phase of the system's lifetime need to be seriously considered to better understand the origin of this enigmatic planet. Based on observations collected at the Lick Observatory, University of California.Based on observations collected at the
NASA Astrophysics Data System (ADS)
Pousse, Alexandre; Robutel, Philippe; Vienne, Alain
2017-02-01
In the framework of the planar and circular restricted three-body problem, we consider an asteroid that orbits the Sun in quasi-satellite motion with a planet. A quasi-satellite trajectory is a heliocentric orbit in co-orbital resonance with the planet, characterized by a nonzero eccentricity and a resonant angle that librates around zero. Likewise, in the rotating frame with the planet, it describes the same trajectory as the one of a retrograde satellite even though the planet acts as a perturbator. In the last few years, the discoveries of asteroids in this type of motion made the term "quasi-satellite" more and more present in the literature. However, some authors rather use the term "retrograde satellite" when referring to this kind of motion in the studies of the restricted problem in the rotating frame. In this paper, we intend to clarify the terminology to use, in order to bridge the gap between the perturbative co-orbital point of view and the more general approach in the rotating frame. Through a numerical exploration of the co-orbital phase space, we describe the quasi-satellite domain and highlight that it is not reachable by low eccentricities by averaging process. We will show that the quasi-satellite domain is effectively included in the domain of the retrograde satellites and neatly defined in terms of frequencies. Eventually, we highlight a remarkable high eccentric quasi-satellite orbit corresponding to a frozen ellipse in the heliocentric frame. We extend this result to the eccentric case (planet on an eccentric motion) and show that two families of frozen ellipses originate from this remarkable orbit.
SUPER-ECCENTRIC MIGRATING JUPITERS
Socrates, Aristotle; Katz, Boaz; Dong Subo; Tremaine, Scott
2012-05-10
An important class of formation theories for hot Jupiters involves the excitation of extreme orbital eccentricity (e = 0.99 or even larger) followed by tidal dissipation at periastron passage that eventually circularizes the planetary orbit at a period less than 10 days. In a steady state, this mechanism requires the existence of a significant population of super-eccentric (e > 0.9) migrating Jupiters with long orbital periods and periastron distances of only a few stellar radii. For these super-eccentric planets, the periastron is fixed due to conservation of orbital angular momentum and the energy dissipated per orbit is constant, implying that the rate of change in semi-major axis a is a-dot {proportional_to}a{sup 1/2} and consequently the number distribution satisfies dN/d log a{proportional_to}a{sup 1/2}. If this formation process produces most hot Jupiters, Kepler should detect several super-eccentric migrating progenitors of hot Jupiters, allowing for a test of high-eccentricity migration scenarios.
Extreme orbital evolution from hierarchical secular coupling of two giant planets
Teyssandier, Jean; Naoz, Smadar; Lizarraga, Ian; Rasio, Frederic A.
2013-12-20
Observations of exoplanets over the last two decades have revealed a new class of Jupiter-size planets with orbital periods of a few days, the so-called 'hot Jupiters'. Recent measurements using the Rossiter-McLaughlin effect have shown that many (∼50%) of these planets are misaligned; furthermore, some (∼15%) are even retrograde with respect to the stellar spin axis. Motivated by these observations, we explore the possibility of forming retrograde orbits in hierarchical triple configurations consisting of a star-planet inner pair with another giant planet, or brown dwarf, in a much wider orbit. Recently, it was shown that in such a system, the inner planet's orbit can flip back and forth from prograde to retrograde and can also reach extremely high eccentricities. Here we map a significant part of the parameter space of dynamical outcomes for these systems. We derive strong constraints on the orbital configurations for the outer perturber (the tertiary) that could lead to the formation of hot Jupiters with misaligned or retrograde orbits. We focus only on the secular evolution, neglecting other dynamical effects such as mean-motion resonances, as well as all dissipative forces. For example, with an inner Jupiter-like planet initially on a nearly circular orbit at 5 AU, we show that a misaligned hot Jupiter is likely to be formed in the presence of a more massive planetary companion (>2 M{sub J} ) within ∼140 AU of the inner system, with mutual inclination >50° and eccentricity above ∼0.25. This is in striking contrast to the test particle approximation, where an almost perpendicular configuration can still cause large-eccentricity excitations, but flips of an inner Jupiter-like planet are much less likely to occur. The constraints we derive can be used to guide future observations and, in particular, searches for more distant companions in systems containing a hot Jupiter.
On the Eccentricities of Extrasolar Planets
NASA Astrophysics Data System (ADS)
Marzari, F.; Weidenschilling, S. J.
1999-09-01
Extrasolar planets (ESPs) seem to be divided into two groups: circular orbits very close to their stars, or eccentric orbits at larger distances. The latter may be the result of gravitational scattering of planets that formed in unstable orbits (Weidenschilling and Marzari 1996, Nature 384, 619). For systems of three Jupiter-mass planets, the most common outcome is ejection of one planet, leaving the others in stable orbits with significant eccentricities and mutual inclinations. We have compiled statistics for orbital elements of the survivors. At the time of ejection, the eccentricity of the inner one has a broad distribution with modal value 0.5, ranging from about 0.1 to 0.9; smaller and larger values are rare. In contrast, among observed eccentric ESPs only 2 of 11 have e > 0.5, and none have e > 0.7, although there is no observational bias against detection of planets on eccentric orbits. One possible explanation is a large cross-section for young gas giant planets still in their contraction phase, so that non-collisional encounters yield smaller velocity changes. However, even if the effective radius is twice Jupiter's present value, the eccentricity distribution does not change significantly. The "snapshot" distribution at the time one planet is ejected may be misleading. The orbits of the remaining planets are subject to mutual perturbations. The inner planet's eccentricity may oscillate with large amplitude on timescales of 10(7) - 10(8) y. Peak values bring some periastrons low enough for tides to circularize orbits. For planets with large initial eccentricities, the time-averaged e is lower, yielding better agreement with the observed distribution. Still, some orbits with eccentricities up to 0.9, should be detected in a large enough sample of ESPs. If none are found, their absence would argue against gravitational scattering as a general phenomenon in planetary systems.
Origin of Prometheus Eccentricity
NASA Astrophysics Data System (ADS)
Rappaport, N. J.; Longaretti, P.
2006-12-01
A number of Saturn's small satellites, from Atlas to the coorbital satellites Janus and Epimetheus, move on orbits just outside the main rings of the planet. These satellites undergo extremely rapid resonant interaction with the rings and outward motion, strongly suggesting that they originated in Saturn's A ring. However, their eccentricities, of the order of 1/1000 are several orders of magnitude larger than what could be expected if the small satellites formed in the ring. This paper represents a first step to providing an explanation for this phenomenon, by focusing on the dynamical processes that have affected the eccentricity of Prometheus. The explanation invokes past resonances with the coorbital satellites combined with chaos due to overlapping of these resonances.
Resonant and secular orbital interactions
NASA Astrophysics Data System (ADS)
Zhang, Ke
In stable solar systems, planets remain in nearly elliptical orbits around their stars. Over longer timescales, however, their orbital shapes and sizes change due to mutual gravitational perturbations. Orbits of satellites around a planet vary for the same reason. Because of their interactions, the orbits of planets and satellites today are different from what they were earlier. In order to determine their original orbits, which are critical constraints on formation theories, it is crucial to understand how orbits evolve over the age of the Solar System. Depending on their timescale, we classify orbital interactions as either short-term (orbital resonances) or long-term (secular evolution). My work involves examples of both interaction types. Resonant history of the small Neptunian satellites. In satellite systems, tidal migration brings satellite orbits in and out of resonances. During a resonance passage, satellite orbits change dramatically in a very short period of time. We investigate the resonant history of the six small Neptunian moons. In this unique system, the exotic orbit of the large captured Triton (with a circular, retrograde, and highly tilted orbit) influences the resonances among the small satellites very strongly. We derive an analytical framework which can be applied to Neptune's satellites and to similar systems. Our numerical simulations explain the current orbital tilts of the small satellites as well as constrain key physical parameters of both Neptune and its moons. Secular orbital interactions during eccentricity damping. Long-term periodic changes of orbital shape and orientation occur when two or more planets orbit the same star. The variations of orbital elements are superpositions of the same number of fundamental modes as the number of planets in the system. We investigate how this effect interacts with other perturbations imposed by external disturbances, such as the tides and relativistic effects. Through analytical studies of a
COMPLETENESS OF IMAGING SURVEYS FOR ECCENTRIC EXOPLANETS
Kane, Stephen R.
2013-03-20
The detection of exoplanets through direct imaging has produced numerous new positive identifications in recent years. The technique is biased toward planets at wide separations due to the difficulty in removing the stellar signature at small angular separations. Planets in eccentric orbits will thus move in and out of the detectable region around a star as a function of time. Here we use the known diversity of orbital eccentricities to determine the range of orbits that may lie beneath the detection threshold of current surveys. We quantify the percentage of the orbit that yields a detectable signature as a function of semimajor axis, eccentricity, and orbital inclination and estimate the fraction of planets which likely remain hidden by the flux of the host star.
Eccentricity Pumping Through Circumbinary Disks in Hot Subdwarf Binaries
NASA Astrophysics Data System (ADS)
Vos, J.
2015-12-01
Hot subdwarf-B stars in long-period binaries are found to be on eccentric orbits, even though current binary-evolution theory predicts these objects to be circularized before the onset of Roche-lobe overflow (RLOF). We have tested three different eccentricity pumping processes on their viability to reproduce the observed wide sdB population; tidally-enhanced wind mass-loss, phase-dependent RLOF on eccentric orbits and the interaction between a circumbinary (CB) disk and the binary. The binary module of the stellar-evolution code Modules for Experiments in Stellar Astrophysics (MESA) is extended to include the eccentricity-pumping processes, and a parameter study is carried out. We find that models including phase-dependent RLOF or a CB disk can reach the observed periods and eccentricities. However, the models cannot explain the observed correlation between period and eccentricity. Nor can circular short period systems be formed when eccentricity pumping mechanisms are active.
Retrograde gastroesophageal intussusception.
David, S; Barkin, J S
1992-01-01
This is an initial report of spontaneous retrograde gastroesophageal intussusception in an adult. The patient is a 72-yr-old women with a history of ovarian cancer and hiatal hernia, who presented with symptoms of upper gastrointestinal obstruction. Retrograde intussusception was diagnosed endoscopically and confirmed radiographically with an upper gastrointestinal series. Heightened awareness of this entity may lead to its more frequent diagnosis.
Functional (dissociative) retrograde amnesia.
Markowitsch, H J; Staniloiu, A
2017-01-01
Retrograde amnesia is described as condition which can occur after direct brain damage, but which occurs more frequently as a result of a psychiatric illness. In order to understand the amnesic condition, content-based divisions of memory are defined. The measurement of retrograde memory is discussed and the dichotomy between "organic" and "psychogenic" retrograde amnesia is questioned. Briefly, brain damage-related etiologies of retrograde amnesia are mentioned. The major portion of the review is devoted to dissociative amnesia (also named psychogenic or functional amnesia) and to the discussion of an overlap between psychogenic and "brain organic" forms of amnesia. The "inability of access hypothesis" is proposed to account for most of both the organic and psychogenic (dissociative) patients with primarily retrograde amnesia. Questions such as why recovery from retrograde amnesia can occur in retrograde (dissociative) amnesia, and why long-term new learning of episodic-autobiographic episodes is possible, are addressed. It is concluded that research on retrograde amnesia research is still in its infancy, as the neural correlates of memory storage are still unknown. It is argued that the recollection of episodic-autobiographic episodes most likely involves frontotemporal regions of the right hemisphere, a region which appears to be hypometabolic in patients with dissociative amnesia.
PUMPING THE ECCENTRICITY OF EXOPLANETS BY TIDAL EFFECT
Correia, Alexandre C. M.; Boue, Gwenaeel; Laskar, Jacques
2012-01-10
Planets close to their host stars are believed to undergo significant tidal interactions, leading to a progressive damping of the orbital eccentricity. Here we show that when the orbit of the planet is excited by an outer companion, tidal effects combined with gravitational interactions may give rise to a secular increasing drift on the eccentricity. As long as this secular drift counterbalances the damping effect, the eccentricity can increase to high values. This mechanism may explain why some of the moderate close-in exoplanets are observed with substantial eccentricity values.
NASA Astrophysics Data System (ADS)
Will, Clifford M.; Maitra, Matthew
2017-03-01
We derive the secular evolution of the orbital elements of a stellar-mass object orbiting a spinning massive black hole. We use the post-Newtonian (PN) approximation in harmonic coordinates, with test-body equations of motion for the conservative dynamics that are valid through 3PN order, including spin-orbit, quadrupole and (spin) 2 effects, and with radiation-reaction contributions linear in the mass of the body that are valid through 4.5PN order, including the 4PN damping effects of spin-orbit coupling. The evolution equations for the osculating orbit elements are iterated to high PN orders using a two-time-scale approach and averaging over orbital time scales. We derive a criterion for terminating the orbit when its Carter constant drops below a critical value, whereupon the body plunges across the event horizon at the next closest approach. The results are valid for arbitrary eccentricities and arbitrary inclinations. We then analyze numerically the orbits of objects injected into high-eccentricity orbits via interactions within a surrounding star cluster, obtaining the number of orbits and the elapsed time between injection and plunge, and the residual orbital eccentricity at plunge as a function of inclination. We derive an analytic approximation for the time to plunge in terms of initial orbital variables. We show that, if the black hole is spinning rapidly, the flux of gravitational radiation during the final orbit before plunge may be suppressed by as much as 3 orders of magnitude if the orbit is retrograde on the equatorial plane compared to its prograde counterpart.
NASA Astrophysics Data System (ADS)
Van Eylen, Vincent; Albrecht, Simon
2015-08-01
Solar system planets move on almost circular orbits. In strong contrast, many massive gas giant exoplanets travel on highly elliptical orbits, whereas the shape of the orbits of smaller, more terrestrial, exoplanets remained largely elusive. Knowing the eccentricity distribution in systems of small planets would be important as it holds information about the planet's formation and evolution, and influences its habitability. We make these measurements using photometry from the Kepler satellite and utilizing a method relying on Kepler's second law, which relates the duration of a planetary transit to its orbital eccentricity, if the stellar density is known. Our sample consists of 28 bright stars with precise asteroseismic density measurements. These stars host 74 planets with an average radius of 2.6 R⊕. We find that the eccentricity of planets in Kepler multi-planet systems is low and can be described by a Rayleigh distribution with σ = 0.049 ± 0.013. This is in full agreement with solar system eccentricities, but in contrast to the eccentricity distributions previously derived for exoplanets from radial velocity studies. Our findings are helpful in identifying which planets are habitable because the location of the habitable zone depends on eccentricity, and to determine occurrence rates inferred for these planets because planets on circular orbits are less likely to transit. For measuring eccentricity it is crucial to detect and remove Transit Timing Variations (TTVs), and we present some previously unreported TTVs. Finally transit durations help distinguish between false positives and true planets and we use our measurements to confirm six new exoplanets.
Kim, Chun-Hwey; Song, Mi-Hwa; Yoon, Jo-Na; Jeong, Min-Ji; Han, Wonyong
2014-06-20
A photometric study of BD And was made through the analysis of two sets of new BVR light curves. The light curves with migrating photometric waves outside eclipse show that BD And is a short-period RS CVn-type binary star. The analysis of all available timings reveals that the orbital period has varied in a strictly cyclical way with a period of 9.2 yr. The periodic variation most likely arises from the light-time effect due to a tertiary moving in a highly elliptical orbit (e {sub 3} = 0.76). The Applegate mechanism could not operate properly in the eclipsing pair. The light curves were modeled with two large spots on the hotter star and a large third light amounting to about 14% of the total systemic light. BD And is a triple system: a detached binary system consisting of two nearly equal solar-type stars with an active primary star and a G6-G7 tertiary dwarf. The absolute dimensions of the eclipsing pair and tertiary components were determined. The three components with a mean age of about 5.8 Gyr are located at midpositions in main-sequence bands. The radius of the secondary is about 17% larger than that deduced from stellar models. The orbital and radiometric characteristics of the tertiary are intensively investigated. One important feature is that the mutual inclination between two orbits is larger than 60°, implying that Kozai cycles had occurred very efficiently in the past. The possible past and future evolutions of the BD And system, driven by KCTF and MBTF, are also discussed.
Orbital Behavior of Captured Satellites: The Effect of Solar Gravity on Triton's Post-Capture Orbit
NASA Astrophysics Data System (ADS)
Benner, Lance A. M.; McKinnon, William B.
1995-03-01
The effects of solar perturbations on the postcapture orbital behavior of satellites are investigated in the context of the restricted, circular three-body problem as applied to Neptune, Triton, and the Sun. Highly eccentric and inclined satellite orbits are considered; thus a numerical, phenomenological approach is taken to describe variations of the satellite's orbital elements. We focus on harmonic variations in specific orbital angular momentum h, and thus pericenter distance q, eccentricity e , semimajor axis a, and inclination to Neptune's orbital plane i . From prograde and retrograde simulations over a range of eccentricities and semimajor axes, a momentum oscillation is found with a period of half a Neptune year and an amplitude proportional to a2e2 cos i. Inclined orbits also experience a longer period, secular-torque-driven variation in h associated with orbital precession and nutation, upon which the semiannual oscillation is superimposed. The amplitude of the longer period variation can exceed and dominate the semiannual variation, and the two can combine to produce much larger variations in the elements q, e, and i than is possible for noninclined orbits, leading in some circumstances to "Neptune,grazing." Consequently, if Triton was temporarily gravitationally captured, solar perturbations could have increased e and reduced h sufficiently to drive the pericenter close to Neptune. There, interactions with a gaseous protoplanetary nebula or a collision with an existing satellite could have dissipated enough orbital energy to make capture permanent. It is more likely, though, that Triton was promptly captured by collision or gas drag into a lower q state to begin with. In either situation, capture at lower q ensures that further orbital variation does not bring Triton dangerously close to Neptune. Repeated close flybys following permanent capture are likely (and could also occur in the less likely event of an extended temporary capture). Multiple close
NASA Astrophysics Data System (ADS)
Hanson, Robert M.
2003-06-01
ORBITAL requires the following software, which is available for free download from the Internet: Netscape Navigator, version 4.75 or higher, or Microsoft Internet Explorer, version 5.0 or higher; Chime Plug-in, version compatible with your OS and browser (available from MDL).
NASA Astrophysics Data System (ADS)
Tal-Or, L.; Mazeh, T.; Alonso, R.; Bouchy, F.; Cabrera, J.; Deeg, H. J.; Deleuil, M.; Faigler, S.; Fridlund, M.; Hébrard, G.; Moutou, C.; Santerne, A.; Tingley, B.
2013-05-01
We present the study of the CoRoT transiting planet candidate 101186644, also named LRc01_E1_4780. Analysis of the CoRoT lightcurve and the HARPS spectroscopic follow-up observations of this faint (mV = 16) candidate revealed an eclipsing binary composed of a late F-type primary (Teff = 6090 ± 200 K) and a low-mass, dense late M-dwarf secondary on an eccentric (e = 0.4) orbit with a period of ~20.7 days. The M-dwarf has a mass of 0.096 ± 0.011 M⊙, and a radius of 0.104-0.006+0.026 R⊙, which possibly makes it the smallest and densest late M-dwarf reported so far. Unlike the claim that theoretical models predict radii that are 5-15% smaller than measured for low-mass stars, this one seems to have a radius that is consistent and might even be below the radius predicted by theoretical models. Based on observations made with the 1-m telescope at the Wise Observatory, Israel, the Swiss 1.2-m Leonhard Euler telescope at La Silla Observatory, Chile, the IAC-80 telescope at the Observatory del Teide, Canarias, Spain, and the 3.6-m telescope at La Silla Observatory (ESO), Chile (program 184.C-0639).
FOREVER ALONE? TESTING SINGLE ECCENTRIC PLANETARY SYSTEMS FOR MULTIPLE COMPANIONS
Wittenmyer, Robert A.; Horner, Jonathan; Tinney, C. G.; Bailey, J.; Salter, G. S.; Wright, D.; Wang Songhu; Zhou Jilin; Butler, R. P.; Jones, H. R. A.; O'Toole, S. J.; Carter, B. D.
2013-09-15
Determining the orbital eccentricity of an extrasolar planet is critically important for understanding the system's dynamical environment and history. However, eccentricity is often poorly determined or entirely mischaracterized due to poor observational sampling, low signal-to-noise, and/or degeneracies with other planetary signals. Some systems previously thought to contain a single, moderate-eccentricity planet have been shown, after further monitoring, to host two planets on nearly circular orbits. We investigate published apparent single-planet systems to see if the available data can be better fit by two lower-eccentricity planets. We identify nine promising candidate systems and perform detailed dynamical tests to confirm the stability of the potential new multiple-planet systems. Finally, we compare the expected orbits of the single- and double-planet scenarios to better inform future observations of these interesting systems.
NASA Astrophysics Data System (ADS)
Hamers, Adrian S.; Antonini, Fabio; Lithwick, Yoram; Perets, Hagai B.; Portegies Zwart, Simon F.
2017-01-01
Hot Jupiters (HJs) are Jupiter-like planets that reside very closely to their host star, within ˜0.1 au. Their formation is not well understood. It is generally believed that they cannot have formed in situ, implying that some form of migration must have occurred after their initial formation. We study the production of HJs through secular evolution in multiplanet systems with three to five planets. In this variant of high-e migration, the eccentricity of the orbit of the innermost planet is excited on secular time-scales, triggering orbital migration due to tidal dissipation. We use a secular dynamics code and carry out a population synthesis study. We find that HJs are only produced if the viscous time-scale is short (≈0.014 yr). In contrast, in up to ≈0.3 of systems, the innermost planet is tidally disrupted. The orbital period distribution is peaked around 5 d, consistent with observations. The median HJ mass is 1 MJ with a maximum of ≈2 MJ, similar to observed HJs. Approximately 0.1 of the HJs have retrograde orbits with respect to the stellar spin. We do not find a significant population of warm Jupiters in our simulations, i.e. planets with semimajor axes between 0.1 and 1 au.
Insolation patterns on eccentric exoplanets
NASA Astrophysics Data System (ADS)
Dobrovolskis, Anthony R.
2015-04-01
Several studies have found that synchronously-rotating Earth-like planets in the habitable zones of M-dwarf stars should exhibit an "eyeball" climate pattern, with a pupil of open ocean facing the parent star, and ice everywhere else. Recent work on eccentric exoplanets by Wang et al. (Wang, Y., Tian, F., Hu, Y. [2014b] Astrophys. J. 791, L12) has extended this conclusion to the 2:1 spin-orbit resonance as well, where the planet rotates twice during one orbital period. However, Wang et al. also found that the 3:2 and 5:2 half-odd resonances produce a zonally-striped climate pattern with polar icecaps instead. Unfortunately, they used incorrect insolation functions for the 3:2 and 5:2 resonances whose long-term time averages are essentially independent of longitude. This paper presents the correct insolation patterns for eccentric exoplanets with negligible obliquities in the 0:1, 1:2, 1:1, 3:2, 2:1, 5:2, 3:1, 7:2, and 4:1 spin-orbit resonances. I confirm that the mean insolation is distributed in an eyeball pattern for integer resonances; but for half-odd resonances, the mean insolation takes a "double-eyeball" pattern, identical over the "eastern" and "western" hemispheres. Presuming that liquids, ices, clouds, albedo, and thermal emission are similarly distributed, this has significant implications for the observation and interpretation of potentially habitable exoplanets. Finally, whether a striped ball, eyeball, or double-eyeball pattern emerges, the possibility exists that long-term build-up of ice (or liquid) away from the hot spots may alter the planet's inertia tensor and quadrupole moments enough to re-orient the planet, ultimately changing the distribution of liquid and ice.
Inferred Eccentricity and Period Distributions of Kepler Eclipsing Binaries
NASA Astrophysics Data System (ADS)
Prsa, Andrej; Matijevic, G.
2014-01-01
Determining the underlying eccentricity and orbital period distributions from an observed sample of eclipsing binary stars is not a trivial task. Shen and Turner (2008) have shown that the commonly used maximum likelihood estimators are biased to larger eccentricities and they do not describe the underlying distribution correctly; orbital periods suffer from a similar bias. Hogg, Myers and Bovy (2010) proposed a hierarchical probabilistic method for inferring the true eccentricity distribution of exoplanet orbits that uses the likelihood functions for individual star eccentricities. The authors show that proper inference outperforms the simple histogramming of the best-fit eccentricity values. We apply this method to the complete sample of eclipsing binary stars observed by the Kepler mission (Prsa et al. 2011) to derive the unbiased underlying eccentricity and orbital period distributions. These distributions can be used for the studies of multiple star formation, dynamical evolution, and they can serve as a drop-in replacement to prior, ad-hoc distributions used in the exoplanet field for determining false positive occurrence rates.
Insolation on exoplanets with eccentricity and obliquity
NASA Astrophysics Data System (ADS)
Dobrovolskis, Anthony R.
2013-09-01
The pattern of insolation on an extrasolar planet has profound implications for its climate and habitability. A planet’s insolation regime depends on its orbital eccentricity, the obliquity of its spin axis, its rotation rate, and its longitude of vernal equinox. For example, although a planet receives the same time-averaged insolation at both poles, the peak insolation at its poles can differ by a factor up to 27, depending on its eccentricity and equinox. This is of particular interest for planets with polar icecaps (or lakes and seas), like Mercury, Earth, and Mars (or Titan). The nearly 600 exoplanets now with known eccentricities span a wide range of eccentricity from essentially zero up to near unity; but their obliquities are still unknown, and also may range widely. Including both non-zero eccentricity and obliquity together vastly broadens the variety of global insolation patterns on extrasolar planets. This applies especially to planets in synchronous rotation, or in other spin-orbit resonances (like Mercury), which can exhibit quite complicated and unusual insolation patterns. For example, regions of eternal daylight and endless night occur only on synchronous exoplanets, whose rotation periods equal their orbital periods; but the peak and time-averaged insolation can vary by factors of at least 32 and 88, respectively, over a planet with a rotation period of half its orbital period, an eccentricity of 0.20, and an obliquity of 60°. Patterns of both mean and peak insolation display various symmetries with respect to latitude and longitude on the planet’s surface. Most of these are relatively simple and easily understood; for example, a resonant planet whose orbital period is half of an odd multiple of its rotation period (as in Mercury’s 3/2 resonance) experiences identical insolation patterns at longitudes 180° apart. However, such half-odd resonances also exhibit a totally unexpected symmetry of the time-averaged insolation with respect to the
NASA Astrophysics Data System (ADS)
Iess, L.; Jacobson, R.; Ducci, M.; Stevenson, D. J.; Lunine, J. I.; Armstrong, J. W.; Asmar, S.; Racioppa, P.; Rappaport, N. J.; Tortora, P.
2011-12-01
The large eccentricity (e=0.03) of Titan's orbit causes significant variations in the tidal field from Saturn and induces periodic stresses in the satellite body at the orbital period (about 16 days). Peak-to-peak variations of the tidal field (from pericenter to apocenter) are about 18% (6e). If Titan hosts a liquid layer (such as an internal ocean), the gravity field would exhibit significant periodic variations. The response of the body to fast variations of the external, perturbing field is controlled by the Love numbers, defined for each spherical harmonic as the ratio between the perturbed and perturbing potential. For Titan the largest effect is by far on the quadrupole field, and the corresponding Love number is indicated by k2 (assumed to be identical for all degree 2 harmonics). Models of Titan's interior generally envisage a core made up of silicates, surrounded by a layer of high pressure ice, possibly a liquid water or water-ammonia ocean, and an ice-I outer shell, with variations associated with the dehydration state of the core or the presence of mixed rock-ice layers. Previous analysis of Titan's tidal response [1] shows that k2 depends crucially on the presence or absence of an internal ocean. k2 was found to vary from about 0.03 for a purely rocky interior to 0.48 for a rigid rocky core surrounded by an ocean and a thin (20 km) ice shell. A large k2 entails changes in the satellite's quadrupole coefficients by a few percent, enough to be detected by accurate range rate measurements of the Cassini spacecraft. So far, of the many Cassini's flybys of Titan, six were used for gravity measurements. During gravity flybys the spacecraft is tracked from the antennas of NASA's Deep Space Network using microwave links at X- and Ka-band frequencies. A state-of-the-art instrumentation enables range rate measurements accurate to 10-50 micron/s at integration times of 60 s. The first four flybys provided the static gravity field and the moment of inertia factor
TRANSIT TIMING VARIATIONS FOR INCLINED AND RETROGRADE EXOPLANETARY SYSTEMS
Payne, Matthew J.; Ford, Eric B.; Veras, Dimitri
2010-03-20
We perform numerical calculations of the expected transit timing variations (TTVs) induced on a hot-Jupiter by an Earth-mass perturber. Motivated by the recent discoveries of retrograde transiting planets, we concentrate on an investigation of the effect of varying relative planetary inclinations, up to and including completely retrograde systems. We find that planets in low-order (e.g., 2:1) mean-motion resonances (MMRs) retain approximately constant TTV amplitudes for 0 deg. < i < 170 deg., only reducing in amplitude for i>170 deg. Systems in higher order MMRs (e.g., 5:1) increase in TTV amplitude as inclinations increase toward 45 deg., becoming approximately constant for 45 deg. < i < 135 deg., and then declining for i>135 deg. Planets away from resonance slowly decrease in TTV amplitude as inclinations increase from 0 deg. to 180 deg., whereas planets adjacent to resonances can exhibit a huge range of variability in TTV amplitude as a function of both eccentricity and inclination. For highly retrograde systems (135 deg. < i {<=} 180 deg.), TTV signals will be undetectable across almost the entirety of parameter space, with the exceptions occurring when the perturber has high eccentricity or is very close to an MMR. This high inclination decrease in TTV amplitude (on and away from resonance) is important for the analysis of the known retrograde and multi-planet transiting systems, as inclination effects need to be considered if TTVs are to be used to exclude the presence of any putative planetary companions: absence of evidence is not evidence of absence.
TTVFaster: First order eccentricity transit timing variations (TTVs)
NASA Astrophysics Data System (ADS)
Agol, Eric; Deck, Katherine
2016-04-01
TTVFaster implements analytic formulae for transit time variations (TTVs) that are accurate to first order in the planet-star mass ratios and in the orbital eccentricities; the implementations are available in several languages, including IDL, Julia, Python and C. These formulae compare well with more computationally expensive N-body integrations in the low-eccentricity, low mass-ratio regime when applied to simulated and to actual multi-transiting Kepler planet systems.
Atmospheric circulation of eccentric extrasolar giant planets
NASA Astrophysics Data System (ADS)
Lewis, Nikole Kae
This dissertation explores the three-dimensional coupling between radiative and dynamical processes in the atmospheres of eccentric extrasolar giant planets GJ436b, HAT-P-2b, and HD80606b. Extrasolar planets on eccentric orbits are subject to time-variable heating and probable non-synchronous rotation, which results in significant variations in global circulation and thermal patterns as a function of orbital phase. Atmospheric simulations for the low eccentricity (e=0.15) Neptune sized planet GJ436b reveal that when Neptune-like atmospheric compositions are assumed day/night temperature contrasts and equatorial jet speeds are significantly increased relative to models that assume a solar-like composition. Comparisons between our theoretical light curves and recent observations support a high metallicity atmosphere with disequilibrium carbon chemistry for GJ436b. The analysis of full-orbit light curve observations at 3.6 and 4.5 microns of the HAT-P-2 system reveal swings in the planet's temperature of more than 900 K during its significantly eccentric ( e=0.5) orbit with a four to six hour offset between periapse passage and the peak of the planet's observed flux. Comparisons between our atmospheric model of HAT-P-2b and the observed light curves indicate an increased carbon to oxygen ratio in HAT-P-2b's atmosphere compared to solar values. Atmospheric simulations of the highly eccentric (e=0.9) HD80606b show that flash-heating events completely alter planetary thermal and jet structures and that assumptions about the rotation period of this planet could affect the shape of light curve observations near periapse. Our simulations of HD80606b also show the development an atmospheric shock on the nightside of the planet that is associated with an observable thermal signature in our theoretical light curves. The simulations and observations presented in this dissertation mark an important step in the exploration of atmospheric circulation on the more than 300
VIEW SOUTHEAST, ECCENTRIC HOUSE, INTERIOR, NOTE DOUBLE OVER MOUNTED ECCENTRICS ...
VIEW SOUTHEAST, ECCENTRIC HOUSE, INTERIOR, NOTE DOUBLE OVER MOUNTED ECCENTRICS WITH ATTACHED ROD LINES ON GEAR ASSEMBLY. - South Penn Oil Company, G. M. Mead Lot 492 Lease, Morrison Run Field, Clarendon, Warren County, PA
ARTEMIS Lunar Orbit Insertion and Science Orbit Design Through 2013
NASA Technical Reports Server (NTRS)
Broschart, Stephen B.; Sweetser, Theodore H.; Angelopoulos, Vassilis; Folta, David; Woodard, Mark
2015-01-01
As of late-July 2011, the ARTEMIS mission is transferring two spacecraft from Lissajous orbits around Earth-Moon Lagrange Point #1 into highly-eccentric lunar science orbits. This paper presents the trajectory design for the transfer from Lissajous orbit to lunar orbit insertion, the period reduction maneuvers, and the science orbits through 2013. The design accommodates large perturbations from Earth's gravity and restrictive spacecraft capabilities to enable opportunities for a range of heliophysics and planetary science measurements. The process used to design the highly-eccentric ARTEMIS science orbits is outlined. The approach may inform the design of future planetary moon missions.
CONDITIONS OF PASSAGE AND ENTRAPMENT OF TERRESTRIAL PLANETS IN SPIN-ORBIT RESONANCES
Makarov, Valeri V.
2012-06-10
The dynamical evolution of terrestrial planets resembling Mercury in the vicinity of spin-orbit resonances is investigated using comprehensive harmonic expansions of the tidal torque taking into account the frequency-dependent quality factors and Love numbers. The torque equations are integrated numerically with a small step in time, including the oscillating triaxial torque components but neglecting the layered structure of the planet and assuming a zero obliquity. We find that a Mercury-like planet with a current value of orbital eccentricity (0.2056) is always captured in 3:2 resonance. The probability of capture in the higher 2:1 resonance is approximately 0.23. These results are confirmed by a semi-analytical estimation of capture probabilities as functions of eccentricity for both prograde and retrograde evolutions of spin rate. As follows from analysis of equilibrium torques, entrapment in 3:2 resonance is inevitable at eccentricities between 0.2 and 0.41. Considering the phase space parameters at the times of periastron, the range of spin rates and phase angles for which an immediate resonance passage is triggered is very narrow, and yet a planet like Mercury rarely fails to align itself into this state of unstable equilibrium before it traverses 2:1 resonance.
NASA Astrophysics Data System (ADS)
Pinilla-Alonso, N.; Alvarez-Candal, A.; Melita, M. D.; Lorenzi, V.; Licandro, J.; Carvano, J.; Lazzaro, D.; Carraro, G.; Alí-Lagoa, V.; Costa, E.; Hasselmann, P. H.
2013-02-01
Most of the objects in the trans-Neptunian belt (TNb) and related populations move in prograde orbits with low eccentricity and inclination. However, the list of icy minor bodies moving in orbits with an inclination above 40° has increased in recent years. The origin of these bodies, and in particular of those objects in retrograde orbits, is not well determined, and different scenarios are considered, depending on their inclination and perihelion. In this paper, we present new observational and dynamical data of two objects in retrograde orbits, 2008 YB3 and 2005 VD. We find that the surface of these extreme objects is depleted of ices and does not contain the "ultra-red" matter typical of some Centaurs. Despite small differences, these objects share common colors and spectral characteristics with the Trojans, comet nuclei, and the group of grey Centaurs. All of these populations are supposed to be covered by a mantle of dust responsible for their reddish-to-neutral color. To investigate if the surface properties and dynamical evolution of these bodies are related, we integrate their orbits for 108 years to the past. We find a remarkable difference in their dynamical evolutions: 2005 VD's evolution is dominated by a Kozai resonance with planet Jupiter while that of 2008 YB3 is dominated by close encounters with planets Jupiter and Saturn. Our models suggest that the immediate site of provenance of 2005 VD is the in the Oort Cloud, whereas for 2008 YB3 it is in the trans-Neptunian region. Additionally, the study of their residence time shows that 2005 VD has spent a larger lapse of time moving in orbits in the region of the giant planets than 2008 YB3. Together with the small differences in color between these two objects, with 2005 VD being more neutral than 2008 YB3, this fact suggests that the surface of 2005 VD has suffered a higher degree of processing, which is probably related to cometary activity episodes. Partially based on observations made with ESO
Temporary Capture of Asteroids by an Eccentric Planet
NASA Astrophysics Data System (ADS)
Higuchi, A.; Ida, S.
2017-04-01
We have investigated the probability of temporary capture of asteroids in eccentric orbits by a planet in a circular or eccentric orbit through analytical and numerical calculations. We found that, in the limit of the circular orbit, the capture probability is ∼0.1% of encounters to the planet’s Hill sphere, independent of planetary mass and semimajor axis. In general, temporary capture becomes more difficult as the planet’s eccentricity ({e}{{p}}) increases. We found that the capture probability is almost independent of {e}{{p}} until a critical value ({e}{{p}}{{c}}) that is given by ≃5 times the Hill radius scaled by the planet’s semimajor axis. For {e}{{p}}> {e}{{p}}{{c}}, the probability decreases approximately in proportion to {e}{{p}}-1. The current orbital eccentricity of Mars is several times larger than {e}{{p}}{{c}}. However, since the range of secular change in Martian eccentricity overlaps {e}{{p}}{{c}}, the capture of minor bodies by Mars in the past is not ruled out.
HABITABLE CLIMATES: THE INFLUENCE OF ECCENTRICITY
Dressing, Courtney D.; Spiegel, David S.; Scharf, Caleb A.; Menou, Kristen; Raymond, Sean N. E-mail: dsp@astro.princeton.ed E-mail: caleb@astro.columbia.ed
2010-10-01
In the outer regions of the habitable zone, the risk of transitioning into a globally frozen 'snowball' state poses a threat to the habitability of planets with the capacity to host water-based life. Here, we use a one-dimensional energy balance climate model (EBM) to examine how obliquity, spin rate, orbital eccentricity, and the fraction of the surface covered by ocean might influence the onset of such a snowball state. For an exoplanet, these parameters may be strikingly different from the values observed for Earth. Since, for a constant semimajor axis, the annual mean stellar irradiation scales with (1 - e {sup 2}){sup -1/2}, one might expect the greatest habitable semimajor axis (for fixed atmospheric composition) to scale as (1 - e {sup 2}){sup -1/4}. We find that this standard simple ansatz provides a reasonable lower bound on the outer boundary of the habitable zone, but the influence of both obliquity and ocean fraction can be profound in the context of planets on eccentric orbits. For planets with eccentricity 0.5, for instance, our EBM suggests that the greatest habitable semimajor axis can vary by more than 0.8 AU (78%) depending on obliquity, with higher obliquity worlds generally more stable against snowball transitions. One might also expect that the long winter at an eccentric planet's apoastron would render it more susceptible to global freezing. Our models suggest that this is not a significant risk for Earth-like planets around Sun-like stars, as considered here, since such planets are buffered by the thermal inertia provided by oceans covering at least 10% of their surface. Since planets on eccentric orbits spend much of their year particularly far from the star, such worlds might turnout to be especially good targets for direct observations with missions such as TPF-Darwin. Nevertheless, the extreme temperature variations achieved on highly eccentric exo-Earths raise questions about the adaptability of life to marginally or transiently
Contingency Trajectory Design for a Lunar Orbit Insertion Maneuver Failure by the LADEE Spacecraft
NASA Technical Reports Server (NTRS)
Genova, A. L.
2014-01-01
This paper presents results from a contingency trajectory analysis performed for the Lunar Atmosphere & Dust Environment Explorer (LADEE) mission in the event of a missed lunar-orbit insertion (LOI) maneuver by the LADEE spacecraft. The effects of varying solar perturbations in the vicinity of the weak stability boundary (WSB) in the Sun-Earth system on the trajectory design are analyzed and discussed. It is shown that geocentric recovery trajectory options existed for the LADEE spacecraft, depending on the spacecraft's recovery time to perform an Earth escape-prevention maneuver after the hypothetical LOI maneuver failure and subsequent path traveled through the Sun-Earth WSB. If Earth-escape occurred, a heliocentric recovery option existed, but with reduced science capacapability for the spacecraft in an eccentric, not circular near-equatorial retrograde lunar orbit.
Chloroplast signaling: retrograde regulation revelations.
Beale, Samuel I
2011-05-24
Developing chloroplasts are able to communicate their status to the nucleus and regulate expression of genes whose products are needed for photosynthesis. Heme is revealed to be a signaling molecule for this retrograde communication.
Bayesian priors for the eccentricity of transiting planets
NASA Astrophysics Data System (ADS)
Kipping, David M.
2014-11-01
Planets on eccentric orbits have a higher geometric probability of transiting their host star. By application of Bayes' theorem, we reverse this logic to show that the eccentricity distribution of transiting planets is positively biased. Adopting the flexible Beta distribution as the underlying prior for eccentricity, we derive the marginalized transit probability as well as the a priori joint probability distribution of eccentricity and argument of periastron, given that a planet is known to transit. These results allow us to demonstrate that most planet occurrence rate calculations using Kepler data have overestimated the prevalence of planets by ˜10 per cent. Indeed, the true occurrence of planets from transit surveys is fundamentally intractable without a prior assumption for the eccentricity distribution. Further more, we show that previously extracted eccentricity distributions using Kepler data are positively biased. In cases where one wishes to impose an informative eccentricity prior, we provide a recursive algorithm to apply inverse transform sampling of our joint prior probability distribution. Computer code of this algorithm,
Circular-Orbit Maintenance Strategies for Primitive Body Orbiters
NASA Technical Reports Server (NTRS)
Wallace, Mark S.; Broschart, Stephen
2013-01-01
For missions to smaller primitive bodies, solar radiation pressure (SRP) is a significant perturbation to Keplerian dynamics. For most orbits, SRP drives large oscillations in orbit eccentricity, which leads to large perturbations from the irregular gravity field at periapsis. Ultimately, chaotic motion results that often escapes or impacts that body. This paper presents an orbit maintenance strategy to keep the orbit eccentricity small, thus avoiding the destabilizing secondary interaction with the gravity field. An estimate of the frequency and magnitude of the required maneuvers as a function of the orbit and body parameters is derived from the analytic perturbation equations.
Some Expansions of the Elliptic Motion to High Eccentricities
NASA Astrophysics Data System (ADS)
da Silva Fernandes, Sandro
1995-12-01
Some classic expansions of the elliptic motion — cosmE and sinmE — in powers of the eccentricity are extended to highly eccentric orbits, 0.6627...
Tsang, David; Cumming, Andrew; Turner, Neal J.
2014-02-20
We show that the first order (non-co-orbital) corotation torques are significantly modified by entropy gradients in a non-barotropic protoplanetary disk. Such non-barotropic torques can dramatically alter the balance that, for barotropic cases, results in the net eccentricity damping for giant gap-clearing planets embedded in the disk. We demonstrate that stellar illumination can heat the gap enough for the planet's orbital eccentricity to instead be excited. We also discuss the 'Eccentricity Valley' noted in the known exoplanet population, where low-metallicity stars have a deficit of eccentric planets between ∼0.1 and ∼1 AU compared to metal-rich systems. We show that this feature in the planet distribution may be due to the self-shadowing of the disk by a rim located at the dust sublimation radius ∼0.1 AU, which is known to exist for several T Tauri systems. In the shadowed region between ∼0.1 and ∼1 AU, lack of gap insolation allows disk interactions to damp eccentricity. Outside such shadowed regions stellar illumination can heat the planetary gaps and drive eccentricity growth for giant planets. We suggest that the self-shadowing does not arise at higher metallicity due to the increased optical depth of the gas interior to the dust sublimation radius.
The formation and evolution of eccentric binary systems
NASA Astrophysics Data System (ADS)
Davis, Philip
2014-09-01
Observations are revealing a host of post-mass-transfer binary systems in significantly eccentric orbits, most notably Barium stars [1] and subdwarf-B + main-sequence systems [2]. Their formation is very puzzling in light of the fact that tidal forces efficiently circularise the orbit. Using our state-of-the-art binary stellar evolution code BINSTAR [3], we explore the formation and evolution of eccentric binary systems within the framework of the osculating orbital theory. This scheme describes, in a physically realistic manner, the perturbing forces acting on the orbit arising from mass transfer [4]. Results are presented, showing the impact of wind losses and Roche lobe overflow on the orbital separation and eccentricity for a range of initial stellar and binary parameters. As an interesting case study, we also discuss a promising formation channel for the eccentric white dwarf + main-sequence binary IP Eri [5], which invokes a tidally enhanced wind-loss mechanism. Our approach reproduces the observed system parameters remarkably well [6]. [1] Jorissen A., 1999, IAU Symposium, 191, 437 [2] Vos et al., 2013, A&A, 559, 54 [3] Siess L. et al., 2012, A&A, 550, 100 [4] Hadjidemetriou J., 1969, Ap&SS, 3, 330 [5] Merle et al., 2014, A&A, in press (arXiv:1405.4669) [6] Siess L., Davis P. J., Jorissen A., 2014, A&A, 565, A57
Diffusion of eccentric microswimmers.
Debnath, Debajyoti; Ghosh, Pulak K; Li, Yunyun; Marchesoni, Fabio; Li, Baowen
2016-02-21
We model the two-dimensional diffusive dynamics of an eccentric artificial microswimmer in a highly viscous medium. We assume that the swimmer's propulsion results from an effective force applied to a center distinct from its center of mass, both centers resting on a body's axis parallel to its average self-propulsion velocity. Moreover, we allow for angular fluctuations of the velocity about the body's axis. We prove, both analytically and numerically, that the ensuing active diffusion of the swimmer is suppressed to an extent that strongly depends on the model parameters. In particular, the active diffusion constant undergoes a transition from a quadratic to a linear dependence on the self-propulsion speed, with practical consequences on the interpretation of the experimental data. Finally, we extend our model to describe the diffusion of chiral eccentric swimmers.
Highly eccentric inspirals into a black hole
NASA Astrophysics Data System (ADS)
Osburn, Thomas; Warburton, Niels; Evans, Charles R.
2016-03-01
We model the inspiral of a compact stellar-mass object into a massive nonrotating black hole including all dissipative and conservative first-order-in-the-mass-ratio effects on the orbital motion. The techniques we develop allow inspirals with initial eccentricities as high as e ˜0.8 and initial separations as large as p ˜50 to be evolved through many thousands of orbits up to the onset of the plunge into the black hole. The inspiral is computed using an osculating elements scheme driven by a hybridized self-force model, which combines Lorenz-gauge self-force results with highly accurate flux data from a Regge-Wheeler-Zerilli code. The high accuracy of our hybrid self-force model allows the orbital phase of the inspirals to be tracked to within ˜0.1 radians or better. The difference between self-force models and inspirals computed in the radiative approximation is quantified.
NASA Astrophysics Data System (ADS)
Jontof-Hutter, Daniel; Van Laerhoven, Christa L.; Ford, Eric B.
2016-05-01
Hundreds of multi-transiting systems discovered by the Kepler mission show Transit Timing Variations (TTV). In cases where the TTVs are uniquely attributable to transiting planets, the TTVs enable precise measurements of planetary masses and orbital parameters. Of particular interest are the constraints on eccentricity vectors that can be inferred in systems of low-mass exoplanets.The TTVs in these systems are dominated by a signal caused by near-resonant mean motions. This causes the well-known near-degeneracy between planetary masses and orbital eccentricities. In addition, it causes a degeneracy between the eccentricities of interacting planet pairs.For many systems, the magnitude of individual eccentricities are weakly constrained, yet the data typically provide a tight constraint on the posterior joint distribution for the eccentricity vector components. This permits tight constraints on the relative eccentricity and degree of alignment of interacting planets.For a sample of two and three-planet systems with TTVs, we highlight the effects of these correlations. While the most eccentric orbital solutions for these systems show apsidal alignment, this is often due to the degeneracy that causes correlated constraints on the eccentricity vector components. We compare the likelihood of apsidal alignment for two choices of eccentricity prior: a wide prior using a Rayleigh distribution of scale length 0.1 and a narrower prior with scale length 0.02. In all cases the narrower prior decreased the fraction of samples that exhibited apsidal alignment. However, apsidal alignment persisted in the majority of cases with a narrower eccentricity prior. For a sample of our TTV solutions, we ran simulations of these systems over secular timescales, and decomposed their eccentricity eigenmodes over time, confirming that in most cases, the eccentricities were dominated by parallel eigenmodes which favor apsidal alignment.
An Orbit Fit for the Grillmair Dionatos Cold Stellar Stream
Willett, Benjamin A.; Newberg, Heidi Jo; Zhang, Haotong; Yanny, Brian; Beers, Timothy C.
2009-01-01
We use velocity and metallicity information from Sloan Digital Sky Survey and Sloan Extension for Galactic Understanding and Exploration stellar spectroscopy to fit an orbit to the narrow 63{sup o} stellar stream of Grillmair and Dionatos. The stars in the stream have a retrograde orbit with eccentricity e = 0.33 (perigalacticon of 14.4 kpc and apogalacticon of 28.7 kpc) and inclination approximately i {approx} 35{sup o}. In the region of the orbit which is detected, it has a distance of about 7-11 kpc from the Sun. Assuming a standard disk plus bulge and logarithmic halo potential for the Milky Way stars plus dark matter, the stream stars are moving with a large space velocity of approximately 276 km s{sup -1} at perigalacticon. Using this stream alone, we are unable to determine if the dark matter halo is oblate or prolate. The metallicity of the stream is [Fe/H] = -2.1 {+-} 0.1. Observed proper motions for individual stream members above the main sequence turnoff are consistent with the derived orbit. None of the known globular clusters in the Milky Way have positions, radial velocities, and metallicities that are consistent with being the progenitor of the GD-1 stream.
NASA Astrophysics Data System (ADS)
Huerta, Eliu; Agarwal, Bhanu; Chua, Alvin; George, Daniel; Haas, Roland; Hinder, Ian; Kumar, Prayush; Moore, Christopher; Pfeiffer, Harald
2017-01-01
We recently constructed an inspiral-merger-ringdown (IMR) waveform model to describe the dynamical evolution of compact binaries on eccentric orbits, and used this model to constrain the eccentricity with which the gravitational wave transients currently detected by LIGO could be effectively recovered with banks of quasi-circular templates. We now present the second generation of this model, which is calibrated using a large catalog of eccentric numerical relativity simulations. We discuss the new features of this model, and show that its enhance accuracy makes it a powerful tool to detect eccentric signals with LIGO.
Eccentric exercise testing and training
NASA Technical Reports Server (NTRS)
Clarkson, Priscilla M.
1994-01-01
Some researchers and practitioners have touted the benefits of including eccentric exercise in strength training programs. However, others have challenged its use because they believe that eccentric actions are dangerous and lead to injuries. Much of the controversy may be based on a lack of understanding of the physiology of eccentric actions. This review will present data concerning eccentric exercise in strength training, the physiological characteristics of eccentric exercise, and the possible stimulus for strength development. Also a discussion of strength needs for extended exposure to microgravity will be presented. Not only is the use of eccentric exercise controversial, but the name itself is fraught with problems. The correct pronunciation is with a hard 'c' so that the word sounds like ekscentric. The confusion in pronunciation may have been prevented if the spelling that Asmussen used in 1953, excentric, had been adopted. Another problem concerns the expressions used to describe eccentric exercise. Commonly used expressions are negatives, eccentric contractions, lengthening contractions, resisted muscle lengthenings, muscle lengthening actions, and eccentric actions. Some of these terms are cumbersome (i.e., resisted muscle lengthenings), one is slang (negatives), and another is an oxymoron (lengthening contractions). Only eccentric action is appropriate and adoption of this term has been recommended by Cavanagh. Despite the controversy that surrounds eccentric exercise, it is important to note that these types of actions play an integral role in normal daily activities. Eccentric actions are used during most forms of movement, for example, in walking when the foot touches the ground and the center of mass is decelerated and in lowering objects, such as placing a bag of groceries in the car.
Constraining Planetary Migration Mechanisms with Highly Eccentric Hot Jupiter Progenitors
NASA Astrophysics Data System (ADS)
Dawson, Rebekah I.; Johnson, J. A.; Murray-Clay, R.; Morton, T.; Crepp, J. R.; Fabrycky, D. C.; Howard, A.
2013-01-01
Abstract: Hot Jupiters --- Jupiter-mass planets orbiting within 0.1 AU of their host stars --- are unlikely to have formed in situ and thus serve as evidence for the prevalence of planetary migration. However, it is debated whether the typical hot Jupiter migrated smoothly inward through the protoplanetary disk or was perturbed onto an eccentric orbit, which tidal dissipation subsequently shrank and circularized during close passages to the star. In the latter class of model, the perturber may be a stellar or planetary companion, which causes the Jupiter to undergo a temporary epoch with high eccentricity (e> 0.9). Socrates and et al. (2012) predicted that these super-eccentric hot Jupiter progenitors should be readily discoverable through the transit method by the Kepler Mission. However, eccentricities of individual transiting planets primarily come from Doppler measurements, which are unfortunately precluded by the faintness of most Kepler targets. To solve this problem, we developed a Bayesian method (the “photoeccentric effect”) for measuring an individual planet's eccentricity solely from its Kepler light curve, allowing for a tight measurement of large eccentricities. We applied this new approach to the Kepler giant planet candidates and identified KOI-1474.01 as an eccentric planet (e = 0.81+0.10/-0.07) with an average orbital period of 69.7340 days, varying by approximately 1 hour due to perturbations by a massive outer companion, which is possibly the culprit responsible for KOI-1474.01’s highly eccentric orbit. KOI-1474.01 is likely a failed hot Jupiter, too far from its host star to be tidally transformed into a hot Jupiter. We found a significant lack of super-eccentric proto-hot Jupiters compared to the number expected, allowing us to place a strong upper limit on the fraction of hot Jupiters created by stellar binaries. Our results are consistent with disks or planetary companions being the primary channel for hot Jupiter creation. Supported by
Hereditary effects in eccentric compact binary inspirals to third post-Newtonian order
NASA Astrophysics Data System (ADS)
Loutrel, Nicholas; Yunes, Nicolás
2017-02-01
While there has been much success in understanding the orbital dynamics and gravitational wave emission of eccentric compact binaries in the post-Newtonian formalism, some problems still remain. The largest of these concerns hereditary effects: non-linear phenomena related to the scattering off of the background curved spacetime (tails) and to the generation of gravitational waves by gravitational waves (memory). Currently, these hereditary effects are only known numerically for arbitrary eccentricity through infinite sums of Bessel functions, with closed-form, analytic results only available in the small eccentricity limit. We here calculate, for the first time, closed-form, analytic expressions for all hereditary effects to third post-Newtonian order in binaries with arbitrary eccentricity. For the tails, we first asymptotically expand all Bessel functions in high eccentricity and find a superasymptotic series for each enhancement factor, accurate to better than 10‑3 relative to post-Newtonian numerical calculations at all eccentricities. We further improve the small-eccentricity behavior of the superasymptotic series by generating hyperasymptotic expressions for each enhancement factor, typically accurate to better than 10‑8 at all eccentricities. For the memory, we discuss its computation within the context of an osculating approximation of the binary’s orbit and the difficulties that arise. Our closed-form analytic expressions for the hereditary fluxes allow us to numerically compute orbital phases that are identical to those found using an infinite sum of Bessel functions to double numerical precision.
Evidence for Reflected Light from the Most Eccentric Exoplanet Known
NASA Astrophysics Data System (ADS)
Kane, Stephen R.; Wittenmyer, Robert A.; Hinkel, Natalie R.; Roy, Arpita; Mahadevan, Suvrath; Dragomir, Diana; Matthews, Jaymie M.; Henry, Gregory W.; Chakraborty, Abhijit; Boyajian, Tabetha S.; Wright, Jason T.; Ciardi, David R.; Fischer, Debra A.; Butler, R. Paul; Tinney, C. G.; Carter, Brad D.; Jones, Hugh R. A.; Bailey, Jeremy; O'Toole, Simon J.
2016-04-01
Planets in highly eccentric orbits form a class of objects not seen within our solar system. The most extreme case known among these objects is the planet orbiting HD 20782, with an orbital period of 597 days and an eccentricity of 0.96. Here we present new data and analysis for this system as part of the Transit Ephemeris Refinement and Monitoring Survey. We obtained CHIRON spectra to perform an independent estimation of the fundamental stellar parameters. New radial velocities from Anglo-Australian Telescope and PARAS observations during periastron passage greatly improve our knowledge of the eccentric nature of the orbit. The combined analysis of our Keplerian orbital and Hipparcos astrometry show that the inclination of the planetary orbit is \\gt 1\\_\\_AMP\\_\\_fdg;22, ruling out stellar masses for the companion. Our long-term robotic photometry show that the star is extremely stable over long timescales. Photometric monitoring of the star during predicted transit and periastron times using Microvariability and Oscillations of STars rule out a transit of the planet and reveal evidence of phase variations during periastron. These possible photometric phase variations may be caused by reflected light from the planet’s atmosphere and the dramatic change in star-planet separation surrounding the periastron passage.
How to Maneuver Around in Eccentricity Vector Space
NASA Technical Reports Server (NTRS)
Sweetser, Theodore H.
2010-01-01
The GRAIL mission to the Moon will be the first time that two separate robotic orbiters will be placed into formation in orbit around a body other than Earth. The need to design an efficient series of maneuvers to shape the orbits and phasing of the two orbiters after arrival presents a significant challenge to mission designers. This paper presents a simple geometric method for relating in-plane impulsive maneuvers to changes in the eccentricity vector, which determines the shape and orientation of an orbit in the orbit plane. Examples then show how such maneuvers can accommodate desired changes to other orbital elements such as period, incination, and longitude of the ascending node.
APSIDAL MOTION IN ECCENTRIC ECLIPSING BINARY WW CAMELOPARDALIS
Wolf, M.; Kotkova, L.; Kocian, R.; Dreveny, R.; Hanzl, D.
2010-03-15
WW Camelopardalis is a relatively bright eclipsing binary system with a slightly eccentric orbit. A dozen of its new eclipse times were measured as part of our long-term observational project of eccentric eclipsing binaries. Based on a new solution of the current O - C diagram, we found for the first time an apsidal motion in good agreement with theory. Its period is about 370 {+-} 50 years. The determined internal structure constant is close to the theoretically expected value. The relativistic effect is significant, being about 13% of the total apsidal motion rate.
A massive millisecond pulsar in an eccentric binary
NASA Astrophysics Data System (ADS)
Barr, E. D.; Freire, P. C. C.; Kramer, M.; Champion, D. J.; Berezina, M.; Bassa, C. G.; Lyne, A. G.; Stappers, B. W.
2017-02-01
The recent discovery of a population of eccentric (e ∼ 0.1) millisecond pulsar (MSP) binaries with low-mass white dwarf companions in the Galactic field represents a challenge to evolutionary models that explain MSP formation as recycling: All such models predict that the orbits become highly circularized during a long period of accretion. The members of this new population exhibit remarkably similar properties (orbital periods, eccentricities, companion masses, spin periods), and several models have been put forward that suggest a common formation channel. In this work, we present the results of an extensive timing campaign focusing on one member of this new population, PSR J1946+3417. Through the measurement of both the advance of periastron and the Shapiro delay for this system, we determine the mass of the pulsar, mass of the companion and the inclination of the orbit to be 1.828(22) M⊙, 0.2656(19) M⊙ and 76.4 ± 0.6 degrees, respectively, under the assumption that general relativity is the true description of gravity. Notably, this is the third highest mass measured for any pulsar. Using these masses and the astrometric properties of PSR J1946+3417, we examine three proposed formation channels for eccentric MSP binaries. While our results are consistent with circumbinary disc-driven eccentricity growth or neutron star to strange star phase transition, we rule out rotationally delayed accretion-induced collapse as the mechanism responsible for the configuration of the PSR J1946+3417 system.
On Mercury's entrapment into the 3:2 spin-orbit resonance
NASA Astrophysics Data System (ADS)
Noyelles, Benoit; Frouard, J.; Makarov, V.; Efroimsky, M.
2013-10-01
The rotational dynamics of Mercury is a peculiar case in the Solar System, since it is a supersynchronous, 3:2 resonant state, with the spin period being 2/3 of the orbital one. While it is widely accepted that the significant eccentricity (0.206) favours this configuration, the history of Mercury's despinning remains nonetheless a matter of discussion. At least three scenarios can be found in the scientific literature. The first one considers a homogeneous Mercury that was trapped after several crossings of the resonance, these crossings made possible by the chaotic evolution of the eccentricity (Correia & Laskar 2004). The second scenario includes friction at the core-mantle boundary, which increases the probabilities of capture during one crossing (Peale & Boss 1977, Correia & Laskar 2009). The third scenario assumes that Mercury had had a retrograde rotation, then a synchronous one, and only later came into the current 3:2 resonance. We here use a realistic model of tides, based on the Darwin-Kaula expansions combined with both the elastic rebound and anelastic creep of solids. Within this model, we find that the 3:2 spin-orbit resonance is the most probable for a homogeneous Mercury. Moreover, we find that leaving a resonance after being trapped is impossible or virtually impossible, thus excluding the possibility of a past 2:1 resonance. This also indicates that entrapment is likely to happen before the differentiation of Mercury takes place.
RESONANT POST-NEWTONIAN ECCENTRICITY EXCITATION IN HIERARCHICAL THREE-BODY SYSTEMS
Naoz, Smadar; Kocsis, Bence; Loeb, Abraham; Yunes, Nicolas
2013-08-20
We study the secular, hierarchical three-body problem to first-order in a post-Newtonian expansion of general relativity (GR). We expand the first-order post-Newtonian Hamiltonian to leading-order in the ratio of the semi-major axis of the two orbits. In addition to the well-known terms that correspond to the GR precession of the inner and outer orbits, we find a new secular post-Newtonian interaction term that can affect the long-term evolution of the triple. We explore the parameter space for highly inclined and eccentric systems, where the Kozai-Lidov mechanism can produce large-amplitude oscillations in the eccentricities. The standard lore, i.e., that GR effects suppress eccentricity, is only consistent with the parts of phase space where the GR timescales are several orders of magnitude shorter than the secular Newtonian one. In other parts of phase space, however, post-Newtonian corrections combined with the three-body ones can excite eccentricities. In particular, for systems where the GR timescale is comparable to the secular Newtonian timescales, the three-body interactions give rise to a resonant-like eccentricity excitation. Furthermore, for triples with a comparable-mass inner binary, where the eccentric Kozai-Lidov mechanism is suppressed, post-Newtonian corrections can further increase the eccentricity and lead to orbital flips even when the timescale of the former is much longer than the timescale of the secular Kozai-Lidov quadrupole perturbations.
Reactionless orbital propulsion using tether deployment
NASA Technical Reports Server (NTRS)
Landis, Geoffrey A.
1990-01-01
Examples of tether propulsion in orbit without the use of reaction mass are discussed. These include (1) using tether extension to reposition a satellite in orbit without fuel expenditure by extending a mass on the end of the tether; (2) using a tether for eccentricity pumping to add energy to the orbit for boosting and orbital transfer; and (3) length modulation of a spinning tether to transfer angular momentum between the orbit and tether spin, thus allowing changes in orbital angular momentum.
Transit Timing Variations for Eccentric and Inclined Exoplanets
NASA Astrophysics Data System (ADS)
Nesvorný, David
2009-08-01
The Transit Timing Variation (TTV) method relies on monitoring changes in timing of transits of known exoplanets. Nontransiting planets in the system can be inferred from TTVs by their gravitational interactions with the transiting planet. The TTV method is sensitive to low-mass planets that cannot be detected by other means. Inferring the orbital elements and mass of the nontransiting planets from TTVs, however, is more challenging than for other planet detection schemes. It is a difficult inverse problem. Here, we extended the new inversion method proposed by Nesvorný & Morbidelli to eccentric transiting planets and inclined orbits. We found that the TTV signal can be significantly amplified for hierarchical planetary systems with substantial orbital inclinations and/or for an eccentric transiting planet with anti-aligned orbit of the planetary companion. Thus, a fortuitous orbital setup of an exoplanetary system may significantly enhance our chances of TTV detection. We also showed that the detailed shape of the TTV signal is sensitive to the orbital inclination of the nontransiting planetary companion. The TTV detection method may thus provide important constraints on the orbital inclination of exoplanets and be used to test theories of planetary formation and evolution.
TRANSIT TIMING VARIATIONS FOR ECCENTRIC AND INCLINED EXOPLANETS
Nesvorny, David
2009-08-20
The Transit Timing Variation (TTV) method relies on monitoring changes in timing of transits of known exoplanets. Nontransiting planets in the system can be inferred from TTVs by their gravitational interactions with the transiting planet. The TTV method is sensitive to low-mass planets that cannot be detected by other means. Inferring the orbital elements and mass of the nontransiting planets from TTVs, however, is more challenging than for other planet detection schemes. It is a difficult inverse problem. Here, we extended the new inversion method proposed by Nesvorny and Morbidelli to eccentric transiting planets and inclined orbits. We found that the TTV signal can be significantly amplified for hierarchical planetary systems with substantial orbital inclinations and/or for an eccentric transiting planet with anti-aligned orbit of the planetary companion. Thus, a fortuitous orbital setup of an exoplanetary system may significantly enhance our chances of TTV detection. We also showed that the detailed shape of the TTV signal is sensitive to the orbital inclination of the nontransiting planetary companion. The TTV detection method may thus provide important constraints on the orbital inclination of exoplanets and be used to test theories of planetary formation and evolution.
Retrograde binaries of massive black holes in circumbinary accretion discs
NASA Astrophysics Data System (ADS)
Amaro-Seoane, Pau; Maureira-Fredes, Cristián; Dotti, Massimo; Colpi, Monica
2016-06-01
accretion only explores the late evolution stages of the binary in an otherwise unperturbed retrograde disc to illustrate how eccentricity evolves with time in relation to the shape of the underlying surface density distribution.
Gravitational-wave phasing for low-eccentricity inspiralling compact binaries to 3PN order
NASA Astrophysics Data System (ADS)
Moore, Blake; Favata, Marc; Arun, K. G.; Mishra, Chandra Kant
2016-06-01
Although gravitational radiation causes inspiralling compact binaries to circularize, a variety of astrophysical scenarios suggest that binaries might have small but non-negligible orbital eccentricities when they enter the low-frequency bands of ground- and space-based gravitational-wave detectors. If not accounted for, even a small orbital eccentricity can cause a potentially significant systematic error in the mass parameters of an inspiralling binary [M. Favata, Phys. Rev. Lett. 112, 101101 (2014)]. Gravitational-wave search templates typically rely on the quasicircular approximation, which provides relatively simple expressions for the gravitational-wave phase to 3.5 post-Newtonian (PN) order. Damour, Gopakumar, Iyer, and others have developed an elegant but complex quasi-Keplerian formalism for describing the post-Newtonian corrections to the orbits and waveforms of inspiralling binaries with any eccentricity. Here, we specialize the quasi-Keplerian formalism to binaries with low eccentricity. In this limit, the nonperiodic contribution to the gravitational-wave phasing can be expressed explicitly as simple functions of frequency or time, with little additional complexity beyond the well-known formulas for circular binaries. These eccentric phase corrections are computed to 3PN order and to leading order in the eccentricity for the standard PN approximants. For a variety of systems, these eccentricity corrections cause significant corrections to the number of gravitational-wave cycles that sweep through a detector's frequency band. This is evaluated using several measures, including a modification of the useful cycles. By comparing to numerical solutions valid for any eccentricity, we find that our analytic solutions are valid up to e0≲0.1 for comparable-mass systems, where e0 is the eccentricity when the source enters the detector band. We also evaluate the role of periodic terms that enter the phasing and discuss how they can be incorporated into some of
LOSP: Liège Orbital Solution Package
NASA Astrophysics Data System (ADS)
Sana, Hugues
2013-09-01
LOSP is a FORTRAN77 numerical package that computes the orbital parameters of spectroscopic binaries. The package deals with SB1 and SB2 systems and is able to adjust either circular or eccentric orbits through a weighted fit.
NASA Astrophysics Data System (ADS)
Storch, Natalia I.; Lai, Dong; Anderson, Kassandra R.
2017-03-01
Many exoplanetary systems containing hot Jupiters (HJs) exhibit significant misalignment between the spin axes of the host stars and the orbital angular momentum axes of the planets ('spin-orbit misalignment'). High-eccentricity migration involving Lidov-Kozai oscillations of the planet's orbit induced by a distant perturber is a possible channel for producing such misaligned HJ systems. Previous works have shown that the dynamical evolution of the stellar spin axis during the high-e migration plays a dominant role in generating the observed spin-orbit misalignment. Numerical studies have also revealed various patterns of the evolution of the stellar spin axis leading to the final misalignment. Here, we develop an analytic theory to elucidate the evolution of spin-orbit misalignment during the Lidov-Kozai migration of planets in stellar binaries. Secular spin-orbit resonances play a key role in the misalignment evolution. We include the effects of short-range forces and tidal dissipation, and categorize the different possible paths to spin-orbit misalignment as a function of various physical parameters (e.g. planet mass and stellar rotation period). We identify five distinct spin-orbit evolution paths and outcomes, only two of which are capable of producing retrograde orbits. We show that these paths to misalignment and the outcomes depend only on two dimensionless parameters, which compare the stellar spin precession frequency with the rate of change of the planet's orbital axis, and the Lidov-Kozai oscillation frequency. Our analysis reveals a number of novel phenomena for the stellar spin evolution, ranging from bifurcation, adiabatic advection, to fully chaotic evolution of spin-orbit angles.
Analyzing information contained in the OARMA Binary Orbit Catalog
NASA Astrophysics Data System (ADS)
Docobo, J. A.; Ling, J. F.; Campo, P. P.
2012-05-01
This poster displays a statistical summary based on the information contained in the Double Star Orbit Catalog of the Ramon Maria Aller Astronomical Observatory (OARMA). Among other findings, the current aleatory period-eccentricity distribution is particularly interesting. We have correlated eccentricities, periods, spectral types, Hipparcos parallaxes and the orientations of the orbital planes. A list is included that contains all of the names of the authors of the orbits as well as the number of orbits calculated by the authors (February 2011).
An eccentric binary millisecond pulsar in the galactic plane.
Champion, David J; Ransom, Scott M; Lazarus, Patrick; Camilo, Fernando; Bassa, Cees; Kaspi, Victoria M; Nice, David J; Freire, Paulo C C; Stairs, Ingrid H; van Leeuwen, Joeri; Stappers, Ben W; Cordes, James M; Hessels, Jason W T; Lorimer, Duncan R; Arzoumanian, Zaven; Backer, Don C; Bhat, N D Ramesh; Chatterjee, Shami; Cognard, Ismaël; Deneva, Julia S; Faucher-Giguère, Claude-André; Gaensler, Bryan M; Han, Jinlin; Jenet, Fredrick A; Kasian, Laura; Kondratiev, Vlad I; Kramer, Michael; Lazio, Joseph; McLaughlin, Maura A; Venkataraman, Arun; Vlemmings, Wouter
2008-06-06
Binary pulsar systems are superb probes of stellar and binary evolution and the physics of extreme environments. In a survey with the Arecibo telescope, we have found PSR J1903+0327, a radio pulsar with a rotational period of 2.15 milliseconds in a highly eccentric (e = 0.44) 95-day orbit around a solar mass (M(middle dot in circle)) companion. Infrared observations identify a possible main-sequence companion star. Conventional binary stellar evolution models predict neither large orbital eccentricities nor main-sequence companions around millisecond pulsars. Alternative formation scenarios involve recycling a neutron star in a globular cluster, then ejecting it into the Galactic disk, or membership in a hierarchical triple system. A relativistic analysis of timing observations of the pulsar finds its mass to be 1.74 +/- 0.04 M solar symbol, an unusually high value.
An Eccentric Binary Millisecond Pulsar in the Galactic Plane
NASA Technical Reports Server (NTRS)
Champion, David J.; Ransom, Scott M.; Lazarus, Patrick; Camilo, Fernando; Bassa, Cess; Kaspi, Victoria M.; Nice, David J.; Freire, Paulo C. C.; Stairs, Ingrid H.; vanLeeuwen, Joeri; Stappers, Ben W.; Cordes, James M.; Hessels, Jason W. T.; Lorimer, Duncan R.; Arzoumanian, Zaven; Backer, Don C.; Bhat, N. D. Ramesh; Chatterjee, Shami; Cognard, Ismael; Deneva, Julia S.; Faucher-Giguere, Claude-Andre; Gaensler, Bryan M.; Han, JinLin; Jenet, Fredrick A.; Kasian, Laura
2008-01-01
Binary pulsar systems are superb probes of stellar and binary evolution and the physics of extreme environments. In a survey with the Arecibo telescope, we have found PSR J1903+0327, a radio pulsar with a rotational period of 2.15 milliseconds in a highly eccentric (e = 0.44) 95-day orbit around a solar mass (M.) companion. Infrared observations identify a possible main-sequence companion star. Conventional binary stellar evolution models predict neither large orbital eccentricities nor main-sequence companions around millisecond pulsars. Alternative formation scenarios involve recycling a neutron star in a globular cluster, then ejecting it into the Galactic disk, or membership in a hierarchical triple system. A relativistic analysis of timing observations of the pulsar finds its mass to be 1.74 +/- 0.04 Solar Mass, an unusually high value.
Spin-orbit evolution of Mercury revisited
NASA Astrophysics Data System (ADS)
Noyelles, Benoît; Frouard, Julien; Makarov, Valeri V.; Efroimsky, Michael
2014-10-01
Although it is accepted that the significant eccentricity of Mercury (0.206) favours entrapment into the 3:2 spin-orbit resonance, open are the questions of how and when the capture took place. A recent work by Makarov (Makarov, V.V. [2012]. Astrophys. J., 752, 73) has proven that trapping into this state is certain for eccentricities larger than 0.2, provided we use a realistic tidal model based on the Darwin-Kaula expansion of the tidal torque. While in Ibid. a Mercury-like planet had its eccentricity fixed, we take into account its evolution. To that end, a family of possible histories of the eccentricity is generated, based on synthetic time evolution consistent with the expected statistics of the distribution of eccentricity. We employ a model of tidal friction, which takes into account both the rheology and self-gravitation of the planet. As opposed to the commonly used constant time lag (CTL) and constant phase lag (CPL) models, the physics-based tidal model changes dramatically the statistics of the possible final spin states. First, we discover that after only one encounter with the spin-orbit 3:2 resonance this resonance becomes the most probable end-state. Second, if a capture into this (or any other) resonance takes place, the capture becomes final, several crossings of the same state being forbidden by our model. Third, within our model the trapping of Mercury happens much faster than previously believed: for most histories, 10-20 Myr are sufficient. Fourth, even a weak laminar friction between the solid mantle and a molten core would most likely result in a capture in the 2:1 or even higher resonance, which is confirmed both semi-analytically and by limited numerical simulations. So the principal novelty of our paper is that the 3:2 end-state is more ancient than the same end-state obtained when the constant time lag model is employed. The swift capture justifies our treatment of Mercury as a homogeneous, unstratified body whose liquid core had not
Assaghir, Yasser
2017-03-01
The piriformis fossa is the ideal portal of entry for antegrade interlocking nailing. Localizing this portal can be difficult and its eccentricity leads to complications. This prospective comparative study was designed to compare an innovative way to obtain the ideal portal from inside the medullary canal in cases of plate failure and compare it to the classic antegrade portal. It included 41 cases (19 antegrade and 22 retrograde). The retrograde portal was significantly better in terms of entry time, radiation time, blood-loss, and wound length. The proper portal was rapidly and easily achieved in all retrograde cases without complications; while four in antegrade cases had complications. Minimum follow-up was 2 years. Level of evidence III.
NEPTUNE'S WILD DAYS: CONSTRAINTS FROM THE ECCENTRICITY DISTRIBUTION OF THE CLASSICAL KUIPER BELT
Dawson, Rebekah I.; Murray-Clay, Ruth
2012-05-01
Neptune's dynamical history shaped the current orbits of Kuiper Belt objects (KBOs), leaving clues to the planet's orbital evolution. In the 'classical' region, a population of dynamically 'hot' high-inclination KBOs overlies a flat 'cold' population with distinct physical properties. Simulations of qualitatively different histories for Neptune, including smooth migration on a circular orbit or scattering by other planets to a high eccentricity, have not simultaneously produced both populations. We explore a general Kuiper Belt assembly model that forms hot classical KBOs interior to Neptune and delivers them to the classical region, where the cold population forms in situ. First, we present evidence that the cold population is confined to eccentricities well below the limit dictated by long-term survival. Therefore, Neptune must deliver hot KBOs into the long-term survival region without excessively exciting the eccentricities of the cold population. Imposing this constraint, we explore the parameter space of Neptune's eccentricity and eccentricity damping, migration, and apsidal precession. We rule out much of parameter space, except where Neptune is scattered to a moderately eccentric orbit (e > 0.15) and subsequently migrates a distance {Delta}a{sub N} = 1-6 AU. Neptune's moderate eccentricity must either damp quickly or be accompanied by fast apsidal precession. We find that Neptune's high eccentricity alone does not generate a chaotic sea in the classical region. Chaos can result from Neptune's interactions with Uranus, exciting the cold KBOs and placing additional constraints. Finally, we discuss how to interpret our constraints in the context of the full, complex dynamical history of the solar system.
Climate of an Earth-Like World with Changing Eccentricity
NASA Astrophysics Data System (ADS)
Kohler, Susanna
2017-02-01
Having a giant planet like Jupiter next door can really wreak havoc on your orbit! A new study examines what such a bad neighbor might mean for the long-term climate of an Earth-like planet.Influence of a Bad NeighborThe presence of a Jupiter-like giant planet in a nearby orbit can significantly affect how terrestrial planets evolve dynamically, causing elements like the planets orbital eccentricities and axial tilts to change over time. Earth is saved this inconvenience Jupiter isnt close enough to significantly influence us, and our large moon stabilizes our orbit against Jupiters tugs.Top panels: Authors simulationoutcomes for Case1, in which the planets eccentricity varies from 0 to 0.283 over 6500 years. Bottom panels: Outcomes for Case 2, in which the planets eccentricity varies from 0 to 0.066 over 4500 years. The highereccentricities reached in Case 1 causes the climate parameters to vary more widely. Click for a better look! [Way Georgakarakos 2017]Mars, on the other hand, isnt as lucky: its possible that Jupiters gravitational pull causes Marss axial tilt, for instance, to evolve through a range as large as 0 to 60 degrees on timescales of millions of years! Marss orbital eccentricity is similarly thought to vary due to Jupiters influence, and both of these factors play a major role in determining Marss climate.As exoplanet missions discover more planets many of which are Earth-like we must carefully consider which among these are most likely to be capable of sustaining life. If having a nearby neighbor like a Jupiter can tug an Earth-like world into an orbit with varying eccentricity, how does this affect the planets climate? Will the planet remain temperate? Or will it develop a runaway heating or cooling effect as it orbits, rendering it uninhabitable?Oceans and OrbitsTo examine these questions, two scientists have built the first ever 3D global climate model simulations of an Earth-like world using a fully coupled ocean (necessary for understanding
CHEMICAL TIMESCALES IN THE ATMOSPHERES OF HIGHLY ECCENTRIC EXOPLANETS
Visscher, Channon
2012-09-20
Close-in exoplanets with highly eccentric orbits are subject to large variations in incoming stellar flux between periapse and apoapse. These variations may lead to large swings in atmospheric temperature, which in turn may cause changes in the chemistry of the atmosphere from higher CO abundances at periapse to higher CH{sub 4} abundances at apoapse. Here, we examine chemical timescales for CO{r_reversible}CH{sub 4} interconversion compared to orbital timescales and vertical mixing timescales for the highly eccentric exoplanets HAT-P-2b and CoRoT-10b. As exoplanet atmospheres cool, the chemical timescales for CO{r_reversible}CH{sub 4} tend to exceed orbital and/or vertical mixing timescales, leading to quenching. The relative roles of orbit-induced thermal quenching and vertical quenching depend upon mixing timescales relative to orbital timescales. For both HAT-P-2b and CoRoT-10b, vertical quenching will determine disequilibrium CO{r_reversible}CH{sub 4} chemistry at faster vertical mixing rates (K{sub zz} > 10{sup 7} cm{sup 2} s{sup -1}), whereas orbit-induced thermal quenching may play a significant role at slower mixing rates (K{sub zz} < 10{sup 7} cm{sup 2} s{sup -1}). The general abundance and chemical timescale results-calculated as a function of pressure, temperature, and metallicity-can be applied for different atmospheric profiles in order to estimate the quench level and disequilibrium abundances of CO and CH{sub 4} on hydrogen-dominated exoplanets. Observations of CO and CH{sub 4} on highly eccentric exoplanets may yield important clues to the chemical and dynamical properties of their atmospheres.
An objective statistical test for eccentricity forcing of Oligo-Miocene climate
NASA Astrophysics Data System (ADS)
Proistosescu, C.; Huybers, P.; Maloof, A. C.
2008-12-01
We seek a maximally objective test for the presence of orbital features in Oligocene and Miocene δ18O records from marine sediments. Changes in Earth's orbital eccentricity are thought to be an important control on the long term variability of climate during the Oligocene and Miocene Epochs. However, such an important control from eccentricity is surprising because eccentricity has relatively little influence on Earth's annual average insolation budget. Nevertheless, if significant eccentricity variability is present, it would provide important insight into the operation of the climate system at long timescales. Here we use previously published data, but using a chronology which is initially independent of orbital assumptions, to test for the presence of eccentricity period variability in the Oligocene/Miocene sediment records. In contrast to the sawtooth climate record of the Pleistocene, the Oligocene and Miocene climate record appears smooth and symmetric and does not reset itself every hundred thousand years. This smooth variation, as well as the time interval spanning many eccentricity periods makes Oligocene and Miocene paleorecords very suitable for evaluating the importance of eccentricity forcing. First, we construct time scales depending only upon the ages of geomagnetic reversals with intervening ages linearly interpolated with depth. Such a single age-depth relationship is, however, too uncertain to assess whether orbital features are present. Thus, we construct a second depth-derived age-model by averaging ages across multiple sediment cores which have, at least partly, independent accumulation rate histories. But ages are still too uncertain to permit unambiguous detection of orbital variability. Thus we employ limited tuning assumptions and measure the degree by orbital period variability increases using spectral power estimates. By tuning we know that we are biasing the record toward showing orbital variations, but we account for this bias in our
NASA Astrophysics Data System (ADS)
Kjurkchieva, Diana; Vasileva, Doroteya; Dimitrov, Dinko
2016-12-01
The eccentricity, periastron angle, orbital inclination, mass ratio, stellar temperatures, and relative stellar radii of 12 eclipsing eccentric binaries were determined on the basis of Kepler data. The analysis of their out-of-eclipse variability led to the following results: (i) KIC 10490980 exhibits rotational (spot-type) variability. (ii) Four new heartbeat stars were found: KIC 9344623 and KIC 10296163, which have wide tidally induced light humps, and KIC 9119405 and KIC 9673173, which have narrow “W-shape” features. (iii) KIC 4932691 shows oscillations with approximately the 18th harmonic of the orbital period. We established that the eccentric Kepler binaries fall below the envelope P{(1-{e}2)}3/2≈ 5 days on the period-eccentricity diagram and that there is a surprising lack of eccentric binaries with periods of 25-35 days.
Orbital Evolution in Extrasolar Planetary Systems
NASA Astrophysics Data System (ADS)
Zhang, Ke; Hamilton, D. P.
2006-09-01
We investigate the long-term orbital evolution of exoplanets in a planar two-planet system, subject to an applied dissipative force. Without dissipation, the orbits of the two planets oscillate with two fundamental eigenmodes due to their secular gravitational interactions: a slow mode in which the two pericenters are aligned and a fast mode in which they are anti-aligned. In each eigenmode, the two orbits precess as a rigid body at a rate determined purely by planet masses and orbital semi-major axes. In addition, the ratio between the two eccentricities is fixed. Any system of two planets can be represented by a linear combination of these two modes, with initial conditions (eccentricities and longitudes of pericenters) determining the precise mix. When eccentricities are slowly damped by perturbations such as planetary tides or disk interactions, the mode frequencies and eccentricity ratios shift slightly, and the two modes decay separately at different rates. We solve for these rates analytically -- usually one mode damps much faster than the other, and the system ends up locked in either an apsidally aligned or anti-aligned state. This mechanism provides a possible explanation for the nonzero eccentricities of "hot-Jupiters", assuming that they have companions in more eccentric orbits. Some perturbations may also cause planetary migration. For slow migration rates, two adiabatic invariants, which are functions of mode parameters (frequencies and amplitudes), exist. Through analytical study of these integrals, we seek to explain the diverse appearance of planetary orbits.
NASA Technical Reports Server (NTRS)
Faramaz, V.; Beust, H.; Thebault, P.; Augereau, J.-C.; Bonsor, A.; delBurgo, C.; Ertel, S.; Marshall, J. P.; Milli, J.; Montesinos, B.; Mora, A.; Bryden, G.; Danchi, William C.; Eiroa, C.; White, G. J.; Wolf, S.
2014-01-01
Context. Imaging of debris disks has found evidence for both eccentric and offset disks. One hypothesis is that they provide evidence for massive perturbers, for example, planets or binary companions, which sculpt the observed structures. One such disk was recently observed in the far-IR by the Herschel Space Observatory around Zeta2 Reticuli. In contrast with previously reported systems, the disk is significantly eccentric, and the system is several Gyr old. Aims. We aim to investigate the long-term evolution of eccentric structures in debris disks caused by a perturber on an eccentric orbit around the star. We hypothesise that the observed eccentric disk around Zeta2 Reticuli might be evidence of such a scenario. If so, we are able to constrain the mass and orbit of a potential perturber, either a giant planet or a binary companion. Methods. Analytical techniques were used to predict the effects of a perturber on a debris disk. Numerical N-body simulations were used to verify these results and further investigate the observable structures that may be produced by eccentric perturbers. The long-term evolution of the disk geometry was examined, with particular application to the Zeta2 Reticuli system. In addition, synthetic images of the disk were produced for direct comparison with Herschel observations. Results. We show that an eccentric companion can produce both the observed offsets and eccentric disks. These effects are not immediate, and we characterise the timescale required for the disk to develop to an eccentric state (and any spirals to vanish). For Zeta2 Reticuli, we derive limits on the mass and orbit of the companion required to produce the observations. Synthetic images show that the pattern observed around Zeta2 Reticuli can be produced by an eccentric disk seen close to edge-on, and allow us to bring additional constraints on the disk parameters of our model (disk flux and extent). Conclusions. We conclude that eccentric planets or stellar companions
Dynamics of binary and planetary-system interaction with disks - Eccentricity changes
NASA Technical Reports Server (NTRS)
Atrymowicz, Pawel
1992-01-01
Protostellar and protoplanetary systems, as well as merging galactic nuclei, often interact tidally and resonantly with the astrophysical disks via gravity. Underlying our understanding of the formation processes of stars, planets, and some galaxies is a dynamical theory of such interactions. Its main goals are to determine the geometry of the binary-disk system and, through the torque calculations, the rate of change of orbital elements of the components. We present some recent developments in this field concentrating on eccentricity driving mechanisms in protoplanetary and protobinary systems. In those two types of systems the result of the interaction is opposite. A small body embedded in a disk suffers a decrease of orbital eccentricity, whereas newly formed binary stars surrounded by protostellar disks may undergo a significant orbital evolution increasing their eccentricities.
EXPLORING A 'FLOW' OF HIGHLY ECCENTRIC BINARIES WITH KEPLER
Dong Subo; Katz, Boaz; Socrates, Aristotle
2013-01-20
With 16-month of Kepler data, 15 long-period (40-265 days) eclipsing binaries on highly eccentric orbits (minimum e between 0.5 and 0.85) are identified from their closely separated primary and secondary eclipses ({Delta}t{sub I,II} = 3-10 days). These systems confirm the existence of a previously hinted binary population situated near a constant angular momentum track at P(1 - e {sup 2}){sup 3/2} {approx} 15 days, close to the tidal circularization period P{sub circ}. They may be presently migrating due to tidal dissipation and form a steady-state 'flow' ({approx}1% of stars) feeding the close-binary population (few % of stars). If so, future Kepler data releases will reveal a growing number (dozens) of systems at longer periods, following dN/dlgP {proportional_to} P {sup 1/3} with increasing eccentricities reaching e {yields} 0.98 for P {yields} 1000 days. Radial-velocity follow-up of long-period eclipsing binaries with no secondary eclipses could offer a significantly larger sample. Orders of magnitude more (hundreds) may reveal their presence from periodic 'eccentricity pulses', such as tidal ellipsoidal variations near pericenter passages. Several new few-day-long eccentricity-pulse candidates with long periods (P = 25-80 days) are reported.
Jiang, Long; Li, Xiang-Dong; Dey, Jishnu; Dey, Mira
2015-07-01
According to the recycling scenario, millisecond pulsars (MSPs) have evolved from low-mass X-ray binaries (LMXBs). Their orbits are expected to be circular due to tidal interactions during binary evolution, as observed in most binary MSPs. There are some peculiar systems that do not fit this picture. Three recent examples are the PSRs J2234+06, J1946+3417, and J1950+2414, all of which are MSPs in eccentric orbits but with mass functions compatible with expected He white dwarf (WD) companions. It has been suggested these MSPs may have formed from delayed accretion-induced collapse of massive WDs, or the eccentricity may be induced by dynamical interaction between the binary and a circumbinary disk. Assuming that the core density of accreting neutron stars (NSs) in LMXBs may reach the density of quark deconfinement, which can lead to phase transition from NSs to strange quark stars, we show that the resultant MSPs are likely to have an eccentric orbit, due to the sudden loss of the gravitational mass of the NS during the transition. The eccentricities can be reproduced with a reasonable estimate of the mass loss. This scenario might also account for the formation of the youngest known X-ray binary Cir X–1, which also possesses a low-field compact star in an eccentric orbit.
Chloroplast retrograde signal regulates flowering
Feng, Peiqiang; Guo, Hailong; Chi, Wei; Chai, Xin; Sun, Xuwu; Xu, Xiumei; Ma, Jinfang; Rochaix, Jean-David; Leister, Dario; Wang, Haiyang; Lu, Congming; Zhang, Lixin
2016-01-01
Light is a major environmental factor regulating flowering time, thus ensuring reproductive success of higher plants. In contrast to our detailed understanding of light quality and photoperiod mechanisms involved, the molecular basis underlying high light-promoted flowering remains elusive. Here we show that, in Arabidopsis, a chloroplast-derived signal is critical for high light-regulated flowering mediated by the FLOWERING LOCUS C (FLC). We also demonstrate that PTM, a PHD transcription factor involved in chloroplast retrograde signaling, perceives such a signal and mediates transcriptional repression of FLC through recruitment of FVE, a component of the histone deacetylase complex. Thus, our data suggest that chloroplasts function as essential sensors of high light to regulate flowering and adaptive responses by triggering nuclear transcriptional changes at the chromatin level. PMID:27601637
Compact Planetary Systems Perturbed by an Inclined Companion. II. Stellar Spin-Orbit Evolution
NASA Astrophysics Data System (ADS)
Boué, Gwenaël; Fabrycky, Daniel C.
2014-07-01
The stellar spin orientation relative to the orbital planes of multiplanet systems is becoming accessible to observations. Here, we analyze and classify different types of spin-orbit evolution in compact multiplanet systems perturbed by an inclined outer companion. Our study is based on classical secular theory, using a vectorial approach developed in a separate paper. When planet-planet perturbations are truncated at the second order in eccentricity and mutual inclination, and the planet-companion perturbations are developed at the quadrupole order, the problem becomes integrable. The motion is composed of a uniform precession of the whole system around the total angular momentum, and in the rotating frame, the evolution is periodic. Here, we focus on the relative motion associated with the oscillations of the inclination between the planet system and the outer orbit and of the obliquities of the star with respect to the two orbital planes. The solution is obtained using a powerful geometric method. With this technique, we identify four different regimes characterized by the nutation amplitude of the stellar spin axis relative to the orbital plane of the planets. In particular, the obliquity of the star reaches its maximum when the system is in the Cassini regime where planets have more angular momentum than the star and where the precession rate of the star is similar to that of the planets induced by the companion. In that case, spin-orbit oscillations exceed twice the inclination between the planets and the companion. Even if the mutual inclination is only ~= 20°, this resonant case can cause the spin-orbit angle to oscillate between perfectly aligned and retrograde values.
Compact planetary systems perturbed by an inclined companion. II. Stellar spin-orbit evolution
Boué, Gwenaël; Fabrycky, Daniel C.
2014-07-10
The stellar spin orientation relative to the orbital planes of multiplanet systems is becoming accessible to observations. Here, we analyze and classify different types of spin-orbit evolution in compact multiplanet systems perturbed by an inclined outer companion. Our study is based on classical secular theory, using a vectorial approach developed in a separate paper. When planet-planet perturbations are truncated at the second order in eccentricity and mutual inclination, and the planet-companion perturbations are developed at the quadrupole order, the problem becomes integrable. The motion is composed of a uniform precession of the whole system around the total angular momentum, and in the rotating frame, the evolution is periodic. Here, we focus on the relative motion associated with the oscillations of the inclination between the planet system and the outer orbit and of the obliquities of the star with respect to the two orbital planes. The solution is obtained using a powerful geometric method. With this technique, we identify four different regimes characterized by the nutation amplitude of the stellar spin axis relative to the orbital plane of the planets. In particular, the obliquity of the star reaches its maximum when the system is in the Cassini regime where planets have more angular momentum than the star and where the precession rate of the star is similar to that of the planets induced by the companion. In that case, spin-orbit oscillations exceed twice the inclination between the planets and the companion. Even if the mutual inclination is only ≅ 20°, this resonant case can cause the spin-orbit angle to oscillate between perfectly aligned and retrograde values.
The Retrograde Motion of Mars.
ERIC Educational Resources Information Center
Erlichson, Herman
1999-01-01
Describes a laboratory activity in a liberal-arts physics course entitled "Galileo to Newton and Beyond" in which students examine the orbits of Earth and Mars from heliocentric and geocentric viewpoints. (WRM)
On the orbital dependence of the asteroidal collision process
NASA Technical Reports Server (NTRS)
Ip, W.-H.
1977-01-01
Collision of asteroids with the main-belt asteroid population is considered with the effect of the impact kinetic energy taken into account. It is found that objects in eccentric orbits have a larger probability of destructive collision as compared to objects in orbits with mean values of eccentricity (equal to 0.15) and inclination (equal to 10 deg); also orbits with small semimajor axes (about 2.3 AU) are found to have peak values of the probability of destructive collision.
NASA Astrophysics Data System (ADS)
Shabram, Megan; Jontof-Hutter, Daniel; Ford, Eric B.
2015-12-01
We characterize the mass-radius-eccentricity distribution of transiting planets near first-order mean motion resonances using Transit Timing Variation (TTV) observations from NASA's Kepler mission. Kepler's precise measurements of transit times (Mazeh et al. 2014; Rowe et al. 2015) constrain the planet-star mass ratio, eccentricity and pericenter directions for hundreds of planets. Strongly-interacting planetary systems allow TTVs to provide precise measurements of masses and orbital eccentricities separately (e.g., Kepler-36, Carter et al. 2012). In addition to these precisely characterized planetary systems, there are several systems harboring at least two planets near a mean motion resonance (MMR) for which TTVs provide a joint constraint on planet masses, eccentricities and pericenter directions (Hadden et al. 2015). Unfortunately, a near degeneracy between these parameters leads to a posterior probability density with highly correlated uncertainties. Nevertheless, the population encodes valuable information about the distribution of planet masses, orbital eccentricities and the planet mass-radius relationship. We characterize the distribution of masses and eccentricities for near-resonant transiting planets by combining a hierarchical Bayesian model with an analytic model for the TTV signatures of near-resonant planet pairs (Lithwick & Wu 2012). By developing a rigorous statistical framework for analyzing the TTV signatures of a population of planetary systems, we significantly improve upon previous analyses. For example, our analysis includes transit timing measurements of near-resonant transiting planet pairs regardless of whether there is a significant detection of TTVs, thereby avoiding biases due to only including TTV detections.
Eccentric Inspirals with Self-Force and Spin-Force
NASA Astrophysics Data System (ADS)
Evans, Charles; Osburn, Thomas; Warburton, Niels
2017-01-01
Eccentric inspirals of a small mass about a more massive Schwarzschild black hole (EMRIs or IMRIs) are calculated using the gravitational self-force and the Mathisson-Papapetrou spin-force. These calculations include all dissipative and conservative effects that are first order in the mass ratio. We compute systems with initial eccentricities as high as e = 0.8, initial separations as large as 50 M, and arbitrary spin orientations. Including the spin-force causes the orbital plane to precess. Inspirals are calculated using an osculating-orbits scheme that is driven by self-force data from a hybrid self-force code and time-domain spin-force calculations. The hybrid approach uses both self-force data from a Lorenz gauge code and highly accurate flux data from a Regge-Wheeler-Zerilli code, allowing the hybrid model to track orbital phase of inspirals to within 0.1 radians or better over hundreds or thousands of orbits. NSF PHY15-06182.
NASA Astrophysics Data System (ADS)
Taylor, S. R.; Huerta, E. A.; Gair, J. R.; McWilliams, S. T.
2016-01-01
The couplings between supermassive black hole binaries (SMBHBs) and their environments within galactic nuclei have been well studied as part of the search for solutions to the final parsec problem. The scattering of stars by the binary or the interaction with a circumbinary disk may efficiently drive the system to sub-parsec separations, allowing the binary to enter a regime where the emission of gravitational waves can drive it to merger within a Hubble time. However, these interactions can also affect the orbital parameters of the binary. In particular, they may drive an increase in binary eccentricity which survives until the system’s gravitational-wave (GW) signal enters the pulsar-timing array (PTA) band. Therefore, if we can measure the eccentricity from observed signals, we can potentially deduce some of the properties of the binary environment. To this end, we build on previous techniques to present a general Bayesian pipeline with which we can detect and estimate the parameters of an eccentric SMBHB system with PTAs. Additionally, we generalize the PTA {{ F }}{{e}}-statistic to eccentric systems, and show that both this statistic and the Bayesian pipeline are robust when studying circular or arbitrarily eccentric systems. We explore how eccentricity influences the detection prospects of single GW sources, as well as the detection penalty incurred by employing a circular waveform template to search for eccentric signals, and conclude by identifying important avenues for future study.
Neptune's Eccentricity and the Nature of the Kuiper Belt
NASA Technical Reports Server (NTRS)
Ward, William R.; Hahn, Joseph M.
1998-01-01
The small eccentricity of Neptune may be a direct consequence of apsidal wave interaction with the trans-Neptune population of debris called the Kuiper belt. The Kuiper belt is subject to resonant perturbations from Neptune, so that the transport of angular momentum by density waves can result in orbital evolution of Neptune as well as changes in the structure of the Kuiper belt. In particular, for a belt eroded out to the vicinity of Neptune's 2:1 resonance at about 48 astronomical units, Neptune's eccentricity can damp to its current value over the age of the solar system if the belt contains slightly more than an earth mass of material out to about 75 astronomical units.
Neptune's eccentricity and the nature of the kuiper belt
Ward; Hahn
1998-06-26
The small eccentricity of Neptune may be a direct consequence of apsidal wave interaction with the trans-Neptune population of debris called the Kuiper belt. The Kuiper belt is subject to resonant perturbations from Neptune, so that the transport of angular momentum by density waves can result in orbital evolution of Neptune as well as changes in the structure of the Kuiper belt. In particular, for a belt eroded out to the vicinity of Neptune's 2:1 resonance at about 48 astronomical units, Neptune's eccentricity can damp to its current value over the age of the solar system if the belt contains slightly more than an earth mass of material out to about 75 astronomical units.
Planet-induced Stellar Pulsations in HAT-P-2's Eccentric System
NASA Astrophysics Data System (ADS)
de Wit, Julien; Lewis, Nikole K.; Knutson, Heather A.; Fuller, Jim; Antoci, Victoria; Fulton, Benjamin J.; Laughlin, Gregory; Deming, Drake; Shporer, Avi; Batygin, Konstantin; Cowan, Nicolas B.; Agol, Eric; Burrows, Adam S.; Fortney, Jonathan J.; Langton, Jonathan; Showman, Adam P.
2017-02-01
Extrasolar planets on eccentric short-period orbits provide a laboratory in which to study radiative and tidal interactions between a planet and its host star under extreme forcing conditions. Studying such systems probes how the planet’s atmosphere redistributes the time-varying heat flux from its host and how the host star responds to transient tidal distortion. Here, we report the insights into the planet–star interactions in HAT-P-2's eccentric planetary system gained from the analysis of ∼350 hr of 4.5 μm observations with the Spitzer Space Telescope. The observations show no sign of orbit-to-orbit variability nor of orbital evolution of the eccentric planetary companion, HAT-P-2 b. The extensive coverage allows us to better differentiate instrumental systematics from the transient heating of HAT-P-2 b’s 4.5 μm photosphere and yields the detection of stellar pulsations with an amplitude of approximately 40 ppm. These pulsation modes correspond to exact harmonics of the planet’s orbital frequency, indicative of a tidal origin. Transient tidal effects can excite pulsation modes in the envelope of a star, but, to date, such pulsations had only been detected in highly eccentric stellar binaries. Current stellar models are unable to reproduce HAT-P-2's pulsations, suggesting that our understanding of the interactions at play in this system is incomplete.
On the Formation of Eccentric Millisecond Pulsars with Helium White-dwarf Companions
NASA Astrophysics Data System (ADS)
Antoniadis, John
2014-12-01
Millisecond pulsars (MSPs) orbiting helium white dwarfs (WDs) in eccentric orbits challenge the established binary-evolution paradigm that predicts efficient orbital circularization during the mass-transfer episode that spins up the pulsar. Freire & Tauris recently proposed that these binary MSPs may instead form from the rotationally delayed accretion-induced collapse of a massive WD. However, their hypothesis predicts that eccentric systems preferably host low-mass pulsars and travel with small systemic velocities—in tension with new observational constraints. Here, I show that a substantial growth in eccentricity may alternatively arise from the dynamical interaction of the binary with a circumbinary disk. Such a disk may form from ejected donor material during hydrogen flash episodes, when the neutron star is already an active radio pulsar and tidal forces can no longer circularize the binary. I demonstrate that a short-lived (104-105 yr) disk can result in eccentricities of e ~= 0.01-0.15 for orbital periods between 15 and 50 days. Finally, I propose that, more generally, the disk hypothesis may explain the lack of circular binary pulsars for the aforementioned orbital-period range.
ON THE FORMATION OF ECCENTRIC MILLISECOND PULSARS WITH HELIUM WHITE-DWARF COMPANIONS
Antoniadis, John
2014-12-20
Millisecond pulsars (MSPs) orbiting helium white dwarfs (WDs) in eccentric orbits challenge the established binary-evolution paradigm that predicts efficient orbital circularization during the mass-transfer episode that spins up the pulsar. Freire and Tauris recently proposed that these binary MSPs may instead form from the rotationally delayed accretion-induced collapse of a massive WD. However, their hypothesis predicts that eccentric systems preferably host low-mass pulsars and travel with small systemic velocities—in tension with new observational constraints. Here, I show that a substantial growth in eccentricity may alternatively arise from the dynamical interaction of the binary with a circumbinary disk. Such a disk may form from ejected donor material during hydrogen flash episodes, when the neutron star is already an active radio pulsar and tidal forces can no longer circularize the binary. I demonstrate that a short-lived (10{sup 4}-10{sup 5} yr) disk can result in eccentricities of e ≅ 0.01-0.15 for orbital periods between 15 and 50 days. Finally, I propose that, more generally, the disk hypothesis may explain the lack of circular binary pulsars for the aforementioned orbital-period range.
Study of certain launching techniques using long orbiting tethers
NASA Technical Reports Server (NTRS)
Colombo, G.; Arnold, D. A.
1981-01-01
A study of the basic equations governing orbital transfers using long orbiting tethers is presented. A very simple approximation to the general transfer equation is derived for the case of short tethers and low eccentricity orbits. Numerical examples are calculated for the case of injection into a circular orbit from a platform in eccentric orbit and injection into eccentric orbit from a platform in circular orbit. For the case of long tethers, a method is derived for reducing tether mass and increasing payload mass by tapering the tether to maintain constant stress per unit of tether cross section. Formulas are presented for calculating the equilibrium orbital parameters taking into account the mass of the platform, tether, and payload.
CHONDRULE FORMATION IN BOW SHOCKS AROUND ECCENTRIC PLANETARY EMBRYOS
Morris, Melissa A.; Desch, Steven J.; Athanassiadou, Themis; Boley, Aaron C.
2012-06-10
Recent isotopic studies of Martian meteorites by Dauphas and Pourmand have established that large ({approx}3000 km radius) planetary embryos existed in the solar nebula at the same time that chondrules-millimeter-sized igneous inclusions found in meteorites-were forming. We model the formation of chondrules by passage through bow shocks around such a planetary embryo on an eccentric orbit. We numerically model the hydrodynamics of the flow and find that such large bodies retain an atmosphere with Kelvin-Helmholtz instabilities allowing mixing of this atmosphere with the gas and particles flowing past the embryo. We calculate the trajectories of chondrules flowing past the body and find that they are not accreted by the protoplanet, but may instead flow through volatiles outgassed from the planet's magma ocean. In contrast, chondrules are accreted onto smaller planetesimals. We calculate the thermal histories of chondrules passing through the bow shock. We find that peak temperatures and cooling rates are consistent with the formation of the dominant, porphyritic texture of most chondrules, assuming a modest enhancement above the likely solar nebula average value of chondrule densities (by a factor of 10), attributable to settling of chondrule precursors to the midplane of the disk or turbulent concentration. We calculate the rate at which a planetary embryo's eccentricity is damped and conclude that a single planetary embryo scattered into an eccentric orbit can, over {approx}10{sup 5} years, produce {approx}10{sup 24} g of chondrules. In principle, a small number (1-10) of eccentric planetary embryos can melt the observed mass of chondrules in a manner consistent with all known constraints.
Does Perceptual Learning Suffer from Retrograde Interference?
Aberg, Kristoffer C.; Herzog, Michael H.
2010-01-01
In motor learning, training a task B can disrupt improvements of performance of a previously learned task A, indicating that learning needs consolidation. An influential study suggested that this is the case also for visual perceptual learning [1]. Using the same paradigm, we failed to reproduce these results. Further experiments with bisection stimuli also showed no retrograde disruption from task B on task A. Hence, for the tasks tested here, perceptual learning does not suffer from retrograde interference. PMID:21151868
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 Observed Orbital Properties of Binary Minor Planets
NASA Astrophysics Data System (ADS)
Naoz, Smadar; Perets, Hagai B.; Ragozzine, Darin
2010-08-01
Many binary minor planets (BMPs; both binary asteroids and binary trans-Neptunian objects) are known to exist in the solar system. The currently observed orbital and physical properties of BMPs hold essential information and clues about their origin, their evolution, and the conditions under which they evolved. Here, we study the orbital properties of BMPs with currently known mutual orbits. We find that BMPs are typically highly inclined relative to their orbit around the Sun, with a distribution consistent with an isotropic distribution. BMPs not affected by tidal forces are found to have high eccentricities with non-thermal eccentricity distribution peaking at intermediate eccentricities (typically 0.4-0.6). The high inclinations and eccentricities of the BMPs suggest that BMPs evolved in a dense collisional environment, in which gravitational encounters in addition to tidal and secular Kozai effects played an important role in their orbital evolution.
Chronic Eccentric Exercise and the Older Adult.
Gluchowski, Ashley; Harris, Nigel; Dulson, Deborah; Cronin, John
2015-10-01
Eccentric exercise has gained increasing attention as a suitable and promising intervention to delay or mitigate the known physical and physiological declines associated with aging. Determining the relative efficacy of eccentric exercise when compared with the more conventionally prescribed traditional resistance exercise will support evidence-based prescribing for the aging population. Thus, original research studies incorporating chronic eccentric exercise interventions in the older adult population were included in this review. The effects of a range of eccentric exercise modalities on muscular strength, functional capacity, body composition, muscle architecture, markers of muscle damage, the immune system, cardiovascular system, endocrine system, and rating of perceived exertion were all reviewed as outcomes of particular interest in the older adult. Muscular strength was found to increase most consistently compared with results from traditional resistance exercise. Functional capacity and body composition showed significant improvements with eccentric endurance protocols, especially in older, frail or sedentary cohorts. Muscle damage was avoided with the gradual progression of novel eccentric exercise, while muscle damage from intense acute bouts was significantly attenuated with repeated sessions. Eccentric exercise causes little cardiovascular stress; thus, it may not generate the overload required to elicit cardiovascular adaptations. An anabolic state may be achievable following eccentric exercise, while improvements to insulin sensitivity have not been found. Finally, rating of perceived exertion during eccentric exercise was often significantly lower than during traditional resistance exercise. Overall, evidence supports the prescription of eccentric exercise for the majority of outcomes of interest in the diverse cohorts of the older adult population.
Dawson, Rebekah I.; Johnson, John Asher
2012-09-10
Exoplanet orbital eccentricities offer valuable clues about the history of planetary systems. Eccentric, Jupiter-sized planets are particularly interesting: they may link the 'cold' Jupiters beyond the ice line to close-in hot Jupiters, which are unlikely to have formed in situ. To date, eccentricities of individual transiting planets primarily come from radial-velocity measurements. Kepler has discovered hundreds of transiting Jupiters spanning a range of periods, but the faintness of the host stars precludes radial-velocity follow-up of most. Here, we demonstrate a Bayesian method of measuring an individual planet's eccentricity solely from its transit light curve using prior knowledge of its host star's density. We show that eccentric Jupiters are readily identified by their short ingress/egress/total transit durations-part of the 'photoeccentric' light curve signature of a planet's eccentricity-even with long-cadence Kepler photometry and loosely constrained stellar parameters. A Markov Chain Monte Carlo exploration of parameter posteriors naturally marginalizes over the periapse angle and automatically accounts for the transit probability. To demonstrate, we use three published transit light curves of HD 17156 b to measure an eccentricity of e = 0.71{sup +0.16}{sub -0.09}, in good agreement with the discovery value e = 0.67 {+-} 0.08 based on 33 radial-velocity measurements. We present two additional tests using Kepler data. In each case, the technique proves to be a viable method of measuring exoplanet eccentricities and their confidence intervals. Finally, we argue that this method is the most efficient, effective means of identifying the extremely eccentric, proto-hot Jupiters predicted by Socrates et al.
Montgomery, M. M.
2012-02-15
Accretion disks around black hole, neutron star, and white dwarf systems are thought to sometimes tilt, retrogradely precess, and produce hump-shaped modulations in light curves that have a period shorter than the orbital period. Although artificially rotating numerically simulated accretion disks out of the orbital plane and around the line of nodes generate these short-period superhumps and retrograde precession of the disk, no numerical code to date has been shown to produce a disk tilt naturally. In this work, we report the first naturally tilted disk in non-magnetic cataclysmic variables using three-dimensional smoothed particle hydrodynamics. Our simulations show that after many hundreds of orbital periods, the disk has tilted on its own and this disk tilt is without the aid of radiation sources or magnetic fields. As the system orbits, the accretion stream strikes the bright spot (which is on the rim of the tilted disk) and flows over and under the disk on different flow paths. These different flow paths suggest the lift force as a source to disk tilt. Our results confirm the disk shape, disk structure, and negative superhump period and support the source to disk tilt, source to retrograde precession, and location associated with X-ray and He II emission from the disk as suggested in previous works. Our results identify the fundamental negative superhump frequency as the indicator of disk tilt around the line of nodes.
ORBITAL DEPENDENCE OF GALAXY PROPERTIES IN SATELLITE SYSTEMS OF GALAXIES
Hwang, Ho Seong; Park, Changbom E-mail: cbp@kias.re.k
2010-09-01
We study the dependence of satellite galaxy properties on the distance to the host galaxy and the orbital motion (prograde and retrograde orbits) using the Sloan Digital Sky Survey (SDSS) data. From SDSS Data Release 7, we find 3515 isolated satellite systems of galaxies at z < 0.03 that contain 8904 satellite galaxies. Using this sample, we construct a catalog of 635 satellites associated with 215 host galaxies whose spin directions are determined by our inspection of the SDSS color images and/or by spectroscopic observations in the literature. We divide satellite galaxies into prograde and retrograde orbit subsamples depending on their orbital motion with respect to the spin direction of the host. We find that the number of galaxies in prograde orbit is nearly equal to that of retrograde orbit galaxies: the fraction of satellites in prograde orbit is 50% {+-} 2%. The velocity distribution of satellites with respect to their hosts is found to be almost symmetric: the median bulk rotation of satellites is -1 {+-} 8 km s{sup -1}. It is found that the radial distribution of early-type satellites in prograde orbit is strongly concentrated toward the host while that of retrograde ones shows much less concentration. We also find the orbital speed of late-type satellites in prograde orbit increases as the projected distance to the host (R) decreases while the speed decreases for those in retrograde orbit. At R less than 0.1 times the host virial radius (R < 0.1r{sub vir,host}), the orbital speed decreases in both prograde and retrograde orbit cases. Prograde satellites are on average fainter than retrograde satellites for both early and late morphological types. The u - r color becomes redder as R decreases for both prograde and retrograde orbit late-type satellites. The differences between prograde and retrograde orbit satellite galaxies may be attributed to their different origin or the different strength of physical processes that they have experienced through
Planetary Migration and Eccentricity and Inclination Resonances in Extrasolar Planetary Systems
NASA Astrophysics Data System (ADS)
Lee, Man Hoi; Thommes, E. W.
2007-07-01
The differential migration of two planets due to planet-disk interaction can result in capture into the 2:1 eccentricity-type resonances. Both the sequence of 2:1 eccentricity-type resonances that the system is driven through by continued migration and the possibility of a subsequent capture into the 4:2 inclination-type resonances are sensitive to the migration rate within the range expected for type II migration due to planet-disk interaction. If the migration rate is fast, the resonant pair can evolve into a family of 2:1 eccentricity-type resonances different from those found by Lee (2004). This new family has outer orbital eccentricity e2 > 0.4-0.5, asymmetric librations of both eccentricity-type mean-motion resonance variables, and orbits that intersect if they are exactly coplanar. Although this family exists for an inner-to-outer planet mass ratio m1/m2 > 0.2, it is possible to evolve into this family by fast migration only for m1/m2 > 2. Thommes & Lissauer (2003) have found that a capture into the 4:2 inclination resonances is possible only for m1/m2 < 2. We show that this capture is also possible for m1/m2 > 2 if the migration rate is slower than that adopted by Thommes & Lissauer. There is significant theoretical uncertainty in both the sign and the magnitude of the net effect of planet-disk interaction on the orbital eccentricity of a planet. If the eccentricity is damped on a timescale equal to or shorter than the migration timescale, the eccentricities may not be able to reach the values needed to enter either the new 2:1 eccentricity resonances or the inclination resonances. Thus the discovery of extrasolar planetary systems with certain combinations of mass ratio and 2:1 resonance geometry would place a constraint on the strength of eccentricity damping during migration, as well as on the rate of migration itself.
Retrogradation enthalpy does not always reflect the retrogradation behavior of gelatinized starch.
Wang, Shujun; Li, Caili; Zhang, Xiu; Copeland, Les; Wang, Shuo
2016-02-10
Starch retrogradation is a term used to define the process in which gelatinized starch undergoes a disorder-to-order transition. A thorough understanding of starch retrogradation behavior plays an important role in maintaining the quality of starchy foods during storage. By means of DSC, we have demonstrated for the first time that at low water contents, the enthalpy change of retrograded starch is higher than that of native starch. In terms of FTIR and Raman spectroscopic results, we showed that the molecular order of reheated retrograded starch samples is lower than that of DSC gelatinized starch. These findings have led us to conclude that enthalpy change of retrograded starch at low water contents involves the melting of recrystallized starch during storage and residual starch crystallites after DSC gelatinization, and that the endothermic transition of retrograded starch gels at low water contents does not fully represent the retrogradation behavior of starch. Very low or high water contents do not favor the occurrence of starch retrogradation.
Retrogradation enthalpy does not always reflect the retrogradation behavior of gelatinized starch
Wang, Shujun; Li, Caili; Zhang, Xiu; Copeland, Les; Wang, Shuo
2016-01-01
Starch retrogradation is a term used to define the process in which gelatinized starch undergoes a disorder-to-order transition. A thorough understanding of starch retrogradation behavior plays an important role in maintaining the quality of starchy foods during storage. By means of DSC, we have demonstrated for the first time that at low water contents, the enthalpy change of retrograded starch is higher than that of native starch. In terms of FTIR and Raman spectroscopic results, we showed that the molecular order of reheated retrograded starch samples is lower than that of DSC gelatinized starch. These findings have led us to conclude that enthalpy change of retrograded starch at low water contents involves the melting of recrystallized starch during storage and residual starch crystallites after DSC gelatinization, and that the endothermic transition of retrograded starch gels at low water contents does not fully represent the retrogradation behavior of starch. Very low or high water contents do not favor the occurrence of starch retrogradation. PMID:26860788
Formation of terrestrial planets in eccentric and inclined giant-planet systems
NASA Astrophysics Data System (ADS)
Sotiriadis, Sotiris; Libert, Anne-Sophie; Raymond, Sean
2016-10-01
The orbits of extrasolar planets are more various than the circular and coplanar ones of the Solar system. We study the impact of inclined and eccentric massive giant planets on the terrestrial planet formation process. The physical and orbital parameters of the giant planets considered in this study arise from n-body simulations of three giant planets in the late stage of the gas disc, under the combined action of Type II migration and planet-planet scattering. At the dispersal of the gas disc, the two- and three-planet systems interact then with an inner disc of planetesimals and planetary embryos. We discuss the mass and orbital parameters of the terrestrial planets formed by our simulations, as well as their water content. We also investigate how the disc of planetesimals and planetary embryos modifies the eccentric and inclined orbits of the giant planets.
Eccentric crank variable compression ratio mechanism
Lawrence, Keith Edward; Moser, William Elliott; Roozenboom, Stephan Donald; Knox, Kevin Jay
2008-05-13
A variable compression ratio mechanism for an internal combustion engine that has an engine block and a crankshaft is disclosed. The variable compression ratio mechanism has a plurality of eccentric disks configured to support the crankshaft. Each of the plurality of eccentric disks has at least one cylindrical portion annularly surrounded by the engine block. The variable compression ratio mechanism also has at least one actuator configured to rotate the plurality of eccentric disks.
Origin of the peculiar eccentricity distribution of the inner cold Kuiper belt
NASA Astrophysics Data System (ADS)
Morbidelli, A.; Gaspar, H. S.; Nesvorny, D.
2014-04-01
Dawson and Murray-Clay (Dawson and Murray-Clay [2012]. Astrophys. J., 750, 43) pointed out that the inner part of the cold population in the Kuiper belt (that with semi major axis a<43.5 AU) has orbital eccentricities significantly smaller than the limit imposed by stability constraints. Here, we confirm their result by looking at the orbital distribution and stability properties in proper element space. We show that the observed distribution could have been produced by the slow sweeping of the 4/7 mean motion resonance with Neptune that accompanied the end of Neptune’s migration process. The orbital distribution of the hot Kuiper belt is not significantly affected in this process, for the reasons discussed in the main text. Therefore, the peculiar eccentricity distribution of the inner cold population cannot be unequivocally interpreted as evidence that the cold population formed in situ and was only moderately excited in eccentricity; it can simply be the signature of Neptune’s radial motion, starting from a moderately eccentric orbit. We discuss how this agrees with a scenario of giant planet evolution following a dynamical instability and, possibly, with the radial transport of the cold population.
Heartbeat Stars: A Class Of Tidally Excited Eccentric Binaries
NASA Astrophysics Data System (ADS)
Barclay, Thomas; Thompson, S. E.; Mullally, F.; Everett, M.; Howell, S. B.; Still, M.; Christiansen, J. L.; Rowe, J.; Kurtz, D. W.; Hambleton, K.
2012-01-01
We have discovered a class of eccentric binary systems undergoing dynamic tidal distortions and tidally induced pulsations in the Kepler data. Each has a uniquely shaped light curve that is characterized by periodic brightening or variability at time scales of 4-20 days which is frequently accompanied by shorter period oscillations. We can explain the dominant features of the entire class with changing tidal forces that occur in close, eccentric binary systems. In this case the large variety of light curve shapes arises from viewing systems at different angles. A hypothesis that is confirmed with radial velocity measurements that show an eccentric orbit. Prior to the discovery of these 17 new systems, KOI-54 was the only system with direct detection of these dynamic tides and tidally induced oscillations. While significant work remains to include all the physics required to accurately model these systems and begin to understand how tidal effects influence the system, in this presentation we present preliminary fits to the light curves and describe the properties of this class of stars as a whole.
Dynamics of eccentric disks with application to superhump binaries
NASA Astrophysics Data System (ADS)
Lubow, Stephen H.
1992-12-01
Three related problems of interest to models of eccentric disks in close binary systems are investigated. For the 3:1 resonance model of superhump binaries, it is found that nonresonant stresses from the m = 2 tidal potential component phi2 weaken the tidal eccentric instability mechanism at the 3:1 resonance driven by phi3. The phi2 potential attempts to expel material from the 3:1 resonance, leading to a lower density there and hence lower resonant angular momentum flux. This process can be understood in terms of the effects of orbit crossing in limiting the radial extent of the disk. Disk precession is found to be due to a combination of the effects of pressure waves in the eccentric mode resonant wave stresses and direct axisymmetric tidal forces from the companion. Wave stresses give rise to a time-varying precession rate. The observed secular increase in the superhump period during superoutburst can be explained as due to a slight ongoing contraction of the disk by about 10-15 percent in radius.
The origin of the eccentricity of the hot Jupiter in CI Tau
NASA Astrophysics Data System (ADS)
Rosotti, G. P.; Booth, R. A.; Clarke, C. J.; Teyssandier, J.; Facchini, S.; Mustill, A. J.
2017-01-01
Following the recent discovery of the first radial velocity planet in a star still possessing a protoplanetary disc (CI Tau), we examine the origin of the planet's eccentricity (e ˜0.3). We show through long time-scale (105 orbits) simulations that the planetary eccentricity can be pumped by the disc, even when its local surface density is well below the threshold previously derived from short time-scale integrations. We show that the disc may be able to excite the planet's orbital eccentricity in <1 Myr for the system parameters of CI Tau. We also perform two-planet scattering experiments and show that alternatively the observed planet may plausibly have acquired its eccentricity through dynamical scattering of a migrating lower mass planet, which has either been ejected from the system or swallowed by the central star. In the latter case the present location and eccentricity of the observed planet can be recovered if it was previously stalled within the disc's magnetospheric cavity.
Orbits of Two-Body Problem From the Lenz Vector
ERIC Educational Resources Information Center
Caplan, S.; And Others
1978-01-01
Obtains the orbits with reference to the center of mass of two bodies under mutual universe square law interaction by use of the eccentricity vector which is equivalent to the Lenz vector within a numerical factor. (Author/SL)
NASA Astrophysics Data System (ADS)
Higuchi, A.; Ida, S.
2016-01-01
We have investigated the dependence of the prograde/retrograde temporary capture of asteroids by a planet on their original heliocentric semimajor axes through analytical arguments and numerical orbital integrations in order to discuss the origins of irregular satellites of giant planets. We found that capture is mostly retrograde for the asteroids near the planetary orbit and is prograde for those from farther orbits. An analytical investigation reveals the intrinsic dynamics of these dependences and gives boundary semimajor axes for the change in prograde/retrograde capture. The numerical calculations support the idea of deriving analytical formulae and confirm their dependence. Our numerical results show that the capture probability is much higher for bodies from the inner region than for outer ones. These results imply that retrograde irregular satellites of Jupiter are most likely captured bodies from the nearby orbits of Jupiter that may have the same origin as Trojan asteroids, while prograde irregular satellites originate from far inner regions such as the main-belt asteroid region.
Constant orbit elements under the third body effect
NASA Astrophysics Data System (ADS)
Condoleo, Ennio; Circi, Christian; Ortore, Emiliano
2017-03-01
An analysis to determine solutions with constant orbit elements has been carried out through a vectorial formulation of the perturbation equations, under the long-term influence due to the attraction of a disturbing body moving over an inclined elliptical orbit. After having gained a frozen orbital plane by assuming an orbital pole parallel or perpendicular to the perturbing body pole, the feasibility to get a frozen condition also on eccentricity or argument of pericentre has been demonstrated and several solutions have been proposed. Moreover, when the orbital pole is perpendicular to the perturbing body pole, a prime integral of motion, linking orbit eccentricity and argument of pericentre, has been retrieved. This prime integral has permitted the identification of solutions characterised by slow variations of eccentricity. A study to obtain orbits at constant eccentricity or argument of pericentre has also been carried out, regardless of the orbital plane evolution. This has highlighted how, while the solutions with a frozen apsidal line have to be determined by means of numerical methods, not pursued in this paper, the ones characterised by a null variation of eccentricity can be retrieved analytically. Examples, for a probe orbiting Mercury, have also been presented.
NASA Astrophysics Data System (ADS)
Dawson, Rebekah I.; Johnson, John Asher
2012-09-01
Exoplanet orbital eccentricities offer valuable clues about the history of planetary systems. Eccentric, Jupiter-sized planets are particularly interesting: they may link the "cold" Jupiters beyond the ice line to close-in hot Jupiters, which are unlikely to have formed in situ. To date, eccentricities of individual transiting planets primarily come from radial-velocity measurements. Kepler has discovered hundreds of transiting Jupiters spanning a range of periods, but the faintness of the host stars precludes radial-velocity follow-up of most. Here, we demonstrate a Bayesian method of measuring an individual planet's eccentricity solely from its transit light curve using prior knowledge of its host star's density. We show that eccentric Jupiters are readily identified by their short ingress/egress/total transit durations—part of the "photoeccentric" light curve signature of a planet's eccentricity—even with long-cadence Kepler photometry and loosely constrained stellar parameters. A Markov Chain Monte Carlo exploration of parameter posteriors naturally marginalizes over the periapse angle and automatically accounts for the transit probability. To demonstrate, we use three published transit light curves of HD 17156 b to measure an eccentricity of e = 0.71+0.16 - 0.09, in good agreement with the discovery value e = 0.67 ± 0.08 based on 33 radial-velocity measurements. We present two additional tests using Kepler data. In each case, the technique proves to be a viable method of measuring exoplanet eccentricities and their confidence intervals. Finally, we argue that this method is the most efficient, effective means of identifying the extremely eccentric, proto-hot Jupiters predicted by Socrates et al.
Process for forming retrograde profiles in silicon
Weiner, K.H.; Sigmon, T.W.
1996-10-15
A process is disclosed for forming retrograde and oscillatory profiles in crystalline and polycrystalline silicon. The process consisting of introducing an n- or p-type dopant into the silicon, or using prior doped silicon, then exposing the silicon to multiple pulses of a high-intensity laser or other appropriate energy source that melts the silicon for short time duration. Depending on the number of laser pulses directed at the silicon, retrograde profiles with peak/surface dopant concentrations which vary are produced. The laser treatment can be performed in air or in vacuum, with the silicon at room temperature or heated to a selected temperature.
Process for forming retrograde profiles in silicon
Weiner, Kurt H.; Sigmon, Thomas W.
1996-01-01
A process for forming retrograde and oscillatory profiles in crystalline and polycrystalline silicon. The process consisting of introducing an n- or p-type dopant into the silicon, or using prior doped silicon, then exposing the silicon to multiple pulses of a high-intensity laser or other appropriate energy source that melts the silicon for short time duration. Depending on the number of laser pulses directed at the silicon, retrograde profiles with peak/surface dopant concentrations which vary from 1-1e4 are produced. The laser treatment can be performed in air or in vacuum, with the silicon at room temperature or heated to a selected temperature.
Planetary Migration and Eccentricity and Inclination Resonances in Extrasolar Planetary Systems
NASA Astrophysics Data System (ADS)
Lee, M. H.; Thommes, E. W.
2004-11-01
The differential migration of two planets due to planet-disk interaction can result in capture into the 2:1 eccentricity-type resonances. Both the sequence of 2:1 eccentricity-type resonances that the system is driven through by continued migration and the possibility of a subsequent capture into the 4:2 inclination-type resonances are sensitive to the migration rate within the range expected for type II migration due to planet-disk interaction. If the migration rate is fast, the resonant pair can evolve into a family of 2:1 eccentricity-type resonances different from those found by Lee (2004). This new family has outer orbital eccentricity e2 ⪆ 0.4--0.5, asymmetric librations of both eccentricity-type mean-motion resonance variables, and orbits that intersect if they are exactly coplanar. Although this family exists for an inner-to-outer planet mass ratio m1}/m{2 ⪆ 0.2, it is possible to evolve into this family by fast migration only for m1}/m{2 ⪆ 2. Thommes & Lissauer (2003) have found that a capture into the 4:2 inclination resonances is possible only for m1}/m{2 ⪉ 2. We show that this capture is also possible for m1}/m{2 ⪆ 2 if the migration rate is slightly slower than that adopted by Thommes & Lissauer. There is significant theoretical uncertainty in both the sign and the magnitude of the net effect of planet-disk interaction on the orbital eccentricity of a planet. If the eccentricity is damped on a timescale equal to or shorter than the migration timescale, e2 may not be able to reach the values needed to enter either the new 2:1 eccentricity resonances or the inclination resonances for m1}/m{2 ⪆ 2. Thus, if future observations were to reveal such a combination of mass ratio and resonant configuration, it would place a constraint on the strength of eccentricity damping during migration, as well as on the rate of the migration itself.
Planetary Migration and Eccentricity and Inclination Resonances in Extrasolar Planetary Systems
NASA Astrophysics Data System (ADS)
Lee, Man Hoi; Thommes, Edward W.
2009-09-01
The differential migration of two planets due to planet-disk interaction can result in capture into the 2:1 eccentricity-type mean-motion resonances. Both the sequence of 2:1 eccentricity resonances that the system is driven through by continued migration and the possibility of a subsequent capture into the 4:2 inclination resonances are sensitive to the migration rate within the range expected for type II migration due to planet-disk interaction. If the migration rate is fast, the resonant pair can evolve into a family of 2:1 eccentricity resonances different from those found by Lee. This new family has outer orbital eccentricity e 2 gsim 0.4-0.5, asymmetric librations of both eccentricity resonance variables, and orbits that intersect if they are exactly coplanar. Although this family exists for an inner-to-outer planet mass ratio m 1/m 2 gsim 0.2, it is possible to evolve into this family by fast migration only for m 1/m 2 gsim 2. Thommes and Lissauer have found that a capture into the 4:2 inclination resonances is possible only for m 1/m 2 lsim 2. We show that this capture is also possible for m 1/m 2 gsim 2 if the migration rate is slightly slower than that adopted by Thommes and Lissauer. There is significant theoretical uncertainty in both the sign and the magnitude of the net effect of planet-disk interaction on the orbital eccentricity of a planet. If the eccentricity is damped on a timescale comparable to or shorter than the migration timescale, e 2 may not be able to reach the values needed to enter either the new 2:1 eccentricity resonances or the 4:2 inclination resonances. Thus, if future observations of extrasolar planetary systems were to reveal certain combinations of mass ratio and resonant configuration, they would place a constraint on the strength of eccentricity damping during migration, as well as on the rate of the migration itself.
Eccentric Exercise: Physiological Characteristics and Acute Responses.
Douglas, Jamie; Pearson, Simon; Ross, Angus; McGuigan, Mike
2017-04-01
An eccentric contraction involves the active lengthening of muscle under an external load. The molecular and neural mechanisms underpinning eccentric contractions differ from those of concentric and isometric contractions and remain less understood. A number of molecular theories have been put forth to explain the unexplained observations during eccentric contractions that deviate from the predictions of the established theories of muscle contraction. Postulated mechanisms include a strain-induced modulation of actin-myosin interactions at the level of the cross-bridge, the activation of the structural protein titin, and the winding of titin on actin. Accordingly, neural strategies controlling eccentric contractions also differ with a greater, and possibly distinct, cortical activation observed despite an apparently lower activation at the level of the motor unit. The characteristics of eccentric contractions are associated with several acute physiological responses to eccentrically-emphasised exercise. Differences in neuromuscular, metabolic, hormonal and anabolic signalling responses during, and following, an eccentric exercise bout have frequently been observed in comparison to concentric exercise. Subsequently, the high levels of muscular strain with such exercise can induce muscle damage which is rarely observed with other contraction types. The net result of these eccentric contraction characteristics and responses appears to be a novel adaptive signal within the neuromuscular system.
A TIME-DEPENDENT RADIATIVE MODEL FOR THE ATMOSPHERE OF THE ECCENTRIC EXOPLANETS
Iro, N.; Deming, L. D. E-mail: leo.d.deming@nasa.go
2010-03-20
We present a time-dependent radiative model for the atmosphere of extrasolar planets that takes into account the eccentricity of their orbit. In addition to the modulation of stellar irradiation by the varying planet-star distance, the pseudo-synchronous rotation of the planets may play a significant role. We include both of these time-dependent effects when modeling the planetary thermal structure. We investigate the thermal structure and spectral characteristics for time-dependent stellar heating for two highly eccentric planets. Finally, we discuss observational aspects for those planets suitable for Spitzer measurements and investigate the role of the rotation rate.
Eccentricity distribution in the main asteroid belt
NASA Astrophysics Data System (ADS)
Malhotra, Renu; Wang, Xianyu
2017-03-01
The observationally complete sample of the main belt asteroids now spans more than two orders of magnitude in size and numbers more than 64 000 (excluding collisional family members). We undertook an analysis of asteroids' eccentricities and their interpretation with simple physical models. We find that a century old conclusion that the asteroids' eccentricities follow a Rayleigh distribution holds for the osculating eccentricities of large asteroids, but the proper eccentricities deviate from a Rayleigh distribution; there is a deficit of eccentricities smaller than ∼0.1 and an excess of larger eccentricities. We further find that the proper eccentricities do not depend significantly on asteroid size but have strong dependence on heliocentric distance; the outer asteroid belt follows a Rayleigh distribution, but the inner belt is strikingly different. Eccentricities in the inner belt can be modelled as a vector sum of a primordial eccentricity vector of random orientation and magnitude drawn from a Rayleigh distribution of parameter ∼0.06, and an excitation of random phase and magnitude ∼0.13. These results imply that when a late dynamical excitation of the asteroids occurred, it was independent of asteroid size and was stronger in the inner belt than in the outer belt. We discuss implications for the primordial asteroid belt and suggest that the observationally complete sample size of main belt asteroids is large enough that more sophisticated model-fitting of the eccentricities is warranted and could serve to test alternative theoretical models of the dynamical excitation history of asteroids and its links to the migration history of the giant planets.
Fundamental parameters and origin of the very eccentric binary 41 Dra
NASA Astrophysics Data System (ADS)
Tokovinin, A.; Balega, Y. Y.; Pluzhnik, E. A.; Shatsky, N. I.; Gorynya, N. A.; Weigelt, G.
2003-10-01
The evolutionary status and origin of the most eccentric known binary in a quadruple system, 41 Dra (e=0.9754, period 3.413 yr), are discussed. New observations include the much improved combined speckle-interferometric orbit, resolved photometry of the components and their spectroscopic analysis. The age of the system is 2.5 +/- 0.2 Gyr; all four components are likely coeval. The high eccentricity of the orbit together with known age and masses provide a constraint on the tidal circularization theory: it seems that the eccentric orbit survived because the convective zones of the F-type dwarfs were very thin. Now as the components of 41 Dra are leaving the Main Sequence, their increased interaction at each periastron passage may result in detectable changes in period and eccentricity. Tables 1, 2, and 3 are 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/409/245
The Influence of Eccentricity Cycles on Exoplanet Habitability
NASA Astrophysics Data System (ADS)
Baskin, N. J. K.; Fabrycky, D. C.; Abbot, D. S.
2015-12-01
In our search for habitable exoplanets, it is important to understand how planetary habitability is influenced by orbital configurations that differ from those of the terrestrial planets in our Solar system. In particular, observational surveys have revealed the prevalence of planetary systems around binary stars. Within these systems, the gravitational influence of a companion star can induce libration in the eccentricity of the planet's orbit (referred to as Kozai Cycles) on timescales as short as thousands of years. The resulting fluctuations in stellar flux at the top of the atmosphere can potentially induce dramatic variations in surface temperatures, with direct implications for the planet's habitability prospects. We investigate this research problem using two steps. First, we utilize the MERCURY N-body integrator in order to calculate the eccentricity of a hypothetical Earth-analogue under the gravitational influence of a stellar companion. Second, we run a coupled Global Climate Model (GCM) at various stages of a cycle provided by the MERCURY runs in order to examine if the increase in insolation renders the planet uninhabitable. This work will allow us to better understand how Kozai cycles influence the boundaries of a planet's habitable zone.
SECULAR ORBITAL EVOLUTION OF COMPACT PLANET SYSTEMS
Zhang, Ke; Hamilton, Douglas P.; Matsumura, Soko E-mail: soko@astro.umd.edu
2013-11-20
Recent observations have shown that at least some close-in exoplanets maintain eccentric orbits despite tidal circularization timescales that are typically much shorter than stellar ages. We explore gravitational interactions with a more distant planetary companion as a possible cause of these unexpected non-zero eccentricities. For simplicity, we focus on the evolution of a planar two-planet system subject to slow eccentricity damping and provide an intuitive interpretation of the resulting long-term orbital evolution. We show that dissipation shifts the two normal eigenmode frequencies and eccentricity ratios of the standard secular theory slightly, and we confirm that each mode decays at its own rate. Tidal damping of the eccentricities drives orbits to transition relatively quickly between periods of pericenter circulation and libration, and the planetary system settles into a locked state in which the pericenters are nearly aligned or nearly anti-aligned. Once in the locked state, the eccentricities of the two orbits decrease very slowly because of tides rather than at the much more rapid single-planet rate, and thus eccentric orbits, even for close-in planets, can often survive much longer than the age of the system. Assuming that an observed close-in planet on an elliptical orbit is apsidally locked to a more distant, and perhaps unseen companion, we provide a constraint on the mass, semi-major axis, and eccentricity of the companion. We find that the observed two-planet system HAT-P-13 might be in just such an apsidally locked state, with parameters that obey our constraint reasonably well. We also survey close-in single planets, some with and some without an indication of an outer companion. None of the dozen systems that we investigate provides compelling evidence for unseen companions. Instead, we suspect that (1) orbits are in fact circular, (2) tidal damping rates are much slower than we have assumed, or (3) a recent event has excited these
Effects of the eccentricity of the primaries in powered Swing-By maneuvers
NASA Astrophysics Data System (ADS)
Ferreira, Alessandra F. S.; Prado, Antônio F. B. A.; Winter, Othon C.; Santos, Denilson P. S.
2017-04-01
The present paper studies the powered Swing-By maneuver when performed in an elliptical system of primaries. It means that there is a spacecraft travelling in a system governed by the gravity fields of two bodies that are in elliptical orbits around their center of mass. The paper particularly analyzes the effects of the parameters relative to the Swing-By (Vinf-,rp, ψ), the orbit of the secondary body around the primary one (e, ν) and the elements that specify the impulse applied (δV, α) to the spacecraft. The impulse is applied when the spacecraft passes by the periapsis of its orbit around the body, where it performs the Swing-By, with different magnitudes and directions. The inclusion of the orbital eccentricity of the primaries in this problem makes it closer to reality, considering that there are many known systems with eccentricities different from zero. In particular, there are several moons in the Solar System which orbits are not circular, as well as some smaller bodies, like the dwarf planet Haumea and its moons, which have eccentricities of 0.25 or even larger. The behavior of the energy variation of the spacecraft is shown in details, as well as the cases where captures and collisions occur. The results show the conditions that optimize this maneuver, according to some given parameters, and how much can be obtained in terms of gains or losses of energy using the best conditions found by the algorithm developed here.
Studies of retrograde memory: A long-term view
Warrington, Elizabeth K.
1996-01-01
Studies of retrograde amnesia are reviewed. First, the issues of temporal gradients of retrograde amnesia are discussed. Second, the question of the anatomical substrates of this syndrome are considered. Finally, some evidence for fractionation of different classes of memoranda within the retrograde time period are presented. PMID:8942966
Orbital Interactions in Extrasolar Planetary Systems
NASA Astrophysics Data System (ADS)
Zhang, Ke; Hamilton, D. P.
2007-07-01
We investigate the long-term orbital evolution of exoplanets in a planar two-planet system, subject to an applied dissipative force. Without dissipation, the orbits of the two planets oscillate with two fundamental eigenmodes due to their secular gravitational interactions: a slow mode in which the two pericenters are aligned and a fast mode in which they are anti-aligned. In each mode, the two orbits precess as a rigid body at a rate determined purely by planet masses and orbital semi-major axes. In addition, the ratio between the two eccentricities is fixed. Any system of two planets can be represented by a linear combination of these two modes, with initial conditions (eccentricities and longitudes of pericenters) determining the precise mix. When eccentricities are slowly damped by perturbations such as planetary tides or disk interactions, the mode frequencies and eccentricity ratios shift slightly, and the two modes decay separately at different rates. We solve for these rates analytically -- usually one mode damps much faster than the other, and the system ends up locked in either an apsidally aligned or anti-aligned state. Numerical integrations of both the first-order secular equations and direct N-body equations show close agreement with our analytical results. This mechanism provides a possible explanation for the nonzero eccentricities of "hot-Jupiters", assuming that they have companions in more eccentric orbits. Some perturbations may also cause planetary migration. For slow migration rates, adiabatic invariants exist, which are functions of mode parameters (frequencies and amplitudes). Similar invariants can be found for the case where mass loss is important. Through analytical study of these integrals, we seek to explain the diverse appearance of planetary orbits.
Highly eccentric Kozai mechanism and gravitational-wave observation for neutron-star binaries.
Seto, Naoki
2013-08-09
The Kozai mechanism for a hierarchical triple system could reduce the merger time of inner eccentric binary emitting gravitational waves (GWs) and has been qualitatively explained with the secular theory that is derived by averaging short-term orbital revolutions. However, with the secular theory, the minimum value of the inner pericenter distance could be excessively limited by the averaging operation. Compared with traditional predictions, the actual evolution of an eccentric inner binary could be accompanied by (i) a higher characteristic frequency of the pulselike GWs around its pericenter passages and (ii) a larger residual eccentricity at its final inspiral phase. These findings would be important for GW astronomy with the forthcoming advanced detectors.
Frozen orbits in the J2 + J3 problem. [orbital mechanics
NASA Technical Reports Server (NTRS)
Kiedron, Krystyna; Cook, Richard
1992-01-01
An analytical derivation of frozen orbit eccentricities and their location over the range of possible orbital inclinations in the J2 + J3 problem is presented. A gravitational field with only J2 and J3 terms is considered, because the equation defining frozen orbits in this field is an algebraic equation of the third order and an analytical formula for roots of this equation exists. An equation for the frozen orbit eccentricity is derived in a convenient form using only two independent parameters: the inclination and a parameter which is the product of the ratio of the radius of the central body to the orbital semimajor axis and the ratio of the J2 and J3 coefficients. The equation is solved, and, on the basis of its roots, frozen orbits in the J2 + J3 problem are classified.
Doppler-guided retrograde catheterization system
NASA Astrophysics Data System (ADS)
Frazin, Leon J.; Vonesh, Michael J.; Chandran, Krishnan B.; Khasho, Fouad; Lanza, George M.; Talano, James V.; McPherson, David D.
1991-05-01
The purpose of this study was to investigate a Doppler guided catheterization system as an adjunctive or alternative methodology to overcome the disadvantages of left heart catheterization and angiography. These disadvantages include the biological effects of radiation and the toxic and volume effects of iodine contrast. Doppler retrograde guidance uses a 20 MHz circular pulsed Doppler crystal incorporated into the tip of a triple lumen multipurpose catheter and is advanced retrogradely using the directional flow information provided by the Doppler waveform. The velocity detection limits are either 1 m/second or 4 m/second depending upon the instrumentation. In a physiologic flow model of the human aortic arch, multiple data points revealed a positive wave form when flow was traveling toward the catheter tip indicating proper alignment for retrograde advancement. There was a negative wave form when flow was traveling away from the catheter tip if the catheter was in a branch or bent upon itself indicating improper catheter tip position for retrograde advancement. In a series of six dogs, the catheter was able to be accurately advanced from the femoral artery to the left ventricular chamber under Doppler signal guidance without the use of x-ray. The potential applications of a Doppler guided retrograde catheterization system include decreasing time requirements and allowing safer catheter guidance in patients with atherosclerotic vascular disease and suspected aortic dissection. The Doppler system may allow left ventricular pressure monitoring in the intensive care unit without the need for x-ray and it may allow left sided contrast echocardiography. With pulse velocity detection limits of 4 m/second, this system may allow catheter direction and passage into the aortic root and left ventricle in patients with aortic stenosis. A modification of the Doppler catheter may include transponder technology which would allow precise catheter tip localization once the
A new Orbit for Comet C/1819 N1 (Great Comet of 1819)
NASA Astrophysics Data System (ADS)
Branham, R. L., Jr.
2017-04-01
A new orbit is calculated for Comet C/1819 N1 (Great Comet of 1819) to replace Peck's parabolic orbit of 1906. The orbit is based upon 402 observations in right ascension and 294 in declination, made between July and October of 1819. The orbit is a high eccentricity ellipse.
ORBITS AROUND BLACK HOLES IN TRIAXIAL NUCLEI
Merritt, David; Vasiliev, Eugene E-mail: eugvas@lpi.ru
2011-01-10
We discuss the properties of orbits within the influence sphere of a supermassive black hole (BH), in the case that the surrounding star cluster is non-axisymmetric. There are four major orbit families; one of these, the pyramid orbits, have the interesting property that they can approach arbitrarily closely to the BH. We derive the orbit-averaged equations of motion and show that in the limit of weak triaxiality, the pyramid orbits are integrable: the motion consists of a two-dimensional libration of the major axis of the orbit about the short axis of the triaxial figure, with eccentricity varying as a function of the two orientation angles and reaching unity at the corners. Because pyramid orbits occupy the lowest angular momentum regions of phase space, they compete with collisional loss cone repopulation and with resonant relaxation (RR) in supplying matter to BHs. General relativistic advance of the periapse dominates the precession for sufficiently eccentric orbits, and we show that relativity imposes an upper limit to the eccentricity: roughly the value at which the relativistic precession time is equal to the time for torques to change the angular momentum. We argue that this upper limit to the eccentricity should also apply to evolution driven by RR, with potentially important consequences for the rate of extreme-mass-ratio inspirals in low-luminosity galaxies. In giant galaxies, we show that capture of stars on pyramid orbits can dominate the feeding of BHs, at least until such a time as the pyramid orbits are depleted; however this time can be of order a Hubble time.
Ultrasonic guided waves in eccentric annular pipes
Pattanayak, Roson Kumar; Balasubramaniam, Krishnan; Rajagopal, Prabhu
2014-02-18
This paper studies the feasibility of using ultrasonic guided waves to rapidly inspect tubes and pipes for possible eccentricity. While guided waves are well established in the long range inspection of structures such as pipes and plates, studies for more complex cross sections are limited and analytical solutions are often difficult to obtain. Recent developments have made the Semi Analytical Finite Element (SAFE) method widely accessible for researchers to study guided wave properties in complex structures. Here the SAFE method is used to study the effect of eccentricity on the modal structures and velocities of lower order guided wave modes in thin pipes of diameters typically of interest to the industry. Results are validated using experiments. The paper demonstrates that even a small eccentricity in the pipe can strongly affect guided wave mode structures and velocities and hence shows potential for pipe eccentricity inspection.
Conjugate natural convection between horizontal eccentric cylinders
NASA Astrophysics Data System (ADS)
Nasiri, Davood; Dehghan, Ali Akbar; Hadian, Mohammad Reza
2017-03-01
This study involved the numerical investigation of conjugate natural convection between two horizontal eccentric cylinders. Both cylinders were considered to be isothermal with only the inner cylinder having a finite wall thickness. The momentum and energy equations were discretized using finite volume method and solved by employing SIMPLER algorithm. Numerical results were presented for various solid-fluid conductivity ratios ( KR) and various values of eccentricities in different thickness of inner cylinder wall and also for different angular positions of inner cylinder. From the results, it was observed that in an eccentric case, and for KR < 10, an increase in thickness of inner cylinder wall resulted in a decrease in the average equivalent conductivity coefficient (overline{{K_{eq} }}); however, a KR > 10 value caused an increase in overline{{K_{eq} }}. It was also concluded that in any angular position of inner cylinder, the value of overline{{K_{eq} }} increased with increase in the eccentricity.
Retrograde transport on the COG railway.
Ungar, Daniel; Oka, Toshihiko; Krieger, Monty; Hughson, Frederick M
2006-02-01
The conserved oligomeric Golgi (COG) complex is essential for establishing and/or maintaining the structure and function of the Golgi apparatus. The Golgi apparatus, in turn, has a central role in protein sorting and glycosylation within the eukaryotic secretory pathway. As a consequence, COG mutations can give rise to human genetic diseases known as congenital disorders of glycosylation. We review recent results from studies of yeast, worm, fly and mammalian COG that provide evidence that COG might function in retrograde vesicular trafficking within the Golgi apparatus. This hypothesis explains the impact of COG mutations by postulating that they impair the retrograde flow of resident Golgi proteins needed to maintain normal Golgi structure and function.
Orbital Operations for Phobos and Deimos Exploration
NASA Technical Reports Server (NTRS)
Wallace, Mark S.; Parker, Jeffrey S.; Strange, Nathan J.; Grebow, Daniel
2012-01-01
One of the deep-space human exploration activities proposed for the post-Shuttle era is a mission to one of the moons of Mars, Phobos or Deimos. There are several options available to the mission architect for operations around these bodies. These options include distant retrograde orbits (DROs), Lagrange-point orbits such as halos and Lyapunov orbits, and fixed-point stationkeeping or "hovering." These three orbit options are discussed in the context of the idealized circular restricted three body problem, full-dynamics propagations, and a concept of operations. The discussion is focused on Phobos, but all results hold for Deimos
General relativity and satellite orbits
NASA Technical Reports Server (NTRS)
Rubincam, D. P.
1975-01-01
The general relativistic correction to the position of a satellite is found by retaining Newtonian physics for an observer on the satellite and introducing a potential. The potential is expanded in terms of the Keplerian elements of the orbit and substituted in Lagrange's equations. Integration of the equations shows that a typical earth satellite with small orbital eccentricity is displaced by about 17 cm. from its unperturbed position after a single orbit, while the periodic displacement over the orbit reaches a maximum of about 3 cm. The moon is displaced by about the same amounts. Application of the equations to Mercury gives a total displacement of about 58 km. after one orbit and a maximum periodic displacement of about 12 km.
NASA Astrophysics Data System (ADS)
Hauser, Heather M.; Marcy, Geoffrey W.
1999-03-01
The high orbital eccentricity of the planet around 16 Cygni B may have been induced by the companion star, 16 Cygni A, but only if the stellar binary has sufficiently small periastron distance. The long period of the stellar binary, ~3x10^4 yr, implies that less than 1% of the orbit has transpired since its first astrometric measurements in 1830. Therefore, we compute the orbit from the measured instantaneous velocity and position vectors, based on new precise Doppler and astrometric data, along with the Hipparcos parallax. The only unknown parameter is the separation between AB along the line of sight, constrained by the demand that the orbit be bound, which leads to a family of possible orbits for 16 Cygni AB. The physically plausible orbits have 18,200 yr
orbit is definitely eccentric, with e=0.54-0.96. All orbital parameters here are in approximate agreement with the previous computation by Romanenko. The new stellar binary orbit remains consistent with the possibility that perturbations from 16 Cygni A cause the eccentricity in the planet around 16 Cygni B. Recently a red point source has been detected 3.2" from 16 Cygni A, but its membership remains unknown (Trilling et al.). We assess its membership based on astrometry and velocities of 16 Cygni A. The point source is either a low-mass M dwarf separated by ~80 AU from component A or it is a higher mass star of perhaps ~0.5 M_solar, separated by at least 150 AU from 16 Cygni A-indeed possibly a background star. If the new companion is bound, 16 Cygni A and B never approach each other closer than ~500 AU, which diminishes the prospects that 16 Cygni A induces the eccentricity of the planet around 16 Cygni B.
Kepler Planet Masses and Eccentricities from Transit Timing Variations
NASA Astrophysics Data System (ADS)
Hadden, Sam; Lithwick, Yoram
2017-01-01
The Kepler mission’s census of transiting exoplanets has shown that planets between one and four times the radius of Earth with short orbital periods are extremely common. Given their small sizes, the properties of these planets can be difficult or impossible to constrain via radial velocity observations. Mutual gravitational interactions in multi-planet systems induce variations in the arrival times of planets’ transits. These variations can used to probe planets’ masses and eccentricities, which in turn constrain their compositions and formation histories. I will discuss the results of our analysis of the transit timing variations (TTVs) of 145 Kepler planets from 55 multi-planet systems. Bulk densities inferred from TTVs imply that many of these planets are covered in gaseous envelopes ranging from a few percent to ~20% of their total mass. Eccentricities in these systems are small but in a many instances definitively non-zero. These results support theoretical predictions for super-Earth/sub-Neptune planets accreting their envelopes from a depleting proto-planetary disk.
Secretly Eccentric: The Giant Planet and Activity Cycle of GJ 328
NASA Astrophysics Data System (ADS)
Robertson, Paul; Endl, Michael; Cochran, William D.; MacQueen, Phillip J.; Boss, Alan P.
2013-09-01
We announce the discovery of a ~2 Jupiter-mass planet in an eccentric 11 yr orbit around the K7/M0 dwarf GJ 328. Our result is based on 10 years of radial velocity (RV) data from the Hobby-Eberly and Harlan J. Smith telescopes at McDonald Observatory, and from the Keck Telescope at Mauna Kea. Our analysis of GJ 328's magnetic activity via the Na I D features reveals a long-period stellar activity cycle, which creates an additional signal in the star's RV curve with amplitude 6-10 m s-1. After correcting for this stellar RV contribution, we see that the orbit of the planet is more eccentric than suggested by the raw RV data. GJ 328b is currently the most massive, longest-period planet discovered around a low-mass dwarf.
SECRETLY ECCENTRIC: THE GIANT PLANET AND ACTIVITY CYCLE OF GJ 328
Robertson, Paul; Endl, Michael; Cochran, William D.; MacQueen, Phillip J.; Boss, Alan P.
2013-09-10
We announce the discovery of a {approx}2 Jupiter-mass planet in an eccentric 11 yr orbit around the K7/M0 dwarf GJ 328. Our result is based on 10 years of radial velocity (RV) data from the Hobby-Eberly and Harlan J. Smith telescopes at McDonald Observatory, and from the Keck Telescope at Mauna Kea. Our analysis of GJ 328's magnetic activity via the Na I D features reveals a long-period stellar activity cycle, which creates an additional signal in the star's RV curve with amplitude 6-10 m s{sup -1}. After correcting for this stellar RV contribution, we see that the orbit of the planet is more eccentric than suggested by the raw RV data. GJ 328b is currently the most massive, longest-period planet discovered around a low-mass dwarf.
Rational orbits around charged black holes
Misra, Vedant; Levin, Janna
2010-10-15
We show that all eccentric timelike orbits in Reissner-Nordstroem spacetime can be classified using a taxonomy that draws upon an isomorphism between periodic orbits and the set of rational numbers. By virtue of the fact that the rationals are dense, the taxonomy can be used to approximate aperiodic orbits with periodic orbits. This may help reduce computational overhead for calculations in gravitational wave astronomy. Our dynamical systems approach enables us to study orbits for both charged and uncharged particles in spite of the fact that charged particle orbits around a charged black hole do not admit a simple one-dimensional effective potential description. Finally, we show that comparing periodic orbits in the Reissner-Nordstroem and Schwarzschild geometries enables us to distinguish charged and uncharged spacetimes by looking only at the orbital dynamics.
Simple Theory of Geosynchronous-Orbit Perturbations
NASA Astrophysics Data System (ADS)
Kawase, Sei-Ichiro
A simple perturbation theory is introduced for modeling geosynchronous orbits. The theory uses diagrammatic representations of orbits, and derives the perturbations in a direct manner without using differential equations. Perturbations of major importance are derived, including satellite-longitude changes due to the earth’s asymmetric shape, orbital eccentricity increase due to the sun-radiation pressure, and orbital plane inclination due to the sun/moon attraction. The theory clarifies the physical/geometrical meaning of the perturbations while using minimal mathematical analysis.
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.
ATMOSPHERIC CIRCULATION OF ECCENTRIC HOT NEPTUNE GJ436b
Lewis, Nikole K.; Showman, Adam P.; Fortney, Jonathan J.; Marley, Mark S.; Freedman, Richard S.; Lodders, Katharina
2010-09-01
GJ436b is a unique member of the transiting extrasolar planet population being one of the smallest and least irradiated and possessing an eccentric orbit. Because of its size, mass, and density, GJ436b could plausibly have an atmospheric metallicity similar to Neptune (20-60 times solar abundances), which makes it an ideal target to study the effects of atmospheric metallicity on dynamics and radiative transfer in an extrasolar planetary atmosphere. We present three-dimensional atmospheric circulation models that include realistic non-gray radiative transfer for 1, 3, 10, 30, and 50 times solar atmospheric metallicity cases of GJ436b. Low metallicity models (1 and 3 times solar) show little day/night temperature variation and strong high-latitude jets. In contrast, higher metallicity models (30 and 50 times solar) exhibit day/night temperature variations and a strong equatorial jet. Spectra and light curves produced from these simulations show strong orbital phase dependencies in the 50 times solar case and negligible variations with orbital phase in the 1 times solar case. Comparisons between the predicted planet/star flux ratio from these models and current secondary eclipse measurements support a high metallicity atmosphere (30-50 times solar abundances) with disequilibrium carbon chemistry at play for GJ436b. Regardless of the actual atmospheric composition of GJ436b, our models serve to illuminate how metallicity influences the atmospheric circulation for a broad range of warm extrasolar planets.
Pulsed Accretion onto Eccentric and Circular Binaries
NASA Astrophysics Data System (ADS)
Muñoz, Diego J.; Lai, Dong
2016-08-01
We present numerical simulations of circumbinary accretion onto eccentric and circular binaries using the moving-mesh code AREPO. This is the first set of simulations to tackle the problem of binary accretion using a finite-volume scheme on a freely moving mesh, which allows for accurate measurements of accretion onto individual stars for arbitrary binary eccentricity. While accretion onto a circular binary shows bursts with period of ˜ 5 times the binary period P b, accretion onto an eccentric binary is predominantly modulated at the period ˜ 1{P}{{b}}. For an equal-mass circular binary, the accretion rates onto individual stars are quite similar to each other, following the same variable pattern in time. By contrast, for eccentric binaries, one of the stars can accrete at a rate 10-20 times larger than its companion. This “symmetry breaking” between the stars, however, alternates over timescales of order 200P b and can be attributed to a slowly precessing, eccentric circumbinary disk. Over longer timescales, the net accretion rates onto individual stars are the same, reaching a quasi-steady state with the circumbinary disk. These results have important implications for the accretion behavior of binary T Tauri stars and supermassive binary black holes.
Revised Orbits of Saturn's Small Inner Satellites
NASA Technical Reports Server (NTRS)
Jacobson, R. A.; Spitale, J.; Porco, C. C.; Beurle, K.; Cooper, N. J.; Evans, M. W.; Murray, C. D.
2007-01-01
We have updated the orbits of the small inner Saturnian satellites using additional Cassini imaging observations through 2007 March. Statistically significant changes from previously published values appear in the eccentricities and inclinations of Pan and Daphnis, but only small changes have been found in the estimated orbits of the other satellites. We have also improved our knowledge of the masses of Janus and Epimetheus as a result of their close encounter observed in early 2006.
Revised Orbits of Saturn's Small Inner Satellites
NASA Astrophysics Data System (ADS)
Jacobson, R. A.; Spitale, J.; Porco, C. C.; Beurle, K.; Cooper, N. J.; Evans, M. W.; Murray, C. D.
2008-01-01
We have updated the orbits of the small inner Saturnian satellites using additional Cassini imaging observations through 2007 March. Statistically significant changes from previously published values appear in the eccentricities and inclinations of Pan and Daphnis, but only small changes have been found in the estimated orbits of the other satellites. We have also improved our knowledge of the masses of Janus and Epimetheus as a result of their close encounter observed in early 2006.
Jumping Jupiter Can Explain Mercury’s Orbit
NASA Astrophysics Data System (ADS)
Roig, Fernando; Nesvorný, David; DeSouza, Sandro Ricardo
2016-04-01
The orbit of Mercury has large values of eccentricity and inclination that cannot be easily explained if this planet formed on a circular and coplanar orbit. Here, we study the evolution of Mercury’s orbit during the instability related to the migration of the giant planets in the framework of the jumping-Jupiter model. We found that some instability models are able to produce the correct values of Mercury’s eccentricity and inclination, provided that relativistic effects are included in the precession of Mercury’s perihelion. The orbital excitation is driven by the fast change of the normal oscillation modes of the system corresponding to the perihelion precession of Jupiter (for the eccentricity) and the nodal regression of Uranus (for the inclination).
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…
Limits on stellar companions to exoplanet host stars with eccentric planets
Kane, Stephen R.; Hinkel, Natalie R.; Howell, Steve B.; Horch, Elliott P.; Feng, Ying; Wright, Jason T.; Ciardi, David R.; Everett, Mark E.; Howard, Andrew W.
2014-04-20
Though there are now many hundreds of confirmed exoplanets known, the binarity of exoplanet host stars is not well understood. This is particularly true of host stars that harbor a giant planet in a highly eccentric orbit since these are more likely to have had a dramatic dynamical history that transferred angular momentum to the planet. Here we present observations of four exoplanet host stars that utilize the excellent resolving power of the Differential Speckle Survey Instrument on the Gemini North telescope. Two of the stars are giants and two are dwarfs. Each star is host to a giant planet with an orbital eccentricity >0.5 and whose radial velocity (RV) data contain a trend in the residuals to the Keplerian orbit fit. These observations rule out stellar companions 4-8 mag fainter than the host star at passbands of 692 nm and 880 nm. The resolution and field of view of the instrument result in exclusion radii of 0.''05-1.''4, which excludes stellar companions within several AU of the host star in most cases. We further provide new RVs for the HD 4203 system that confirm that the linear trend previously observed in the residuals is due to an additional planet. These results place dynamical constraints on the source of the planet's eccentricities, place constraints on additional planetary companions, and inform the known distribution of multiplicity amongst exoplanet host stars.
TOWARD A DETERMINISTIC MODEL OF PLANETARY FORMATION. VII. ECCENTRICITY DISTRIBUTION OF GAS GIANTS
Ida, S.; Lin, D. N. C.
2013-09-20
The ubiquity of planets and diversity of planetary systems reveal that planet formation encompasses many complex and competing processes. In this series of papers, we develop and upgrade a population synthesis model as a tool to identify the dominant physical effects and to calibrate the range of physical conditions. Recent planet searches have led to the discovery of many multiple-planet systems. Any theoretical models of their origins must take into account dynamical interactions between emerging protoplanets. Here, we introduce a prescription to approximate the close encounters between multiple planets. We apply this method to simulate the growth, migration, and dynamical interaction of planetary systems. Our models show that in relatively massive disks, several gas giants and rocky/icy planets emerge, migrate, and undergo dynamical instability. Secular perturbation between planets leads to orbital crossings, eccentricity excitation, and planetary ejection. In disks with modest masses, two or less gas giants form with multiple super-Earths. Orbital stability in these systems is generally maintained and they retain the kinematic structure after gas in their natal disks is depleted. These results reproduce the observed planetary mass-eccentricity and semimajor axis-eccentricity correlations. They also suggest that emerging gas giants can scatter residual cores to the outer disk regions. Subsequent in situ gas accretion onto these cores can lead to the formation of distant (∼> 30 AU) gas giants with nearly circular orbits.
The First Transmission Spectrum of an Eccentric Cool Jupiter
NASA Astrophysics Data System (ADS)
Huitson, Catherine
2012-10-01
The techniques of transmission/emission spectroscopy are at the forefront of the characterization of exoplanetary atmospheres, allowing for a direct determination of elemental abundances, chemistry and temperature-pressure profiles. Hot Jupiters have dominated such studies due to their large spectroscopic signals. Despite this well-studied sample of similar exoplanets, the measured spectra exhibit surprising diversity, a fact which remains poorly understood. Since the hotter gas giants are well-observed, advancing our understanding of exoplanetary atmospheres requires the multi-wavelength detection of transits for exoplanets residing in cooler temperature regimes. We propose the very first transit observations, from the optical to the near-infrared, of a moderately-irradiated { 650-960 K}, Jupiter-like exoplanet residing on an eccentric orbit {e=0.346}: HAT-P-17b. Besides being in a previously unobserved temperature regime, its eccentric orbit allows the atmosphere of HAT-P-17b to periodically cross the condensation curves of sodium and potassium, implying that these alkali metals exist in the gas phase at periapsis and condense out into clouds/hazes at apoapsis. Furthermore, the range of temperatures allow for the carbon budget to be based on comparable amounts of CO and CH4. Our proposed observations will determine if the spectral features of K I, Na I, CH4 and H2O are present or absent from the optical to the near-infrared, thereby allowing us to constrain elemental abundances and atmospheric temperatures. This first dataset of a unique transition object will provide an insightful compliment to existing transmission observations of hot Jupiters.
Highly inclined and eccentric massive planets. II. Planet-planet interactions during the disc phase
NASA Astrophysics Data System (ADS)
Sotiriadis, Sotiris; Libert, Anne-Sophie; Bitsch, Bertram; Crida, Aurélien
2017-02-01
Context. Observational evidence indicates that the orbits of extrasolar planets are more various than the circular and coplanar ones of the solar system. Planet-planet interactions during migration in the protoplanetary disc have been invoked to explain the formation of these eccentric and inclined orbits. However, our companion paper (Paper I) on the planet-disc interactions of highly inclined and eccentric massive planets has shown that the damping induced by the disc is significant for a massive planet, leading the planet back to the midplane with its eccentricity possibly increasing over time. Aims: We aim to investigate the influence of the eccentricity and inclination damping due to planet-disc interactions on the final configurations of the systems, generalizing previous studies on the combined action of the gas disc and planet-planet scattering during the disc phase. Methods: Instead of the simplistic K-prescription, our N-body simulations adopt the damping formulae for eccentricity and inclination provided by the hydrodynamical simulations of our companion paper. We follow the orbital evolution of 11 000 numerical experiments of three giant planets in the late stage of the gas disc, exploring different initial configurations, planetary mass ratios and disc masses. Results: The dynamical evolutions of the planetary systems are studied along the simulations, with a particular emphasis on the resonance captures and inclination-growth mechanisms. Most of the systems are found with small inclinations (≤ 10°) at the dispersal of the disc. Even though many systems enter an inclination-type resonance during the migration, the disc usually damps the inclinations on a short timescale. Although the majority of the multiple systems in our simulations are quasi-coplanar, 5% of them end up with high mutual inclinations (≥ 10°). Half of these highly mutually inclined systems result from two- or three-body mean-motion resonance captures, the other half being
Retrograde ejaculation, painful ejaculation and hematospermia
Parnham, Arie
2016-01-01
Although there has been an increased interest on premature ejaculation in the recent years, our understanding regarding the disorders of retrograde ejaculation, painful ejaculation and hematospermia remain limited. All three of these conditions require a keen clinical acumen and willingness to engage in thinking outside of the standard established treatment paradigm. The development of novel investigational techniques and treatments has led to progress in the management of these conditions symptoms; however, the literature almost uniformly is limited to small series and rare randomised trials. Further investigation and randomised controlled trials are needed for progress in these often challenging cases. PMID:27652230
Retrograde ejaculation, painful ejaculation and hematospermia.
Parnham, Arie; Serefoglu, Ege Can
2016-08-01
Although there has been an increased interest on premature ejaculation in the recent years, our understanding regarding the disorders of retrograde ejaculation, painful ejaculation and hematospermia remain limited. All three of these conditions require a keen clinical acumen and willingness to engage in thinking outside of the standard established treatment paradigm. The development of novel investigational techniques and treatments has led to progress in the management of these conditions symptoms; however, the literature almost uniformly is limited to small series and rare randomised trials. Further investigation and randomised controlled trials are needed for progress in these often challenging cases.
Skylab 1 rocket /1973-27B/ - Orbit determination and analysis
NASA Astrophysics Data System (ADS)
King-Hele, D. G.
1980-04-01
The paper analyzes Skylab 1 rocket orbit and describes the geopotential resonance, atmospheric rotation, and variations in eccentricity due to drag. The final stage rocket which projected Skylab into orbit itself entered a nearly circular orbit which was determined at 62 epochs, with the orbital accuracy in perigee height and orbital inclination of 90 km. As the orbit contracted under influence of air drag, it passed slowly through the 31:2 geopotential resonance, when the track over the earth repeats every 31 revolutions at intervals of 2 days. The variations in inclination and eccentricity during the resonance phase were analyzed to determine the atmospheric rotation rate; the eccentricity variations were compared with the predicted values for orbit contraction in an atmosphere with a strong day-to-night variation in density.
Unstable force analysis for induction motor eccentricity
NASA Astrophysics Data System (ADS)
Han, Xu; Palazzolo, Alan
2016-05-01
The increasing popularity of motors in machinery trains has led to an intensified interest in the forces they produce that may influence machinery vibration. Motor design typically assumes a uniform air gap, however in practice all motors operate with the rotor slightly displaced from the motor centerline in what is referred to as an eccentric position. Rotor center eccentricity can cause a radially unbalanced magnetic field when the motor is operating. This will results in both a radial force pulling the motor further away from the center, and a tangential force which can induce a vibration stability problem. In this paper, a magnetic equivalent circuit MEC modeling method is proposed to calculate both the radial and tangential motor eccentric force. The treatment of tangential force determination is rarely addressed, but it is very important for rotordynamic vibration stability evaluation. The proposed model is also coupled with the motor electric circuit model to provide capability for transient vibration simulations. FEM is used to verify the MEC model. A parametric study is performed on the motor radial and tangential eccentric forces. Also a Jeffcott rotor model is used to study the influence of the motor eccentric force on mechanical vibration stability and nonlinear behavior. Furthermore, a stability criteria for the bearing damping is provided. The motor radial and tangential eccentric forces are both curved fitted to include their nonlinearity in time domain transient simulation for both a Jeffcott rotor model and a geared machinery train with coupled torsional-lateral motion. Nonlinear motions are observed, including limit cycles and bifurcation induced vibration amplitude jumps.
A Third Exoplanetary System with Misaligned Orbital and Stellar Spin Axes
NASA Technical Reports Server (NTRS)
Johnosn, John A.; Winn, Joshua N.; Albrecht, Simon; Howard, Andrew W.; Marcy, Geoffrey W.; Gazak, J. Zachary
2009-01-01
We presented evidence that the WASP-14 exoplanetary system has misaligned orbital and stellar-rotational axes, with an angle of 33.1 plus or minus 7.4 degrees between their sky projections. At the time of this publication, WASP-14 was the third system known to have a significant spin-orbit misalignment, and all three systems had super- Jupiter planets and eccentric orbits. Therefore we hypothesized that the migration and subsequent orbital evolution of massive, eccentric exoplanets is somehow different from that of less massive close-in Jupiters, the majority of which have well-aligned orbits.
Concentric and eccentric shoulder rehabilitation biomechanics.
Kohles, S S; Gregorczyk, K N; Phillips, T C; Brody, L T; Orwin, I F; Vanderby, R
2007-04-01
The use of an impulse-momentum (IM) exercise technique was investigated for end-stage shoulder rehabilitation. The objectives of this study were to: (a) quantify the net shoulder joint forces and moments while using an IM system and (b) test the influence of gender and muscle loading type (concentric or eccentric) on kinetic and kinematic parameters. Fourteen healthy adults (eight males, six females) performed a repeated measures experiment on an instrumented device utilizing a cabled shuttle system. While maintaining 90 degrees of shoulder abduction and 90 degrees of elbow flexion, the subjects externally rotated their upper arm from 0 degrees to 90 degrees (concentric acceleration) and then internally rotated their upper arm back from 90 degrees to the 0 degrees position (eccentric deceleration). Shoulder joint forces and moments as well as rotational work and power were calculated using inverse dynamics (free-body forces and moments calculated at intersegmental joint centres). Overall concentric peak forces and moments were greater than eccentric peak forces and moments (P < 0.0001). Joint forces and moments reached a maximum during the initial phase of concentric loading (0 degrees to 45 degrees) compared with any other rotational position in the loading cycle (concentric 45 degrees to 90 degrees or eccentric 90 degrees to 0 degrees). The results also indicate that males experienced higher (P < 0.0001) average resultant peak joint forces (concentric 0 degrees to 45 degrees = 108.0 N and eccentric 90 degrees to 45 degrees = 87.2 N) than females (concentric 0 degrees to 45 degrees = 74.7 N and eccentric 45 degrees to 0 degrees = 56.0 N). In addition, males experienced higher (P < 0.0001) average resultant peak joint moments (concentric 0 degrees to 45 degrees = 30.4 N m and eccentric 45 degrees to 0 degrees = 21.0 N m) than females (concentric 0 degrees to 45 degrees = 19.7 N m and eccentric 45 degrees to 0 degrees = 12.8 N m).
NASA Astrophysics Data System (ADS)
Libert, A.-S.; Delsate, N.
2012-05-01
We study the dynamics of the 3D three-body problem of a small body moving under the attractions of a star and a giant planet which orbits the star on a much wider and elliptic orbit. In particular, we focus on the influence of an eccentric orbit of the outer perturber on the dynamics of a small highly inclined inner body. Our analytical study of the secular perturbations relies on the classical octupole Hamiltonian expansion (third-order theory in the ratio of the semimajor axes), as third-order terms are needed to consider the secular variations of the outer perturber and potential secular resonances between the arguments of the pericentre and/or longitudes of the node of both bodies. Short-period averaging and node reduction (by adoption of the Laplace plane reference frame) reduce the problem to two degrees of freedom. The 4D dynamics is analysed through representative planes which identify the main equilibria of the problem. As in the circular problem (i.e. perturber on a circular orbit), the 'Kozai-bifurcated' equilibria play a major role in the dynamics of an inner body on a quasi-circular orbit: its eccentricity variations are very limited for mutual inclination between the orbital planes smaller than ˜40°, while they become large and chaotic for higher mutual inclination. Particular attention is also given to a region around 35° of mutual inclination, detected numerically by Funk et al. and consisting of long-time stable and particularly low-eccentricity orbits of the small body. Using a 12th-order Hamiltonian expansion in eccentricities and inclinations, in particular its action-angle formulation obtained by Lie transforms from Libert & Henrard, we show that this region presents an equality of two fundamental frequencies and can be regarded as a secular resonance. Our results also apply to binary star systems where a planet is revolving around one of the two stars.
Subtrochanteric fractures after retrograde femoral nailing
Mounasamy, Varatharaj; Mallu, Sathya; Khanna, Vishesh; Sambandam, Senthil
2015-01-01
Secondary fractures around femoral nails placed for the management of hip fractures are well known. We report, two cases of a fracture of the femur at the interlocking screw site in the subtrochanteric area after retrograde femoral nailing of a femoral shaft fracture. Only a few reports in the existing literature have described these fractures. Two young men after sustaining a fall presented to us with pain, swelling and deformity in the upper thigh region. On enquiring, examining and radiographing them, peri-implant fractures of subtrochanteric nature through the distal interlocking screws were revealed in both patients who also had histories of previous falls for which retrograde intramedullary nailing was performed for their respective femora. Both patients were managed with similar surgical routines including removal of the existing hardware, open reduction and ace cephallomedullary antegrade nailing. The second case did show evidence of delayed healing and was additionally stabilized with cerclage wires. Both patients had uneventful postoperative outcomes and union was evident at the end of 6 mo postoperatively with a good range of motion at the hip and knee. Our report suggests that though seldom reported, peri-implant fractures around the subtrochanteric region can occur and pose a challenge to the treating orthopaedic surgeon. We suggest these be managed, after initial stabilization and resuscitation, by implant removal, open reduction and interlocking intramedullary antegrade nailing. Good results and progression to union can be expected in these patients by adhering to basic principles of osteosynthesis. PMID:26495251
Terminal retrograde turn of rolling rings
NASA Astrophysics Data System (ADS)
Jalali, Mir Abbas; Sarebangholi, Milad S.; Alam, Mohammad-Reza
2015-09-01
We report an unexpected reverse spiral turn in the final stage of the motion of rolling rings. It is well known that spinning disks rotate in the same direction of their initial spin until they stop. While a spinning ring starts its motion with a kinematics similar to disks, i.e., moving along a cycloidal path prograde with the direction of its rigid body rotation, the mean trajectory of its center of mass later develops an inflection point so that the ring makes a spiral turn and revolves in a retrograde direction around a new center. Using high speed imaging and numerical simulations of models featuring a rolling rigid body, we show that the hollow geometry of a ring tunes the rotational air drag resistance so that the frictional force at the contact point with the ground changes its direction at the inflection point and puts the ring on a retrograde spiral trajectory. Our findings have potential applications in designing topologically new surface-effect flying objects capable of performing complex reorientation and translational maneuvers.
VIEW NORTHEAST, WEST GABLE ELEVATIONS AND OF ECCENTRIC HOUSE IN ...
VIEW NORTHEAST, WEST GABLE ELEVATIONS AND OF ECCENTRIC HOUSE IN FOREGROUND AND ENGINE HOUSE IN REAR, NOTE ROD LINES EXITING ECCENTRIC HOUSE. - Golden Oil Company, Lot 410 Lease, Sheffield Field, Donaldson, Warren County, PA
Technology Transfer Automated Retrieval System (TEKTRAN)
Plastid-to-nucleus retrograde signals emitted by dysfunctional chloroplasts impact photomorphogenic development, but the molecular link between retrograde and photosensory-receptor signaling has remained undefined. Here, we show that the phytochrome (phy) and retrograde signaling pathways converge a...
Using Kinesthetic Activities to Teach Ptolemaic and Copernican Retrograde Motion
ERIC Educational Resources Information Center
Richards, Ted
2012-01-01
This paper describes a method for teaching planetary retrograde motion, and the Ptolemaic and Copernican accounts of retrograde motion, by means of a series kinesthetic learning activities (KLAs). In the KLAs described, the students literally walk through the motions of the planets in both systems. A retrospective statistical analysis shows that…
CYCLIC TRANSIT PROBABILITIES OF LONG-PERIOD ECCENTRIC PLANETS DUE TO PERIASTRON PRECESSION
Kane, Stephen R.; Von Braun, Kaspar; Horner, Jonathan
2012-09-20
The observed properties of transiting exoplanets are an exceptionally rich source of information that allows us to understand and characterize their physical properties. Unfortunately, only a relatively small fraction of the known exoplanets discovered using the radial velocity technique are known to transit their host due to the stringent orbital geometry requirements. For each target, the transit probability and predicted transit time can be calculated to great accuracy with refinement of the orbital parameters. However, the transit probability of short period and eccentric orbits can have a reasonable time dependence due to the effects of apsidal and nodal precession, thus altering their transit potential and predicted transit time. Here we investigate the magnitude of these precession effects on transit probabilities and apply this to the known radial velocity exoplanets. We assess the refinement of orbital parameters as a path to measuring these precessions and cyclic transit probabilities.
Eccentric superconducting RF cavity separator structure
Aggus, John R.; Giordano, Salvatore T.; Halama, Henry J.
1976-01-01
Accelerator apparatus having an eccentric-shaped, iris-loaded deflecting cavity for an rf separator for a high energy high momentum, charged particle accelerator beam. In one embodiment, the deflector is superconducting, and the apparatus of this invention provides simplified machining and electron beam welding techniques. Model tests have shown that the electrical characteristics provide the desired mode splitting without adverse effects.
Chain hexagonal cacti with the extremal eccentric distance sum.
Qu, Hui; Yu, Guihai
2014-01-01
Eccentric distance sum (EDS), which can predict biological and physical properties, is a topological index based on the eccentricity of a graph. In this paper we characterize the chain hexagonal cactus with the minimal and the maximal eccentric distance sum among all chain hexagonal cacti of length n, respectively. Moreover, we present exact formulas for EDS of two types of hexagonal cacti.
Chain Hexagonal Cacti with the Extremal Eccentric Distance Sum
Qu, Hui
2014-01-01
Eccentric distance sum (EDS), which can predict biological and physical properties, is a topological index based on the eccentricity of a graph. In this paper we characterize the chain hexagonal cactus with the minimal and the maximal eccentric distance sum among all chain hexagonal cacti of length n, respectively. Moreover, we present exact formulas for EDS of two types of hexagonal cacti. PMID:24741365
Force matching errors following eccentric exercise.
Proske, U; Gregory, J E; Morgan, D L; Percival, P; Weerakkody, N S; Canny, B J
2004-10-01
During eccentric exercise contracting muscles are forcibly lengthened, to act as a brake to control motion of the body. A consequence of eccentric exercise is damage to muscle fibres. It has been reported that following the damage there is disturbance to proprioception, in particular, the senses of force and limb position. Force sense was tested in an isometric force-matching task using the elbow flexor muscles of both arms before and after the muscles in one arm had performed 50 eccentric contractions at a strength of 30% of a maximum voluntary contraction (MVC). The exercise led to an immediate reduction of about 40%, in the force generated during an MVC followed by a slow recovery over the next four days, and to the development of delayed onset muscle soreness (DOMS) lasting about the same time. After the exercise, even though participants believed they were making an accurate match, they made large matching errors, in a direction where the exercised arm developed less force than the unexercised arm. This was true whichever arm was used to generate the reference forces, which were in a range of 5-30% of the reference arm's MVC, with visual feedback of the reference arm's force levels provided to the participant. The errors were correlated with the fall in MVC following the exercise, suggesting that participants were not matching force, but the subjective effort needed to generate the force: the same effort producing less force in a muscle weakened by eccentric exercise. The errors were, however, larger than predicted from the measured reduction in MVC, suggesting that factors other than effort might also be contributing. One factor may be DOMS. To test this idea, force matches were done in the presence of pain, induced in unexercised muscles by injection of hypertonic (5%) saline or by the application of noxious heat to the skin over the muscle. Both procedures led to errors in the same direction as those seen after eccentric exercise.
THEORY OF SECULAR CHAOS AND MERCURY'S ORBIT
Lithwick, Yoram; Wu Yanqin
2011-09-20
We study the chaotic orbital evolution of planetary systems, focusing on secular (i.e., orbit-averaged) interactions, which dominate on long timescales. We first focus on the evolution of a test particle that is forced by multiple planets. To linear order in eccentricity and inclination, its orbit precesses with constant frequencies. But nonlinearities modify the frequencies, and can shift them into and out of resonance with either the planets' eigenfrequencies (forming eccentricity or inclination secular resonances), or with linear combinations of those frequencies (forming mixed high-order secular resonances). The overlap of these nonlinear secular resonances drives secular chaos. We calculate the locations and widths of nonlinear secular resonances, display them together on a newly developed map (the 'map of the mean momenta'), and find good agreement between analytical and numerical results. This map also graphically demonstrates how chaos emerges from overlapping secular resonances. We then apply this newfound understanding to Mercury to elucidate the origin of its orbital chaos. We find that since Mercury's two free precession frequencies (in eccentricity and inclination) lie within {approx}25% of two other eigenfrequencies in the solar system (those of the Jupiter-dominated eccentricity mode and the Venus-dominated inclination mode), secular resonances involving these four modes overlap and cause Mercury's chaos. We confirm this with N-body integrations by showing that a slew of these resonant angles alternately librate and circulate. Our new analytical understanding allows us to calculate the criterion for Mercury to become chaotic: Jupiter and Venus must have eccentricity and inclination of a few percent. The timescale for Mercury's chaotic diffusion depends sensitively on the forcing. As it is, Mercury appears to be perched on the threshold for chaos, with an instability timescale comparable to the lifetime of the solar system.
[Retrograde nailing in a tibial fracture].
Valls-Mellado, M; Martí-Garín, D; Fillat-Gomà, F; Marcano-Fernández, F A; González-Vargas, J A
2014-01-01
We describe a case of a severely comminuted type iiia open tibial fracture, with distal loss of bone stock (7 cm), total involvement of the tibial joint surface, and severe instability of the fibular-talar joint. The treatment performed consisted of thorough cleansing, placing a retrograde reamed calcaneal-talar-tibial nail with proximal and distal blockage, as well as a fibular-talar Kirschner nail. Primary closure of the skin was achieved. After 3 weeks, an autologous iliac crest bone graft was performed to fill the bone defect, and the endomedullary nail, which had protruded distally was reimpacted and dynamized distally. The bone defect was eventually consolidated after 16 weeks. Currently, the patient can walk without pain the tibial-astragal arthrodesis is consolidated.
Evidence for retrograde lithospheric subduction on Venus
NASA Technical Reports Server (NTRS)
Sandwell, David T.; Schubert, Gerald
1992-01-01
Annular moats and outer rises around large Venus coronas such as Artemis, Latona, and Eithinoha are similar in arcuate planform and topography to the trenches and outer rises of terrestrial subduction zones. On earth, trenches and outer rises are modeled as the flexural response of a thin elastic lithosphere to the bending moment of the subducted slab; this lithospheric flexure model also accounts for the trenches and outer rises outboard of the major coronas on Venus. Accordingly, it is proposed that retrograde lithospheric subduction may be occurring on the margins of the large Venus coronas while compensating back-arc extension is occurring in the expanding coronas interiors. Similar processes may be taking place at other deep arcuate trenches or chasmata on Venus such as those in the Dali-Diana chasmata area of aestern Aphrodite Terra.
Schwab, ME; Suda, K; Thoenen, H
1979-01-01
The fate of tetanus toxin (mol wt 150,000) subsequent to its retrograde axonal transport in peripheral sympathetic neurons of the rat was studied by both electron microscope autoradiography and cytochemistry using toxin-horseradish peroxidase (HRP) coupling products, and compared to that of nerve growth factor (NGF), cholera toxin, and the lectins wheat germ agglutinin (WGA), phytohaemagglutinin (PHA), and ricin. All these macromolecules are taken up by adrenergic nerve terminals and transported retrogradely in a selective, highly efficient manner. This selective uptake and transport is a consequence of the binding of these macromolecules to specific receptive sites on the nerve terminal membrane. All these ligands are transported in the axons within smooth vesicles, cisternae, and tubules. In the cell bodies these membrane compartments fuse and most of the transported macromolecules are finally incorporated into lysosomes. The cell nuclei, the parallel golgi cisternae, and the extracellular space always remain unlabeled. In case the tetanus toxin, however, a substantial fraction of the labeled material appears in presynaptic cholinergic nerve terminals which innervate the labeled ganglion cells. In these terminals tetanus toxin-HRP is localized in 500-1,000 A diam vesicles. In contrast, such a retrograde transsynaptic transfer is not at all or only very rarely detectable after retrograde transport of cholera toxin, NGF, WGA, PHA, or ricin. An atoxic fragment of the tetanus toxin, which contains the ganglioside-binding site, behaves like intact toxin. With all these macromolecules, the extracellular space and the glial cells in the ganglion remain unlabeled. We conclude that the selectivity of this transsynaptic transfer of tetanus toxin is due to a selective release of the toxin from the postsynaptic dendrites. This release is immediately followed by an uptake into the presynaptic terminals. PMID:92475
On Orbital Elements of Extrasolar Planetary Candidates and Spectroscopic Binaries
NASA Technical Reports Server (NTRS)
Stepinski, T. F.; Black, D. C.
2001-01-01
We estimate probability densities of orbital elements, periods, and eccentricities, for the population of extrasolar planetary candidates (EPC) and, separately, for the population of spectroscopic binaries (SB) with solar-type primaries. We construct empirical cumulative distribution functions (CDFs) in order to infer probability distribution functions (PDFs) for orbital periods and eccentricities. We also derive a joint probability density for period-eccentricity pairs in each population. Comparison of respective distributions reveals that in all cases EPC and SB populations are, in the context of orbital elements, indistinguishable from each other to a high degree of statistical significance. Probability densities of orbital periods in both populations have P(exp -1) functional form, whereas the PDFs of eccentricities can he best characterized as a Gaussian with a mean of about 0.35 and standard deviation of about 0.2 turning into a flat distribution at small values of eccentricity. These remarkable similarities between EPC and SB must be taken into account by theories aimed at explaining the origin of extrasolar planetary candidates, and constitute an important clue us to their ultimate nature.
... hemolytic streptococci may also cause orbital cellulitis. Orbital cellulitis infections in children may get worse very quickly and ... in the space around the eye. An orbital cellulitis infection can get worse very quickly. A person with ...
Synthetic aperture radar in geosynchronous orbit
NASA Technical Reports Server (NTRS)
Tomiyasu, K.
1978-01-01
Radar images of the earth were taken with a synthetic aperture radar (SAR) from geosynchronous orbital ranges by utilizing satellite motion relative to a geostationary position. A suitable satellite motion was obtained by having an orbit plane inclined relative to the equatorial plane and by having an eccentric orbit. Potential applications of these SAR images are topography, water resource management and soil moisture determination. Preliminary calculations show that the United States can be mapped with 100 m resolution cells in about 4 hours. With the use of microwave signals the mapping can be performed day or night, through clouds and during adverse weather.
Closed loop orbit trim using GPS
NASA Technical Reports Server (NTRS)
Parkinson, B. W.; Axelrad, P.
1989-01-01
This paper describes an onboard closed-loop navigation and control system capable of executing extremely precise orbit maneuvers. It uses information from the Global Positioning System (GPS) and an onboard controller to perform orbit adjustments. As a result, the system circumvents the need for extensive ground support. The particular application considered is an orbit injection system for NASA's Gravity Probe B (GP-B) spacecraft. Eccentricity adjustments of 0.0004 to 0.005, and inclination and node changes of 0.001 to 0.01 deg are demonstrated. The same technique can be adapted to other satellite missions.
Poynting-Robertson effect - 'Circular' orbit
NASA Astrophysics Data System (ADS)
Klacka, J.; Kaufmannova, J.
1992-11-01
The study investigates time evolution of the interplanetary dust particle under the action of the solar electromagnetic radiation (Poynting-Robertson effect). The evolution of the initially circular orbit in terms of the orbital elements present in the standard equations for their secular changes is considered. It is shown that the osculating eccentricity is virtually constant during the motion in spite of the generally accepted opinion that the standard equations for the secular changes of orbital elements represent the time evolution of the osculating elements.
Highly eccentric inspirals into a Schwarzschild black hole using self-force calculations
NASA Astrophysics Data System (ADS)
Osburn, Thomas; Warburton, Niels; Evans, Charles
2016-03-01
Eccentric-orbit inspirals into a massive black hole are calculated using the gravitational self-force. Both extreme-mass-ratio inspirals (EMRIs) and intermediate-mass-ratio inspirals (IMRIs) are modeled. These calculations include all dissipative and conservative first-order-in-the-mass-ratio effects for inspirals into a Schwarzschild black hole. We compute systems with initial eccentricities as high as e = 0.8 and initial separations as large as 100 M. In the case of EMRIs, the calculations follow the decay through many thousands of orbits up to the onset of the plunge. Inspirals are computed using an osculating-orbits scheme that is driven by self-force data from a hybridized self-force code. A Lorenz gauge self-force code is combined with highly accurate flux data from a Regge-Wheeler-Zerilli code, allowing the hybrid self-force model to track orbital phase in the inspirals to within 0.1 radians or better. Extensions of the method to include other physical effects are considered.
On the Orbit of the Circumbinary Planet Kepler-16b
NASA Astrophysics Data System (ADS)
Lee, Man Hoi; Leung, C. K.
2012-05-01
The orbit of the circumbinary planet Kepler-16b is significantly non-Keplerian because of the large secondary-to-primary mass ratio (0.29) and orbital eccentricity (0.15) of the binary, as well as the proximity of the planet to the binary (orbital period ratio 5.6). We present an analytic theory which models the motion of the planet (treated as a test particle) by the superposition of the circular motion of a guiding center, the forced oscillations due to the non-axisymmetric components of the binary's potential, the epicyclic motion, and the vertical motion. In this analytic theory, the periapse and ascending node of the planet precess at nearly equal rates in opposite directions, and the largest forced oscillation term corresponds to a forced eccentricity of 0.035. The nodal precession period (42 years) found in direct numerical orbit integration is in excellent agreement with the analytic theory, while the periapse precession period (49 years) and forced eccentricity (0.038) are slightly larger than the analytic values. The comparison with direct numerical orbit integration also shows that the planet's orbit has a nonzero epicyclic (or free) eccentricity of 0.027. This work is supported in part by Hong Kong RGC grant HKU 7034/09P.
Transit Timing Variations for Planets near Eccentricity-type Mean Motion Resonances
NASA Astrophysics Data System (ADS)
Deck, Katherine M.; Agol, Eric
2016-04-01
We derive the transit timing variations (TTVs) of two planets near a second-order mean motion resonance (MMR) on nearly circular orbits. We show that the TTVs of each planet are given by sinusoids with a frequency of {{jn}}2-(j-2){n}1, where j≥slant 3 is an integer characterizing the resonance and n2 and n1 are the mean motions of the outer and inner planets, respectively. The amplitude of the TTV depends on the mass of the perturbing planet, relative to the mass of the star, and on both the eccentricities and longitudes of pericenter of each planet. The TTVs of the two planets are approximated anti-correlated, with phases of ϕ and ≈ φ +π , where the phase ϕ also depends on the eccentricities and longitudes of pericenter. Therefore, the TTVs caused by proximity to a second-order MMR do not in general uniquely determine both planet masses, eccentricities, and pericenters. This is completely analogous to the case of TTVs induced by two planets near a first-order MMR. We explore how other TTV signals, such as the short-period synodic TTV or a first-order resonant TTV, in combination with the second-order resonant TTV, can break degeneracies. Finally, we derive approximate formulae for the TTVs of planets near any order eccentricity-type MMR; this shows that the same basic sinusoidal TTV structure holds for all eccentricity-type resonances. Our general formula reduces to previously derived results near first-order MMRs.
Influence of age on the late retrograde effects of sciatic nerve section in the rat.
Kerezoudi, E; King, R H; Muddle, J R; O'Neill, J A; Thomas, P K
1995-01-01
The influence of age on the late retrograde effects of unilateral sciatic nerve section was investigated in rats. Operations were performed on young rats aged 3 months and older rats aged 15 and 18 months, with survival times ranging from 6 to 15 months depending upon age at the time of operation. As in previous studies, axonal atrophy was found in myelinated fibres proximal to nerve transection. This was observed to be greater in animals operated upon at 3 months of age than in those in which the sciatic nerve was transected at 15 and 18 months. In the sciatic nerve, focal intramyelinic oedema was present at a low frequency on the operated side just proximal to the section at all survival times but not on the unoperated side except in 1 old animal. Its frequency increased with age both in the dorsal and ventral roots on both sides but it was not more common on the operated side. Retrograde axonal atrophy is therefore unlikely to contribute to its occurrence. In the dorsal root ganglia the main abnormality was the presence of vacuolated neurons on the operated side. Nuclear eccentricity was also observed on the operated side in young animals in a proportion of the neurons; its frequency increased with age on the normal side and there was no difference in the older animals between operated and control sides. The possibility is discussed that growth factor deprivation secondary to axotomy is implicated in these changes. If so, there are age differences in its effect in giving rise to axonal atrophy and neuronal vacuolation. Images Fig. 1 Fig. 2 Fig. 3 Fig. 4 Fig. 5 Fig. 6 PMID:7591983
Samsing, Johan; MacLeod, Morgan; Ramirez-Ruiz, Enrico
2014-03-20
The inspiral and merger of eccentric binaries leads to gravitational waveforms distinct from those generated by circularly merging binaries. Dynamical environments can assemble binaries with high eccentricity and peak frequencies within the LIGO band. In this paper, we study binary-single stellar scatterings occurring in dense stellar systems as a source of eccentrically inspiraling binaries. Many interactions between compact binaries and single objects are characterized by chaotic resonances in which the binary-single system undergoes many exchanges before reaching a final state. During these chaotic resonances, a pair of objects has a non-negligible probability of experiencing a very close passage. Significant orbital energy and angular momentum are carried away from the system by gravitational wave (GW) radiation in these close passages, and in some cases this implies an inspiral time shorter than the orbital period of the bound third body. We derive the cross section for such dynamical inspiral outcomes through analytical arguments and through numerical scattering experiments including GW losses. We show that the cross section for dynamical inspirals grows with increasing target binary semi-major axis a and that for equal-mass binaries it scales as a {sup 2/7}. Thus, we expect wide target binaries to predominantly contribute to the production of these relativistic outcomes. We estimate that eccentric inspirals account for approximately 1% of dynamically assembled non-eccentric merging binaries. While these events are rare, we show that binary-single scatterings are a more effective formation channel than single-single captures for the production of eccentrically inspiraling binaries, even given modest binary fractions.
A MODEL FOR THERMAL PHASE VARIATIONS OF CIRCULAR AND ECCENTRIC EXOPLANETS
Cowan, Nicolas B.; Agol, Eric
2011-01-10
We present a semi-analytic model atmosphere for close-in exoplanets that captures the essential physics of phase curves: orbital and viewing geometry, advection, and re-radiation. We calibrate the model with the well-characterized transiting planet, HD 189733b, then compute light curves for seven of the most eccentric transiting planets: Gl 436b, HAT-P-2b, HAT-P-11b, HD 17156b, HD 80606b, WASP-17b, and XO-3b. We present phase variations for a variety of different radiative times and wind speeds. In the limit of instant re-radiation, the light-curve morphology is entirely dictated by the planet's eccentricity and argument of pericenter: the light curve maximum leads or trails the eclipse depending on whether the planet is receding from or approaching the star at superior conjunction, respectively. For a planet with non-zero radiative timescales, the phase peak occurs early for super-rotating winds, and late for sub-rotating winds. We find that for a circular orbit, the timing of the phase variation maximum with respect to superior conjunction indicates the direction of the dominant winds, but cannot break the degeneracy between wind speed and radiative time. For circular planets the phase minimum occurs half an orbit away from the phase maximum-despite the fact that the coolest longitudes are always near the dawn terminator-and therefore does not convey any additional information. In general, increasing the advective frequency or the radiative time has the effect of reducing the peak-to-trough amplitude of phase variations, but there are interesting exceptions to these trends. Lastly, eccentric planets with orbital periods significantly longer than their radiative time exhibit 'ringing', whereby the hot spot generated at periastron rotates in and out of view. The existence of ringing makes it possible to directly measure the wind speed (the frequency of the ringing) and the radiative time constant (the damping of the ringing).
Using Kinesthetic Activities to Teach Ptolemaic and Copernican Retrograde Motion
NASA Astrophysics Data System (ADS)
Richards, Ted
2012-06-01
This paper describes a method for teaching planetary retrograde motion, and the Ptolemaic and Copernican accounts of retrograde motion, by means of a series kinesthetic learning activities (KLAs). In the KLAs described, the students literally walk through the motions of the planets in both systems. A retrospective statistical analysis shows that students who participated in these activities performed better on examination questions pertaining to retrograde motion than students who did not. Potential explanations for this result, including the breaking of classroom routine, the effect of body movement on conceptual memory, and egocentric spatial proprioception, are considered.
NASA Astrophysics Data System (ADS)
Huerta, E. A.; McWilliams, Sean T.; Gair, Jonathan R.; Taylor, Stephen R.
2015-09-01
We present a detailed analysis of the expected signal-to-noise ratios of supermassive black hole binaries on eccentric orbits observed by pulsar timing arrays. We derive several analytical relations that extend the results of Peters and Mathews [Phys. Rev. D 131, 435 (1963)] to quantify the impact of eccentricity in the detection of single resolvable binaries in the pulsar timing array band. We present ready-to-use expressions to compute the increase/loss in signal-to-noise ratio of eccentric single resolvable sources whose dominant harmonic is located in the low/high frequency sensitivity regime of pulsar timing arrays. Building upon the work of Phinney (arXiv:astro-ph/0108028) and Enoki and Nagashima [Prog. Theor. Phys. 117, 241 (2007)], we present an analytical framework that enables the construction of rapid spectra for a stochastic gravitational-wave background generated by a cosmological population of eccentric sources. We confirm previous findings which indicate that, relative to a population of quasicircular binaries, the strain of a stochastic, isotropic gravitational-wave background generated by a cosmological population of eccentric binaries will be suppressed in the frequency band of pulsar timing arrays. We quantify this effect in terms of signal-to-noise ratios in a pulsar timing array.
Buckling tests on eccentrically loaded beam columns
NASA Technical Reports Server (NTRS)
Cassens, J
1941-01-01
Formulas are obtained for computing the buckling load of rods eccentrically loaded at each end, the computation being extended in particular to the inelastic range. The test results are graphically presented on three sets of curves. Two of these, at least for the elastic range, are independent of the material tested. The third set, which is independent of the material, possesses greater clearness and is therefore used for comparing the test results with the theoretical.
THE STATISTICAL MECHANICS OF PLANET ORBITS
Tremaine, Scott
2015-07-10
The final “giant-impact” phase of terrestrial planet formation is believed to begin with a large number of planetary “embryos” on nearly circular, coplanar orbits. Mutual gravitational interactions gradually excite their eccentricities until their orbits cross and they collide and merge; through this process the number of surviving bodies declines until the system contains a small number of planets on well-separated, stable orbits. In this paper we explore a simple statistical model for the orbit distribution of planets formed by this process, based on the sheared-sheet approximation and the ansatz that the planets explore uniformly all of the stable region of phase space. The model provides analytic predictions for the distribution of eccentricities and semimajor axis differences, correlations between orbital elements of nearby planets, and the complete N-planet distribution function, in terms of a single parameter, the “dynamical temperature,” that is determined by the planetary masses. The predicted properties are generally consistent with N-body simulations of the giant-impact phase and with the distribution of semimajor axis differences in the Kepler catalog of extrasolar planets. A similar model may apply to the orbits of giant planets if these orbits are determined mainly by dynamical evolution after the planets have formed and the gas disk has disappeared.
Age Attenuates Leucine Oxidation after Eccentric Exercise
Kullman, E. L.; Campbell, W. W.; Krishnan, R. K.; Yarasheski, K. E.; Evans, W. J.; Kirwan, J. P.
2013-01-01
Aging may alter protein metabolism during periods of metabolic and physiologic challenge. The purpose of this study was to assess the effects of age on whole-body amino acid turnover in response to eccentric exercise and hyperglycemia-induced hyperinsulinemia. 16 healthy men were divided into young (N = 8) and older (N = 8) groups. Protein metabolism was assessed using a [1-13C]-leucine isotopic tracer approach. Measures were obtained under fasted basal conditions and during 3-h hyperglycemic clamps that were performed without (control) and 48 h after eccentric exercise. Exercise reduced leucine oxidation in the younger men (P < 0.05), but not in older men. Insulin sensitivity was inversely correlated with leucine oxidation (P < 0.05), and was lower in older men (P < 0.05). Healthy aging is associated with an impaired capacity to adjust protein oxidation in response to eccentric exercise. The decreased efficiency of protein utilization in older men may contribute to impaired maintenance, growth, and repair of body tissues with advancing age. PMID:23325713
Analytical representations of precise orbit predictions for Earth orbiting space objects
NASA Astrophysics Data System (ADS)
Sang, Jizhang; Li, Bin; Chen, Junyu; Zhang, Pin; Ning, Jinsheng
2017-01-01
Accurate orbits of Earth orbiting space objects are usually generated from an orbit determination/prediction process using numerical integrators, and presented to users in a tabulated form or a state vector including force model parameters. When dealing with hundreds of thousands of space objects such as in the space conjunction assessment, the memory required for the tabulated orbits or the computing time for propagating orbits using the state vector are both confronting to users. This paper presents two methods of analytically representing numerical orbits considering the accuracy, computing efficiency and memory. The first one is a two-step TLE-based method in which the numerical orbits are first fitted into a TLE set and then correction functions are applied to improve the position accuracy. In the second method, the orbit states are represented in equinoctial elements first, and then again correction functions are applied to reduce the position errors. Experiments using six satellite laser ranging (SLR) satellites and 12 debris objects with accurate orbits show that both methods can represent the accurate orbits over 5 days in an accuracy of a few dozens of meters for the circular orbits and several hundred meters for the eccentric orbits. The computing time is similar to that using the NORAD TLE/SGP4 algorithm, and storage for the orbit elements and function coefficients is about 3-5 KB. These features could make the two methods beneficial for the maintenance of orbit catalog of large numbers of space objects.
Effects of eccentric cycle ergometry in alpine skiers.
Gross, M; Lüthy, F; Kroell, J; Müller, E; Hoppeler, H; Vogt, M
2010-08-01
Eccentric cycling, where the goal is to resist the pedals, which are driven by a motor, increases muscle strength and size in untrained subjects. We hypothesized that it could also be beneficial for athletes, particularly in alpine skiing, which involves predominantly eccentric contractions at longer muscle lengths. We investigated the effects of replacing part of regular weight training with eccentric cycling in junior male alpine skiers using a matched-pair design. Control subjects ( N=7) executed 1-h weight sessions 3 times per week, which included 4-5 sets of 4 leg exercises. The eccentric group ( N=8) performed only 3 sets, followed by continuous sessions on the eccentric ergometer for the remaining 20 min. After 6 weeks, lean thigh mass increased significantly only in the eccentric group. There was a groupxtime effect on squat-jump height favouring the eccentric group, which also experienced a 6.5% improvement in countermovement-jump height. The ability to finely modulate muscle force during variable eccentric cycling improved 50% (p=0.004) only in the eccentric group. Although eccentric cycling did not significantly enhance isometric leg strength, we believe it is beneficial for alpine skiers because it provides an efficient means for hypertrophy while closely mimicking the type of muscle actions encountered while skiing.
Fundamental studies of retrograde reactions in direct liquefaction
Serio, M.A.; Solomon, P.R.; Bassilakis, R.; Kroo, E.
1989-01-01
Most of the proposed processing schemes for improving liquefaction yields involve favoring bond-breaking and radical stabilization reactions over the retrograde reactions. The retrograde reactions are often encountered before liquefaction temperatures are reached. The objective of this program is to elucidate and model the retrograde reaction chemistry in direct coal liquefaction through the application of experimental techniques and theoretical models which have been successfully employed at Advanced Fuel Research (AFR) and SRI International (a subcontractor) to understand and predict coal reaction behavior. The study of retrograde reactions is being done using an integrated approach using extensive characterization of the liquefaction chemistry of three kinds of systems: (1) model polymers; (2) coal; and (3) modified coals.
Inhibition of retrograde transport protects mice from lethal ricin challenge.
Stechmann, Bahne; Bai, Siau-Kun; Gobbo, Emilie; Lopez, Roman; Merer, Goulven; Pinchard, Suzy; Panigai, Laetitia; Tenza, Danièle; Raposo, Graça; Beaumelle, Bruno; Sauvaire, Didier; Gillet, Daniel; Johannes, Ludger; Barbier, Julien
2010-04-16
Bacterial Shiga-like toxins are virulence factors that constitute a significant public health threat worldwide, and the plant toxin ricin is a potential bioterror weapon. To gain access to their cytosolic target, ribosomal RNA, these toxins follow the retrograde transport route from the plasma membrane to the endoplasmic reticulum, via endosomes and the Golgi apparatus. Here, we used high-throughput screening to identify small molecule inhibitors that protect cells from ricin and Shiga-like toxins. We identified two compounds that selectively block retrograde toxin trafficking at the early endosome-TGN interface, without affecting compartment morphology, endogenous retrograde cargos, or other trafficking steps, demonstrating an unexpected degree of selectivity and lack of toxicity. In mice, one compound clearly protects from lethal nasal exposure to ricin. Our work discovers the first small molecule that shows efficacy against ricin in animal experiments and identifies the retrograde route as a potential therapeutic target.
The 'SAFARI' Technique Using Retrograde Access Via Peroneal Artery Access
Zhuang, Kun Da; Tan, Seck Guan; Tay, Kiang Hiong
2012-08-15
The 'SAFARI' technique or subintimal arterial flossing with antegrade-retrograde intervention is a method for recanalisation of chronic total occlusions (CTOs) when subintimal angioplasty fails. Retrograde access is usually obtained via the popliteal, distal anterior tibial artery (ATA)/dorsalis pedis (DP), or distal posterior tibial artery (PTA). Distal access via the peroneal artery has not been described and has a risk of continued bleeding, leading to compartment syndrome due to its deep location. We describe our experience in two patients with retrograde access via the peroneal artery and the use of balloon-assisted hemostasis for these retrograde punctures. This approach may potentially give more options for endovascular interventions in lower limb CTOs.
Plant Intracellular Transport: Tracing Functions of the Retrograde Kinesin.
Müller, Sabine
2015-09-21
Adding to its varied repertoire of functions in cell morphogenesis and cell division, a molecular motor protein of the kinesin-14 class has recently been implicated in rapid retrograde transport along cellular tracks in moss.
Relevance of ellipse eccentricity for camera calibration
NASA Astrophysics Data System (ADS)
Mordwinzew, W.; Tietz, B.; Boochs, F.; Paulus, D.
2015-05-01
Plane circular targets are widely used within calibrations of optical sensors through photogrammetric set-ups. Due to this popularity, their advantages and disadvantages are also well studied in the scientific community. One main disadvantage occurs when the projected target is not parallel to the image plane. In this geometric constellation, the target has an elliptic geometry with an offset between its geometric and its projected center. This difference is referred to as ellipse eccentricity and is a systematic error which, if not treated accordingly, has a negative impact on the overall achievable accuracy. The magnitude and direction of eccentricity errors are dependent on various factors. The most important one is the target size. The bigger an ellipse in the image is, the bigger the error will be. Although correction models dealing with eccentricity have been available for decades, it is mostly seen as a planning task in which the aim is to choose the target size small enough so that the resulting eccentricity error remains negligible. Besides the fact that advanced mathematical models are available and that the influence of this error on camera calibration results is still not completely investigated, there are various additional reasons why bigger targets can or should not be avoided. One of them is the growing image resolution as a by-product from advancements in the sensor development. Here, smaller pixels have a lower S/N ratio, necessitating more pixels to assure geometric quality. Another scenario might need bigger targets due to larger scale differences whereas distant targets should still contain enough information in the image. In general, bigger ellipses contain more contour pixels and therefore more information. This supports the target-detection algorithms to perform better even at non-optimal conditions such as data from sensors with a high noise level. In contrast to rather simple measuring situations in a stereo or multi-image mode, the impact
A reappraisal of retrograde cerebral perfusion
2013-01-01
Brain protection during aortic arch surgery by perfusing cold oxygenated blood into the superior vena cava was first reported by Lemole et al. In 1990 Ueda and associates first described the routine use of continuous retrograde cerebral perfusion (RCP) in thoracic aortic surgery for the purpose of cerebral protection during the interval of obligatory interruption of anterograde cerebral flow. The beneficial effects of RCP may be its ability to sustain brain hypothermia during hypothermic circulatory arrest (HCA) and removal of embolic material from the arterial circulation of the brain. RCP can offer effective brain protection during HCA for about 40 to 60 minutes. Animal experiments revealed that RCP provided inadequate cerebral perfusion and that neurological recovery was improved with selective antegrade cerebral perfusion (ACP), however, both RCP and ACP provide comparable clinical outcomes regarding both the mortality and stroke rates by risk-adjusted and case-matched comparative study. RCP still remains a valuable adjunct for brain protection during aortic arch repair in particular pathologies and patients. PMID:23977600
San Andreas Fault tremor and retrograde metamorphism
NASA Astrophysics Data System (ADS)
Fagereng, Åke; Diener, Johann F. A.
2011-12-01
Tectonic tremor is an enigmatic low-frequency seismic phenomenon mainly observed in subduction zones, but also documented along the deep extension of the central San Andreas Fault. The physical mechanisms behind this unusual seismic event are not yet determined for any tectonic setting; however, low effective stress conditions arising from metamorphic fluid production are commonly inferred for subduction-related tremor. We investigate the petrologic conditions at which the San Andreas tectonic tremor is inferred to occur through calculations of the pressure - temperature - time evolution of stable mineral assemblages and their water content in the dominant lithologies of the Franciscan Complex. We find that tremor locations around Parkfield and Cholame are currently experiencing retrograde metamorphic conditions. Within the temperature-depth conditions of observed tremor activity, at approximately 500°C and 20 km depth, several mineralogical transitions may occur in cooling greywacke and mafic rocks, leading to localised, significant removal of free water and an associated volume decrease. This indicates that, contrary to subduction-related tremor, tremor on the San Andreas Fault is not linked to prograde, crustal metamorphic fluid production within the fault zone; rather it might be related to mantle-derived fluids from below the tremor zone, and/or fault zone weakening that occurs as phyllosilicates replace more competent and granular mineral phases.
Endoscopic Retrograde Cholangiopancreatography in Bilioenteric Anastomosis
Park, Eun Taek
2016-01-01
For diagnosis and treatment of pancreatobiliary diseases, endoscopic retrograde cholangiopancreatography (ERCP) is useful method nowadays and its technically success rate is usually in about 90%-95% of patients with normal gastric and pancreaticobiliary anatomy. Recently ERCP is significantly challenging after intestinal reconstruction, particularly in patients who have undergone pancreaticoduodenectomy (PD, classic Whipple’s operation) or pylorus-preserving pancreatoduodenectomy (PPPD) with reconstruction. PD and PPPD relate to numerous techniques have been presented for reconstruction of the digestive tract and pancreaticobiliary tree during the resection bilioenteric stricture commonly occurs later in the postoperative course and developed in 5-year cumulative probability of biliary stricture rate of 8.2% and pancreaticoenteric stricture of 4.6%. This complication was no difference in incidence between patients with benign or malignant disease. In PD or PPPD with reconstruction, short pancreatobiliary limb with biliojejunal anastomosis site is made usually, modestly success rate of intubation to blind loop and cannulation with conventional endoscope. However, in combined Reux-en-Y anastomosis, longer pancreatobiliary limb and additional Reux limb are obstacle to success intubation and cannulation by using conventional endoscope. In this situation, new designed enetroscope with dedicated accessories is efficient. PMID:27838918
Pleuropancreatic fistula: endoscopic retrograde cholangiopancreatography and computed tomography
McCarthy, S.; Pellegrini, C.A.; Moss, A.A.; Way, L.W.
1984-06-01
The complementary use of endoscopic retrograde cholangiopancreatography and computed tomography in the diagnosis and management of pleuropancreatic fistulas is described in relation to four cases in which computed tomography revealedthe thoracic extension of a pancreatic fistula not demonstrable by endoscopic retrograde cholangiopancreatography, although the latter indicated an abnormal pancreatic duct. The complementary use of both techniques may be necessary to define the pathologic anatomy so that the appropriate therapy, particularly the surgical approach, can be decided.
Retrograde Melting and Internal Liquid Gettering in Silicon
Hudelson, Steve; Newman, Bonna K.; Bernardis, Sarah; Fenning, David P.; Bertoni, Mariana I.; Marcus, Matthew A.; Fakra, Sirine C.; Lai, Barry; Buonassisi, Tonio
2011-07-01
Retrograde melting (melting upon cooling) is observed in silicon doped with 3d transition metals, via synchrotron-based temperature-dependent X-ray microprobe measurements. Liquid metal-silicon droplets formed via retrograde melting act as efficient sinks for metal impurities dissolved within the silicon matrix. Cooling results in decomposition of the homogeneous liquid phase into solid multiple-metal alloy precipitates. These phenomena represent a novel pathway for engineering impurities in semiconductor-based systems.
20 Myr of eccentricity paced lacustrine cycles in the Cenozoic Ebro Basin
NASA Astrophysics Data System (ADS)
Valero, Luis; Garcés, Miguel; Cabrera, Lluís; Costa, Elisenda; Sáez, Alberto
2014-12-01
Long-period orbital forcing is a crucial component of the major global climate shifts during the Cenozoic as revealed in marine pelagic records. A complementary regional perspective of climate change can be assessed from internally drained lake basins, which are directly affected by insolation and precipitation balance. The Ebro Basin in northeastern Iberia embraces a 20 Myr long continuous sedimentary record where recurrent expansions and retractions of the central lacustrine system suggest periodic shifts of water balance due to orbital oscillations. In order to test climatic (orbital) forcing a key-piece of the basin, the Los Monegros lacustrine system, has been analyzed in detail. The cyclostratigraphic analysis points to orbital eccentricity as pacemaker of short to long-term lacustrine sequences, and reveals a correlation of maxima of the 100-kyr, 400-kyr and 2.4-Myr eccentricity cycles with periods of lake expansion. A magnetostratigraphy-based chronostratigraphy of the complete continental record allows further assessing long-period orbital forcing at basin scale, a view that challenges alternate scenarios where the stratigraphic architecture in foreland systems is preferably associated to tectonic processes. We conclude that while the location of lacustrine depocenters reacted to the long-term tectonic-driven accommodation changes, shorter wavelenght oscillations of lake environments, still million-year scale, claims for a dominance of orbital forcing. We suggest a decoupling between (tectonic) supply-driven clastic sequences fed from basin margins and (climatic) base level-driven lacustrine sequences in active settings with medium to large sediment transfer systems.
HEO space debris orbit predictions.
NASA Astrophysics Data System (ADS)
Gregorowicz, Dorota; Pospieszynski, Remigiusz; Golembiewska, Justyna; Wnuk, Edwin
2012-07-01
HEO (Highly Elliptical Orbit) satellites are objects with an elliptic orbit with a low-altitude perigee and a high-altitude apogee. Perigee mainly cross the LEO orbits and apogee reaches regions above GEO orbits. Number of satellites on the orbits are old racket bodies and other space debris. Most of HEO objects has the eccentricity more than 0.7. Many trackable objects are included in the NORAD TLE Catalogue but much more small debris exist which we could not track. Objects on as highly elliptical orbit are very danger for satellites in LEO region because of increasing velocity near the perigee. In order to calculate the trajectory of space debris we have to take into account force model consisting of geopotential, luni-solar effects, solar radiation pressure and for objects with low-altitude of perigee, atmospheric drag. This last perturbation is very important to calculate orbits with high accuracy but also one of the hardest to predict. Many atmospheric space debris objects parameters should be taken into account in this case, but we do not have sufficient data from observations, in particular S/M (area-to-mass) ratio. Fortunately we have some archival data for some debris included in TLE Catalogue, which are very helpful to estimate the approximate value of the parameter. In this paper we present the results of calculations of orbit predictions for short and medium time span (up to several weeks). We tried to designate the S/M parameter for some HEO objects from archival data from the TLE Catalogue and predict its orbital elements for several weeks. With better knowledge about approximate mean value of the S/M parameter we are able to improve the accuracy of predicted orbits.
Home Sweet Home?: Determining Habitability From the Eccentricities of Kepler-186
NASA Astrophysics Data System (ADS)
McTier, Moiya; Kipping, David M.
2016-01-01
In the search for habitable exoplanets, astronomers' primary criterion has historically been that the planet's equilibrium temperature be suitable for liquid water. Equilibrium temperature is often determined assuming a circular orbit and, therefore, a constant star-planet separation, especially for low-mass transiting exoplanets. Using photometric data from the first Kepler mission, we analyze the transit light curves of Kepler 186, an exoplanetary system located approximately 150pc from Earth. In this poster, we report new lower limits on the eccentricities of the system found using the astrodensity profiling method and discuss how those values effect habitabilty. We also report other orbital, stellar, and planetary properties, which are consistent with, though slightly more precise than, the values reported in Quintana et al, 2014. We assert that, with an eccentricity of 0.092, a semimajor axis of 0.35 AU, and a radius of 1.06 Earth radii, Kepler 186f is an Earth-sized exoplanet that spends its entire orbit in the habitable zone of its star.
HD 285507b: An eccentric hot Jupiter in the hyades open cluster
Quinn, Samuel N.; White, Russel J.; Latham, David W.; Buchhave, Lars A.; Torres, Guillermo; Stefanik, Robert P.; Berlind, Perry; Bieryla, Allyson; Calkins, Michael C.; Esquerdo, Gilbert A.; Fűrész, Gabor; Geary, John C.; Szentgyorgyi, Andrew H.
2014-05-20
We report the discovery of the first hot Jupiter in the Hyades open cluster. HD 285507b orbits a V = 10.47 K4.5V dwarf (M {sub *} = 0.734 M {sub ☉}; R {sub *} = 0.656 R {sub ☉}) in a slightly eccentric (e=0.086{sub −0.019}{sup +0.018}) orbit with a period of 6.0881{sub −0.0018}{sup +0.0019} days. The induced stellar radial velocity corresponds to a minimum companion mass of M {sub P}sin i = 0.917 ± 0.033 M {sub Jup}. Line bisector spans and stellar activity measures show no correlation with orbital phase, and the radial velocity amplitude is independent of wavelength, supporting the conclusion that the variations are caused by a planetary companion. Follow-up photometry indicates with high confidence that the planet does not transit. HD 285507b joins a small but growing list of planets in open clusters, and its existence lends support to a planet formation scenario in which a high stellar space density does not inhibit giant planet formation and migration. We calculate the circularization timescale for HD 285507b to be larger than the age of the Hyades, which may indicate that this planet's non-zero eccentricity is the result of migration via interactions with a third body. We also demonstrate a significant difference between the eccentricity distributions of hot Jupiters that have had time to tidally circularize and those that have not, which we interpret as evidence against Type II migration in the final stages of hot Jupiter formation. Finally, the dependence of the circularization timescale on the planetary tidal quality factor, Q {sub P}, allows us to constrain the average value for hot Jupiters to be logQ{sub P}=6.14{sub −0.25}{sup +0.41}.
Orbital resonances and Poynting-Robertson drag
NASA Technical Reports Server (NTRS)
Weidenschilling, S. J.; Jackson, A. A.
1993-01-01
The phenomenon of resonance trapping with Poynting-Robertson drag in the simplest case - the circular restricted three-body problem - is elucidated. Attention is given to what determines whether a grain of a given size passes through a given resonance or is trapped there, to how and why a trapped particle's orbit evolves with time, and to why Poynting-Robertson drag resonances are only temporary, while gas-drag resonances appear to be stable. The possibility of trapping a grain into resonance with a planet depends on the combination of the following parameters: the ratio of radiation pressure force to solar gravity, the mass of the perturbing planet normalized to the solar mass, an integer, and eccentricity. In general, the peak eccentricity and sometimes the threshold value are large enough so that crossing orbits and close approaches to the planet can inhibit capture and aid escape from resonance.
On the formation of hot and warm Jupiters via secular high-eccentricity migration in stellar triples
NASA Astrophysics Data System (ADS)
Hamers, Adrian S.
2017-01-01
Hot Jupiters (HJs) are Jupiter-like planets orbiting their host star in tight orbits of a few days. They are commonly believed not to have formed in situ, requiring inwards migration towards the host star. One of the proposed migration scenarios is secular high-eccentricity or high-e migration, in which the orbit of the planet is perturbed to high eccentricity by secular processes, triggering strong tidal evolution and orbital migration. Previous theoretical studies have considered secular excitation in stellar binaries. Recently, a number of HJs have been observed in stellar triple systems. In the latter, the secular dynamics are much richer compared to stellar binaries, and HJs could potentially be formed more efficiently. Here, we investigate this possibility by modeling the secular dynamical and tidal evolution of planets in two hierarchical configurations in stellar triple systems. We find that the HJ formation efficiency is higher compared to stellar binaries, but only by at most a few tens of per cent. The orbital properties of the HJs formed in the simulations are very similar to HJs formed in stellar binaries, and similarly to studies of the latter we find no significant number of warm Jupiters. HJs are only formed in our simulations for triples with specific orbital configurations, and our constraints are approximately consistent with current observations. In future, this allows to rule out high-e migration in stellar triples if a HJ is detected in a triple grossly violating these constraints.
Eisenstein, Emmanuel D; Waterman, Brian R; Kanlic, Enes M; Abdelgawad, Amr A
Bone grafting is one of the most common orthopedic procedures. We conducted a study to assess the possibility of passing a Reamer/Irrigator/Aspirator (RIA; DePuy Synthes) retrograde through the nonunion site in distal femur cases. This technique would avoid the complications and discomfort associated with a separate entry site for RIA. All patients with a distal femur nonunion treated with RIA bone grafting between 2009 and 2013 were included in the study. Nonunions were mobilized with excision of fibrous tissues. The distal part was angulated into varus, and then the guide wire was passed from the nonunion site laterally. Five patients had a RIA passed retrograde through the nonunion site. Mean age of these patients was 40.4 years (range, 22-66 years). Mean reamer size was 13.4 mm (mode, 14 mm), producing an average bone graft volume of 33 mL. There were no intraoperative or postoperative fractures. In 1 case, the reamer shaft broke. Passing a RIA retrograde through the nonunion site in distal femur cases is reproducible, and the technique avoids the discomfort and pain associated with a separate entry point as well as the complication of eccentric reaming of the proximal and distal part of the femoral canal.
Stability of Frozen Orbits Around Europa
NASA Astrophysics Data System (ADS)
Cardoso Dos Santos, Josué; Vilhena de Moraes, R.; Carvalho, J. S.
2013-05-01
Abstract (2,250 Maximum Characters): A planetary satellite of interest at the present moment for the scientific community is Europa, one of the four largest moons of Jupiter. There are some missions planned to visit Europa in the next years, for example, Jupiter Europa Orbiter (JEO, NASA) and Jupiter IcyMoon Explorer (JUICE, ESA). In this work we are formulating theories and constructing computer programs to be used in the design of aerospace tasks as regards the stability of artificial satellite orbits around planetary satellites. The studies are related to translational motion of orbits around planetary satellites considering polygenic perturbations due to forces, such as the nonspherical shape of the central body and the perturbation of the third body. The equations of motion will be developed in closed form to avoid expansions in eccentricity and inclination. For a description of canonical formalism are used the Delaunay canonical variables. The canonical set of equations, which are nonlinear differential equations, will be used to study the stability of orbits around Europa. We will use a simplified dynamic model, which considers the effects caused by non-uniform distribution of mass of Europa (J2, J3 and C22) and the gravitational attraction of Jupiter. Emphasis will be given to the case of frozen orbits, defined as having almost constant values of eccentricity, inclination, and argument of pericentre. An approach will be used to search for frozen orbits around planetary satellites and study their stability by applying a process of normalization of Hamiltonian. Acknowledges: FAPESP
Absolute Dimensions of the Eccentric Eclipsing Binary V541 Cygni
NASA Astrophysics Data System (ADS)
Torres, Guillermo; McGruder, Chima D.; Siverd, Robert J.; Rodriguez, Joseph E.; Pepper, Joshua; Stevens, Daniel J.; Stassun, Keivan G.; Lund, Michael B.; James, David
2017-02-01
We report new spectroscopic and photometric observations of the main-sequence, detached, eccentric, double-lined eclipsing binary V541 Cyg (P = 15.34 days, e = 0.468). Using these observations together with existing measurements, we determine the component masses and radii to better than 1% precision: {M}1={2.335}-0.013+0.017 {M}ȯ , {M}2={2.260}-0.013+0.016 {M}ȯ , {R}1={1.859}-0.009+0.012 {R}ȯ , and {R}2={1.808}-0.013+0.015 {R}ȯ . The nearly identical B9.5 stars have estimated effective temperatures of 10650 ± 200 K and 10350 ± 200 K. A comparison of these properties with current stellar evolution models shows excellent agreement at an age of about 190 Myr and [Fe/H] ≈ ‑0.18. Both components are found to be rotating at the pseudo-synchronous rate. The system displays a slow periastron advance that is dominated by general relativity (GR), and has previously been claimed to be slower than predicted by theory. Our new measurement, \\dot{ω }={0.859}-0.017+0.042 deg century‑1, has an 88% contribution from GR and agrees with the expected rate within the uncertainties. We also clarify the use of the gravity darkening coefficients in the light-curve fitting Eclipsing Binary Orbit Program (EBOP), a version of which we use here.
DENSITY AND ECCENTRICITY OF KEPLER PLANETS
Wu Yanqin; Lithwick, Yoram
2013-07-20
We analyze the transit timing variations (TTV) obtained by the Kepler mission for 22 sub-Jovian planet pairs (19 published, 3 new) that lie close to mean motion resonances. We find that the TTV phases for most of these pairs lie close to zero, consistent with an eccentricity distribution that has a very low root-mean-squared value of e {approx} 0.01; but about a quarter of the pairs possess much higher eccentricities, up to e {approx} 0.1-0.4. For the low-eccentricity pairs, we are able to statistically remove the effect of eccentricity to obtain planet masses from TTV data. These masses, together with those measured by radial velocity, yield a best-fit mass-radius relation M {approx} 3 M{sub Circled-Plus }(R/R{sub Circled-Plus }). This corresponds to a constant surface escape velocity of {approx}20 km s{sup -1}. We separate the planets into two distinct groups: ''mid-sized'' (those greater than 3 R{sub Circled-Plus }) and 'compact' (those smaller). All mid-sized planets are found to be less dense than water and therefore must contain extensive H/He envelopes that are comparable in mass to that of their cores. We argue that these planets have been significantly sculpted by photoevaporation. Surprisingly, mid-sized planets, a minority among Kepler candidates, are discovered exclusively around stars more massive than 0.8 M{sub Sun }. The compact planets, on the other hand, are often denser than water. Combining our density measurements with those from radial velocity studies, we find that hotter compact planets tend to be denser, with the hottest ones reaching rock density. Moreover, hotter planets tend to be smaller in size. These results can be explained if the compact planets are made of rocky cores overlaid with a small amount of hydrogen, {<=}1% in mass, with water contributing little to their masses or sizes. Photoevaporation has exposed bare rocky cores in cases of the hottest planets. Our conclusion that these planets are likely not water worlds contrasts
Eccentricity effects upon the flow field inside a whirling annular seal
NASA Technical Reports Server (NTRS)
Morrison, Gerald L.; Deotte, Robert E., Jr.; Das, Purandar G.; Thames, H. Davis
1994-01-01
The flow field inside a whirling annular seal operating at a Reynolds number of 24,000 and a Taylor number of 6600 has been measured using a 3-D laser Doppler anemometer system. Two eccentricity ratios were considered, 0.10 and 0.50. The seal has a diameter of 164 mm, is 37.3 mm long, and has a clearance of 1.27 mm. The rotor was mounted eccentrically on the shaft such that the whirl ratio is 1.0 and the rotor follows a circular orbit. The mean axial velocity is not uniform around the circumference of the seal; near the inlet a region characterized by high velocity of the seal. By the exit, another region of high axial velocity is not uniform around the circumference of the seal; near the inlet a region characterized by high velocity of the seal. By the exit, another region of high axial velocity has developed, this time on the suction side of the seal. The magnitude and azimuthal distance of the migration increased with increasing whirl amplitude (eccentricity). Throughout the seal length, the azimuthal mean velocity varied inversely with the mean axial velocity. Increasing the whirl amplitude did not increase the magnitude of the azimuthal velocity at the seal exit.
Constraining stellar binary black hole formation scenarios with eLISA eccentricity measurements
NASA Astrophysics Data System (ADS)
Nishizawa, Atsushi; Sesana, Alberto; Berti, Emanuele; Klein, Antoine
2017-03-01
A space-based interferometer such as the evolved Laser Interferometer Space Antenna (eLISA) could observe a few to a few thousands of progenitors of black hole binaries (BHBs) similar to those recently detected by Advanced LIGO. Gravitational radiation circularizes the orbit during inspiral, but some BHBs retain a measurable eccentricity at the low frequencies where eLISA is the most sensitive. The eccentricity of a BHB carries precious information about its formation channel: BHBs formed in the field, in globular clusters, or close to a massive black hole (MBH) have distinct eccentricity distributions in the eLISA band. We generate mock eLISA observations, folding in measurement errors, and using a Bayesian model selection, we study whether eLISA measurements can identify the BHB formation channel. We find that a handful of observations would suffice to tell whether BHBs were formed in the gravitational field of an MBH. Conversely, several tens of observations are needed to tell apart field formation from globular cluster formation. A 5-yr eLISA mission with the longest possible armlength is desirable to shed light on BHB formation scenarios.
Merging binaries in the Galactic Center: the eccentric Kozai-Lidov mechanism with stellar evolution
NASA Astrophysics Data System (ADS)
Stephan, Alexander P.; Naoz, Smadar; Ghez, Andrea M.; Witzel, Gunther; Sitarski, Breann N.; Do, Tuan; Kocsis, Bence
2016-08-01
Most, if not all, stars in the field are born in binary configurations or higher multiplicity systems. In dense stellar environment such as the Galactic Center (GC), many stars are expected to be in binary configurations as well. These binaries form hierarchical triple-body systems, with the massive black hole (MBH) as the third, distant object. The stellar binaries are expected to undergo large-amplitude eccentricity and inclination oscillations via the so-called `eccentric Kozai-Lidov' mechanism. These eccentricity excitations, combined with post-main-sequence stellar evolution, can drive the inner stellar binaries to merge. We study the mergers of stellar binaries in the inner 0.1 pc of the GC caused by gravitational perturbations due to the MBH. We run a large set of Monte Carlo simulations that include the secular evolution of the orbits, general relativistic precession, tides and post-main-sequence stellar evolution. We find that about 13 per cent of the initial binary population will have merged after a few Myr and about 29 per cent after a few Gyr. These expected merged systems represent a new class of objects at the GC, and we speculate that they are connected to G2-like objects and the young stellar population.
A CLASS OF ECCENTRIC BINARIES WITH DYNAMIC TIDAL DISTORTIONS DISCOVERED WITH KEPLER
Thompson, Susan E.; Barclay, Thomas; Howell, Steve B.; Still, Martin; Ibrahim, Khadeejah A.; Everett, Mark; Mullally, Fergal; Rowe, Jason; Christiansen, Jessie L.; Twicken, Joseph D.; Clarke, Bruce D.; Kurtz, Donald W.; Hambleton, Kelly
2012-07-01
We have discovered a class of eccentric binary systems within the Kepler data archive that have dynamic tidal distortions and tidally induced pulsations. Each has a uniquely shaped light curve that is characterized by periodic brightening or variability at timescales of 4-20 days, frequently accompanied by shorter period oscillations. We can explain the dominant features of the entire class with orbitally varying tidal forces that occur in close, eccentric binary systems. The large variety of light curve shapes arises from viewing systems at different angles. This hypothesis is supported by spectroscopic radial velocity measurements for five systems, each showing evidence of being in an eccentric binary system. Prior to the discovery of these 17 new systems, only four stars, where KOI-54 is the best example, were known to have evidence of these dynamic tides and tidally induced oscillations. We perform preliminary fits to the light curves and radial velocity data, present the overall properties of this class, and discuss the work required to accurately model these systems.
Constraining stellar binary black hole formation scenarios with LISA eccentricity measurements
NASA Astrophysics Data System (ADS)
Berti, Emanuele; Nishizawa, Atsushi; Sesana, Alberto; Klein, Antoine
2017-01-01
A space-based interferometer such as LISA could observe few to few thousands progenitors of black hole binaries (BHBs) similar to those recently detected by Advanced LIGO. Gravitational radiation circularizes the orbit during inspiral, but some BHBs retain a measurable eccentricity at the low frequencies where LISA is most sensitive. The eccentricity of a BHB carries precious information about its formation channel: BHBs formed in the field, in globular clusters, or close to a massive black hole (MBH) have distinct eccentricity distributions in the LISA band. We generate mock LISA observations, folding in measurement errors, and using Bayesian model selection we study whether LISA measurements can identify the BHB formation channel. We find that a handful of observations would suffice to tell whether BHBs were formed in the gravitational field of a MBH. Conversely, several tens of observations are needed to tell apart field formation from globular cluster formation. A five-year LISA mission with the longest possible armlength is desirable to shed light on BHB formation scenarios. NSF CAREER Grant No. PHY-1055103, NSF Grant No. PHY-1607130, FCT contract IF/00797/2014/CP1214/CT0012.
Influence of High Eccentricity Objects in the Evolution of the GEO Environment
NASA Astrophysics Data System (ADS)
Rossi, Alessandro; Anselmo, Luciano; Pardini, Carmen
2009-03-01
The long term influence of objects crossing or abandoned in GEO was evaluated, based on current practices, using the new Space Debris Mitigation model SDM 4.0. It was the latest version of a long term evolution code originally developed in the early 1990's, specifically designed to model with high accuracy the high Earth orbit regimes.Starting from the MASTER-2005 debris population, the long term evolution of the GEO environment was simulated under a few realistic scenarios, based on increasingly aggressive mitigation strategies. Beyond the high eccentricity objects, also the influence of the rocket stages separated from GEO spacecraft and left in geosynchronous drift orbits was analyzed. The main mitigation measures considered included the re-orbiting of GEO spacecraft at the end-of-life in the super-GEO graveyard zone, the de-orbiting of GTO/HEO upper stages and the re-orbiting of the rocket stages usually abandoned in drift orbits.These simulations allowed the quantitative estimation of the collision probability related to all the above mentioned classes of objects. The effectiveness of the current mitigation measures was assessed and the rationale of new mitigation guidelines devised to minimize the future collision risk in GEO was discussed.
Kepler does not orbit the Earth, rather it orbits the Sun in concert with the Earth, slowly drifting away from Earth. Every 61 Earth years, Kepler and Earth will pass by each other. Throughout the ...
Dawson, Rebekah I.; Clubb, Kelsey I.; Johnson, John Asher; Murray-Clay, Ruth A.; Fabrycky, Daniel C.; Foreman-Mackey, Daniel; Buchhave, Lars A.; Cargile, Phillip A.; Fulton, Benjamin J.; Howard, Andrew W.; Hebb, Leslie; Huber, Daniel; Shporer, Avi; Valenti, Jeff A.
2014-08-20
We establish the three-dimensional architecture of the Kepler-419 (previously KOI-1474) system to be eccentric yet with a low mutual inclination. Kepler-419b is a warm Jupiter at semi-major axis a=0.370{sub −0.006}{sup +0.007} AU with a large eccentricity (e = 0.85{sub −0.07}{sup +0.08}) measured via the 'photoeccentric effect'. It exhibits transit timing variations (TTVs) induced by the non-transiting Kepler-419c, which we uniquely constrain to be a moderately eccentric (e = 0.184 ± 0.002), hierarchically separated (a = 1.68 ± 0.03 AU) giant planet (7.3 ± 0.4 M {sub Jup}). We combine 16 quarters of Kepler photometry, radial-velocity (RV) measurements from the HIgh Resolution Echelle Spectrometer on Keck, and improved stellar parameters that we derive from spectroscopy and asteroseismology. From the RVs, we measure the mass of the inner planet to be 2.5 ± 0.3 M {sub Jup} and confirm its photometrically measured eccentricity, refining the value to e = 0.83 ± 0.01. The RV acceleration is consistent with the properties of the outer planet derived from TTVs. We find that despite their sizable eccentricities, the planets are coplanar to within 9{sub −6}{sup +8} degrees, and therefore the inner planet's large eccentricity and close-in orbit are unlikely to be the result of Kozai migration. Moreover, even over many secular cycles, the inner planet's periapse is most likely never small enough for tidal circularization. Finally, we present and measure a transit time and impact parameter from four simultaneous ground-based light curves from 1 m class telescopes, demonstrating the feasibility of ground-based follow-up of Kepler giant planets exhibiting large TTVs.
Strength After Bouts of Eccentric or Concentric Actions
NASA Technical Reports Server (NTRS)
Golden, Catherine L.; Dudley, Gary A.
1992-01-01
This study examined the influence of an initial bout of eccentric or concentric actions and a subsequent bout of eccentric actions on muscular strength. Twenty-four healthy males, 24-45 yr old, were placed in three groups that performed eccentric actions in bouts 1 and 2 (ECC/ECC, N = 8), concentric actions in bout 1, and eccentric actions in bout 2 (CON/ECC, N = 8) or served as controls (N = 8). Bouts involved unilateral actions with the left and right quadriceps femoris. Ten sets of 10 repetitions with an initial resistance equal to 85% of the eccentric or concentric one repetition maximum (1 RM) were performed for each bout. Three minutes of rest were given between sets and 3 wk between bouts. Two weeks before bout 1 and 1, 4, 7, and 10 d after bouts 1 and 2, eccentric and concentric 1 RM were measured for the right quadriceps femoris and a speed-torque relation established for the left quadriceps femoris. Eccentric and concentric 1 RM decreased (P less than 0.05) 32% 1 d after bout 1 for group ECC/ECC. The speed-torque relation was down-shifted (P less than 0.05) 38%. Eccentric 1 RM and eccentric and isometric torque returned to normal 6 d later. Concentric 1 RM and torque at 3.14 rad-s(exp -1) had not recovered on day 10 (-7% for both, P less than 0.05). Decreases in strength after bout 2 for group ECC/ECC only occurred on day 1 (-9% for concentric 1 RM and 16% downshift of the speed- torque relation). Group CONIECC showed the opposite responses; marked decreases in strength after bout 2 but not bout 1. The results indicate that the initial decrease in strength after performance of a novel bout of eccentric exercise is comparable for eccentric, concentric and isometric muscle actions. Recovery of strength, however, appears to occur more rapidly for eccentric and isometric actions. They suggest that performance of a prior bout of eccentric but not concentric actions, as done in this study, can essentially eradicate decreases in strength after a subsequent bout
Moderate Load Eccentric Exercise; A Distinct Novel Training Modality
Hoppeler, Hans
2016-01-01
Over the last 20 years a number of studies have been published using progressive eccentric exercise protocols on motorized ergometers or similar devices that allow for controlled application of eccentric loads. Exercise protocols ramp eccentric loads over an initial 3 weeks period in order to prevent muscle damage and delayed onset muscle soreness. Final training loads reach 400–500 W in rehabilitative settings and over 1200 W in elite athletes. Training is typically carried out three times per week for durations of 20–30 min. This type of training has been characterizes as moderate load eccentric exercise. It has also been denoted RENEW (Resistance Exercise via Negative Eccentric Work by LaStayo et al., 2014). It is distinct from plyometric exercises (i.e., drop jumps) that impose muscle loads of several thousand Watts on muscles and tendons. It is also distinct from eccentric overload training whereby loads in a conventional strength training setting are increased in the eccentric phase of the movement to match concentric loads. Moderate load eccentric exercise (or RENEW) has been shown to be similarly effective as conventional strength training in increasing muscle strength and muscle volume. However, as carried out at higher angular velocities of joint movement, it reduces joint loads. A hallmark of moderate load eccentric exercise is the fact that the energy requirements are typically 4-fold smaller than in concentric exercise of the same load. This makes moderate load eccentric exercise training the tool of choice in medical conditions with limitations in muscle energy supply. The use and effectiveness of moderate load eccentric exercise has been demonstrated mostly in small scale studies for cardiorespiratory conditions, sarcopenia of old age, cancer, diabetes type 2, and neurological conditions. It has also been used effectively in the prevention and rehabilitation of injuries of the locomotor system in particular the rehabilitation after anterior
Moderate Load Eccentric Exercise; A Distinct Novel Training Modality.
Hoppeler, Hans
2016-01-01
Over the last 20 years a number of studies have been published using progressive eccentric exercise protocols on motorized ergometers or similar devices that allow for controlled application of eccentric loads. Exercise protocols ramp eccentric loads over an initial 3 weeks period in order to prevent muscle damage and delayed onset muscle soreness. Final training loads reach 400-500 W in rehabilitative settings and over 1200 W in elite athletes. Training is typically carried out three times per week for durations of 20-30 min. This type of training has been characterizes as moderate load eccentric exercise. It has also been denoted RENEW (Resistance Exercise via Negative Eccentric Work by LaStayo et al., 2014). It is distinct from plyometric exercises (i.e., drop jumps) that impose muscle loads of several thousand Watts on muscles and tendons. It is also distinct from eccentric overload training whereby loads in a conventional strength training setting are increased in the eccentric phase of the movement to match concentric loads. Moderate load eccentric exercise (or RENEW) has been shown to be similarly effective as conventional strength training in increasing muscle strength and muscle volume. However, as carried out at higher angular velocities of joint movement, it reduces joint loads. A hallmark of moderate load eccentric exercise is the fact that the energy requirements are typically 4-fold smaller than in concentric exercise of the same load. This makes moderate load eccentric exercise training the tool of choice in medical conditions with limitations in muscle energy supply. The use and effectiveness of moderate load eccentric exercise has been demonstrated mostly in small scale studies for cardiorespiratory conditions, sarcopenia of old age, cancer, diabetes type 2, and neurological conditions. It has also been used effectively in the prevention and rehabilitation of injuries of the locomotor system in particular the rehabilitation after anterior cruciate
An infrared eccentric photo-optometer.
Roorda, A; Bobier, W R; Campbell, M C
1998-06-01
An objective infrared optometer has been designed, based on the optical principles of eccentric photorefraction. A CCD camera with an eccentric infrared light source images the subject's pupil through a Badal optometer. The slope of the light distribution across the pupil is continuously recorded. Accommodative state is measured by moving the camera behind the Badal lens until the slope is zero. This position corresponds to the case where the camera is conjugate with the retina of the observer. In this Badal optometer, the irradiance of light at the pupil plane, the sensitivity of the photorefractor, and the focal setting of the camera lens remain constant for all positions of the camera from the eye. The repeatability of a single measure of refractive state in a cyclopleged eye was less than 0.05 D. Static accommodative responses taken from 3 subjects in both closed and open loop conditions provided expected stimulus/response measures. The instrument can also be adapted to measure dynamic accommodation.
An Eccentric Binary Millisecond Pulsar with a Helium White Dwarf Companion in the Galactic field
NASA Astrophysics Data System (ADS)
Antoniadis, John; Kaplan, David L.; Stovall, Kevin; Freire, Paulo C. C.; Deneva, Julia S.; Koester, Detlev; Jenet, Fredrick; Martinez, Jose G.
2016-10-01
Low-mass white dwarfs (LMWDs) are believed to be exclusive products of binary evolution, as the universe is not old enough to produce them from single stars. Because of the strong tidal forces operating during the binary interaction phase, the remnant systems observed today are expected to have negligible eccentricities. Here, we report on the first unambiguous identification of an LMWD in an eccentric (e = 0.13) orbit around the millisecond pulsar PSR J2234+0511, which directly contradicts this picture. We use our spectra and radio-timing solution (derived elsewhere) to infer the WD temperature ({T}{{eff}}=8600+/- 190 K), and peculiar systemic velocity relative to the local standard of rest (≃ 31 km s-1). We also place model-independent constraints on the WD radius ({R}{{WD}}={0.024}-0.002+0.004 {R}⊙ ) and surface gravity ({log} g={7.11}-0.16+0.08 dex). The WD and kinematic properties are consistent with the expectations for low-mass X-ray binary evolution and disfavor a dynamic three-body formation channel. In the case of the high eccentricity being the result of a spontaneous phase transition, we infer a mass of ˜1.60 M ⊙ for the pulsar progenitor, which is too low for the quark-nova mechanism proposed by Jiang et al., and too high for the scenario of Freire & Tauris, in which a WD collapses into a neutron star via a rotationally delayed accretion-induced collapse. We find that eccentricity pumping via interaction with a circumbinary disk is consistent with our inferred parameters. Finally, we report tentative evidence for pulsations that, if confirmed, would transform the star into an unprecedented laboratory for WD physics.
DYNAMICS AND ECCENTRICITY FORMATION OF PLANETS IN OGLE-06-109L SYSTEM
Wang Su; Zhao Gang; Zhou Jilin
2009-11-20
Recent observation of the microlensing technique reveals two giant planets at 2.3 AU and 4.6 AU around the star OGLE-06-109L. The eccentricity of the outer planet (e{sub c} ) is estimated to be 0.11{sup +0.17}{sub -0.04}, comparable to that of Saturn (0.01-0.09). The similarities between the OGLE-06-109L system and the solar system indicate that they may have passed through similar histories during their formation stage. In this paper, we investigate the dynamics and formation of the orbital architecture in the OGLE-06-109L system. For the present two planets with their nominal locations, the secular motions are stable as long as their eccentricities (e{sub b} , e{sub c} ) fulfill e {sup 2} {sub b} + e {sup 2} {sub c} <= 0.3{sup 2}. Earth-size bodies might be formed and are stable in the habitable zone (0.25-0.36 AU) of the system. Three possible scenarios may be accounted for the formation of e{sub b} and e{sub c} : (1) convergent migration of two planets and the 3:1 mean motion resonance (MMR) trapping; (2) planetary scattering; and (3) divergent migration and the 3:1 MMR crossing. As we showed that the probability for the two giant planets in 3:1 MMR is low (approx3%), scenario (1) is less likely. According to models (2) and (3), the final eccentricity of inner planet (e{sub b} ) may oscillate between [0-0.06], comparable to that of Jupiter (0.03-0.06). An inspection of e{sub b} , e{sub c} 's secular motion may be helpful to understand which model is really responsible for the eccentricity formation.
Impact of Eccentricity Build-Up and Graveyard Disposal Strategies on Meo Navigation Constellations
NASA Astrophysics Data System (ADS)
Radtke, Jonas; Flegel, Sven Kevin; Sanchez-Ortiz, Noelia; Dominguez-Gonzalez, Raul; Merz, Klaus
With currently two constellations being in or close to the build-up phase, in a few years the Medium Earth Orbit (MEO) region will be populated with four complete navigation systems in relatively close orbital altitudes: The American GPS, Russian GLONASS, European Galileo and Chinese Beidou. To guarantee an appropriate visibility of constellation satellites from Earth, these constellations rely on certain defined orbits. For these, both the repeat pattern, which is basically defined by the semi-major axis and inclination, as well as the orbital planes, which are defined by the right ascension of ascending node, are important. To avoid an overcrowding of the region of interest, the disposal of satellites after their end-of-life is recommended. Because of their distances to Earth, ordinary disposal manoeuvers leading to a direct or delayed re-entry due to atmospheric drag are not feasible: The needed fuel masses for such manoeuvers are by far above the reasonable limits and available fuel budgets. Thus, additional approaches have to be applied. For this, in general two options do exist: Disposal to graveyard orbits or the disposal to eccentricity build-up orbits. For the graveyard strategy, the key criterium for the disposed spacecraft is that they must keep a safe minimum distance to altitude of the active constellation on a long-term time scale of up to 200 years. This constraint imposes stringent requirements on the stability of the graveyard orbit. Similar disposals are also performed for high LEO satellites. The eccentricity build-up strategy on the other hand uses an effect that is characteristic for the orbital regime of MEO navigation constellations: Due to resonant effects between the Earth's geopotential, the Sun and the Moon, depending on the initial conditions, a large eccentricity build-up takes place, which can lead to a re-entry of the satellite. In this paper, the effects of applying either the first or the second disposal strategy on all payloads
The habitable zone and extreme planetary orbits.
Kane, Stephen R; Gelino, Dawn M
2012-10-01
The habitable zone for a given star describes the range of circumstellar distances from the star within which a planet could have liquid water on its surface, which depends upon the stellar properties. Here we describe the development of the habitable zone concept, its application to our own solar system, and its subsequent application to exoplanetary systems. We further apply this to planets in extreme eccentric orbits and show how they may still retain life-bearing properties depending upon the percentage of the total orbit which is spent within the habitable zone. Key Words: Extrasolar planets-Habitable zone-Astrobiology.
A solution of the variational equations for elliptic orbits in rotating coordinates
NASA Technical Reports Server (NTRS)
Jones, J. B.
1980-01-01
For elliptic reference orbits, formulas are given for the perturbation state transition matrix of the two-body problem. The formulas relate perturbations expressed in a local vertical rotating coordinate system and are valid for motion in the linear neighborhood of reference orbits with e in the range of 0 to 1. The elements of the state transition matrix are expressed in terms of natural parameters (horizontal and radial velocity, radius, eccentricity, true anomaly, etc.) at the initial and final points. In addition to the general form, a simplified version, valid for small eccentricity orbits, is given.
Seasonal Variations of the James Webb Space Telescope Orbital Dynamics
NASA Technical Reports Server (NTRS)
Brown, Jonathan; Petersen, Jeremy; Villac, Benjamin; Yu, Wayne
2015-01-01
While spacecraft orbital variations due to the Earth's tilt and orbital eccentricity are well-known phenomena, the implications for the James Webb Space Telescope present unique features. We investigate the variability of the observatory trajectory characteristics, and present an explanation of some of these effects using invariant manifold theory and local approximation of the dynamics in terms of the restricted three-body problem.
Formation of the Long-Period Eccentric Binary IP Eri
NASA Astrophysics Data System (ADS)
Davis, P. J.; Siess, L.; Jorissen, A.
2015-08-01
We present a formation channel that is able to reproduce the observational properties of the K0 + He white dwarf binary IP Eri, in particular its high eccentricity (e≍ 0.25). Our scheme invokes a tidally-enhanced wind-loss mechanism on the red giant branch that can counteract the circularising effect of tides, thereby preserving or even increasing the eccentricity.
Time course of neuromuscular adaptations to knee extensor eccentric training.
Baroni, B M; Rodrigues, R; Franke, R A; Geremia, J M; Rassier, D E; Vaz, M A
2013-10-01
This study investigated the chronology of neural and morphological adaptations to knee extensor eccentric training and their contribution to strength gains in isometric, concentric and eccentric muscle actions. 20 male healthy subjects performed a 12-week eccentric training program on an isokinetic dynamometer, and neuromuscular evaluations of knee extensors were performed every 4 weeks. After 12 training weeks, significant increases were observed for: isometric (24%), concentric (15%) and eccentric (29%) torques; isometric (29%) and eccentric (33%) electromyographic activity; muscle thickness (10%) and anatomical cross-sectional area (19%). Eccentric and isometric torques increased progressively until the end of the program. Concentric torque and muscle mass parameters increased until the eighth training week, but did not change from this point to the twelfth training week. Eccentric and isometric activation increased at 4 and 8 training weeks, respectively, while no change was found in concentric activation. These results suggest that: 1) the relative increment in concentric strength was minor and does not relate to neural effects; 2) eccentric and isometric strength gains up to 8 training weeks are explained by the increased neural activation and muscle mass, whereas the increments in the last 4 training weeks seem to be associated with other mechanisms.
Mab's orbital motion explained
NASA Astrophysics Data System (ADS)
Kumar, K.; de Pater, I.; Showalter, M. R.
2015-07-01
We explored the hypothesis that Mab's anomalous orbital motion, as deduced from Hubble Space Telescope (HST) data (Showalter, M.R., Lissauer, J.J. [2006]. Science (New York, NY) 311, 973-977), is the result of gravitational interactions with a putative suite of large bodies in the μ-ring. We conducted simulations to compute the gravitational effect of Mab (a recently discovered Uranian moon) on a cloud of test particles. Subsequently, by employing the data extracted from the test particle simulations, we executed random walk simulations to compute the back-reaction of nearby perturbers on Mab. By generating simulated observation metrics, we compared our results to the data retrieved from the HST. Our results indicate that the longitude residual change noted in the HST data (Δλr,Mab ≈ 1 deg) is well matched by our simulations. The eccentricity variations (ΔeMab ≈10-3) are however typically two orders of magnitude too small. We present a variety of reasons that could account for this discrepancy. The nominal scenario that we investigated assumes a perturber ring mass (mring) of 1 mMab (Mab's mass) and a perturber ring number density (ρn,ring) of 10 perturbers per 3 RHill,Mab (Mab's Hill radius). This effectively translates to a few tens of perturbers with radii of approximately 2-3 km, depending on the albedo assumed. The results obtained also include an interesting litmus test: variations of Mab's inclination on the order of the eccentricity changes should be observable. Our work provides clues for further investigation into the tantalizing prospect that the Mab/μ-ring system is undergoing re-accretion after a recent catastrophic disruption.
Analytic Orbit Propagation for Transiting Circumbinary Planets
NASA Astrophysics Data System (ADS)
Georgakarakos, Nikolaos; Eggl, Siegfried
2015-04-01
The analytical framework presented herein fully describes the motion of coplanar systems consisting of a stellar binary and a planet orbiting both stars on orbital as well as secular timescales. Perturbations of the Runge-Lenz vector are used to derive short-period evolution of the system, while octupole secular theory is applied to describe its long-term behavior. A post-Newtonian correction on the stellar orbit is included. The planetary orbit is initially circular and the theory developed here assumes that the planetary eccentricity remains relatively small ({{e}2}\\lt 0.2). Our model is tested against results from numerical integrations of the full equations of motion and is then applied to investigate the dynamical history of some of the circumbinary planetary systems discovered by NASA’s Kepler spacecraft. Our results suggest that the formation history of the systems Kepler-34 and Kepler-413 has most likely been different from that of Kepler-16, Kepler-35, Kepler-38 and Kepler-64, since the observed planetary eccentricities for those systems are not compatible with the assumption of initially circular orbits.
Fundamental studies of retrograde reactions in direct liquefaction
Serio, M.A.; Solomon, P.R.; Kroo, E.; Charpenay, S.; Bassilakis, R.
1991-12-17
The overall objective of the program was to improve the understanding of retrograde reactions and their dependencies on coal rank and structure, and/or coal modifications and reaction conditions. Because retrograde reactions are competitive with bond breaking reactions, an understanding of both is required to shift the competition in favor of the latter. Related objectives were to clarify the conflicting observations reported in literature on such major topics as the role of oxygen groups in retrograde reactions and to provide a bridge from very fundamental studies on pure compounds to phenomenological studies on actual coal. This information was integrated into the FG-DVC model, which was improved and extended to the liquefaction context.
Retrograde resonance in the planar three-body problem
NASA Astrophysics Data System (ADS)
Morais, M. H. M.; Namouni, F.
2013-12-01
We continue the investigation of the dynamics of retrograde resonances initiated in Morais and Giuppone (Mon Notices R Astron Soc 424:52-64, doi:10.1111/j.1365-2966.2012.21151.x, 2012). After deriving a procedure to deduce the retrograde resonance terms from the standard expansion of the three-dimensional disturbing function, we concentrate on the planar problem and construct surfaces of section that explore phase-space in the vicinity of the main retrograde resonances (2/1, 1/1 and 1/2). In the case of the 1/1 resonance for which the standard expansion is not adequate to describe the dynamics, we develop a semi-analytic model based on numerical averaging of the unexpanded disturbing function, and show that the predicted libration modes are in agreement with the behavior seen in the surfaces of section.
Be discs in binary systems - I. Coplanar orbits
NASA Astrophysics Data System (ADS)
Panoglou, Despina; Carciofi, Alex C.; Vieira, Rodrigo G.; Cyr, Isabelle H.; Jones, Carol E.; Okazaki, Atsuo T.; Rivinius, Thomas
2016-09-01
Be stars are surrounded by outflowing circumstellar matter structured in the form of decretion discs. They are often members of binary systems, where it is expected that the decretion disc interacts both radiatively and gravitationally with the companion. In this work we study how various orbital (period, mass ratio and eccentricity) and disc (viscosity) parameters affect the disc structure in coplanar binaries. The main effects of the secondary on the disc are its truncation and the accumulation of material inwards of truncation. We find two limiting cases with respect to the effects of eccentricity: in circular or nearly circular prograde orbits, the disc maintains a rotating, constant in shape, configuration, which is locked to the orbital phase. The disc structure appears smaller in size, more elongated and more massive for small viscosity parameter, small orbital separation and/or high mass ratio. In highly eccentric orbits, the effects are more complex, with the disc structure strongly dependent on the orbital phase. We also studied the effects of binarity in the disc continuum emission. Since the infrared and radio SED are sensitive to the disc size and density slope, the truncation and matter accumulation result in considerable modifications in the emergent spectrum. We conclude that binarity can serve as an explanation for the variability exhibited in observations of Be stars, and that our model can be used to detect invisible companions.
DETECTION OF A LOW-ECCENTRICITY AND SUPER-MASSIVE PLANET TO THE SUBGIANT HD 38801
Harakawa, Hiroki; Ida, Shigeru; Hori, Yasunori; Sato, Bun'ei; Fischer, Debra A.; Omiya, Masashi; Johnson, John A.; Marcy, Geoffrey W.; Howard, Andrew W.; Toyota, Eri
2010-05-20
We report the detection of a large mass planet orbiting around the K0 metal-rich subgiant HD38801 (V = 8.26) by precise radial velocity (RV) measurements from the Subaru Telescope and the Keck Telescope. The star has a mass of 1.36 M{sub sun} and a metallicity of [Fe/H] = +0.26. The RV variations are consistent with a circular orbit with a period of 696.0 days and a velocity semiamplitude of 200.0 m s{sup -1}, which yield a minimum mass for the companion of 10.7 M{sub JUP} and a semimajor axis of 1.71 AU. Such super-massive objects with very low eccentricities and periods of hundreds of days are uncommon among the ensemble of known exoplanets.
Impact of eccentricity build-up and graveyard disposal Strategies on MEO navigation constellations
NASA Astrophysics Data System (ADS)
Radtke, Jonas; Domínguez-González, Raúl; Flegel, Sven K.; Sánchez-Ortiz, Noelia; Merz, Klaus
2015-12-01
With currently two constellations being in or close to the build-up phase, in a few years the Medium Earth Orbit (MEO) region will be populated with four complete navigation systems in relatively close orbital altitudes: The American GPS, Russian GLONASS, European Galileo, and Chinese BeiDou. To guarantee an appropriate visibility of constellation satellites from Earth, these constellations rely on certain defined orbits. For this, both the repeat pattern, which is basically defined by the semimajor axis and inclination, as well as the orbital planes, which are defined by the right ascension of ascending node, are determining values. To avoid an overcrowding of the region of interest, the disposal of satellites after their end-of-life is recommended. However, for the MEO region, no internationally agreed mitigation guidelines exist. Because of their distances to Earth, ordinary disposal manoeuvres leading to a direct or delayed re-entry due to atmospheric drag are not feasible: The needed fuel masses for such manoeuvres are by far above the reasonable limits and available fuel budgets. Thus, additional approaches have to be applied. For this, in general two options exist: disposal to graveyard orbits or the disposal to eccentricity build-up orbits. In the study performed, the key criterion for the graveyard strategy is that the disposed spacecraft must keep a safe minimum distance to the altitude of the active constellation on a long-term time scale of up to 200 years. This constraint imposes stringent requirements on the stability of the graveyard orbit. Similar disposals are also performed for high LEO satellites and disposed GEO payloads. The eccentricity build-up strategy on the other hand uses resonant effects between the Earth's geopotential, the Sun and the Moon. Depending on the initial conditions, these can cause a large eccentricity build-up, which finally can lead to a re-entry of the satellite. In this paper, the effects of applying either the first or
Scalar self-force on eccentric geodesics in Schwarzschild spacetime: A time-domain computation
Haas, Roland
2007-06-15
We calculate the self-force acting on a particle with scalar charge moving on a generic geodesic around a Schwarzschild black hole. This calculation requires an accurate computation of the retarded scalar field produced by the moving charge; this is done numerically with the help of a fourth-order convergent finite-difference scheme formulated in the time domain. The calculation also requires a regularization procedure, because the retarded field is singular on the particle's world line; this is handled mode-by-mode via the mode-sum regularization scheme first introduced by Barack and Ori. This paper presents the numerical method, various numerical tests, and a sample of results for mildly eccentric orbits as well as ''zoom-whirl'' orbits.
Retrograde tibial nail: anatomical implantation and surgical feasibility study.
Kuhn, S; Appelmann, P; Pairon, P; Gruszka, D; Rommens, P M
2015-01-01
PURPOSE OF THE STUDY The treatment of distal tibial fractures requires a stable fixation while minimizing the secondary trauma to the soft tissues by the surgical approach and implant. The experimental Retrograde Tibial Nail is currently investigated as a minimally invasive alternative to plating and antegrade nailing. The purpose of this study was to evaluate the surgical feasibility in a cadaver model for all distal tibial fracture types generally considered treatable by nailing. MATERIAL AND METHODS Five different fracture types (AO/OTA 43-A1/A2/A3 and 43-C1/C2) were created on separate cadaveric limbs. In simple fractures (AO/OTA 43-A1/A2/A3) primary nailing was performed. In intraarticular fractures (AO/OTA 43-C1/2) reduction of the articular block and lag screw fixation was performed before nailing. Intraoperative complications, quality of reduction, fluoroscopy duration and operative time were evaluated. RESULTS Retrograde intramedullary nailing is feasible in simple fracture types by closed manual reduction and percutaneous reduction forceps. Retrograde nailing is possible in fractures with simple intraarticular involvement after primary lag screw fixation. The duration of surgery averaged 51.8 minutes (range 40-62 min). No major complications occurred during nailing. CONCLUSIONS The minimally invasive retrograde nail combines a minimally invasive local osteosynthesis with the ability to adequately fix extraarticular and simple intraarticular distal tibial fractures. The results suggests that retrograde tibia nailing is a promising new concept for the treatment of distal tibia fractures. Key words: minimally invasive surgery, tibia, metaphyseal fractures, intramedullary nailing, retrograde nailing.
Ketchum, Jacob A.; Adams, Fred C.; Bloch, Anthony M.
2011-01-01
Pairs of migrating extrasolar planets often lock into mean motion resonance as they drift inward. This paper studies the convergent migration of giant planets (driven by a circumstellar disk) and determines the probability that they are captured into mean motion resonance. The probability that such planets enter resonance depends on the type of resonance, the migration rate, the eccentricity damping rate, and the amplitude of the turbulent fluctuations. This problem is studied both through direct integrations of the full three-body problem and via semi-analytic model equations. In general, the probability of resonance decreases with increasing migration rate, and with increasing levels of turbulence, but increases with eccentricity damping. Previous work has shown that the distributions of orbital elements (eccentricity and semimajor axis) for observed extrasolar planets can be reproduced by migration models with multiple planets. However, these results depend on resonance locking, and this study shows that entry into-and maintenance of-mean motion resonance depends sensitively on the migration rate, eccentricity damping, and turbulence.
Importance of tides for periastron precession in eccentric neutron star-white dwarf binaries
Sravan, N.; Valsecchi, F.; Kalogera, V.; Althaus, L. G.
2014-09-10
Although not nearly as numerous as binaries with two white dwarfs, eccentric neutron star-white dwarf (NS-WD) binaries are important gravitational-wave (GW) sources for the next generation of space-based detectors sensitive to low frequency waves. Here we investigate periastron precession in these sources as a result of general relativistic, tidal, and rotational effects; such precession is expected to be detectable for at least some of the detected binaries of this type. Currently, two eccentric NS-WD binaries are known in the galactic field, PSR J1141–6545 and PSR B2303+46, both of which have orbits too wide to be relevant in their current state to GW observations. However, population synthesis studies predict the existence of a significant Galactic population of such systems. Though small in most of these systems, we find that tidally induced periastron precession becomes important when tides contribute to more than 3% of the total precession rate. For these systems, accounting for tides when analyzing periastron precession rate measurements can improve estimates of the inferred WD component mass and, in some cases, will prevent us from misclassifying the object. However, such systems are rare, due to rapid orbital decay. To aid the inclusion of tidal effects when using periastron precession as a mass measurement tool, we derive a function that relates the WD radius and periastron precession constant to the WD mass.
DAY-SIDE z'-BAND EMISSION AND ECCENTRICITY OF WASP-12b
Lopez-Morales, Mercedes; Rogers, Justin C.; Coughlin, Jeffrey L.; Sing, David K.; Burrows, Adam; Spiegel, David S.; Apai, Daniel; Adams, Elisabeth R.
2010-06-10
We report the detection of the eclipse of the very hot Jupiter WASP-12b via z'-band time-series photometry obtained with the 3.5 m Astrophysical Research Consortium telescope at Apache Point Observatory. We measure a decrease in flux of 0.082% {+-} 0.015% during the passage of the planet behind the star. That planetary flux is equally well reproduced by atmospheric models with and without extra absorbers, and blackbody models with f {>=} 0.585 {+-} 0.080. It is therefore necessary to measure the planet at other wavelengths to further constrain its atmospheric properties. The eclipse appears centered at phase {phi} = 0.5100{sup +0.0072}{sub -0.0061}, consistent with an orbital eccentricity of |ecos {omega}| = 0.016{sup +0.011}{sub -0.009} (see note at the end of Section 4). If the orbit of the planet is indeed eccentric, the large radius of WASP-12b can be explained by tidal heating.
Physiology and pathology of endosome-to-Golgi retrograde sorting.
Burd, Christopher G
2011-08-01
Bidirectional traffic between the Golgi apparatus and the endosomal system sustains the functions of the trans-Golgi network (TGN) in secretion and organelle biogenesis. Export of cargo from the TGN via anterograde trafficking pathways depletes the organelle of sorting receptors, processing proteases, SNARE molecules, and other factors, and these are subsequently retrieved from endosomes via the retrograde pathway. Recent studies indicate that retrograde trafficking is vital to early metazoan development, nutrient homeostasis, and for processes that protect against Alzheimer's and other neurological diseases.
A periodic table for black hole orbits
Levin, Janna; Perez-Giz, Gabe
2008-05-15
Understanding the dynamics around rotating black holes is imperative to the success of future gravitational wave observatories. Although integrable in principle, test-particle orbits in the Kerr spacetime can also be elaborate, and while they have been studied extensively, classifying their general properties has been a challenge. This is the first in a series of papers that adopts a dynamical systems approach to the study of Kerr orbits, beginning with equatorial orbits. We define a 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 multileaf clovers in the final stages of inspiral. Furthermore, for any black hole, there is some point in the strong-field regime past which zoom-whirl behavior becomes unavoidable. Finally, we sketch the potential application of the taxonomy to problems of astrophysical interest, in particular its utility for computationally intensive gravitational wave calculations.
Hayasaki, K.; Sohn, B.W.; Jung, T.; Zhao, G.; Okazaki, A.T.; Naito, T. E-mail: bwsohn@kasi.re.kr E-mail: thjung@kasi.re.kr E-mail: tsuguya@ygu.ac.jp
2015-07-01
We study the warping and tearing of a geometrically thin, non-self-gravitating disk surrounding binary supermassive black holes on an eccentric orbit. The circumbinary disk is significantly misaligned with the binary orbital plane, and is subject to the time-dependent tidal torques. In principle, such a disk is warped and precesses, and is torn into mutually misaligned rings in the region, where the tidal precession torques are stronger than the local viscous torques. We derive the tidal-warp and tearing radii of the misaligned circumbinary disks around eccentric SMBH binaries. We find that in disks with the viscosity parameter α larger than a critical value depending on the disk aspect ratio, the disk warping appears outside the tearing radius. This condition is expressed for small amplitude warps as α > √H/(3r) for H/r∼<0.1, where H is the disk scale height. If α < √H/(3r), only the disk tearing occurs because the tidal warp radius is inside the tearing radius, where most of disk material is likely to rapidly accrete onto SMBHs. In warped and torn disks, both the tidal-warp and the tearing radii most strongly depend on the binary semi-major axis, although they also mildly depend on the other orbital and disk parameters. This strong dependence enables us to estimate the semi-major axis, once the tidal warp or tearing radius is determined observationally: for the tidal warp radius of 0.1 pc, the semi-major axis is estimated to be ∼10{sup −2} pc for 10{sup 7} M{sub ⊙} black hole with typical orbital and disk parameters. We also briefly discuss the possibility that central objects of observed warped maser disks in active galactic nuclei are supermassive black hole binaries.
Modification of Eccentric Gaze-Holding
NASA Technical Reports Server (NTRS)
Reschke, M. F.; Paloski, W. H.; Somers, J. T.; Leigh, R. J.; Wood, S. J.; Kornilova, L.
2006-01-01
Clear vision and accurate localization of objects in the environment are prerequisites for reliable performance of motor tasks. Space flight confronts the crewmember with a stimulus rearrangement that requires adaptation to function effectively with the new requirements of altered spatial orientation and motor coordination. Adaptation and motor learning driven by the effects of cerebellar disorders may share some of the same demands that face our astronauts. One measure of spatial localization shared by the astronauts and those suffering from cerebellar disorders that is easily quantified, and for which a neurobiological substrate has been identified, is the control of the angle of gaze (the "line of sight"). The disturbances of gaze control that have been documented to occur in astronauts and cosmonauts, both in-flight and postflight, can be directly related to changes in the extrinsic gravitational environment and intrinsic proprioceptive mechanisms thus, lending themselves to description by simple non-linear statistical models. Because of the necessity of developing robust normal response populations and normative populations against which abnormal responses can be evaluated, the basic models can be formulated using normal, non-astronaut test subjects and subsequently extended using centrifugation techniques to alter the gravitational and proprioceptive environment of these subjects. Further tests and extensions of the models can be made by studying abnormalities of gaze control in patients with cerebellar disease. A series of investigations were conducted in which a total of 62 subjects were tested to: (1) Define eccentric gaze-holding parameters in a normative population, and (2) explore the effects of linear acceleration on gaze-holding parameters. For these studies gaze-holding was evaluated with the subjects seated upright (the normative values), rolled 45 degrees to both the left and right, or pitched back 30 and 90 degrees. In a separate study the further
NASA Astrophysics Data System (ADS)
Ghosh, Arindam; Chakrabarti, Sandip Kumar
2016-07-01
X-ray binary orbits are expected to have some eccentricity, albeit small. Stellar companion of a black hole orbiting in an eccentric orbit will experience modulating tidal force with a periodicity same as that of the orbital period which will result in a modulation of accretion rates, seed photon flux, and flux of inverse Comptonized harder X-rays as well. Timing analysis of long-term X-ray data (1.5-12 keV) of RXTE/ASM and all sky survey data (15-50 keV) of Swift/BAT satellites reveal this periodicity in several black hole candidates. If this modulation is assumed to be solely due to tidal effects (without taking other effects, such as eclipses, reflection from winds, super-hump phenomena etc. into account), the RMS-value of the peak in power density spectrum allows us to estimate eccentricities of these orbits. We present these very interesting results. We show that our results generally agree with independent studies of these parameters.
ν Octantis: a conjectured S-type retrograde planet in a spectroscopic binary system
NASA Astrophysics Data System (ADS)
Nelson, Benjamin E.; Ramm, David; Endl, Michael
2016-01-01
ν Octantis is a single-lined spectroscopic binary system consisting of a K-giant primary and a secondary orbiting near 1050 days. Radial velocity observations reveal an additional ~400 day periodicity with a semi-amplitude of 40 m/s. If this signal is planetary in nature, the ν Octantis system would be unique amongst all known exoplanet systems in that long-term stability can only be achieved if the orbit is retrograde with respect to the stellar companions (i.e. mutual inclination ~ 180°).Spectral line analyses suggest this signal is unlikely to be due to surface activity or pulsations (Ramm 2015). We also rule out an exotic scenario where the secondary itself is a binary.We report an analysis of 1437 radial velocity measurements taken with HERCULES at the Mt. John Observatory spanning nearly 13 years, 1180 being new iodine iodine-cell velocities (2009-2013). The sensitive orbital dynamics of the two-companion model allow us to constrain the three-dimensional orbital architecture directly from the observations. Posterior samples obtained from an n-body Markov chain Monte Carlo (Nelson et al. 2014) yields a mutual inclination of 158.4 ± 1.2°. None of these are dynamically stable beyond 106 years. However, a grid search around the posterior sample suggests that they are in close proximity to a region of parameter space that is stable for at least 106 years.If real, the tight orbital architecture here imposes a considerable challenge for formation of this dynamically extreme system.
More support for the extreme S-type retrograde planet in the spectroscopic binary ν Octantis
NASA Astrophysics Data System (ADS)
Nelson, Benjamin Earl; Ramm, David; Endl, Michael; Gunn, Fraser; Hearnshaw, John; Kilmartin, Pam; Bergmann, Christoph; Brogt, Erik
2015-12-01
ν Octantis is a single-lined spectroscopic binary system consisting of a K-giant primary and a secondary orbiting near 1050 days. Radial velocity observations reveal an additional ~400 day periodicity with a semi-amplitude of 40 m/s. If this signal is planetary in nature, the ν Octantis system would be unique amongst all known exoplanet systems in that long-term stability can only be achieved if the orbit is retrograde with respect to the stellar companions (i.e. mutual inclination ~ 180°).Spectral line analyses suggest this signal is unlikely to be due to surface activity or pulsations (Ramm 2015). We also rule out an exotic scenario where the secondary itself is a binary.We report an analysis of 1437 radial velocity measurements taken with HERCULES at the Mt. John Observatory spanning nearly 13 years, 1180 being new iodine iodine-cell velocities (2009-2013). The sensitive orbital dynamics of the two-companion model allow us to constrain the three-dimensional orbital architecture directly from the observations. Posterior samples obtained from an n-body Markov chain Monte Carlo (Nelson et al. 2014) yields a mutual inclination of 158.4 ± 1.2°. None of these are dynamically stable beyond 106 years. However, a grid search around the posterior sample suggests that they are in close proximity to a region of parameter space that is stable for at least 106 years.If real, the tight orbital architecture here imposes a considerable challenge for formation of this dynamically extreme system.
Factors Affecting Crowded Acuity: Eccentricity and Contrast
Coates, Daniel R.; Chin, Jeremy M.; Chung, Susana T. L.
2013-01-01
Purpose Acuity measurement is a fundamental method to assess visual performance in the clinic. Little is known about how acuity measured in the presence of neighboring letters, as in the case of letter charts, changes with contrast and with non-foveal viewing. This information is crucial for acuity measurement using low-contrast charts and when patients cannot use their fovea. In this study, we evaluated how optotype acuity, with and without flankers, is affected by contrast and eccentricity. Methods Five young adults with normal vision identified the orientation of a Tumbling-E alone or in the presence of four flanking Tumbling-Es. Edge-to-edge letter spacing ranged from 1 to 20 bar widths. Stimuli were presented on a white background for 150 ms with Weber contrast ranging from −2.5% to −99%. Flankers had the same size and contrast as the target. Testings were performed at the fovea, 3, 5 and 10 degrees in the inferior visual field. Results When plotted as a function of letter spacing, acuity remains unaffected by the presence of flankers until the flankers are within the critical spacing, which averages an edge-to-edge spacing of 4.4 bar widths at the fovea, and approximately 16 bar widths at all three eccentricities. Critical spacing decreases with a reduction in contrast. When plotted as a function of contrast, acuity only worsens when the contrast falls below approximately 24% at the fovea and 17% in the periphery, for flanked and unflanked conditions alike. Conclusions The letter spacing on conventional letter charts exceeds the critical spacing for acuity measurement at the fovea, at all contrast levels. Thus these charts are appropriate for assessing foveal acuity. In the periphery, the critical spacing is larger than the letter spacing on conventional charts. Consequently, these charts may underestimate the acuity measured in the periphery due to the effects of crowding. PMID:23770657
Chronic tendinopathy: effectiveness of eccentric exercise
Woodley, Brett L; Newsham‐West, Richard J; Baxter, G David
2007-01-01
Objectives: To determine the effectiveness of eccentric exercise (EE) programmes in the treatment of common tendinopathies. Data sources: Relevant randomised controlled trials (RCTs) were sourced using the OVID website databases: MEDLINE (1966–Jan 2006), CINAHL (1982–Jan 2006), AMED (1985–Jan 2006), EMBASE (1988–Jan 2006), and all EBM reviews – Cochrane DSR, ACP Journal Club, DARE, and CCTR (Jan 2006). The Physiotherapy Evidence Database (PEDro) was also searched using the keyword: eccentric. Review methods: The PEDro and van Tulder scales were employed to assess methodological quality. Levels of evidence were then obtained according to predefined thresholds: Strong–consistent findings among multiple high‐quality RCTs. Moderate–consistent findings among multiple low‐quality RCTs and/or clinically controlled trials (CCTs) and/or one high‐quality RCT. Limited–one low‐quality RCT and/or CCT. Conflicting–inconsistent findings among multiple trials (RCTs and/or CCTs). No evidence–no RCTs or CCTs. Results: Twenty relevant studies were sourced, 11 of which met the inclusion criteria. These included studies of Achilles tendinopathy (AT), patella tendinopathy (PT) and tendinopathy of the common wrist extensor tendon of the lateral elbow (LET). Limited levels of evidence exist to suggest that EE has a positive effect on clinical outcomes such as pain, function and patient satisfaction/return to work when compared to various control interventions such as concentric exercise (CE), stretching, splinting, frictions and ultrasound. Levels of evidence were found to be variable across the tendinopathies investigated. Conclusions: This review demonstrates the dearth of high‐quality research in support of the clinical effectiveness of EE over other treatments in the management of tendinopathies. Further adequately powered studies that include appropriate randomisation procedures, standardised outcome measures and long‐term follow‐up are required
Orbital Resonances in the Solar Nebula: Strengths and Weaknesses
NASA Technical Reports Server (NTRS)
Malhotra, Renu
1993-01-01
A planetesimal moving in the Solar Nebula experiences an aero- dynamic drag which causes its orbit to circularize and shrink. However, resonant perturbations from a protoplanet interior to the planetesimal's orbit ran counteract both the orbital decay and the damping of the eccentricity: the planetesimal can be captured into an orbital resonance and its eccentricity pumped up to a modestly high equilibrium value. Thus, orbital resonances constitute (partial) barriers to the delivery of planetesimals into the feeding zone of the protoplanet. We have established the characteristics of the phenomenon of resonance capture by gas drag in the circular restricted three-body approximation. We have determined the strengths of the equilibrium resonant orbits with respect to impulsive velocity perturbations. We conclude that planetesimals captured in orbital resonances are quite vulnerable to being dislocated from these orbits by mutual planetesimal interactions, but that the resonances are effective in slowing down the rate of orbital decay of planetesimals. Only very small bodies, less or approx. equal to 100 m, are able to reach a approx. 1 mass of the earth protoplanet without being slowed down by resonances.
Secular orbital evolution of Jupiter family comets
NASA Astrophysics Data System (ADS)
Rickman, H.; Gabryszewski, R.; Wajer, P.; Wiśniowski, T.; Wójcikowski, K.; Szutowicz, S.; Valsecchi, G. B.; Morbidelli, A.
2017-02-01
Context. The issue of the long term dynamics of Jupiter family comets (JFCs) involves uncertain assumptions about the physical evolution and lifetimes of these comets. Contrary to what is often assumed, real effects of secular dynamics cannot be excluded and therefore merit investigation. Aims: We use a random sample of late heavy bombardment cometary projectiles to study the long-term dynamics of JFCs by a Monte Carlo approach. In a steady-state picture of the Jupiter family, we investigate the orbital distribution of JFCs, including rarely visited domains like retrograde orbits or orbits within the outer parts of the asteroid main belt. Methods: We integrate 100 000 objects over a maximum of 100 000 orbital revolutions including the Sun, a comet, and four giant planets. Considering the steady-state number of JFCs to be proportional to the total time spent in the respective orbital domain, we derive the capture rate based on observed JFCs with small perihelia and large nuclei. We consider a purely dynamical model and one where the nuclei are eroded by ice sublimation. Results: The JFC inclination distribution is incompatible with our erosional model. This may imply that a new type of comet evolution model is necessary. Considering that comets may live for a long time, we show that JFCs can evolve into retrograde orbits as well as asteroidal orbits in the outer main belt or Cybele regions. The steady-state capture rate into the Jupiter family is consistent with 1 × 109 scattered disk objects with diameters D > 2 km. Conclusions: Our excited scattered disk makes it difficult to explain the JFC inclination distribution, unless the physical evolution of JFCs is more intricate than assumed in standard, erosional models. Independent of this, the population size of the Jupiter family is consistent with a relatively low-mass scattered disk.
Correlations between Compositions and Orbits Established by the Giant Impact Era of Planet Formation
NASA Astrophysics Data System (ADS)
Dawson, Rebekah I.; Lee, Eve J.; Chiang, Eugene
2016-05-01
The giant impact phase of terrestrial planet formation establishes connections between super-Earths’ orbital properties (semimajor axis spacings, eccentricities, mutual inclinations) and interior compositions (the presence or absence of gaseous envelopes). Using N-body simulations and analytic arguments, we show that spacings derive not only from eccentricities, but also from inclinations. Flatter systems attain tighter spacings, a consequence of an eccentricity equilibrium between gravitational scatterings, which increase eccentricities, and mergers, which damp them. Dynamical friction by residual disk gas plays a critical role in regulating mergers and in damping inclinations and eccentricities. Systems with moderate gas damping and high solid surface density spawn gas-enveloped super-Earths with tight spacings, small eccentricities, and small inclinations. Systems in which super-Earths coagulate without as much ambient gas, in disks with low solid surface density, produce rocky planets with wider spacings, larger eccentricities, and larger mutual inclinations. A combination of both populations can reproduce the observed distributions of spacings, period ratios, transiting planet multiplicities, and transit duration ratios exhibited by Kepler super-Earths. The two populations, both formed in situ, also help to explain observed trends of eccentricity versus planet size, and bulk density versus method of mass measurement (radial velocities versus transit timing variations). Simplifications made in this study—including the limited time span of the simulations, and the approximate treatments of gas dynamical friction and gas depletion history—should be improved on in future work to enable a detailed quantitative comparison to the observations.
NEAR-EARTH BINARIES AND TRIPLES: ORIGIN AND EVOLUTION OF SPIN-ORBITAL PROPERTIES
Fang, Julia; Margot, Jean-Luc
2012-01-15
In the near-Earth asteroid population, binary and triple systems have been discovered with mutual orbits that have significant eccentricities as well as large semimajor axes. All known systems with eccentric orbits and all widely separated primary-satellite pairs have rapidly rotating satellites. Here, we study processes that can elucidate the origin of these spin-orbital properties. Binary formation models based on rotational fissioning can reproduce asynchronous satellites on orbits with high eccentricities and a wide range of separations, but do not match observed properties. We explore whether any evolutionary mechanisms can link the spin and orbital parameters expected from post-fission dynamics to those observed today. We investigate four processes: tidal torques, radiative perturbations (BYORP), close planetary encounters, and Kozai oscillations. We find that a combination of post-fission dynamics and tidal evolution can explain nearly all the spin-orbit properties in a sample of nine well-characterized near-Earth binaries and triples. The other mechanisms may act as well but are not required to explain the observed data. Lastly, we describe evolutionary pathways between observed spin-orbital states including synchronous and circular, asynchronous and circular, and asynchronous and eccentric configurations.
Eccentricity effect of micropatterned surface on contact angle.
Kashaninejad, Navid; Chan, Weng Kong; Nguyen, Nam-Trung
2012-03-13
This article experimentally shows that the wetting property of a micropatterned surface is a function of the center-to-center offset distance between successive pillars in a column, referred to here as eccentricity. Studies were conducted on square micropatterns which were fabricated on a silicon wafer with pillar eccentricity ranging from 0 to 6 μm for two different pillar diameters and spacing. Measurement results of the static as well as the dynamic contact angles on these surfaces revealed that the contact angle decreases with increasing eccentricity and increasing relative spacing between the pillars. Furthermore, quantification of the contact angle hysteresis (CAH) shows that, for the case of lower pillar spacing, CAH could increase up to 41%, whereas for the case of higher pillar spacing, this increment was up to 35%, both corresponding to the maximum eccentricity of 6 μm. In general, the maximum obtainable hydrophobicity corresponds to micropillars with zero eccentricity. As the pillar relative spacing decreases, the effect of eccentricity on hydrophobicity becomes more pronounced. The dependence of the wettability conditions of the micropatterned surface on the pillar eccentricity is attributed to the contact line deformation resulting from the changed orientation of the pillars. This finding provides additional insights in design and fabrication of efficient micropatterned surfaces with controlled wetting properties.
An alternative approach for computing seismic response with accidental eccentricity
NASA Astrophysics Data System (ADS)
Fan, Xuanhua; Yin, Jiacong; Sun, Shuli; Chen, Pu
2014-09-01
Accidental eccentricity is a non-standard assumption for seismic design of tall buildings. Taking it into consideration requires reanalysis of seismic resistance, which requires either time consuming computation of natural vibration of eccentric structures or finding a static displacement solution by applying an approximated equivalent torsional moment for each eccentric case. This study proposes an alternative modal response spectrum analysis (MRSA) approach to calculate seismic responses with accidental eccentricity. The proposed approach, called the Rayleigh Ritz Projection-MRSA (RRP-MRSA), is developed based on MRSA and two strategies: (a) a RRP method to obtain a fast calculation of approximate modes of eccentric structures; and (b) an approach to assemble mass matrices of eccentric structures. The efficiency of RRP-MRSA is tested via engineering examples and compared with the standard MRSA (ST-MRSA) and one approximate method, i.e., the equivalent torsional moment hybrid MRSA (ETM-MRSA). Numerical results show that RRP-MRSA not only achieves almost the same precision as ST-MRSA, and is much better than ETM-MRSA, but is also more economical. Thus, RRP-MRSA can be in place of current accidental eccentricity computations in seismic design.
Insights into the neural control of eccentric contractions.
Duchateau, Jacques; Baudry, Stéphane
2014-06-01
The purpose of this brief review is to examine our current knowledge of the neural control of eccentric contractions. The review focuses on three main issues. The first issue considers the ability of individuals to activate muscles maximally during eccentric contractions. Most studies indicate that, regardless of the experimental approach (surface EMG amplitude, twitch superimposition, and motor unit recordings), it is usually more difficult to achieve full activation of a muscle by voluntary command during eccentric contractions than during concentric and isometric contractions. The second issue is related to the specificity of the control strategy used by the central nervous system during submaximal eccentric contractions. This part underscores that although the central nervous system appears to employ a single size-related strategy to activate motoneurons during the different types of contractions, the discharge rate of motor units is less during eccentric contractions across different loading conditions. The last issue addresses the mechanisms that produce this specific neural activation. This section indicates that neural adjustments at both supraspinal and spinal levels contribute to the specific modulation of voluntary activation during eccentric contractions. Although the available information on the control of eccentric contractions has increased during the last two decades, this review indicates that the exact mechanisms underlying the unique neural modulation observed in this type of contraction at spinal and supraspinal levels remains unknown and their understanding represents, therefore, a major challenge for future research on this topic.
EXTRACTING PLANET MASS AND ECCENTRICITY FROM TTV DATA
Lithwick, Yoram; Xie Jiwei; Wu Yanqin
2012-12-20
Most planet pairs in the Kepler data that have measured transit time variations (TTVs) are near first-order mean-motion resonances. We derive analytical formulae for their TTV signals. We separate planet eccentricity into free and forced parts, where the forced part is purely due to the planets' proximity to resonance. This separation yields simple analytical formulae. The phase of the TTV depends sensitively on the presence of free eccentricity: if the free eccentricity vanishes, the TTV will be in phase with the longitude of conjunctions. This effect is easily detectable in current TTV data. The amplitude of the TTV depends on planet mass and free eccentricity, and it determines planet mass uniquely only when the free eccentricity is sufficiently small. We analyze the TTV signals of six short-period Kepler pairs. We find that three of these pairs (Kepler 18, 24, 25) have a TTV phase consistent with zero. The other three (Kepler 23, 28, 32) have small TTV phases, but ones that are distinctly non-zero. We deduce that the free eccentricities of the planets are small, {approx}< 0.01, but not always vanishing. Furthermore, as a consequence of this, we deduce that the true masses of the planets are fairly accurately determined by the TTV amplitudes, within a factor of {approx}< 2. The smallness of the free eccentricities suggests that the planets have experienced substantial dissipation. This is consistent with the hypothesis that the observed pile-up of Kepler pairs near mean-motion resonances is caused by resonant repulsion. But the fact that some of the planets have non-vanishing free eccentricity suggests that after resonant repulsion occurred there was a subsequent phase in the planets' evolution when their eccentricities were modestly excited, perhaps by interplanetary interactions.
Water dynamics and retrogradation of ultrahigh pressurized wheat starch.
Doona, Christopher J; Feeherry, Florence E; Baik, Moo-Yeol
2006-09-06
The water dynamics and retrogradation kinetics behavior of gelatinized wheat starch by either ultrahigh pressure (UHP) processing or heat are investigated. Wheat starch completely gelatinized in the condition of 90, 000 psi at 25 degrees C for 30 min (pressurized gel) or 100 degrees C for 30 min (heated gel). The physical properties of the wheat starches were characterized in terms of proton relaxation times (T2 times) measured using time-domain nuclear magnetic resonance spectroscopy and evaluated using commercially available continuous distribution modeling software. Different T2 distributions in both micro- and millisecond ranges between pressurized and heated wheat starch gels suggest distinctively different water dynamics between pressurized and heated wheat starch gels. Smaller water self-diffusion coefficients were observed for pressurized wheat starch gels and are indicative of more restricted translational proton mobility than is observed with heated wheat starch gels. The physical characteristics associated with changes taking place during retrogradation were evaluated using melting curves obtained with differential scanning calorimetry. Less retrogradation was observed in pressurized wheat starch, and it may be related to a smaller quantity of freezable water in pressurized wheat starch. Starches comprise a major constituent of many foods proposed for commercial potential using UHP, and the present results furnish insight into the effect of UHP on starch gelatinization and the mechanism of retrogradation during storage.
Light intensity-dependent retrograde signalling in higher plants.
Szechyńska-Hebda, Magdalena; Karpiński, Stanisław
2013-11-15
Plants are able to acclimate to highly fluctuating light environment and evolved a short- and long-term light acclimatory responses, that are dependent on chloroplasts retrograde signalling. In this review we summarise recent evidences suggesting that the chloroplasts act as key sensors of light intensity changes in a wide range (low, high and excess light conditions) as well as sensors of darkness. They also participate in transduction and synchronisation of systemic retrograde signalling in response to differential light exposure of distinct leaves. Regulation of intra- and inter-cellular chloroplast retrograde signalling is dependent on the developmental and functional stage of the plastids. Therefore, it is discussed in following subsections: firstly, chloroplast biogenic control of nuclear genes, for example, signals related to photosystems and pigment biogenesis during early plastid development; secondly, signals in the mature chloroplast induced by changes in photosynthetic electron transport, reactive oxygen species, hormones and metabolite biosynthesis; thirdly, chloroplast signalling during leaf senescence. Moreover, with a help of meta-analysis of multiple microarray experiments, we showed that the expression of the same set of genes is regulated specifically in particular types of signals and types of light conditions. Furthermore, we also highlight the alternative scenarios of the chloroplast retrograde signals transduction and coordination linked to the role of photo-electrochemical signalling.
Baudet, Juan-Salvador; Arguiñarena, Xabier; Redondo, Ignacio; Tadeo, Eva; Navazo, Lucía; Mendiz, Javier; Montiel, Raquel
2011-02-01
This report describes the case of a patient who developed a subcapsular hepatic hematoma 48 hours after endoscopic retrograde cholangiopancreatography. She was treated by embolizing the sites of bleeding and by surgically resecting the area. We review the literature and discuss the potential mechanisms that cause this complication.
Selected properties of acetylated adipate of retrograded starch.
Zięba, T; Gryszkin, A; Kapelko, M
2014-01-01
Native potato starch (NS) and retrograded starch (R - obtained via freezing and defrosting of a starch paste) were used to prepare starch acetates: NS-A and R-A, and then acetylated distarch adipates: NS-ADA and R-ADA. The chemically-modified preparations produced from retrograded starch (R-A; R-ADA) were characterized by a higher degree of esterification compared to the modified preparations produced under the same conditions from native potato starch (NS-A; NS-ADA). Starch resistance to amylolysis was observed to increase (to 30-40 g/100 g) as a result of starch retrogradation and acetylation. Starch cross-linking had a significant impact on the increased viscosity of the paste in the entire course of pasting characteristics and on the increased values of rheological coefficients determined from the equations describing flow curves. The produced preparation of acetylated retrograded starch cross-linked with adipic acid (R-ADA) may be deemed an RS3/4 preparation to be used as a food thickening agent.
Chloroplast Retrograde Regulation of Heat Stress Responses in Plants
Sun, Ai-Zhen; Guo, Fang-Qing
2016-01-01
It is well known that intracellular signaling from chloroplast to nucleus plays a vital role in stress responses to survive environmental perturbations. The chloroplasts were proposed as sensors to heat stress since components of the photosynthetic apparatus housed in the chloroplast are the major targets of thermal damage in plants. Thus, communicating subcellular perturbations to the nucleus is critical during exposure to extreme environmental conditions such as heat stress. By coordinating expression of stress specific nuclear genes essential for adaptive responses to hostile environment, plants optimize different cell functions and activate acclimation responses through retrograde signaling pathways. The efficient communication between plastids and the nucleus is highly required for such diverse metabolic and biosynthetic functions during adaptation processes to environmental stresses. In recent years, several putative retrograde signals released from plastids that regulate nuclear genes have been identified and signaling pathways have been proposed. In this review, we provide an update on retrograde signals derived from tetrapyrroles, carotenoids, reactive oxygen species (ROS) and organellar gene expression (OGE) in the context of heat stress responses and address their roles in retrograde regulation of heat-responsive gene expression, systemic acquired acclimation, and cellular coordination in plants. PMID:27066042
An Eccentric Accretion Disk In V691 Cra?
NASA Astrophysics Data System (ADS)
Peris, Charith; Vrtilek, S. D.
2011-09-01
We present phase-resolved spectroscopic observations over a full orbital period (5.6 hr) of the low-mass X-ray binary, V691 CrA, obtained with IMACS on the 6.5-m Walter Baade telescope at Las Campanas Observatory in June 2010. This is part of an on-going program to construct modulated tomograms in selected optical lines that enable us to study the geometry of the accretion flow and to examine spectral signatures that differentiate between neutron stars and black holes. The images constructed via tomography provide one of the few paths toward detailed insight into the structure of spatially unresolved accretion processes and the dependence of that structure on the nature of the central condensed object. Apparent in the V691 CrA spectrum are emission lines from H, He, and Fe with Hα and HeII 4686 showing clear double peaks varying with phase. Using K1= 94.5 km/s (Casares et al., 2010) and K2 = 324 km/s (Jonker et al 2003) we confirm a systemic velocity γ = -43 km/s (Casares et al 2003). Using these values to generate Modulation maps in Hα we find strong disk emission and a bright spot at the point where the accreting stream hits the disk. The center of the disk appears significantly offset from the center-of-mass of the system indicating an eccentric disk that may be associated with precession. We will present these results in the context of both black hole and neutron star systems observed by our project. SDV has been supported in part by NSF grant AST-0507637 awarded to the Smithsonian Astrophysical Observatory and a Smithsonian Institution Scholarly Studies Grant.
An Analytic Theory for the Orbits of Circumbinary Planets
NASA Astrophysics Data System (ADS)
Leung, Gene C. K.; Lee, Man Hoi
2013-02-01
Three transiting circumbinary planets (Kepler-16 b, Kepler-34 b, and Kepler-35 b) have recently been discovered from photometric data taken by the Kepler spacecraft. Their orbits are significantly non-Keplerian because of the large secondary-to-primary mass ratio and orbital eccentricity of the binaries, as well as the proximity of the planets to the binaries. We present an analytic theory, with the planet treated as a test particle, which shows that the planetary motion can be represented by the superposition of the circular motion of a guiding center, the forced oscillations due to the non-axisymmetric components of the binary's potential, the epicyclic motion, and the vertical motion. In this analytic theory, the periapse and ascending node of the planet precess at nearly equal rates in opposite directions. The largest forced oscillation term corresponds to a forced eccentricity (which is an explicit function of the parameters of the binary and of the guiding center radius of the planet), and the amplitude of the epicyclic motion (which is a free parameter of the theory) is the free eccentricity. Comparisons with direct numerical orbit integrations show that this analytic theory gives an accurate description of the planetary motion for all three Kepler systems. We find that all three Kepler circumbinary planets have nonzero free eccentricities.
AN ANALYTIC THEORY FOR THE ORBITS OF CIRCUMBINARY PLANETS
Leung, Gene C. K.; Lee, Man Hoi
2013-02-15
Three transiting circumbinary planets (Kepler-16 b, Kepler-34 b, and Kepler-35 b) have recently been discovered from photometric data taken by the Kepler spacecraft. Their orbits are significantly non-Keplerian because of the large secondary-to-primary mass ratio and orbital eccentricity of the binaries, as well as the proximity of the planets to the binaries. We present an analytic theory, with the planet treated as a test particle, which shows that the planetary motion can be represented by the superposition of the circular motion of a guiding center, the forced oscillations due to the non-axisymmetric components of the binary's potential, the epicyclic motion, and the vertical motion. In this analytic theory, the periapse and ascending node of the planet precess at nearly equal rates in opposite directions. The largest forced oscillation term corresponds to a forced eccentricity (which is an explicit function of the parameters of the binary and of the guiding center radius of the planet), and the amplitude of the epicyclic motion (which is a free parameter of the theory) is the free eccentricity. Comparisons with direct numerical orbit integrations show that this analytic theory gives an accurate description of the planetary motion for all three Kepler systems. We find that all three Kepler circumbinary planets have nonzero free eccentricities.
NASA Astrophysics Data System (ADS)
Beust, H.; Bonfils, X.; Montagnier, G.; Delfosse, X.; Forveille, T.
2012-09-01
Context. The close-in planet orbiting GJ 436 presents a puzzling orbital eccentricity (e ≃ 0.14) considering its very short orbital period. Given the age of the system, this planet should have been tidally circularized a long time ago. Many attempts to explain this were proposed in recent years, either involving abnormally weak tides, or the perturbing action of a distant companion. Aims: In this paper, we address the latter issue based on Kozai migration. We propose that GJ 436b was formerly located further away from the star and that it underwent a migration induced by a massive, inclined perturber via Kozai mechanism. In this context, the perturbations by the companion trigger high-amplitude variations to GJ 436b that cause tides to act at periastron. Then the orbit tidally shrinks to reach its present day location. Methods: We numerically integrate the 3-body system including tides and general relativity correction. We use a modified symplectic integrator as well as a fully averaged integrator. The former is slower but accurate to any order in semi-major axis ratio, while the latter is first truncated to some order (4th) in semi-major axis ratio before averaging. Results: We first show that starting from the present-day location of GJ 436b inevitably leads to damping the Kozai oscillations and to rapidly circularizing the planet. Conversely, starting from 5-10 times further away allows the onset of Kozai cycles. The tides act in peak eccentricity phases and reduce the semi-major axis of the planet. The net result is a two-fold evolution, characterized by two phases: a first one with Kozai cycles and a slowly shrinking semi-major axis, and a second one once the planet gets out of the Kozai resonance characterized by a more rapid decrease. The timescale of this process appears in most cases much longer than the standard circularization time of the planet by a factor of 50 or above. Conclusions: This model can provide a solution to the eccentricity paradox of GJ
Eccentric Exercise Program Design: A Periodization Model for Rehabilitation Applications
Harris-Love, Michael O.; Seamon, Bryant A.; Gonzales, Tomas I.; Hernandez, Haniel J.; Pennington, Donte; Hoover, Brian M.
2017-01-01
The applied use of eccentric muscle actions for physical rehabilitation may utilize the framework of periodization. This approach may facilitate the safe introduction of eccentric exercise and appropriate management of the workload progression. The purpose of this data-driven Hypothesis and Theory paper is to present a periodization model for isokinetic eccentric strengthening of older adults in an outpatient rehabilitation setting. Exemplar and group data are used to describe the initial eccentric exercise prescription, structured familiarization procedures, workload progression algorithm, and feasibility of the exercise regimen. Twenty-four men (61.8 ± 6.3 years of age) completed a 12-week isokinetic eccentric strengthening regimen involving the knee extensors. Feasibility and safety of the regimen was evaluated using serial visual analog scale (VAS, 0–10) values for self-reported pain, and examining changes in the magnitude of mean eccentric power as a function of movement velocity. Motor learning associated with the familiarization sessions was characterized through torque-time curve analysis. Total work was analyzed to identify relative training plateaus or diminished exercise capacity during the progressive phase of the macrocycle. Variability in the mean repetition interval decreased from 68 to 12% during the familiarization phase of the macrocycle. The mean VAS values were 2.9 ± 2.7 at the start of the regimen and 2.6 ± 2.9 following 12 weeks of eccentric strength training. During the progressive phase of the macrocycle, exercise workload increased from 70% of the estimated eccentric peak torque to 141% and total work increased by 185% during this training phase. The slope of the total work performed across the progressive phase of the macrocycle ranged from −5.5 to 29.6, with the lowest slope values occurring during microcycles 8 and 11. Also, mean power generation increased by 25% when eccentric isokinetic velocity increased from 60 to 90° s−1
Eccentric Exercise Program Design: A Periodization Model for Rehabilitation Applications.
Harris-Love, Michael O; Seamon, Bryant A; Gonzales, Tomas I; Hernandez, Haniel J; Pennington, Donte; Hoover, Brian M
2017-01-01
The applied use of eccentric muscle actions for physical rehabilitation may utilize the framework of periodization. This approach may facilitate the safe introduction of eccentric exercise and appropriate management of the workload progression. The purpose of this data-driven Hypothesis and Theory paper is to present a periodization model for isokinetic eccentric strengthening of older adults in an outpatient rehabilitation setting. Exemplar and group data are used to describe the initial eccentric exercise prescription, structured familiarization procedures, workload progression algorithm, and feasibility of the exercise regimen. Twenty-four men (61.8 ± 6.3 years of age) completed a 12-week isokinetic eccentric strengthening regimen involving the knee extensors. Feasibility and safety of the regimen was evaluated using serial visual analog scale (VAS, 0-10) values for self-reported pain, and examining changes in the magnitude of mean eccentric power as a function of movement velocity. Motor learning associated with the familiarization sessions was characterized through torque-time curve analysis. Total work was analyzed to identify relative training plateaus or diminished exercise capacity during the progressive phase of the macrocycle. Variability in the mean repetition interval decreased from 68 to 12% during the familiarization phase of the macrocycle. The mean VAS values were 2.9 ± 2.7 at the start of the regimen and 2.6 ± 2.9 following 12 weeks of eccentric strength training. During the progressive phase of the macrocycle, exercise workload increased from 70% of the estimated eccentric peak torque to 141% and total work increased by 185% during this training phase. The slope of the total work performed across the progressive phase of the macrocycle ranged from -5.5 to 29.6, with the lowest slope values occurring during microcycles 8 and 11. Also, mean power generation increased by 25% when eccentric isokinetic velocity increased from 60 to 90° s(-1) while
ON THE TRANSIT POTENTIAL OF THE PLANET ORBITING IOTA DRACONIS
Kane, Stephen R.; Reffert, Sabine; Schwab, Christian; Bergmann, Christoph; Henry, Gregory W.; Fischer, Debra; Clubb, Kelsey I.
2010-09-10
Most of the known transiting exoplanets are in short-period orbits, largely due to the bias inherent in detecting planets through the transit technique. However, the eccentricity distribution of the known radial velocity planets results in many of those planets having a non-negligible transit probability. One such case is the massive planet orbiting the giant star iota Draconis, a situation where both the orientation of the planet's eccentric orbit and the size of the host star inflate the transit probability to a much higher value than for a typical hot Jupiter. Here we present a revised fit of the radial velocity data with new measurements and a photometric analysis of the stellar variability. We provide a revised transit probability, an improved transit ephemeris, and discuss the prospects for observing a transit of this planet from both ground and space.
A general time element for orbit integration in Cartesian coordinates
NASA Technical Reports Server (NTRS)
Janin, G.; Bond, V. R.
1981-01-01
Two techniques are discussed for increasing the accuracy of the numerical integration of eccentric orbits in Cartesian coordinates. One involves the use of an independent variable different from time; this increases the efficiency of the numerical integration. The other uses a time element, which reduces the in-track error. A general expression is given of a time element valid for an arbitrary independent variable. It is pointed out that this time element makes it possible to switch the independent variable merely by applying a scaling factor; there is no need to change the differential equations of the motion. Eccentric, true, and elliptic anomalies are used as independent variables in the case of a transfer orbit for a geosynchronous orbit. The elliptic anomaly is shown to perform much better than the other classical anomalies.
The Equilibrium Temperature of Planets in Elliptical Orbits
NASA Astrophysics Data System (ADS)
Méndez, Abel; Rivera-Valentín, Edgard G.
2017-03-01
There exists a positive correlation between orbital eccentricity and the average stellar flux that planets receive from their parent star. Often, though, it is assumed that the average equilibrium temperature would correspondingly increase with eccentricity. Here, we test this assumption by calculating and comparing analytic solutions for both the spatial and temporal averages of orbital distance, stellar flux, and equilibrium temperature. Our solutions show that the average equilibrium temperature of a planet, with a constant albedo, slowly decreases with eccentricity until converging to a value 90% that of a circular orbit. This might be the case for many types of planets (e.g., hot Jupiters); however, the actual equilibrium and surface temperature of planets also depend on orbital variations of albedo and greenhouse. Our results also have implications in understanding the climate, habitability, and the occurrence of potential Earth-like planets. For instance, it helps explain why the limits of the habitable zone for planets in highly elliptical orbits are wider than expected from the mean flux approximation, as shown by climate models.
Retrograde fluids in granulites: Stable isotope evidence of fluid migration
Morrison, J. ); Valley, J.W. )
1991-07-01
Widespread retrograde alteration assemblages document the migration of mixed H{sub 2}O-CO{sub 2} fluids into granulite facies rocks in the Adirondack Mountains. Fluid migration is manifest by (1) veins and patchy intergrowths of chlorite {plus minus} sericite {plus minus} calcite, (2) small veins of calcite, many only identifiable by cathodoluminescence, and (3) high-density, CO{sub 2}-rich or mixed H{sub 2}O-CO{sub 2} fluid inclusions. The distinct and varied textural occurrences of the alteration minerals indicate that fluid-rock ratios were low and variable on a local scale. Stable isotope ratios of C, O, and S have been determined in retrograde minerals from samples of the Marcy anorthosite massif and adjacent granitic gneisses (charnockites). Retrograde calcite in the anorthosite has a relatively small range in both {delta}{sup 18}O{sub SMOW} and {delta}{sup 13}C{sub PDB} (8.6 to 14.9% and {minus}4.1 to 0.4%, respectively), probably indicating that the hydrothermal fluids that precipitated the calcite had exchanged with a variety of crustal lithologies including marbles and orthogneisses, and that calcite was precipitated over a relatively narrow temperature interval. Values of {delta}{sup 34}S{sub CDT} that range from 2.8 to 8.3% within the anorthosite can also be interpreted to reflect exchange between orthogneisses and metasediments. The recognition of retrograde fluid migration is particularly significant in granulite facies terranes because the controversy surrounding the origin of granulites arises in part from differing interpretations of fluid inclusion data, specifically, the timing of entrapment of high-density, CO{sub 2}-rich inclusions. Results indicate that retrograde fluid migration, which in some samples may leave only cryptic petrographic evidence, is a process capable of producing high-density, CO{sub 2}-rich fluid inclusions.
A Planet Orbiting 47 Ursae Majoris
NASA Astrophysics Data System (ADS)
Butler, R. Paul; Marcy, Geoffrey W.
1996-06-01
The G0 V star 47 UMa exhibits very low amplitude radial velocity variations having a period of 2.98 yr, a velocity amplitude of K = 45.5 m s-1, and small eccentricity. The residuals scatter by 11 m s-1 from a Keplerian fit to the 34 velocity measurements obtained during 8 yr. The minimum mass of the unseen companion is M2 sin i = 2.39 MJ, and for likely orbital inclinations of 30 deg--90 deg, its mass is less than 4.8 MJ. This mass resides in a regime associated with extrasolar giant planets (Burrows and coworkers). Unlike the planet candidates 70 Vir B and 51 Peg B, this companion has an orbital radius (2.1 AU) and eccentricity (e = 0.03) reminiscent of giant planets in our solar system. Its effective temperature will be at least 180 K due simply to absorbed stellar radiation, and probably slightly higher due to intrinsic heating from gravitational contraction (Guillot and coworkers). For 47 UMa B to be, instead, an orbiting brown dwarf of mass M > 40 MJ, the inclination would have to be i < 3.dg4, which occurs for only 0.18% of randomly oriented orbits. In any case, this companion is separated from the primary star by ~0."2, which portends follow-up work by astrometric and direct IR techniques.
Stationkeeping for the Lunar Reconnaissance Orbiter (LRO)
NASA Technical Reports Server (NTRS)
Beckman, Mark; Lamb, Rivers
2007-01-01
The Lunar Reconnaissance Orbiter (LRO) is scheduled to launch in 2008 as the first mission under NASA's Vision for Space Exploration. Following several weeks in a quasi-frozen commissioning orbit, LRO will fly in a 50 km mean altitude lunar polar orbit. During the one year mission duration, the orbital dynamics of a low lunar orbit force LRO to perform periodic sets of stationkeeping maneuvers. This paper explores the characteristics of low lunar orbits and explains how the LRO stationkeeping plan is designed to accommodate the dynamics in such an orbit. The stationkeeping algorithm used for LRO must meet five mission constraints. These five constraints are to maintain ground station contact during maneuvers, to control the altitude variation of the orbit, to distribute periselene equally between northern and southern hemispheres, to match eccentricity at the beginning and the end of the sidereal period, and to minimize stationkeeping deltaV. This paper addresses how the maneuver plan for LRO is designed to meet all of the above constraints.
Stationkeeping for the Lunar Reconnaissance Orbiter (LRO)
NASA Technical Reports Server (NTRS)
Beckman, Mark; Lamb, Rivers
2007-01-01
The Lunar Reconnaissance Orbiter (LRO) is scheduled to launch in 2008 as the first mission under NASA's Vision for Space Exploration. Follo wing several weeks in a quasi-frozen commissioning orbit, LRO will fl y in a 50 km mean altitude lunar polar orbit. During the one year mis sion duration, the orbital dynamics of a low lunar orbit force LRO to perform periodic sets of stationkeeping maneuvers. This paper explor es the characteristics of low lunar orbits and explains how the LRO s tationkeeping plan is designed to accommodate the dynamics in such an orbit. The stationkeeping algorithm used for LRO must meet five miss ion constraints. These five constraints are to maintain ground statio n contact during maneuvers, to control the altitude variation of the orbit, to distribute periselene equally between northern and southern hemispheres, to match eccentricity at the beginning and the end of the sidereal period, and to minimize stationkeeping (Delta)V. This pape r addresses how the maneuver plan for LRO is designed to meet all of the above constraints.
NASA Astrophysics Data System (ADS)
Dawson, Rebekah I.; Johnson, John Asher; Morton, Timothy D.; Crepp, Justin R.; Fabrycky, Daniel C.; Murray-Clay, Ruth A.; Howard, Andrew W.
2012-12-01
The exoplanets known as hot Jupiters—Jupiter-sized planets with periods of less than 10 days—likely are relics of dynamical processes that shape all planetary system architectures. Socrates et al. argued that high eccentricity migration (HEM) mechanisms proposed for situating these close-in planets should produce an observable population of highly eccentric proto-hot Jupiters that have not yet tidally circularized. HEM should also create failed-hot Jupiters, with periapses just beyond the influence of fast circularization. Using the technique we previously presented for measuring eccentricities from photometry (the "photoeccentric effect"), we are distilling a collection of eccentric proto- and failed-hot Jupiters from the Kepler Objects of Interest (KOI). Here, we present the first, KOI-1474.01, which has a long orbital period (69.7340 days) and a large eccentricity e = 0.81+0.10 -0.07, skirting the proto-hot Jupiter boundary. Combining Kepler photometry, ground-based spectroscopy, and stellar evolution models, we characterize host KOI-1474 as a rapidly rotating F star. Statistical arguments reveal that the transiting candidate has a low false-positive probability of 3.1%. KOI-1474.01 also exhibits transit-timing variations of the order of an hour. We explore characteristics of the third-body perturber, which is possibly the "smoking-gun" cause of KOI-1474.01's large eccentricity. We use the host star's period, radius, and projected rotational velocity to measure the inclination of the stellar spin. Comparing KOI 1474.01's inclination, we find that its orbit is marginally consistent with being aligned with the stellar spin axis, although a reanalysis is warranted with future additional data. Finally, we discuss how the number and existence of proto-hot Jupiters will not only demonstrate that hot Jupiters migrate via HEM, but also shed light on the typical timescale for the mechanism.
Dawson, Rebekah I.; Murray-Clay, Ruth A.; Johnson, John Asher; Morton, Timothy D.; Crepp, Justin R.; Fabrycky, Daniel C.; Howard, Andrew W.
2012-12-20
The exoplanets known as hot Jupiters-Jupiter-sized planets with periods of less than 10 days-likely are relics of dynamical processes that shape all planetary system architectures. Socrates et al. argued that high eccentricity migration (HEM) mechanisms proposed for situating these close-in planets should produce an observable population of highly eccentric proto-hot Jupiters that have not yet tidally circularized. HEM should also create failed-hot Jupiters, with periapses just beyond the influence of fast circularization. Using the technique we previously presented for measuring eccentricities from photometry (the ''photoeccentric effect''), we are distilling a collection of eccentric proto- and failed-hot Jupiters from the Kepler Objects of Interest (KOI). Here, we present the first, KOI-1474.01, which has a long orbital period (69.7340 days) and a large eccentricity e 0.81{sup +0.10}{sub -0.07}, skirting the proto-hot Jupiter boundary. Combining Kepler photometry, ground-based spectroscopy, and stellar evolution models, we characterize host KOI-1474 as a rapidly rotating F star. Statistical arguments reveal that the transiting candidate has a low false-positive probability of 3.1%. KOI-1474.01 also exhibits transit-timing variations of the order of an hour. We explore characteristics of the third-body perturber, which is possibly the ''smoking-gun'' cause of KOI-1474.01's large eccentricity. We use the host star's period, radius, and projected rotational velocity to measure the inclination of the stellar spin. Comparing KOI 1474.01's inclination, we find that its orbit is marginally consistent with being aligned with the stellar spin axis, although a reanalysis is warranted with future additional data. Finally, we discuss how the number and existence of proto-hot Jupiters will not only demonstrate that hot Jupiters migrate via HEM, but also shed light on the typical timescale for the mechanism.
NASA Astrophysics Data System (ADS)
Sheppard, Scott S.; Trujillo, Chadwick; Tholen, David J.
2016-07-01
We are conducting a survey for distant solar system objects beyond the Kuiper Belt edge (˜50 au) with new wide-field cameras on the Subaru and CTIO telescopes. We are interested in the orbits of objects that are decoupled from the giant planet region to understand the structure of the outer solar system, including whether a massive planet exists beyond a few hundred astronomical units as first reported in 2014 by Trujillo & Sheppard. In addition to discovering extreme trans-Neptunian objects detailed elsewhere, we found several objects with high perihelia (q > 40 au) that differ from the extreme and inner Oort cloud objects due to their moderate semimajor axes (50 < a < 100 au) and eccentricities (e ≲ 0.3). Newly discovered objects 2014 FZ71 and 2015 FJ345 have the third and fourth highest perihelia known after Sedna and 2012 VP113, yet their orbits are not nearly as eccentric or distant. We found several of these high-perihelion but moderate orbit objects and observe that they are mostly near Neptune mean motion resonances (MMRs) and have significant inclinations (i > 20°). These moderate objects likely obtained their unusual orbits through combined interactions with Neptune’s MMRs and the Kozai resonance, similar to the origin scenarios for 2004 XR190. We also find the distant 2008 ST291 has likely been modified by the MMR+KR mechanism through the 6:1 Neptune resonance. We discuss these moderately eccentric distant objects along with some other interesting low inclination outer classical belt objects like 2012 FH84 discovered in our ongoing survey.
An Assessment of Relativistic Effects for Low Earth Orbiters: The GRACE Satellites
2007-01-01
IOP PUBLISHING METROLOGIA Metrologia 44 (2007) 484–490 doi:10.1088/0026-1394/44/6/007 An assessment of relativistic effects for low Earth orbiters...for the larger-eccentricity orbit is shown in figure 2(b). Metrologia , 44 (2007) 484–490 485 K M Larson et al Figure 1. Amplitude of the once/rev...486 Metrologia , 44 (2007) 484–490 Assessment of relativistic effects for low Earth orbiters combination was launched on TOPEX in 1992. Unfortunately
TOPEX/Poseidon orbit maintenance for the first five years
NASA Technical Reports Server (NTRS)
Bhat, R. S.; Shapiro, B. E.; Frauenholz, R. B.; Leavitt, R. K.
1998-01-01
The TOPEX/Poseidon orbit maintenance strategy was changed following launch to include the effects of observed unmodeled, and hence anomalous, along-track accelerations. The anomalous force causes the semi-major axis, a, to either increase (called "boost") or decrease ("deboost" or "decay") depending on the satellite attitude and solar array pitch angle offset. Although this force is the most uncertain parameter in ground track prediction, it has been used as a passive technique for orbit maintenance, thereby reducing the number of propulsive maneuvers, enhancing maneuver spacing, and to place maneuvers at convenient times. This passive technique was first demonstrated in May 1993. The TOPEX/Poseidon orbit has been uniquely maintained using both passive (non-propulsive) and active (propulsive) maneuvers. Furthermore, the orbit has been maintained using only the passive technique since the ninth orbit maintenance maneuver on January 15, 1996. Only nine orbit maintenance maneuvers have been required to maintain the ground track, including verification site over flights, since achieving the operational orbit on September 21, 1992 (mission requirement: 95% within +/- l km). During this period, a has varied within 7,714,429 +/- 7 m, while the inclination i periodically fluctuated in the range 66.0408 deg. +/- 0.0040 deg. The frozen orbit (required e < 0.001 and omega approximately equals to 90 deg.) has been maintained without any dedicated eccentricity maneuvers. The frozen eccentricity vector has completed two periodic cycles and it is currently tracing its third cycle (period approximately equals 26.7 months).
On the Orbit of Exoplanet WASP-12b
NASA Astrophysics Data System (ADS)
Campo, Christopher J.; Harrington, Joseph; Hardy, Ryan A.; Stevenson, Kevin B.; Nymeyer, Sarah; Ragozzine, Darin; Lust, Nate B.; Anderson, David R.; Collier-Cameron, Andrew; Blecic, Jasmina; Britt, Christopher B. T.; Bowman, William C.; Wheatley, Peter J.; Loredo, Thomas J.; Deming, Drake; Hebb, Leslie; Hellier, Coel; Maxted, Pierre F. L.; Pollaco, Don; West, Richard G.
2011-02-01
We observed two secondary eclipses of the exoplanet WASP-12b using the Infrared Array Camera on the Spitzer Space Telescope. The close proximity of WASP-12b to its G-type star results in extreme tidal forces capable of inducing apsidal precession with a period as short as a few decades. This precession would be measurable if the orbit had a significant eccentricity, leading to an estimate of the tidal Love number and an assessment of the degree of central concentration in the planetary interior. An initial ground-based secondary-eclipse phase reported by López-Morales et al. (0.510 ± 0.002) implied eccentricity at the 4.5σ level. The spectroscopic orbit of Hebb et al. has eccentricity 0.049 ± 0.015, a 3σ result, implying an eclipse phase of 0.509 ± 0.007. However, there is a well-documented tendency of spectroscopic data to overestimate small eccentricities. Our eclipse phases are 0.5010 ± 0.0006 (3.6 and 5.8 μm) and 0.5006 ± 0.0007 (4.5 and 8.0 μm). An unlikely orbital precession scenario invoking an alignment of the orbit during the Spitzer observations could have explained this apparent discrepancy, but the final eclipse phase of López-Morales et al. (0.510 ±+0.007 -0.006) is consistent with a circular orbit at better than 2σ. An orbit fit to all the available transit, eclipse, and radial-velocity data indicates precession at <1σ a non-precessing solution fits better. We also comment on analysis and reporting for Spitzer exoplanet data in light of recent re-analyses.
ON THE ORBIT OF EXOPLANET WASP-12b
Campo, Christopher J.; Harrington, Joseph; Hardy, Ryan A.; Stevenson, Kevin B.; Nymeyer, Sarah; Lust, Nate B.; Blecic, Jasmina; Britt, Christopher B. T.; Bowman, William C.; Ragozzine, Darin; Anderson, David R.; Hellier, Coel; Maxted, Pierre F. L.; Collier-Cameron, Andrew; Wheatley, Peter J.; Loredo, Thomas J.; Deming, Drake; Hebb, Leslie; Pollaco, Don; West, Richard G.
2011-02-01
We observed two secondary eclipses of the exoplanet WASP-12b using the Infrared Array Camera on the Spitzer Space Telescope. The close proximity of WASP-12b to its G-type star results in extreme tidal forces capable of inducing apsidal precession with a period as short as a few decades. This precession would be measurable if the orbit had a significant eccentricity, leading to an estimate of the tidal Love number and an assessment of the degree of central concentration in the planetary interior. An initial ground-based secondary-eclipse phase reported by Lopez-Morales et al. (0.510 {+-} 0.002) implied eccentricity at the 4.5{sigma} level. The spectroscopic orbit of Hebb et al. has eccentricity 0.049 {+-} 0.015, a 3{sigma} result, implying an eclipse phase of 0.509 {+-} 0.007. However, there is a well-documented tendency of spectroscopic data to overestimate small eccentricities. Our eclipse phases are 0.5010 {+-} 0.0006 (3.6 and 5.8 {mu}m) and 0.5006 {+-} 0.0007 (4.5 and 8.0 {mu}m). An unlikely orbital precession scenario invoking an alignment of the orbit during the Spitzer observations could have explained this apparent discrepancy, but the final eclipse phase of Lopez-Morales et al. (0.510 {+-}{sup +0.007}{sub -0.006}) is consistent with a circular orbit at better than 2{sigma}. An orbit fit to all the available transit, eclipse, and radial-velocity data indicates precession at <1{sigma}; a non-precessing solution fits better. We also comment on analysis and reporting for Spitzer exoplanet data in light of recent re-analyses.
Orbits Close to Asteroid 4769 Castalia
NASA Technical Reports Server (NTRS)
Scheeres, D. J.; Ostro, S. J.; Hudson, R. S.; Werner, R. A.
1996-01-01
We use a radar-derived physical model of 4769 Castalia (1989 PB) to investigate close orbit dynamics around that kilometer- sized, uniformly rotating asteroid. Our methods of analysis provide a basis for systematic studies of particle dynamics close to any uniformly rotating asteroid. We establish that a Jacobi integral exists for particles orbiting this asteroid, examine the attendant zero-velocity surfaces, find families of periodic orbits, and determine their stability. All synchronous orbits and direct orbits within approx. 3 mean radii of Castalia are unstable and are subject to impact or escape from Castalia. Retrograde orbits are mostly stable and allow particles to orbit close to the asteroid surface. We derive a model which allows us to predict the escape conditions of a particle in orbit about Castalia and the (temporary) capture conditions for a hyperbolic interloper. Orbits within 1.5 km of Castalia are subject to immediate ejection from the system. Hyperbolic orbits with a V(sub infinity) less than 0.4 m/sec can potentially be captured by Castalia if their periapsis radius Is within approx. 2 km. For Castalia this capture region is small, but the results also apply to larger asteroids whose capture regions would also be larger. We determine bounds on ejecta speeds which either ensure ejecta escape or re-impact as functions of location on Castalia's surface. The speeds that ensure escape range from 0.28 to 0.84 m/sec and the speeds that ensure re-impact range from 0 to 0.18 m/sec. Speeds between these two bounds lead either to escape, re-impact, or potentially finite-time stable orbits. We develop a simple criterion which can establish whether a particle could have been ejected from the asteroid in the past and if it will impact the surface in the future.
Welsh, William F.; Orosz, Jerome A.; Aerts, Conny; Zima, Wolfgang; Brown, Timothy M.; Brugamyer, Erik; Cochran, William D.; Gilliland, Ronald L.; Guzik, Joyce Ann; Kurtz, D. W.; Latham, David W.; Quinn, Samuel N.; Marcy, Geoffrey W.; Allen, Christopher; Bryson, Steve; Caldwell, Douglas A.; Howell, Steve B.; Gautier, Thomas N.
2011-11-01
Kepler observations of the star HD 187091 (KIC 8112039, hereafter KOI-54) revealed a remarkable light curve exhibiting sharp periodic brightening events every 41.8 days with a superimposed set of oscillations forming a beating pattern in phase with the brightenings. Spectroscopic observations revealed that this is a binary star with a highly eccentric orbit, e = 0.83. We are able to match the Kepler light curve and radial velocities with a nearly face-on (i = 5.{sup 0}5) binary star model in which the brightening events are caused by tidal distortion and irradiation of nearly identical A stars during their close periastron passage. The two dominant oscillations in the light curve, responsible for the beating pattern, have frequencies that are the 91st and 90th harmonic of the orbital frequency. The power spectrum of the light curve, after removing the binary star brightening component, reveals a large number of pulsations, 30 of which have a signal-to-noise ratio {approx}>7. Nearly all of these pulsations have frequencies that are either integer multiples of the orbital frequency or are tidally split multiples of the orbital frequency. This pattern of frequencies unambiguously establishes the pulsations as resonances between the dynamic tides at periastron and the free oscillation modes of one or both of the stars. KOI-54 is only the fourth star to show such a phenomenon and is by far the richest in terms of excited modes.
Effects of Variable Eccentricity on the Climate of an Earth-like World
NASA Astrophysics Data System (ADS)
Way, M. J.; Georgakarakos, Nikolaos
2017-01-01
The Kepler era of exoplanetary discovery has presented the astronomical community with a cornucopia of planetary systems that are very different from the one that we inhabit. It has long been known that Jupiter plays a major role in the orbital parameters of Mars and its climate, but there is also a long-standing belief that Jupiter would play a similar role for Earth if not for the Moon. Using a three-dimensional general circulation model (3D GCM) with a fully coupled ocean, we simulate what would happen to the climate of an Earth-like world if Mars did not exist, but a Jupiter-like planet was much closer to Earth’s orbit. We investigate two scenarios that involve the evolution of the Earth-like planet’s orbital eccentricity from 0 to 0.283 over 6500 years, and from 0 to 0.066 on a timescale of 4500 years. In both cases we discover that they would maintain relatively temperate climates over the timescales simulated. More Earth-like planets in multi-planet systems will be discovered as we continue to survey the skies and the results herein show that the proximity of large gas giant planets may play an important role in the habitability of these worlds. These are the first such 3D GCM simulations using a fully coupled ocean with a planetary orbit that evolves over time due to the presence of a giant planet.
Cowey, A; Stoerig, P; Williams, C
1999-10-01
The extent of transneuronal retrograde degeneration of ganglion cells in the primate retina depends on the age at which striate cortex was damaged, the survival time, the species, and retinal eccentricity. We here report on the effect of lesion size beyond striate cortex, which we assessed along with retinal ganglion cell degeneration in three groups of macaque monkeys who, in each group, had undergone striate cortical ablation at similar ages and survived for similar periods, which ranged from 302 days to 8 years. Where possible, the number of surviving projection neurones in the degenerated dLGN and its volume were also estimated. Results confirm that both geniculate and retinal degeneration correlate significantly with survival time but that the differences within a group can exceed differences between groups and are best accounted for by the extent of the damage to extra-striate visual cortex and underlying white matter.
Inner mean-motion resonances with eccentric planets: a possible origin for exozodiacal dust clouds
NASA Astrophysics Data System (ADS)
Faramaz, V.; Ertel, S.; Booth, M.; Cuadra, J.; Simmonds, C.
2017-02-01
High levels of dust have been detected in the immediate vicinity of many stars, both young and old. A promising scenario to explain the presence of this short-lived dust is that these analogues to the zodiacal cloud (or exozodis) are refilled in situ through cometary activity and sublimation. As the reservoir of comets is not expected to be replenished, the presence of these exozodis in old systems has yet to be adequately explained. It was recently suggested that mean-motion resonances with exterior planets on moderately eccentric (ep ≳ 0.1) orbits could scatter planetesimals on to cometary orbits with delays of the order of several 100 Myr. Theoretically, this mechanism is also expected to sustain continuous production of active comets once it has started, potentially over Gyr time-scales. We aim here to investigate the ability of this mechanism to generate scattering on to cometary orbits compatible with the production of an exozodi on long time-scales. We combine analytical predictions and complementary numerical N-body simulations to study its characteristics. We show, using order of magnitude estimates, that via this mechanism, low-mass discs comparable to the Kuiper belt could sustain comet scattering at rates compatible with the presence of the exozodis which are detected around Solar-type stars, and on Gyr time-scales. We also find that the levels of dust detected around Vega could be sustained via our proposed mechanism if an eccentric Jupiter-like planet were present exterior to the system's cold debris disc.
Radiation-driven Warping of Circumbinary Disks around Eccentric Young Star Binaries
NASA Astrophysics Data System (ADS)
Hayasaki, Kimitake; Sohn, Bong Won; Okazaki, Atsuo T.; Jung, Taehyun; Zhao, Guangyao; Naito, Tsuguya
2014-12-01
We study a warping instability of a geometrically thin, non-self-gravitating, circumbinary disk around young binary stars on an eccentric orbit. Such a disk is subject to both the tidal torques due to a time-dependent binary potential and the radiative torques due to radiation emitted from each star. The tilt angle between the circumbinary disk plane and the binary orbital plane is assumed to be very small. We find that there is a radius within/beyond which the circumbinary disk is unstable to radiation-driven warping, depending on the disk density and temperature gradient indices. This marginally stable warping radius is very sensitive to viscosity parameters, a fiducial disk radius and the temperature measured there, the stellar luminosity, and the disk surface density at a radius where the disk changes from optically thick to thin for the irradiation from the central stars. On the other hand, it is insensitive to the orbital eccentricity and binary irradiation parameter, which is a function of the binary mass ratio and luminosity of each star. Since the tidal torques can suppress the warping in the inner part of the circumbinary disk, the disk starts to be warped in the outer part. While the circumbinary disks are most likely to be subject to the radiation-driven warping on an AU to kilo-AU scale for binaries with young massive stars more luminous than 104 L ⊙, the radiation-driven warping does not work for those around young binaries with the luminosity comparable to the solar luminosity.
VIEW NORTH, SOUTH ELEVATION OF (FROM LEFT) ECCENTRIC HOUSE, BELT ...
VIEW NORTH, SOUTH ELEVATION OF (FROM LEFT) ECCENTRIC HOUSE, BELT SHED, AND ENGINE HOUSE, NOTE EXHAUST LOWER RIGHT OF ENGINE HOUSE. - Golden Oil Company, Lot 410 Lease, Sheffield Field, Donaldson, Warren County, PA
VIEW EAST, EAST ELEVATION OF ECCENTRIC HOUSE, NOTE ROD LINES ...
VIEW EAST, EAST ELEVATION OF ECCENTRIC HOUSE, NOTE ROD LINES EXITING THE BUILDING AND ROD LINES WITH SUPPORTS IN FOREGROUND LEFT. - South Penn Oil Company, G. M. Mead Lot 492 Lease, Morrison Run Field, Clarendon, Warren County, PA
Near- and Far-Field Optical Response of Eccentric Nanoshells
NASA Astrophysics Data System (ADS)
Peña-Rodríguez, Ovidio; Díaz-Núñez, Pablo; Rodríguez-Iglesias, Vladimir; Montaño-Priede, Luis; Rivera, Antonio; Pal, Umapada
2017-01-01
We study the optical response of eccentric nanoshells (i.e., spherical nanoparticles with an eccentric spherical inclusion) in the near and the far field through finite-difference time-domain simulations. Plasmon hybridization theory is used to explain the obtained results. The eccentricity generates a far-field optical spectrum with various plasmon peaks. The number, position, and width of the peaks depend on the core offset. Near-field enhancements in the surroundings of these structures are significantly larger than those obtained for equivalent concentric nanoshells and, more importantly, they are almost independent of the illumination conditions. This opens up the door for using eccentric nanoshells in applications requiring intense near-field enhancements.
Near- and Far-Field Optical Response of Eccentric Nanoshells.
Peña-Rodríguez, Ovidio; Díaz-Núñez, Pablo; Rodríguez-Iglesias, Vladimir; Montaño-Priede, Luis; Rivera, Antonio; Pal, Umapada
2017-12-01
We study the optical response of eccentric nanoshells (i.e., spherical nanoparticles with an eccentric spherical inclusion) in the near and the far field through finite-difference time-domain simulations. Plasmon hybridization theory is used to explain the obtained results. The eccentricity generates a far-field optical spectrum with various plasmon peaks. The number, position, and width of the peaks depend on the core offset. Near-field enhancements in the surroundings of these structures are significantly larger than those obtained for equivalent concentric nanoshells and, more importantly, they are almost independent of the illumination conditions. This opens up the door for using eccentric nanoshells in applications requiring intense near-field enhancements.
RESEARCH PAPERS : Geomagnetic induction in multiple eccentrically nested spheres
NASA Astrophysics Data System (ADS)
Martinec, Z.
1998-01-01
We present a semi-analytic solution to the 3-D forward modelling of electromagnetic induction in a heterogeneous model consisting of multiple eccentrically nested spheres. A number of numerical methods for 2-D and 3-D global electromagnetic modelling have been applied recently, including thin-sheet, perturbation-expansion, finite-element and spectral-finite-element schemes. The present semi-analytical approach may be used as an aid for testing more general algorithms of electromagnetic induction modelling. The multiple eccentrically nested spheres solution has been tested by comparing against the analytical solution for electromagnetic induction in a uniform sphere and in two eccentrically nested spheres with an azimuthal structure of electrical conductivity, and good agreements have been obtained. We further solve the electromagnetic induction problem in three and four eccentrically nested spheres configurations and compute the global response function and the spherical components of magnetic intensity within the model.
NASA Astrophysics Data System (ADS)
Schlaufman, Kevin C.; Winn, Joshua N.
2016-07-01
The origin of Jupiter-mass planets with orbital periods of only a few days is still uncertain. It is widely believed that these planets formed near the water-ice line of the protoplanetary disk, and subsequently migrated into much smaller orbits. Most of the proposed migration mechanisms can be classified either as disk-driven migration, or as excitation of a very high eccentricity followed by tidal circularization. In the latter scenario, the giant planet that is destined to become a hot Jupiter spends billions of years on a highly eccentric orbit, with apastron near the water-ice line. Eventually, tidal dissipation at periastron shrinks and circularizes the orbit. If this is correct, then it should be especially rare for hot Jupiters to be accompanied by another giant planet interior to the water-ice line. Using the current sample of giant planets discovered with the Doppler technique, we find that hot Jupiters with P orb < 10 days are no more or less likely to have exterior Jupiter-mass companions than longer-period giant planets with P orb ≥ 10 days. This result holds for exterior companions both inside and outside of the approximate location of the water-ice line. These results are difficult to reconcile with the high-eccentricity migration scenario for hot Jupiter formation.
Seismic response of eccentrically braced tall buildings
Celebi, Mehmet
1993-01-01
Spectral analysis and system identification techniques are used to analyze a set of acceleration reponse records obtained during the Loma Prieta earthquake from the 47-story, moment-resisting framed and eccentrically braced Embarcadero Building (EMB). The EMB was constructed in 1979 based on the 1976 Uniform Building Code requirements and a design response spectra defined by two levels of earthquake performances. The EMB is in the lower market area of San Francisco, which is of great interest to the engineering community because of the area's soft soil characteristics that amplify ground motions originating at long distances, and because the Embarcadero freeway suffered extensive damage during the earthquake and was razed in 1991. The first modal frequencies of the building at approximately 0.19 Hz (north-south) and 0.16 Hz (east-west) are identified. The torsional response and rocking motions of the building are insignificant. Discontinuity of stiffness and mass at the 40th floor level causes significant response issues above that floor such as excessive drift ratios.
Orbits of the ten small satellites of Uranus
Owen, W.M. Jr.; Synnott, S.P.
1987-05-01
Orbital elements are presented for the ten small satellites discovered by Voyager 2 at Uranus. These ten new satellites, whose provisional IAU designations are 1985UI and 1986UI through 1986U9, lie for the most part in equatorial, circular orbits; the most notable exception is 1986U8, the outer epsilon-ring shepherd, whose eccentricity e = 0.0101. Unlike the Voyager discoveries at Saturn, which included two co-orbiting satellites and three librators, the ten small Uranian satellites all have quite different semimajor axes. 11 references.
Orbital Evolution of Jupiter-Family Comets
NASA Astrophysics Data System (ADS)
Ipatov, S. I.; Mather, J. S.
2002-05-01
We investigated the evolution for periods of at least 5-10 Myr of 2500 Jupiter-crossing objects (JCOs) under the gravitational influence of all planets, except for Mercury and Pluto (without dissipative factors). In the first series we considered N=2000 orbits near the orbits of 30 real Jupiter-family comets with period <10 yr, and in the second series we took 500 orbits close to the orbit of Comet 10P Tempel 2. We calculated the probabilities of collisions of objects with the terrestrial planets, using orbital elements obtained with a step equal to 500 yr and then summarized the results for all time intervals and all bodies, obtaining the total probability PΣ of collisions with a planet and the total time interval TΣ during which perihelion distance of bodies was less than a semimajor axis of the planet. The values of P = 106 PΣ /N and T = TΣ /1000 yr are presented in Table together with the ratio r of the total time interval when orbits were of Apollo type (at e<0.999) to that of Amor type. Venus & Venus & Earth & Earth & Mars & Mars & - N & T & P & T & P & T & P & r 2000 & 9.3 & 6.62 & 14.0 & 6.65 & 24.7 & 2.03 & 1.32 500 & 24.9 & 16.3 & 44.0 & 24.5 & 96.2 & 5.92 & 1.49 The probability of collisions with the Earth for 3 former JCOs, each of which moved for more than 1 Myr in Earth-crossing orbits, (usually more than 80% of such collisions with the terrestrial planets were from orbits with aphelion distance <4.2 AU) was 1.5 times greater than that for 1997 other JCOs. About 1 of 300 JCOs collided with the Sun. The total time during which former 2000 JCOs were in Apollo-type and Amor-type orbits was 28.7 and 21.75 Myr, respectively, but 12.7 and 11.4 Myr of the above times were due to three objects. One former JCO spent some time in orbits with aphelia deep inside Jupiter's orbit, and then it moved for tens of Myr in the trans-Neptunian region, partly in low eccentricity and partly in high eccentricity orbits. We acknowledge support of this work by NASA grant
Dance as an eccentric form of exercise: practical implications.
Paschalis, Vassilis; Nikolaidis, Michalis G; Jamurtas, Athanasios Z; Owolabi, Emmanuel O; Kitas, George D; Wyon, Matthew A; Koutedakis, Yiannis
2012-06-01
The eccentric action is an integral part of the stretch-shortening (or eccentric-concentric) cycle of muscle movement, especially when repositioning of the centre of gravity is required. Jumps and landing tasks are examples of this cycle and are incorporated in most dance activities. However, unaccustomed eccentric muscle action can cause muscle damage, which is characterised by the development of delayed-onset muscle soreness and swelling, decline of pain-free range of motion, as well as sustained loss of muscle force and range of motion. Furthermore, unaccustomed eccentric muscle action can induce disturbances in movement economy and energy expenditure, so dancers spend more energy during a routine than usual. Such negative effects are gradually reduced and eventually disappear due to physiological adaptations to this form of muscular activity. Given that eccentric exercises also appear to induce greater muscle performance improvements than other forms of muscle conditioning, it is advised that they should be integrated into dancers' weekly schedules. The purpose of the present review is to examine the possible effects of the eccentric component of dance on the performance and health status of dancers.
Dynamics of black hole pairs. II. Spherical orbits and the homoclinic limit of zoom-whirliness
Grossman, Rebecca; Levin, Janna
2009-02-15
Spinning black hole pairs exhibit a range of complicated dynamical behaviors. An interest in eccentric and zoom-whirl orbits has ironically inspired the focus of this paper: the constant radius orbits. When black hole spins are misaligned, the constant radius orbits are not circles but, rather, they lie on the surface of a sphere and have acquired the name 'spherical orbits'. The spherical orbits are significant as they energetically frame the distribution of all orbits. In addition, each unstable spherical orbit is asymptotically approached by an orbit that whirls an infinite number of times, known as a homoclinic orbit. A homoclinic trajectory is an infinite whirl limit of the zoom-whirl spectrum and has a further significance as the separatrix between inspiral and plunge for eccentric orbits. We work in the context of two spinning black holes of comparable mass as described in the third-order post-Newtonian Hamiltonian with spin-orbit coupling included. As such, the results could provide a testing ground for the accuracy of the post-Newtonian expansion. Further, the spherical orbits could provide useful initial data for numerical relativity. Finally, we comment that the spinning black hole pairs should give way to chaos around the homoclinic orbit when spin-spin coupling is incorporated.
Luo, Denglin; Li, Yun; Xu, Baocheng; Ren, Guangyue; Li, Peiyan; Li, Xuan; Han, Sihai; Liu, Jianxue
2017-08-15
The effects of three types of inulin, including FS (DP≤10), FI (DP of 2-60) and FXL (DP≥23), on the gelatinization and retrogradation characteristics of wheat starch were investigated. As the concentration of inulin added into starch increased, the gelatinization temperature increased whereas the breakdown value decreased, and the value of setback first decreased and then increased slightly. The three types of inulin with lower concentrations (<15%) all showed obvious suppression effects on the short-term retrogradation of wheat starch. After 7days of storage, the three types of inulin showed a significant suppression of starch retrogradation in the addition range of 5-7.5%. They can all inhibit amylose retrogradation, but accelerate amylopectin retrogradation. Inulin with lower DP has stronger effects on the starch retrogradation. Generally, the three types of inulin can all retard the retrogradation performance of wheat starch to some extent in the long-term storage.
Ji, Na; Liu, Chengzhen; Zhang, Shuangling; Yu, Jing; Xiong, Liu; Sun, Qingjie
2017-01-01
Starch is very prone to retrogradation after gelatinization. Inhibition of starch retrogradation has been an important factor in improving the quality of food. For the first time, we investigated the effect of nano-materials, represented by chitin nano-whiskers (CNWs), on the short- and long-term retrogradation of maize and potato starches. Rapid Visco-Analyser results showed that the addition of CNWs significantly decreased the setback values of maize and potato starches, which suggested that CNWs could retard the short-term retrogradation of starch. Differential scanning calorimetry and X-ray diffraction results showed that the percentage of retrogradation of maize and potato starches significantly decreased (P<0.05), suggesting the inhibition of long-term retrogradation. The CNWs could be used as a new inhibitor of starch retrogradation to develop starch-based food with longer shelf life.
NASA Technical Reports Server (NTRS)
2005-01-01
The structure of NASA's Mars Reconnaissance Orbiter spacecraft is constructed from composite panels of carbon layers over aluminum honeycomb, lightweight yet strong. This forms a basic structure or skeleton on which the instruments, electronics, propulsion and power systems can be mounted. The propellant tank is contained in the center of the orbiter's structure. This photo was taken at Lockheed Martin Space Systems, Denver, during construction of the spacecraft.
Naoz, Smadar; Silk, Joseph
2014-11-10
We explore the effects of long-term secular perturbations on the distribution of dark matter particles around supermassive black hole (BH) binaries. We show that in the hierarchical (in separation) three-body problem, one of the BHs and a dark matter particle form an inner binary. Gravitational perturbations from the BH companion, on a much wider orbit, can cause the dark matter particle to reach extremely high eccentricities and even get accreted onto the BH by what is known as the eccentric Kozai-Lidov (EKL) mechanism. We show that this may produce a torus-like configuration for the dark matter distribution around the less massive member of the BH binary. We first consider an intermediate BH (IMBH) in the vicinity of our galactic center, which may be a relic of a past minor merger. We show that if the IMBH is close enough (i.e., near the stellar disk) the EKL mechanism is very efficient in exciting the eccentricity of dark matter particles in near-polar configurations to extremely high values where they are accreted by the IMBH. We show that this mechanism is even more effective if the central BH grows in mass, where we have assumed adiabatic growth. Because near-polar configurations are disrupted, a torus-like shape is formed. We also show that this behavior is also likely to be relevant for supermassive BH binaries. We suggest that if the BHs are spinning, the accreted dark matter particles may linger in the ergosphere, and thereby generate self-annihilations and produce an indirect signature of potential interest.
Low Earth orbit constellations: Orbit control or not
NASA Astrophysics Data System (ADS)
Radzik, Jose; Maral, Gerard
1993-01-01
The aim of the study is to list the arguments for and against the adoption of orbit control. The first section is a semi-analytical calculation of the probability of visibility with minimum elevation angle of a single satellite, to be used for altitudes less than 2000 km. Section two evaluates the number of noncontrolled satellites needed to guarantee a given probability of visibility for the whole constellation. Section three gives a comparison between noncontrolled and controlled constellations in the case of very low altitudes (less than 800 km). The main problem is the effect of atmospheric drag which reduces significantly the coverage performance of the satellite at its end of life. Evaluating the semi-major-axis contraction and eccentricity evolution with time allows us to define the noncontrolled satellite constellations.
The GEOS-3 orbit determination investigation
NASA Technical Reports Server (NTRS)
Pisacane, V. L.; Eisner, A.; Yionoulis, S. M.; Mcconahy, R. J.; Black, H. D.; Pryor, L. L.
1978-01-01
The nature and improvement in satellite orbit determination when precise altimetric height data are used in combination with conventional tracking data was determined. A digital orbit determination program was developed that could singly or jointly use laser ranging, C-band ranging, Doppler range difference, and altimetric height data. Two intervals were selected and used in a preliminary evaluation of the altimeter data. With the data available, it was possible to determine the semimajor axis and eccentricity to within several kilometers, in addition to determining an altimeter height bias. When used jointly with a limited amount of either C-band or laser range data, it was shown that altimeter data can improve the orbit solution.
HAT-P-17b,c: A TRANSITING, ECCENTRIC, HOT SATURN AND A LONG-PERIOD, COLD JUPITER
Howard, A. W.; Marcy, G. W.; Bakos, G. A.; Hartman, J.; Torres, G.; Latham, D. W.; Noyes, R. W.; Esquerdo, G. A.; Beky, B.; Sasselov, D. D.; Stefanik, R. P.; Perumpilly, G.; Shporer, A.; Mazeh, T.; Kovacs, Geza; Fischer, D. A.; Johnson, J. A.; Butler, R. P.; Lazar, J.; Papp, I. E-mail: gbakos@cfa.harvard.edu; and others
2012-04-20
We report the discovery of HAT-P-17b,c, a multi-planet system with an inner transiting planet in a short-period, eccentric orbit and an outer planet in a 4.4 yr, nearly circular orbit. The inner planet, HAT-P-17b, transits the bright V = 10.54 early K dwarf star GSC 2717-00417, with an orbital period P = 10.338523 {+-} 0.000009 days, orbital eccentricity e = 0.342 {+-} 0.006, transit epoch T{sub c} = 2454801.16943 {+-} 0.00020 (BJD: barycentric Julian dates throughout the paper are calculated from Coordinated Universal Time (UTC)), and transit duration 0.1690 {+-} 0.0009 days. HAT-P-17b has a mass of 0.534 {+-} 0.018 M{sub J} and radius of 1.010 {+-} 0.029 R{sub J} yielding a mean density of 0.64 {+-} 0.05 g cm{sup -3}. This planet has a relatively low equilibrium temperature in the range 780-927 K, making it an attractive target for follow-up spectroscopic studies. The outer planet, HAT-P-17c, has a significantly longer orbital period P{sub 2} = 1610 {+-} 20 days and a minimum mass m{sub 2}sin i{sub 2} = 1.31{sup +0.18}{sub -0.15} M{sub J}. The orbital inclination of HAT-P-17c is unknown as transits have not been observed and may not be present. The host star has a mass of 0.86 {+-} 0.04 M{sub Sun }, radius of 0.84 {+-} 0.02 R{sub Sun }, effective temperature 5246 {+-} 80 K, and metallicity [Fe/H] = 0.00 {+-} 0.08. HAT-P-17 is the second multi-planet system detected from ground-based transit surveys.
Relative orbit control of collocated geostationary spacecraft
NASA Astrophysics Data System (ADS)
Rausch, Raoul R.
A relative orbit control concept for collocated geostationary spacecraft is presented. One chief spacecraft, controlled from the ground, is responsible for the orbit determination and control of the remaining vehicles. Any orbit relative to the chief is described in terms of equinoctial orbit element differences and a linear mapping is employed for quick transformation from relative orbit measurements to orbit element differences. It is demonstrated that the concept is well-suited for spacecraft that are collocated using eccentricity-inclination vector separation and this formulation still allows for the continued use of well established and currently employed stationkeeping schemes, such as the Sun-pointing-perigee strategy. The relative approach allows to take determinisitc thruster cross-coupling effects in the computation of stationkeeping corrections into account. The control cost for the proposed concept is comparable to ground-based stationkeeping. A relative line-of-sight constraint between spacecraft separated in longitude is also considered and an algorithm is developed to provide enforcement options. The proposed on-board control approach maintains the deputy spacecraft relative orbit, is competitive in terms of propellant consumption, allows enforcement of a relative line-of-sight constraint and offers increased autonomy and flexibility for future missions.
Retrograde amnesia induced by drugs acting on different molecular systems.
Rossato, Janine I; Bonini, Juliana S; Coitinho, Adriana S; Vianna, Monica R M; Medina, Jorge H; Cammarota, Martín; Izquierdo, Iván
2004-06-01
The gamma aminobutyric acid-A (GABA-sub(A)) agonist, muscimol, the glutamate N-methyl-D-aspartate (NMDA) receptor antagonist, D-2-amino-5-phosphonopentanoic acid (AP5), and the inhibitor of the extracellularly regulated kinases (ERKs), UO 126, cause retrograde amnesia when administered to the hippocampus. In the present study, the authors found that they all cause retrograde amnesia for 1-trial inhibitory avoidance, not only when infused into the dorsal CA1 region of the hippocampus, but also when infused into the basolateral amygdala or the entorhinal, parietal, and posterior cingulate cortices. The posttraining time course of the effect of each drug was, however, quite different across brain structures. Thus, in all of them, NMDA receptors and the ERK pathway are indispensable for memory consolidation, and GABA-sub(A) receptor activation inhibits memory consolidation: but in each case, their influence is interwoven differently.
Photosynthetic light reactions: integral to chloroplast retrograde signalling.
Gollan, Peter J; Tikkanen, Mikko; Aro, Eva-Mari
2015-10-01
Chloroplast retrograde signalling is ultimately dependent on the function of the photosynthetic light reactions and not only guides the acclimation of the photosynthetic apparatus to changing environmental and metabolic cues, but has a much wider influence on the growth and development of plants. New information generated during the past few years about regulation of photosynthetic light reactions and identification of the underlying regulatory proteins has paved the way towards better understanding of the signalling molecules produced in chloroplasts upon changes in the environment. Likewise, the availability of various mutants lacking regulatory functions has made it possible to address the role of excitation energy distribution and electron flow in the thylakoid membrane in inducing the retrograde signals from chloroplasts to the nucleus. Such signalling molecules also induce and interact with hormonal signalling cascades to provide comprehensive information from chloroplasts to the nucleus.
Retrograde amnesia following carbon monoxide poisoning: a case report.
Acland, Peter R; Heaver, Catriona
2008-07-01
Retrograde amnesia is a recognised neurological complication of carbon monoxide poisoning. This article describes the case of a female found dead in her bath where initial post-mortem findings and the surrounding circumstances raised strong suspicions of homicide, especially when there was contradictory evidence from her husband who was the only other person present. He was later diagnosed as having retrograde amnesia between his two visits to the bathroom to attend to his wife which caused him to merge them into one event, thus arousing suspicions of foul play. The discussion explores the current clinical views on non-fatal carbon monoxide poisoning as well as problems of interpretation of information derived from case work.
WLS retrograde transport to the endoplasmic reticulum during Wnt secretion.
Yu, Jia; Chia, Joanne; Canning, Claire Ann; Jones, C Michael; Bard, Frédéric A; Virshup, David M
2014-05-12
Wnts are transported to the cell surface by the integral membrane protein WLS (also known as Wntless, Evi, and GPR177). Previous studies of WLS trafficking have emphasized WLS movement from the Golgi to the plasma membrane (PM) and then back to the Golgi via retromer-mediated endocytic recycling. We find that endogenous WLS binds Wnts in the endoplasmic reticulum (ER), cycles to the PM, and then returns to the ER through the Golgi. We identify an ER-targeting sequence at the carboxyl terminus of native WLS that is critical for ER retrograde recycling and contributes to Wnt secretory function. Golgi-to-ER recycling of WLS requires the COPI regulator ARF as well as ERGIC2, an ER-Golgi intermediate compartment protein that is also required for the retrograde trafficking of the KDEL receptor and certain toxins. ERGIC2 is required for efficient Wnt secretion. ER retrieval is an integral part of the WLS transport cycle.
Propofol use in endoscopic retrograde cholangiopancreatography and endoscopic ultrasound
Cheriyan, Danny G; Byrne, Michael F
2014-01-01
Compared to standard endoscopy, endoscopic retrograde cholangiopancreatography (ERCP) and endoscopic ultrasound (EUS) are often lengthier and more complex, thus requiring higher doses of sedatives for patient comfort and compliance. The aim of this review is to provide the reader with information regarding the use, safety profile, and merits of propofol for sedation in advanced endoscopic procedures like ERCP and EUS, based on the current literature. PMID:24833847
NanoSail - D Orbital and Attitude Dynamics
NASA Technical Reports Server (NTRS)
Heaton, Andrew F.; Faller, Brent F.; Katan, Chelsea K.
2013-01-01
NanoSail-D unfurled January 20th, 2011 and successfully demonstrated the deployment and deorbit capability of a solar sail in low Earth orbit. The orbit was strongly perturbed by solar radiation pressure, aerodynamic drag, and oblate gravity which were modeled using STK HPOP. A comparison of the ballistic coefficient history to the orbit parameters exhibits a strong relationship between orbital lighting, the decay rate of the mean semi-major axis and mean eccentricity. A similar comparison of mean solar area using the STK HPOP solar radiation pressure model exhibits a strong correlation of solar radiation pressure to mean eccentricity and mean argument of perigee. NanoSail-D was not actively controlled and had no capability on-board for attitude or orbit determination. To estimate attitude dynamics we created a 3-DOF attitude dynamics simulation that incorporated highly realistic estimates of perturbing forces into NanoSail-D torque models. By comparing the results of this simulation to the orbital behavior and ground observations of NanoSail-D, we conclude that there is a coupling between the orbit and attitude dynamics as well as establish approximate limits on the location of the NanoSail-D solar center of pressure. Both of these observations contribute valuable data for future solar sail designs and missions.
WASP-8b: CHARACTERIZATION OF A COOL AND ECCENTRIC EXOPLANET WITH SPITZER
Cubillos, Patricio; Harrington, Joseph; Hardy, Ryan A.; Blecic, Jasmina; Hardin, Matthew; Campo, Christopher J.; Madhusudhan, Nikku; Stevenson, Kevin B.; Anderson, David R.
2013-05-01
WASP-8b has 2.18 times Jupiter's mass and is on an eccentric (e = 0.31) 8.16 day orbit. With a time-averaged equilibrium temperature of 948 K, it is one of the least-irradiated hot Jupiters observed with the Spitzer Space Telescope. We have analyzed six photometric light curves of WASP-8b during secondary eclipse observed in the 3.6, 4.5, and 8.0 {mu}m Infrared Array Camera bands. The eclipse depths are 0.113% {+-} 0.018%, 0.069% {+-} 0.007%, and 0.093% {+-} 0.023%, respectively, giving respective brightness temperatures of 1552, 1131, and 938 K. We characterized the atmospheric thermal profile and composition of the planet using a line-by-line radiative transfer code and a Markov-chain Monte Carlo sampler. The data indicated no thermal inversion, independently of any assumption about chemical composition. We noted an anomalously high 3.6 {mu}m brightness temperature (1552 K); by modeling the eccentricity-caused thermal variation, we found that this temperature is plausible for radiative timescales less than {approx}10{sup 2} hr. However, as no model spectra fit all three data points well, the temperature discrepancy remains as an open question.
Formation of the Galactic Stellar Halo: Origin of the Metallicity-Eccentricity Relation.
Bekki; Chiba
2000-05-01
Motivated by the recently improved knowledge on the kinematic and chemical properties of the Galactic metal-poor stars, we present the numerical simulation for the formation of the Galactic stellar halo to interpret the observational results. As a model for the Galaxy contraction, we adopt the currently standard theory of galaxy formation based on the hierarchical assembly of the cold dark matter fluctuations. We find, for the simulated stars with &sqbl0;Fe&solm0;H&sqbr0;orbital eccentricities, in good agreement with the observations. Moreover, the observed fraction of the low-eccentricity stars is reproduced correctly for &sqbl0;Fe&solm0;H&sqbr0;
WASP-8b: Characterization of a Cool and Eccentric Exoplanet with Spitzer
NASA Astrophysics Data System (ADS)
Cubillos, Patricio; Harrington, Joseph; Madhusudhan, Nikku; Stevenson, Kevin B.; Hardy, Ryan A.; Blecic, Jasmina; Anderson, David R.; Hardin, Matthew; Campo, Christopher J.
2013-05-01
WASP-8b has 2.18 times Jupiter's mass and is on an eccentric (e = 0.31) 8.16 day orbit. With a time-averaged equilibrium temperature of 948 K, it is one of the least-irradiated hot Jupiters observed with the Spitzer Space Telescope. We have analyzed six photometric light curves of WASP-8b during secondary eclipse observed in the 3.6, 4.5, and 8.0 μm Infrared Array Camera bands. The eclipse depths are 0.113% ± 0.018%, 0.069% ± 0.007%, and 0.093% ± 0.023%, respectively, giving respective brightness temperatures of 1552, 1131, and 938 K. We characterized the atmospheric thermal profile and composition of the planet using a line-by-line radiative transfer code and a Markov-chain Monte Carlo sampler. The data indicated no thermal inversion, independently of any assumption about chemical composition. We noted an anomalously high 3.6 μm brightness temperature (1552 K) by modeling the eccentricity-caused thermal variation, we found that this temperature is plausible for radiative timescales less than ~102 hr. However, as no model spectra fit all three data points well, the temperature discrepancy remains as an open question.
Formation of the Galactic Stellar Halo: Origin of the Metallicity-Eccentricity Relation
NASA Astrophysics Data System (ADS)
Bekki, Kenji; Chiba, Masashi
2000-05-01
Motivated by the recently improved knowledge on the kinematic and chemical properties of the Galactic metal-poor stars, we present the numerical simulation for the formation of the Galactic stellar halo to interpret the observational results. As a model for the Galaxy contraction, we adopt the currently standard theory of galaxy formation based on the hierarchical assembly of the cold dark matter fluctuations. We find, for the simulated stars with [Fe/H]<=-1.0, that there is no strong correlation between metal abundances and orbital eccentricities, in good agreement with the observations. Moreover, the observed fraction of the low-eccentricity stars is reproduced correctly for [Fe/H]<=-1.6 and approximately for the intermediate abundance range of -1.6<[Fe/H]<=-1.0. We show that this successful reproduction of the kinematics of the Galactic halo is a natural consequence of the hierarchical evolution of the subgalactic clumps seeded from the cold dark matter density fluctuations.
Alkhateeb, Harith M.; Aljanabi, Thaer J.; Al-azzawi, Khairallh H.; Alkarboly, Taha A.
2015-01-01
Background Biliary leak can occur as a complication of biliary surgery, endoscopic retrograde cholangiopancreatography manipulations and endoscopic biliary sphincterotomy. Consequently, bile may collect in the abdominal cavity, a condition called biloma. Rarely, it may reach a massive size. Case presentation A 72-year-old man presented with gastric upset with gradual abdominal distension reaching a large size due to intra-abdominal bile collection (biloma) after endoscopic retrograde cholangiopancreatography plus endoscopic biliary sphincterotomy and stenting for post laparoscopic cholecystectomy common bile duct stricture. This huge biloma was treated by percutaneous insertion of a tube drain for a few days, evacuating the collection successfully without recurrence. Discussion This patient might sustain injury to the common bile duct either by the guide wire or stent, or the injury occurred at the angle between the common bile duct and duodenum during sphincterotomy of the ampulla. Although any of these rents may lead to a bile leak, causing a huge biloma, they could be successfully treated by percutaneous drainage. Conclusions (1) Following endoscopic retrograde cholangiopancreatography, a patient’s complaints should not be ignored. (2) A massive biloma can occur due to such procedures. (3) Conservative treatment with minimal invasive technique can prove to be effective. PMID:26402876
Novel class of potential therapeutics that target ricin retrograde translocation.
Redmann, Veronika; Gardner, Thomas; Lau, Zerlina; Morohashi, Keita; Felsenfeld, Dan; Tortorella, Domenico
2013-12-23
Ricin toxin, an A-B toxin from Ricinus communis, induces cell death through the inhibition of protein synthesis. The toxin binds to the cell surface via its B chain (RTB) followed by its retrograde trafficking through intracellular compartments to the ER where the A chain (RTA) is transported across the membrane and into the cytosol. Ricin A chain is transported across the ER membrane utilizing cellular proteins involved in the disposal of aberrant ER proteins by a process referred to as retrograde translocation. Given the current lack of therapeutics against ricin intoxication, we developed a high-content screen using an enzymatically attenuated RTA chimera engineered with a carboxy-terminal enhanced green fluorescent protein (RTA(E177Q)egfp) to identify compounds that target RTA retrograde translocation. Stabilizing RTA(E177Q)egfp through the inclusion of proteasome inhibitor produced fluorescent peri-nuclear granules. Quantitative analysis of the fluorescent granules provided the basis to discover compounds from a small chemical library (2080 compounds) with known bioactive properties. Strikingly, the screen found compounds that stabilized RTA molecules within the cell and several compounds limited the ability of wild type RTA to suppress protein synthesis. Collectively, a robust high-content screen was developed to discover novel compounds that stabilize intracellular ricin and limit ricin intoxication.
Proxima's orbit around α Centauri
NASA Astrophysics Data System (ADS)
Kervella, P.; Thévenin, F.; Lovis, C.
2017-01-01
Proxima and α Centauri AB have almost identical distances and proper motions with respect to the Sun. Although the probability of such similar parameters is, in principle, very low, the question as to whether they actually form a single gravitationally bound triple system has been open since the discovery of Proxima one century ago. Owing to HARPS high-precision absolute radial velocity measurements and the recent revision of the parameters of the α Cen pair, we show that Proxima and α Cen are gravitationally bound with a high degree of confidence. The orbital period of Proxima is ≈ 550 000 yr. With an eccentricity of , Proxima comes within kau of α Cen at periastron, and is currently close to apastron ( kau). This orbital motion may have influenced the formation or evolution of the recently discovered planet orbiting Proxima, as well as circumbinary planet formation around α Cen. Based on observations collected at the European Organisation for Astronomical Research in the Southern Hemisphere under ESO programs 072.C-0488(E), 082.C-0718(B), 183.C-0437(A), 191.C-0505(A) and 096.C-0082(A).
Wang, Long; Berczik, Peter; Spurzem, Rainer; Kouwenhoven, M. B. N.
2014-01-10
The hierarchical galaxy formation picture suggests that supermassive black holes (SMBHs) observed in galactic nuclei today have grown from coalescence of massive black hole binaries (MBHB) after galaxy merging. Once the components of an MBHB become gravitationally bound, strong three-body encounters between the MBHB and stars dominate its evolution in a 'dry' gas-free environment and change the MBHB's energy and angular momentum (semimajor axis, eccentricity, and orientation). Here we present high-accuracy direct N-body simulations of spherical and axisymmetric (rotating) galactic nuclei with order of 10{sup 6} stars and two MBHs that are initially unbound. We analyze the properties of the ejected stars due to slingshot effects from three-body encounters with the MBHB in detail. Previous studies have investigated the eccentricity and energy changes of MBHs using approximate models or Monte Carlo three-body scatterings. We find general agreement with the average results of previous semi-analytic models for spherical galactic nuclei, but our results show a large statistical variation. Our new results show many more phase space details of how the process works, and also show the influence of stellar system rotation on the process. We detect that the angle between the orbital plane of the MBHBs and that of the stellar system (when it rotates) influences the phase-space properties of the ejected stars. We also find that MBHBs tend to switch stars with counter-rotating orbits into corotating orbits during their interactions.
Photometric orbits of seven detached eclipsing binaries
NASA Astrophysics Data System (ADS)
Popper, D. M.; Etzel, P. B.
1981-01-01
Photoelectric light curves of the detached eclipsing binaries V805 Aql, TV Cet, MY Cyg, V478 Cyg, V1143 Cyg, BS Dra, and BK Peg are analyzed. The systems are among those with good spectrographic orbits of both components that are in need of good photometric solutions in order to obtain the absolute properties of the components. The analyses are carried out with a computer program valid for detached systems of spherical or slightly oblate stars in orbits of arbitrary eccentricity. A range of solutions much greater than implied by the internal mean errors of the parameters, is found to give satisfactory fits to the observations. Some of the fits are displayed for a variety of solutions for each system. For the three systems with measurable light variation between eclipses - V478 Cyg, V805 Aql, and MY Cyg - the effect of reflection appears to be substantially less than predicted. Very small, but nonzero, orbital eccentricities are found for four of the systems. The variations of limb darkening with wavelength and with spectral type are found to be in reasonable agreement with predictions from atmospheric theory.
NASA Astrophysics Data System (ADS)
Rodríguez, A.; Callegari, N.; Correia, A. C. M.
2016-12-01
We investigate the orbital and rotational evolution of the CoRoT-7 two-planet system, assuming that the innermost planet behaves like a Maxwell body. We numerically resolve the coupled differential equations governing the instantaneous deformation of the inner planet together with the orbital motion of the system. We show that, depending on the relaxation time for the deformation of the planet, the orbital evolution has two distinct behaviours: for relaxation times shorter than the orbital period, we reproduce the results from classic tidal theories, for which the eccentricity is always damped. However, for longer relaxation times, the eccentricity of the inner orbit is secularly excited and can grow to high values. This mechanism provides an explanation for the present high eccentricity observed for CoRoT-7 b, as well as for other close-in super-Earths in multiple planetary systems.
Estimates of Planetary System Properties using TTV data and Least-Excited Orbital Configurations
NASA Astrophysics Data System (ADS)
Lee, Daeyoung; Steffen, Jason H.
2015-01-01
Kepler's precise measurements of planetary transit times have enabled the study of transit timing variations (TTVs) caused by gravitational interactions between planets in multi-planet systems. Using analytic models, Hadden and Lithwick (ApJ, 787, 80, 2014) analyzed the TTVs for 139 Kepler planets and obtained nominal masses. However, due to a degeneracy between mass and eccentricity in the analytical formulae, systems with high eccentricity planets have nominal masses larger than their true masses―sometimes significantly larger. We investigate the constraints that can be placed on the eccentricities of the planets in these systems by minimizing the system's angular momentum deficit. This analysis gives an effectives lower bound on the orbital eccentricities and gives insight into their dynamical histories.
Giguere, Matthew J.; Fischer, Debra A.; Spronck, Julien; Howard, Andrew W.; Marcy, Geoffrey W.; Isaacson, Howard T.; Johnson, John A.; Henry, Gregory W.; Wright, Jason T.; Hou Fengji
2012-01-01
We report the detection of three new exoplanets from Keck Observatory. HD 163607 is a metal-rich G5IV star with two planets. The inner planet has an observed orbital period of 75.29 {+-} 0.02 days, a semi-amplitude of 51.1 {+-} 1.4 m s{sup -1}, an eccentricity of 0.73 {+-} 0.02, and a derived minimum mass of M{sub P} sin i = 0.77 {+-} 0.02 M{sub Jup}. This is the largest eccentricity of any known planet in a multi-planet system. The argument of periastron passage is 78.7 {+-} 2.{sup 0}0; consequently, the planet's closest approach to its parent star is very near the line of sight, leading to a relatively high transit probability of 8%. The outer planet has an orbital period of 3.60 {+-} 0.02 years, an orbital eccentricity of 0.12 {+-} 0.06, and a semi-amplitude of 40.4 {+-} 1.3 m s{sup -1}. The minimum mass is M{sub P} sin i = 2.29 {+-} 0.16 M{sub Jup}. HD 164509 is a metal-rich G5V star with a planet in an orbital period of 282.4 {+-} 3.8 days and an eccentricity of 0.26 {+-} 0.14. The semi-amplitude of 14.2 {+-} 2.7 m s{sup -1} implies a minimum mass of 0.48 {+-} 0.09 M{sub Jup}. The radial velocities (RVs) of HD 164509 also exhibit a residual linear trend of -5.1 {+-} 0.7 m s{sup -1} year{sup -1}, indicating the presence of an additional longer period companion in the system. Photometric observations demonstrate that HD 163607 and HD 164509 are constant in brightness to submillimagnitude levels on their RV periods. This provides strong support for planetary reflex motion as the cause of the RV variations.
Orbit Prediction Tool for Different Classes of Space Debris Orbits
NASA Astrophysics Data System (ADS)
Wnuk, Edwin; Wytrzyszczak, Iwona; Golembiewska, Justyna; Klinkrad, Heiner
There are two aspects of the orbital evolution of space debris: the long-term evolution and the short-term prediction of individual object orbits. In the case of the long-term evolution (years or tens of years time span) general characteristics (e.g. total number of objects, spa-tial distribution and density) of a future space environment are predicted with the use of a relatively simple theory of motion for statistical analysis of future orbits of a large number of objects -a cloud of particles". In the short-term orbital evolution of space debris objects, as considered in this paper, future positions and velocities of individual objects are calculated for a few days or a few weeks time span. A much more sophisticated theory of satellite motion is applied in this case. The paper presents the orbital prediction tool that uses an analytical and semi-analytical theories of satellite motion. The force model includes all important perturbing factors: geopotential effects with arbitrary degree and order spherical harmonic coefficients taken into account, luni-solar attractions, solar radiation pressure and atmospheric drag. The analytical theory of motion is of the second order and is not sensitive to singularities for small eccentricities and small inclinations. A new algorithm for the transformation between mean and osculating elements for the second order theory is applied. Predicted positions of a satel-lite on a given level of accuracy are calculated only with the use of terms that essentially influence on predicted satellite orbit, all other terms are omitted. The number of terms in for-mulas for perturbations, and thus complexity of the theory, depends on the defined level of accuracy and the type of orbit. In practice, we create a dynamical model for a given class of satellite orbit. Geopotential and luni-solar perturbations are calculated in the two following steps. In the first step, values of secular terms and all amplitudes of periodic terms are calculated
NASA Technical Reports Server (NTRS)
Kessler, D. J. (