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.
Bayesian inference for orbital eccentricities
NASA Astrophysics Data System (ADS)
Lucy, L. B.
2013-03-01
Highest posterior density intervals (HPDIs) are derived for the true eccentricities ɛ of spectroscopic binaries with measured values e ≈ 0. These yield upper limits when e is below the detection threshold eth and seamlessly transform to upper and lower bounds when e > eth. In the main text, HPDIs are computed with an informative eccentricity prior representing orbital decay due to tidal dissipation. In an appendix, the corresponding HPDIs are computed with a uniform prior and are the basis for a revised version of the Lucy-Sweeney test, with the previous outcome ɛ = 0 now replaced by an upper limit ɛU. Sampling experiments with known prior confirm the validity of the HPDIs.
Evolution of star clusters on eccentric orbits
NASA Astrophysics Data System (ADS)
Cai, Maxwell Xu; Gieles, Mark; Heggie, Douglas C.; Varri, Anna Lisa
2016-01-01
We study the evolution of star clusters on circular and eccentric orbits using direct N-body simulations. We model clusters with initially N = 8k and 16k single stars of the same mass, orbiting around a point-mass galaxy. For each orbital eccentricity that we consider, we find the apogalactic radius at which the cluster has the same lifetime as the cluster with the same N on a circular orbit. We show that then, the evolution of bound particle number and half-mass radius is approximately independent of eccentricity. Secondly, when we scale our results to orbits with the same semimajor axis, we find that the lifetimes are, to first order, independent of eccentricity. When the results of Baumgardt and Makino for a singular isothermal halo are scaled in the same way, the lifetime is again independent of eccentricity to first order, suggesting that this result is independent of the galactic mass profile. From both sets of simulations, we empirically derive the higher order dependence of the lifetime on eccentricity. Our results serve as benchmark for theoretical studies of the escape rate from clusters on eccentric orbits. Finally, our results can be useful for generative models for cold streams and cluster evolution models that are confined to spherical symmetry and/or time-independent tides, such as Fokker-Planck models, Monte Carlo models, and (fast) semi-analytic models.
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
Kinematical evolution of tidally limited star clusters: the role of retrograde stellar orbits
NASA Astrophysics Data System (ADS)
Tiongco, Maria A.; Vesperini, Enrico; Varri, Anna Lisa
2016-06-01
The presence of an external tidal field often induces significant dynamical evolutionary effects on the internal kinematics of star clusters. Previous studies investigating the restricted three-body problem with applications to star cluster dynamics have shown that unbound stars on retrograde orbits (with respect to the direction of the cluster's orbit) are more stable against escape than prograde orbits, and predicted that a star cluster might acquire retrograde rotation through preferential escape of stars on prograde orbits. In this study we present evidence of this prediction, but we also illustrate that there are additional effects that cannot be accounted for by the preferential escape of prograde orbits alone. Specifically, in the early evolution, initially underfilling models increase their fraction of retrograde stars without losing significant mass, and acquire a retrograde angular velocity. We attribute this effect to the development of preferentially eccentric/radial orbits in the outer regions of star clusters as they are expanding into their tidal limitation. We explore the implications of the evolution of the fraction of prograde and retrograde stars for the evolution of the cluster internal rotation, and its dependence on the initial structural properties. Although all the systems studied here evolve towards an approximately solid-body internal rotation with angular velocity equal to about half of the angular velocity of the cluster orbital motion around the host galaxy, the evolutionary history of the radial profile of the cluster internal angular velocity depends on the cluster initial structure.
Kinematical evolution of tidally limited star clusters: the role of retrograde stellar orbits
NASA Astrophysics Data System (ADS)
Tiongco, Maria A.; Vesperini, Enrico; Varri, Anna Lisa
2016-09-01
The presence of an external tidal field often induces significant dynamical evolutionary effects on the internal kinematics of star clusters. Previous studies investigating the restricted three-body problem with applications to star cluster dynamics have shown that unbound stars on retrograde orbits (with respect to the direction of the cluster's orbit) are more stable against escape than prograde orbits, and predicted that a star cluster might acquire retrograde rotation through preferential escape of stars on prograde orbits. In this study, we present evidence of this prediction, but we also illustrate that there are additional effects that cannot be accounted for by the preferential escape of prograde orbits alone. Specifically, in the early evolution, initially underfilling models increase their fraction of retrograde stars without losing significant mass, and acquire a retrograde angular velocity. We attribute this effect to the development of preferentially eccentric/radial orbits in the outer regions of star clusters as they are expanding into their tidal limitation. We explore the implications of the evolution of the fraction of prograde and retrograde stars for the evolution of the cluster internal rotation, and its dependence on the initial structural properties. Although all the systems studied here evolve towards an approximately solid-body internal rotation with angular velocity equal to about half of the angular velocity of the cluster orbital motion around the host galaxy, the evolutionary history of the radial profile of the cluster internal angular velocity depends on the cluster initial structure.
The habitability of eccentric planetary orbits
NASA Astrophysics Data System (ADS)
Pilat-Lohinger, E.; Lammer, H.; Bancelin, D.; Erkaev, N. V.; Bazso, A.; Eggl, S.
2016-02-01
The huge number of exo-planets discovered so far show an unexpected diversity of planetary systems where most planets indicate eccentricity motion. Since Earth is still the only habitable planet we know and the planetary motion in our Solar system is nearly circular we study possible constraints of habitability in case of eccentric planetary motion. Previous dynamical studies have shown that the architecture of the giant planets in a system might influence the motion in the habitable zone (HZ). Such orbital perturbations may change the conditions of habitability for a terrestrial planet in the HZ. In this context, it has been shown that a small change in the mutual distance of Jupiter and Saturn would lead to a secular perturbation of Earth orbit with variations in eccentricity from 0.0 to 0.7. For planetary motion in binary star systems gravitational perturbations play an important role not only for the long-term stability also the habitability can be affected. In this presentation we discuss the problems that will arise in case an Earth-type planet exits the HZ periodically and approaches a Sun-like star up to 0.3 AU where we pay special attention to the Nitrogen-loss from this planet.
Eccentricity and inclination of Miranda's orbit
NASA Technical Reports Server (NTRS)
Whitaker, E.; Greenberg, R.
1973-01-01
Careful re-measurement of all available plates showing Uranus V (Miranda), supplemented by some recently obtained images, shows that this satellite has both a pronounced orbital eccentricity and inclination (to the plane of the other satellites). Observations are sufficient in number and distribution to allow determinations of the precession rates of both pericenter and node, with implications for the dynamical oblateness of Uranus and the gravitational interaction of the satellites. An improved value for the revolution period is a byproduct of the investigation. The success of the study is due to the improved precision of the measures resulting from the adoption of a very simple, direct method of measurement.
Eccentricity and inclination of Miranda's orbit
NASA Technical Reports Server (NTRS)
Whitaker, E.; Greenberg, R.
1973-01-01
Careful re-measurement of all available plates showing Uranus V (Miranda), supplemented by some recently obtained images, shows that this satellite has both a pronounced orbital eccentricity and inclination (to the plane of the other satellites). Observations are sufficient in number and distribution to allow determinations of the precession rates of both pericenter and node, with implications for the dynamical oblateness of Uranus and the gravitational interaction of the satellites. An improved value for the revolution period is a by-product of the investigation. The success of this study is due to the improved precision of the measures resulting from the adoption of a very simple, direct method of measurement.
Single Close Encounters do not make Eccentric Planetary Orbits
NASA Technical Reports Server (NTRS)
Katz, J. I.
1997-01-01
The recent discovery of a planet in an orbit with eccentricity e = 0.63 +/- 0.08 around the solar-type star 16 Cyg B, together with earlier discoveries of other planets in orbits of significant eccentricity, raises the question of the origin of these orbits, so unlike the nearly circular orbits of our solar system. In this paper I consider close encounters between two planets, each initially in a nearly circular orbit (but with sufficient eccentricity to permit the encounter). Such encounters are described by a two-body approximation, in which the effect of the attracting star is neglected, and by the approximation that their separation vector follows a nearly parabolic path. A single encounter cannot produce the present state of these systems, in which one planet is in an eccentric orbit and the other has apparently been lost. Even if the requirement that the second planet be lost is dropped, nearly circular orbits cannot scatter into eccentric ones.
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.
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…
Characterizing spinning black hole binaries in eccentric orbits with LISA
Key, Joey Shapiro; Cornish, Neil J.
2011-04-15
The Laser Interferometer Space Antenna (LISA) is designed to detect gravitational wave signals from astrophysical sources, including those from coalescing binary systems of compact objects such as black holes. Colliding galaxies have central black holes that sink to the center of the merged galaxy and begin to orbit one another and emit gravitational waves. Some galaxy evolution models predict that the binary black hole system will enter the LISA band with significant orbital eccentricity, while other models suggest that the orbits will already have circularized. Using a full 17 parameter waveform model that includes the effects of orbital eccentricity, spin precession, and higher harmonics, we investigate how well the source parameters can be inferred from simulated LISA data. Defining the reference eccentricity as the value one year before merger, we find that for typical LISA sources, it will be possible to measure the eccentricity to an accuracy of parts in a thousand. The accuracy with which the eccentricity can be measured depends only very weakly on the eccentricity, making it possible to distinguish circular orbits from those with very small eccentricities. LISA measurements of the orbital eccentricity can help constraints theories of galaxy mergers in the early universe. Failing to account for the eccentricity in the waveform modeling can lead to a loss of signal power and bias the estimation of parameters such as the black hole masses and spins.
On the Tidal Radius of Satellites on Prograde and Retrograde Orbits
NASA Astrophysics Data System (ADS)
Gajda, Grzegorz; Łokas, Ewa L.
2016-03-01
A tidal radius is the distance from a satellite orbiting in a host potential beyond which its material is stripped by the tidal force. We derive a revised expression for the tidal radius of a rotating satellite that properly takes into account the possibility of prograde and retrograde orbits of stars. Besides the eccentricity of the satellite orbit, the tidal radius also depends on the ratio of the satellite internal angular velocity to the orbital angular velocity. We compare our formula to the results of two N-body simulations of dwarf galaxies orbiting a Milky-Way-like host on a prograde and retrograde orbit. The tidal radius for the retrograde case is larger than for the prograde. We introduce a kinematic radius that separates stars still orbiting the dwarf galaxy from those already stripped and following the potential of the host galaxy. We find that the tidal radius matches the kinematic radius very well. Our results provide a connection between the formalism of the tidal radius derivation and the theory of resonant stripping.
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. PMID:20879864
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.
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.
On disk-planet interactions and orbital eccentricities
NASA Astrophysics Data System (ADS)
Ward, W. R.
1988-02-01
The eccentricity evolution from density wave interaction between a planetesimal and a Keplerian disk is studied. While it is known that Lindblad resonances both interior and exterior to the perturber's orbit excite its eccentricity, the author shows that corotation resonances in these regions become ineffective at eccentricity damping if the object is embedded in a continuous disk without a gap. However, under these conditions another class of Lindblad resonances exists. These operate on disk material co-orbiting with the perturber and become the most important source of eccentricity damping. The author employs a model problem to obtain estimates of the various disk torques and concludes that the eccentricity ultimately suffers decay. The limitations of this model are also discussed.
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.
Exoplanets in binary star systems: on the switch from prograde to retrograde orbits
NASA Astrophysics Data System (ADS)
Carvalho, J. P. S.; Mourão, D. C.; de Moraes, R. Vilhena; Prado, A. F. B. A.; Winter, O. C.
2016-01-01
The eccentric Kozai-Lidov mechanism, based on the secular theory, has been proposed as a mechanism that plays an important role in producing orbits that switch from prograde to retrograde. In the present work we study the secular dynamics of a triple system composed of a Sun-like central star and a Jupiter-like planet, which are under the gravitational influence of another perturbing star (brown dwarf). The perturbation potential is developed in closed form up to the fifth order in a small parameter (α =a1/a2), where a1 is the semimajor axis of the extrasolar planet and a2 is the semimajor axis of the perturbing star. To eliminate the short-period terms of the perturbation potential, the double-average method is applied. In this work we do not eliminate the nodes, a standard method in the literature, before deriving the equations of motion. The main goal is to study the effects of the higher-order terms of the expansion of the perturbing force due to the third body in the orbital evolution of the planet. In particular, we investigate the inclination and the shape (eccentricity) of these orbits. We show the importance of the higher-order terms in changing the inversion times of the flip, i.e., the times where the inclination of the inner planet flips from prograde to retrograde trajectories. We also show the dependence of the first flip with respect to the semimajor axis and eccentricity of the orbit of the planet. The general conclusion is that the analytical model increases its accuracy with the inclusion of higher-order terms. We also performed full numerical integrations using the Bulirsch-Stoer method available in the Mercury package for comparison with the analytical model. The results obtained with the equations developed in this work are in accordance with direct numerical simulations.
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.
Formation Flying in Earth, Libration, and Distant Retrograde Orbits
NASA Technical Reports Server (NTRS)
Folta, David C.
2004-01-01
This slide presentation examines the current and future state of formation flying, LEO formations, control strategies for flight in the vicinity of the libration points, and distant retrograde orbit formations. This discussion of LEO formations includes background on perturbation theory/accelerations and LEO formation flying. The discussion of strategies for formation flight in the vicinity of the libration points includes libration missions and natural and controlled libration orbit formations. A reference list is included.
Orbital evolution of eccentric interacting binary star systems
NASA Astrophysics Data System (ADS)
Sepinsky, Jeremy Francis
2009-06-01
We provide a comprehensive description of the long-term (secular) orbital evolution of eccentric interacting binary systems. The evolution of circular interacting binary systems is a well studied phenomenon, but observations have shown the existence of a small but significant number of eccentric interacting binary systems. We begin by extending the commonly accepted Roche formalism for binary interacting to include eccentric orbits and asynchronously rotating stars. Using this, we calculate orbital trajectories for particles ejected from a Roche lobe-filling donor star at the periastron of the eccentric orbit. These particles admit of three possible trajectories: direct impact onto the secondary star, self accretion back onto the donor star, and the formation of a disk about the accretor. We provide a proscription for determining a priorithe trajectory of the particle given the initial system parameters, as well as describe the secular evolution of the system for each of the three cases described above. We find that these orbital evolution timescales are comparable to the mass transfer timescale which can be significantly longer than expected from the literature. Furthermore, while it is commonly assumed that any mass transfer interactions will act to circularize the orbit, we find that there are regimes of parameter space where mass transfer can cause an increase in eccentricity, and can do so at a timescale comparable to the circularization timescale created by tidal interactions. The formalism presented here can be incorporated into binary evolution and population synthesis models to create a self-consistent treatment of mass transfer in eccentric binaries.
Retrograde closed orbits in a rotating triaxial potential
NASA Astrophysics Data System (ADS)
Heisler, J.; Merritt, D.; Schwarzschild, M.
1982-07-01
Four closed periodic orbit sequences are determined numerically, and their stability is investigated by the standard Floquet method, for the case of a specific, triaxial rotating potential. The sequences comprise (1) stable anomalous orbits that are tipped to the long axis which they circle, so that they also circle the short rotation axis, (2) unstable, anomalous orbits circling the intermediate axis, otherwise behaving like (1), (3) stable, normal retrograde orbits lying in the equatorial plane, which become unstable against perpendicular perturbations in Binney's instability strip, and (4) Z-axis orbits lying on the rotation axis, which, although stable in their inner section, become unstable to perturbations parallel to the intermediate axis farther out, and to the long axis farther out still. The entire set contains one composite sequence which is stable over the entire energy range, consisting of the outer section of the normal retrograde orbits, the sequence of the anomalous orbits, and the inner section of the Z-axis orbits. It is suggested that the composite sequence may be relevant to the dynamics of gas masses captured by rotating triaxial galaxies.
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
2015-01-01
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
On the rotation of co-orbital bodies in eccentric orbits
NASA Astrophysics Data System (ADS)
Leleu, A.; Robutel, P.; Correia, A. C. M.
2016-06-01
We investigate the resonant rotation of co-orbital bodies in eccentric and planar orbits. We develop a simple analytical model to study the impact of the eccentricity and orbital perturbations on the spin dynamics. This model is relevant in the entire domain of horseshoe and tadpole orbit, for moderate eccentricities. We show that there are three different families of spin-orbit resonances, one depending on the eccentricity, one depending on the orbital libration frequency, and another depending on the pericenter's dynamics. We can estimate the width and the location of the different resonant islands in the phase space, predicting which are the more likely to capture the spin of the rotating body. In some regions of the phase space the resonant islands may overlap, giving rise to chaotic rotation.
Approximations of distant retrograde orbits for mission design
NASA Technical Reports Server (NTRS)
Hirani, Anil N.; Russell, Ryan P.
2006-01-01
Distant retrograde orbits (DROs) are stable periodic orbit solutions of the equations of motion in the circular restricted three body problem. Since no closed form expressions for DROs are known, we present methods for approximating a family of planar DROs for an arbitrary, fixed mass ratio. Furthermore we give methods for computing the first and second derivatives of the position and velocity with respect to the variables that parameterize the family. The approximation and derivative methods described allow a mission designer to target specific DROs or a range of DROs with no regard to phasing in contrast to the more limited case of targeting a six-state only.
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
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.
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.
Orbital Eccentricity and the Stability of Planets in the Alpha Centauri System
NASA Astrophysics Data System (ADS)
Lissauer, Jack J.; Quarles, Billy L.
2016-05-01
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.
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.
Sepinsky, J. F.; Willems, B.; Kalogera, V.; Rasio, F. A. E-mail: b-willems@northwestern.ed E-mail: rasio@northwestern.ed
2010-11-20
The rapid circularization and synchronization of the stellar components in an eccentric binary system at the onset of Roche lobe overflow is a fundamental assumption common to all binary stellar evolution and population synthesis codes, even though the validity of this assumption is questionable both theoretically and observationally. Here we calculate the evolution of the orbital elements of an eccentric binary through the direct three-body integration of a massive particle ejected through the inner Lagrangian point of the donor star at periastron. The trajectory of this particle leads to three possible outcomes: direct accretion onto the companion star within a single orbit, self-accretion back onto the donor star within a single orbit, or a quasi-periodic orbit around the companion star, possibly leading to the formation of a disk. We calculate the secular evolution of the binary orbit in the first two cases and conclude that direct impact accretion can increase as well as decrease the orbital semimajor axis and eccentricity, while self-accretion always decreases the orbital semimajor axis and eccentricity. In cases where mass overflow contributes to circularizing the orbit, circularization can set in on timescales as short as a few percent of the mass-transfer timescale. In cases where mass overflow increases the eccentricity, the orbital evolution is governed by competition between mass overflow and tidal torques. In the absence of tidal torques, mass overflow results in direct impact can lead to substantially subsynchronously rotating donor stars. Contrary to assumptions common in the literature, direct impact accretion furthermore does not always provide a strong sink of orbital angular momentum in close mass-transferring binaries; in fact, we instead find that a significant part can be returned to the orbit during the particle orbit. The formulation presented in this paper together with our previous work can be combined with stellar and binary evolution
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.
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.
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.
The enigma of the Uranian satellites' orbital eccentricities
NASA Astrophysics Data System (ADS)
Squyres, S. W.; Reynolds, R. T.; Lissauer, J. J.
1985-02-01
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.
NASA Astrophysics Data System (ADS)
Bourassa, Matthew; Burlton, Bruce; Afagh, Fred; Langlois, Rob
2015-06-01
The lunar and solar gravitational perturbations coupled with the J2 effect acting on Earth-orbiting satellites in critically inclined highly eccentric orbits cause several modes of oscillation in the eccentricity of the orbit. The sign changes in the slope of the eccentricity variations are labelled "switch points" and their development is explored in this paper. Using spherical trigonometry, the switch points can be determined in terms of the position and orbital elements of the perturbing third body (i.e., Moon or Sun) and the orbital elements of the satellite. Furthermore, the concept of switch point angles, used to identify when the switch points occur, is defined and discussed. As a result, the fundamental nature of the interaction between the gravitational perturbations of the third body and the orbit of the satellite is expanded upon. The switch points are also used to analyze the different modes of oscillation that occur in the eccentricity variations, whose periods can vary from two weeks to several years, and as a result cause significant variations in the perigee and apogee altitudes of the highly eccentric orbits. This study provides insight into the behaviour of the satellite's orbit under the lunar and solar perturbations in relation to the position of the Moon and Sun.
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
Discovery of a Highly Eccentric Orbit for Fomalhaut b
NASA Astrophysics Data System (ADS)
Kalas, P.; Graham, J. R.; Fitzgerald, M. P.; Clampin, M.
2013-09-01
Fomalhaut is a bright (mv = 1.3 mag), nearby (d = 7.7 pc) main-sequence star (SpT = A3V) with age 440 Myr [6] that is surrounded by dusty debris from the collisional evolution of comets and asteroids. Optical coronagraphic observations of dust scattered light with the Hubble Space Telescope (HST) in 2004 reveal a sharp inner edge at ~133 AU and a geometric center that is offset from the star by ~15 AU, providing indirect evidence for a dynamical perturbation by a planet mass object [2]. Follow-up observations in 2006 revealed a faint common proper motion companions, Fomalhaut b, that appeared to orbit 18 AU interior to the dust belt [3]. Here we present new optical detections of Fomalhaut b obtained with HST/STIS in 2010 and 2012 (Figure 1). A Markov chain Monte-Carlo analysis [1] of the entire HST astrometric data set reveals that the orbit of Fomalhaut b is highly eccentric (e = 0.8 ± 0.1), and in the sky-plane projection it will appear to cross the dust belt approximately two decades in the future [4]. The current uncertainties in the orbit determination specify that the mutual inclination between Fomalhaut b and the belt is ≤36°, and only 12% of possible orbits have nodes crossing through the belt. Therefore it is not known if Fomalhaut b will directly interact with belt material. With periastron and apastron at approximately 32 AU and 322 AU, respectively, Fomalhaut b may be dynamically linked to other planet mass objects in the system. If hypothetical Fomalhaut planets orbit at 30 AU or at 120 AU, the Tisserand parameter is in the range 2 - 3, similar to highly eccentric solar system objects. The possibility that Fomalhaut b interacts with other planet mass objects suggests that the current orbital configuration is relatively shortlived like that of solar system Centaurs. Fomalhaut b may be optically detectable due to reflection from planetary rings [4] or the collisional evolution of irregular satellites [5]. We suggest that periastron passage will
NASA Astrophysics Data System (ADS)
Tanay, Sashwat; Haney, Maria; Gopakumar, Achamveedu
2016-03-01
Inspiraling compact binaries with non-negligible orbital eccentricities are plausible gravitational wave (GW) sources for the upcoming network of GW observatories. In this paper, we present two prescriptions to compute post-Newtonian (PN) accurate inspiral templates for such binaries. First, we adapt and extend the postcircular scheme of Yunes et al. [Phys. Rev. D 80, 084001 (2009)] to obtain a Fourier-domain inspiral approximant that incorporates the effects of PN-accurate orbital eccentricity evolution. This results in a fully analytic frequency-domain inspiral waveform with Newtonian amplitude and 2PN-order Fourier phase while incorporating eccentricity effects up to sixth order at each PN order. The importance of incorporating eccentricity evolution contributions to the Fourier phase in a PN-consistent manner is also demonstrated. Second, we present an accurate and efficient prescription to incorporate orbital eccentricity into the quasicircular time-domain TaylorT4 approximant at 2PN order. New features include the use of rational functions in orbital eccentricity to implement the 1.5PN-order tail contributions to the far-zone fluxes. This leads to closed form PN-accurate differential equations for evolving eccentric orbits, and the resulting time-domain approximant is accurate and efficient to handle initial orbital eccentricities ≤0.9 . Preliminary GW data analysis implications are probed using match estimates.
Determining the eccentricity of the Moon's orbit without a telescope
NASA Astrophysics Data System (ADS)
Krisciunas, Kevin
2010-08-01
Prior to the invention of the telescope many astronomers worked out models of the motion of the Moon to predict the position of the Moon in the sky. These geometrical models implied a certain range of distances of the Moon from Earth. Ptolemy's most quoted model predicted that the Moon was nearly twice as far away at apogee than at perigee. Measurements of the angular size of the Moon were within the capabilities of pretelescopic astronomers. Such measurements could have helped refine the models of the motion of the Moon, but hardly anyone seems to have made any measurements that have come down to us. We use a piece of cardboard with a small hole in it which slides up and down a yardstick to show that it is possible to determine the eccentricity ɛ~0.039+/-0.006 of the Moon's orbit. A typical measurement uncertainty of the Moon's angular size is +/-0.8 arc min. Because the Moon's angular size ranges from 29.4 to 33.5 arc min, carefully taken naked eye data are accurate enough to demonstrate periodic variations of the Moon's angular size.
Orbit Control of Fly-around Satellite with Highly Eccentric Orbit by Using Solar Radiation Pressure
NASA Astrophysics Data System (ADS)
Hou, Y. G.; Zhao, C. Y.; Zhang, M. J.; Sun, R. Y.
2016-01-01
The method of controlling highly eccentric fly-around orbit using the solar wing is designed in this paper. The formation is maintained by controlling the follower. The in-plane and the out-of-plane control are separated. The follower is rotating around the inertial principal axis with a constant angular velocity. The controlling of the angular between the solar wings and satellite body is obtained. The orbit is controlled by adjusting the geometrical orientation. The in-plane control is prior to the out-of-plane control. The out-of-plane control force is applied when the error of in-plane is eliminated or the in-plane control force can not be supplied. Three different kinds of numerical simulations including the orbit reconfiguration, the error elimination, and the orbit maintenance are performed. It is shown that the method can keep the error less than 5 m, and it is feasible for the space formation.
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.
NASA Astrophysics Data System (ADS)
Salmon, Rachel L.; Sepinsky, Jeremy F.
2015-01-01
As the number of extrasolar planets and planet candidates increases, so does the number of systems that look strikingly different from our own. Hot Jupiters are such a system and are characterized by a Jupiter mass planet with a close-in orbit. Because of the proximity of the planet to its parent star, we would expect these systems to be tidally circularized. However, we observe many with significant eccentricities, suggesting that a mechanism must exist to account for sustained eccentric orbits. Previous analyses found that, in a population of eccentric hot Jupiters generated by planet-planet scattering, a significant fraction will overfill their Roche lobe at periastron. Other work has noted that mass loss in systems similar to hot Jupiters can act to increase the eccentricity of the orbit of a binary system. Here, we consider the effects of tidal circularization and mass loss on the orbital evolution of the hot Jupiters. By analyzing the balance between the tidal circularization and mass loss, we can determine an equilibrium eccentricity as a function of planet mass and the tidal quality factor, Q. If such an equilibrium value exists, then it is possible for this mechanism to be responsible for the sustained eccentric orbits of hot Jupiters that we observe. We present the orbital parameters for these equilibrium orbits over a broad parameter space and compare those results to the current population of observed extrasolar planets.
FIVE LONG-PERIOD EXTRASOLAR PLANETS IN ECCENTRIC ORBITS FROM THE MAGELLAN PLANET SEARCH PROGRAM
Arriagada, Pamela; Minniti, Dante; Butler, R. Paul; Lopez-Morales, Mercedes; Boss, Alan P.; Chambers, John E.; Shectman, Stephen A.; Adams, Fred C.
2010-03-10
Five new planets orbiting G and K dwarfs have emerged from the Magellan velocity survey. These companions are Jovian-mass planets in eccentric (e >= 0.24) intermediate- and long-period orbits. HD 86226b orbits a solar metallicity G2 dwarf. The M{sub P} sin i mass of the planet is 1.5 M{sub JUP}, the semimajor axis is 2.6 AU, and the eccentricity is 0.73. HD 129445b orbits a metal-rich G6 dwarf. The minimum mass of the planet is M{sub P} sin i = 1.6 M{sub JUP}, the semimajor axis is 2.9 AU, and the eccentricity is 0.70. HD 164604b orbits a K2 dwarf. The M{sub P} sin i mass is 2.7 M{sub JUP}, the semimajor axis is 1.3 AU, and the eccentricity is 0.24. HD 175167b orbits a metal-rich G5 star. The M{sub P} sin i mass is 7.8 M{sub JUP}, the semimajor axis is 2.4 AU, and the eccentricity is 0.54. HD 152079b orbits a G6 dwarf. The M{sub P} sin i mass of the planet is 3 M{sub JUP}, the semimajor axis is 3.2 AU, and the eccentricity is 0.60.
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.
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.
Impact of Eccentricity on East-west Stationkeeping for GPS Class of Orbits
NASA Technical Reports Server (NTRS)
Ely, Todd A.
1999-01-01
There exists a strong relationship between eccentricity and the potential for a repeating groundtrack orbit to exhibit chaotic motion. This is true at all values of eccentricity, but, perhaps most dramatic, is that it is true even for orbits that are nearly circular. These complex motions can have a significant impact on the east-west stationkeeping process for maintaining the repeating groundtrack property of a commensurate orbit. Ely and Howell have shown that traditional stationkeeping (SK) methods are unable to maintain a repeating groundtrack in the presence of complex dynamics, such as with chaotic motion. They developed an alternate SK method that is able to maintain a repeating groundtrack for eccentric, commensurate orbits. The focus of the current study is to investigate orbits with characteristics that are similar to GPS satellites except with modestly larger eccentricities. It will be shown that at eccentricities larger than approx. .01 the chaotic regions become significant, and the need arises for a robust stationkeeping approach, such as developed in. FurtheRmore, the investigation will reveal that the influence of luni-solar perturbations contributes to the growth of eccentricity, thus increasing the probability of encountering chaotic motion during a typical satellite lifetime.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Bini, Donato; Damour, Thibault; Geralico, Andrea
2016-06-01
We present the first analytic computation of the Detweiler-Barack-Sago gauge-invariant redshift function for a small mass in eccentric equatorial orbit around a spinning black hole. Our results give the redshift contributions that mix eccentricity and spin effects, through second order in eccentricity, second order in spin parameter, and the eight-and-a-half post-Newtonian order.
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.
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.
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.
THE TRANSIT INGRESS AND THE TILTED ORBIT OF THE EXTRAORDINARILY ECCENTRIC EXOPLANET HD 80606b
Winn, Joshua N.; Howard, Andrew W.; Marcy, Geoffrey W.; Johnson, John Asher; 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
2009-10-01
We present the results of a transcontinental campaign to observe the 2009 June 5 transit of the exoplanet HD 80606b. We report the first detection of the transit ingress, revealing the transit duration to be 11.64 +- 0.25 hr and allowing more robust determinations of the system parameters. Keck spectra obtained at midtransit exhibit an anomalous blueshift, giving definitive evidence that the stellar spin axis and planetary orbital axis are misaligned. The Keck data show that the projected spin-orbit angle lambda is between 32 deg. and 87 deg. with 68.3% confidence and between 14 deg. and 142 deg. with 99.73% confidence. Thus, the orbit of this planet is not only highly eccentric (e = 0.93) 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. Independently of the theory, it is worth noting that all three exoplanetary systems with known spin-orbit misalignments have massive planets on eccentric orbits, suggesting that those systems migrate through a different channel than lower mass planets on circular orbits.
Stellar encounters as the origin of distant Solar System objects in highly eccentric orbits.
Kenyon, Scott J; Bromley, Benjamin C
2004-12-01
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. PMID:15577903
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…
The Influence of Mass Loss on the Eccentricity of Double Star Orbits
NASA Astrophysics Data System (ADS)
Docobo, J. A.; Prieto, C.; Ling, J. F.
In this comunication we study the behaviour of the eccentricity of double star orbits (visual and wide spectroscopic binaries) according to simplified laws of mass loss. Applications to the systems WDS 05245S0224 - HD 35411, WDS 05387S0236 - HD 37468 and WDS 06154S0902 - HD 43362 are included.
ON THE DISTRIBUTION OF ORBITAL ECCENTRICITIES FOR VERY LOW-MASS BINARIES
Dupuy, Trent J.; Liu, Michael C.
2011-06-01
We have compiled a sample of 16 orbits for very low-mass stellar (<0.1 M{sub sun}) and brown dwarf binaries, including updated orbits for HD 130948BC and LP 415-20AB. This sample enables the first comprehensive study of the eccentricity distribution for such objects. We find that very low-mass binaries span a broad range of eccentricities from near-circular to highly eccentric (e {approx} 0.8), with a median eccentricity of 0.34. We have examined potential observational biases in this sample, and for visual binaries we show through Monte Carlo simulations that if we choose appropriate selection criteria then all eccentricities are equally represented ({approx}< 5% difference between input and output eccentricity distributions). The orbits of this sample of very low-mass binaries show some significant differences from their solar-type counterparts. They lack a correlation between orbital period and eccentricity, and display a much higher fraction of near-circular orbits (e < 0.1) than solar-type stars, which together may suggest a different formation mechanism or dynamical history for these two populations. Very low-mass binaries also do not follow the e{sup 2} distribution of Ambartsumian, which would be expected if their orbits were distributed in phase space according to a function of energy alone (e.g., the Boltzmann distribution). We find that current numerical simulations of very low-mass star formation do not completely reproduce the observed properties of our binary sample. The cluster formation model of Bate agrees very well with the overall e distribution, but the lack of any high-e (>0.6) binaries at orbital periods comparable to our sample suggests that tidal damping due to gas disks may play too large of a role in the simulations. In contrast, the circumstellar disk fragmentation model of Stamatellos and Whitworth predicts only high-e binaries and thus is highly inconsistent with our sample. These discrepancies could be explained if multiple formation
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.
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.
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.
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.
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.
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.
Einstein@Home Discovery of a PALFA Millisecond Pulsar in an Eccentric Binary Orbit
NASA Astrophysics Data System (ADS)
Knispel, B.; Lyne, A. G.; Stappers, B. W.; Freire, P. C. C.; Lazarus, P.; Allen, B.; Aulbert, C.; Bock, O.; Bogdanov, S.; Brazier, A.; Camilo, F.; Cardoso, F.; Chatterjee, S.; Cordes, J. M.; Crawford, F.; Deneva, J. S.; Eggenstein, H.-B.; Fehrmann, H.; Ferdman, R.; Hessels, J. W. T.; Jenet, F. A.; Karako-Argaman, C.; Kaspi, V. M.; van Leeuwen, J.; Lorimer, D. R.; Lynch, R.; Machenschalk, B.; Madsen, E.; McLaughlin, M. A.; Patel, C.; Ransom, S. M.; Scholz, P.; Siemens, X.; Spitler, L. G.; Stairs, I. H.; Stovall, K.; Swiggum, J. K.; Venkataraman, A.; Wharton, R. S.; Zhu, W. W.
2015-06-01
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⊙ 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.
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.
NASA Technical Reports Server (NTRS)
Wagner, C. A.
1979-01-01
Two dimensional gravitational spectra are derived from simple harmonic analysis of range rate tracking data on planetary orbiters. The eccentricity of the orbit is arbitrary and results are shown to vary substantially with the aspect angle of the tracking line of sight with the orbit plane. The development for arbitrary start with stop times (with respect to periapsis) uses modified eccentricity functions evaluated by quadrature. Simulations with a point-masses model of Venus using tracking data on the Pioneer Venus Orbiter show excellent predictions of the average orbiter spectrum over one Venus day. The Venus gravitational signal should be above the tracking noise level for arc lengths longer than 40 deg (in true anomaly) about periapsis and for terms as high as 55th degree. analysis has been made of tracking residuals from a short arc fit to Mariner Mars 9 data over the Hellas Basin (using a complete 6th degree field). Results are most consistent with higher residual gravitational power than predicted from Kaula's rule for Mars.
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
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.
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
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.
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.
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. PMID:26417080
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
A numerical investigation on the eccentricity growth of GNSS disposal orbits
NASA Astrophysics Data System (ADS)
Alessi, E. M.; Deleflie, F.; Rosengren, A. J.; Rossi, A.; Valsecchi, G. B.; Daquin, J.; Merz, K.
2016-05-01
We present the results of an extensive numerical exploration performed on the eccentricity growth in MEO associated with two possible end-of-life disposal strategies for GNSS satellites. The study calls attention to the existence of values of initial inclination, longitude of ascending node, and argument of perigee that are more advantageous in terms of long-term stability of the orbit. The important role of the initial epoch and a corresponding periodicity are also shown. The present investigation is influential in view of recent analytical and numerical developments on the chaotic nature of the region due to lunisolar perturbations, but also for the upcoming Galileo and BeiDou constellations.
Initial Data for Binary Neutron Stars with Arbitrary Spin and Orbital Eccentricity
NASA Astrophysics Data System (ADS)
Tsatsin, Petr; Marronetti, Pedro
2013-04-01
The starting point of any general relativistic numerical simulation is a solution of the Hamiltonian and momentum constraint. One characteristic of the Binary Neutron Star (BNS) initial data problem is that, unlike the case of binary black holes, there are no formalisms that permit the construction of initial data for stars with arbitrary spins. For many years, the only options available have been systems either with irrotational or corotating fluid. Ten years ago, Marronetti & Shapiro (2003) introduced an approximation that would produce such arbitrarily spinning systems. More recently, Tichy (2012) presented a new formulation to do the same. However, all these data sets are bound to have a non-zero eccentricity that results from the fact the stars' velocity have initial null radial components. We present here a new approximation for BNS initial data for systems that possess arbitrary spins and arbitrary radial and tangential velocity components. The latter allows for the construction of data sets with arbitrary orbital eccentricity. Through the fine-tuning of the radial component, we were able to reduce the eccentricity by a factor of several compared to that of standard helical symmetry data sets such as those currently used in the scientific community.
NASA Astrophysics Data System (ADS)
Barker, A. J.; Ogilvie, G. I.
2016-06-01
We perform global two-dimensional hydrodynamical simulations of Keplerian discs with free eccentricity over thousands of orbital periods. Our aim is to determine the validity of secular theory in describing the evolution of eccentric discs, and to explore their nonlinear evolution for moderate eccentricities. Linear secular theory is found to correctly predict the structure and precession rates of discs with small eccentricities. However, discs with larger eccentricities (and eccentricity gradients) are observed to precess faster (retrograde relative to the orbital motion), at a rate that depends on their eccentricities (and eccentricity gradients). We derive analytically a nonlinear secular theory for eccentric gas discs, which explains this result as a modification of the pressure forces whenever eccentric orbits in a disc nearly intersect. This effect could be particularly important for highly eccentric discs produced in tidal disruption events, or for narrow gaseous rings; it might also play a role in causing some of the variability in superhump binary systems. In two dimensions, the eccentricity of a moderately eccentric disc is long-lived and persists throughout the duration of our simulations. Eccentric modes are however weakly damped by their interaction with non-axisymmetric spiral density waves (driven by the Papaloizou-Pringle instability, which occurs in our idealized setup with solid walls), as well as numerical diffusion.
NASA Astrophysics Data System (ADS)
Remeikas, Charles; Xu, Yunjun; Pham, Khanh; Chen, Genshe; Jia, Bin; Shen, Dan
2014-06-01
Recently bio-inspired rendezvous strategies have been investigated for applications in space situation awareness. Particularly, closed-loop solutions have been developed for the cases that the target object is in a circular orbit without considering any orbital perturbations. In this paper, the minimum-fuel consumption bio-inspired motions are further studied. The follow cases considering the J2 perturbation, the non-zero eccentricities, and different boundary conditions are analyzed: (1) the target object is at the local vertical local horizontal coordinate origin; (2) the target is moving in the local vertical local horizontal coordinate; (3) the rendezvous object approaches the target object from the R-bar, V-bar, and Z-bar directions, respectively. Fast solutions can be obtained for the rendezvous object to approach the target object with minimum energy consumption.
Analysis of Formation Flying in Eccentric Orbits Using Linearized Equations of Relative Motion
NASA Technical Reports Server (NTRS)
Lane, Christopher; Axelrad, Penina
2004-01-01
Geometrical methods for formation flying design based on the analytical solution to Hill's equations have been previously developed and used to specify desired relative motions in near circular orbits. By generating relationships between the vehicles that are intuitive, these approaches offer valuable insight into the relative motion and allow for the rapid design of satellite configurations to achieve mission specific requirements, such as vehicle separation at perigee or apogee, minimum separation, or a specific geometrical shape. Furthermore, the results obtained using geometrical approaches can be used to better constrain numerical optimization methods; allowing those methods to converge to optimal satellite configurations faster. This paper presents a set of geometrical relationships for formations in eccentric orbits, where Hill.s equations are not valid, and shows how these relationships can be used to investigate formation designs and how they evolve with time.
Fomalhaut's Main Belt Structure and the Eccentric Orbit of Fomalhaut b
NASA Astrophysics Data System (ADS)
Kalas, Paul; Graham, James R.; Fitzgerald, Michael C.; Clampin, Mark
2013-07-01
We present a significant update to the observations and understanding of the planetary system sur- rounding the nearby, 440 Myr old, A3V star Fomalhaut. Our latest HST/STIS high-contrast optical images confirm that the low-mass object Fomalhaut b has a hightly eccentric orbit (e˜0.8). Its periapse is near 30 AU and in the sky-plane projection Fomalhaut b will begin crossing the main belt (a˜140 AU) two decades in the future. An MCMC analysis of the astrometry indicates apsidal alignment between Fomalhaut b and the belt, but the mutual inclination is not necessarily coplanar. We find that only 12 per cent of Fomalhaut b's ascending and descending nodes would physically encounter the belt. The non-detections of Fomalhaut b at infrared wavelengths suggest that its mass is less than a Jupiter mass, and its optical luminosity may be due to a circumplanetary dust ring or an irregular satellite cloud. We suggest that Fomalhaut b's minimum mass is a few times that of the dwarf planet Ceres in order for the circumplanetary cloud to survive shearing during periapse passage. In addition, we give observational evidence that the main belt may have an azimuthal dust depletion approximately 50 AU wide. Taken together, the eccentric orbit of Fomalhaut b and the main belt struc- ture indicate that other, yet-to-be-detected planet-mass objects may dynamically influence the system.
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
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
Gravitational self-force on a particle in eccentric orbit around a Schwarzschild black hole
Barack, Leor; Sago, Norichika
2010-04-15
We present a numerical code for calculating the local gravitational self-force acting on a pointlike particle in a generic (bound) geodesic orbit around a Schwarzschild black hole. The calculation is carried out in the Lorenz gauge: For a given geodesic orbit, we decompose the Lorenz-gauge metric perturbation equations (sourced by the delta-function particle) into tensorial harmonics, and solve for each harmonic using numerical evolution in the time domain (in 1+1 dimensions). The physical self-force along the orbit is then obtained via mode-sum regularization. The total self-force contains a dissipative piece as well as a conservative piece, and we describe a simple method for disentangling these two pieces in a time-domain framework. The dissipative component is responsible for the loss of orbital energy and angular momentum through gravitational radiation; as a test of our code we demonstrate that the work done by the dissipative component of the computed force is precisely balanced by the asymptotic fluxes of energy and angular momentum, which we extract independently from the wave-zone numerical solutions. The conservative piece of the self-force does not affect the time-averaged rate of energy and angular-momentum loss, but it influences the evolution of the orbital phases; this piece is calculated here for the first time in eccentric strong-field orbits. As a first concrete application of our code we recently reported the value of the shift in the location and frequency of the innermost stable circular orbit due to the conservative self-force [Phys. Rev. Lett. 102, 191101 (2009)]. Here we provide full details of this analysis, and discuss future applications.
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
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
State transition matrix for long-distance formation with J2 in eccentric orbits
NASA Astrophysics Data System (ADS)
Kimura, Masaya; Yamada, Katsuhiko
2014-08-01
The relative state transition of spacecraft formation flying is considered in this paper. In eccentric orbits, the Tschauner-Hempel (TH) equations are used to express the relative motion between a deputy spacecraft and a chief spacecraft. Perturbation forces are not considered in the TH equations, and the relative distance between two spacecraft is limited to a short range. In this paper, the effects of the J2 perturbation forces are considered, and the case of relatively long distance between two spacecraft is focused. A state transition matrix applicable to such cases is derived. The state transition matrix is expressed by adding some compensating terms to the state transition matrix of the TH equations. The usefulness of the proposed state transition matrix relative to the state transition matrix of the TH equations is shown through numerical simulations from the viewpoint of position error.
Disc formation from tidal disruptions of stars on eccentric orbits by Schwarzschild black holes
NASA Astrophysics Data System (ADS)
Bonnerot, Clément; Rossi, Elena M.; Lodato, Giuseppe; Price, Daniel J.
2016-01-01
The potential of tidal disruption of stars to probe otherwise quiescent supermassive black holes cannot be exploited, if their dynamics is not fully understood. So far, the observational appearance of these events has been derived from analytical extrapolations of the debris dynamical properties just after disruption. By means of hydrodynamical simulations, we investigate the subsequent fallback of the stream of debris towards the black hole for stars already bound to the black hole on eccentric orbits. We demonstrate that the debris circularize due to relativistic apsidal precession which causes the stream to self-cross. The circularization time-scale varies between 1 and 10 times the period of the star, being shorter for more eccentric and/or deeper encounters. This self-crossing leads to the formation of shocks that increase the thermal energy of the debris. If this thermal energy is efficiently radiated away, the debris settle in a narrow ring at the circularization radius with shock-induced luminosities of ˜10-103 LEdd. If instead cooling is impeded, the debris form an extended torus located between the circularization radius and the semi-major axis of the star with heating rates ˜1-102 LEdd. Extrapolating our results to parabolic orbits, we infer that circularization would occur via the same mechanism in ˜1 period of the most bound debris for deeply penetrating encounters to ˜10 for grazing ones. We also anticipate the same effect of the cooling efficiency on the structure of the disc with associated luminosities of ˜1-10 LEdd and heating rates of ˜0.1-1 LEdd. In the latter case of inefficient cooling, we deduce a viscous time-scale generally shorter than the circularization time-scale. This suggests an accretion rate through the disc tracing the fallback rate, if viscosity starts acting promptly.
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)
Hinnov, L.; Ogg, J. G.
2009-12-01
Mesozoic cyclostratigraphy from around the world is being assessed to construct a continuous Astronomical Time Scale (ATS) based on Earth’s cyclic orbital parameters. The recognition of a prevalent sedimentary cycling with a ~400-kyr period associated with forcing by the stable 405-kyr orbital eccentricity variation is an important development. Numerous formations spanning 10 to 20 myr (and longer) intervals in the Cretaceous, Jurassic and Triassic clearly express this dominant cycle and provide a robust basis for 405-kyr-scale calibration of the ATS. This 405-kyr metronome will enable extension of the well-defined Cenozoic ATS for scaling of the past quarter-billion years of Earth history. This astronomical calibration has a resolution comparable to the 1% to 0.1% precision for radioisotope dating of Mesozoic ash beds, with the added benefit of providing continuous stratigraphic coverage between dated beds. Extended portions of the Mesozoic ATS have already provided new insights into long-standing geologic problems of seafloor spreading, tectonics, eustasy, and paleoclimate change. Ongoing work is focused on closing gaps in coverage and on collecting duplicate cyclostratigraphic records for the entire Mesozoic Era.
HD 147506b: A Supermassive Planet in an Eccentric Orbit Transiting a Bright Star
NASA Astrophysics Data System (ADS)
Bakos, G. Á.; Kovács, G.; Torres, G.; Fischer, D. A.; Latham, D. W.; Noyes, R. W.; Sasselov, D. D.; Mazeh, T.; Shporer, A.; Butler, R. P.; Stefanik, R. P.; Fernández, J. M.; Sozzetti, A.; Pál, A.; Johnson, J.; Marcy, G. W.; Winn, J. N.; Sipőcz, B.; Lázár, J.; Papp, I.; Sári, P.
2007-11-01
We report the discovery of a massive (Mp=9.04+/-0.50 MJ) planet transiting the bright (V=8.7) F8 star HD 147506, with an orbital period of 5.63341+/-0.00013 days and an eccentricity of e=0.520+/-0.010. From the transit light curve we determine that the radius of the planet is Rp=0.982+0.038-0.105 RJ. HD 147506b (also coined HAT-P-2b) has a mass about 9 times the average mass of previously known transiting exoplanets and a density of ρp~12 g cm-3, greater than that of rocky planets like the Earth. Its mass and radius are marginally consistent with theories of structure of massive giant planets composed of pure H and He, and accounting for them may require a large (>~100 M⊕) core. The high eccentricity causes a ninefold variation of insolation of the planet between peri- and apastron. Using follow-up photometry, we find that the center of transit is Tmid=2,454,212.8559+/-0.0007 (HJD) and the transit duration is 0.177+/-0.002 days. Some of the data presented herein were obtained at the W. M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California, and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation. The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain. Keck time has been in part granted by NASA.
NASA Astrophysics Data System (ADS)
Evans, Charles; Forseth, Erik; Hopper, Seth
2015-04-01
Several groups (Fujita 2012; Shah, Friedman, and Whiting 2014; Shah 2014; Fujita 2014) have recently described results from computing gravitational perturbations and the self-force at extraordinarily high precision for binaries with circular orbits in the extreme-mass-ratio limit. These calculations have allowed comparison with post-Newtonian (PN) theory at the lowest order in the mass ratio and uncovered new terms and coefficients in the PN expansion for circular orbits. We describe a new means of extending this analytic function expansion approach to include binaries with eccentric orbits, thus allowing terms in the known 3PN order expansion to be verified and to discover new terms beyond 3PN.
NASA Astrophysics Data System (ADS)
Shibahashi, Hiromoto; Kurtz, Donald W.; Murphy, Simon J.
2015-07-01
Continuous and precise space-based photometry has made it possible to measure the orbital frequency modulation of pulsating stars in binary systems with extremely high precision over long time spans. Frequency modulation caused by binary orbital motion manifests itself as a multiplet with equal spacing of the orbital frequency in the Fourier transform. The amplitudes and phases of the peaks in these multiplets reflect the orbital properties, hence the orbital parameters can be extracted by analysing such precise photometric data alone. We derive analytically the theoretical relations between the multiplet properties and the orbital parameters, and present a method for determining these parameters, including the eccentricity and the argument of periapsis, from a quintuplet or a higher order multiplet. This is achievable with the photometry alone, without spectroscopic radial velocity measurements. We apply this method to Kepler mission data of KIC 8264492, KIC 9651065, and KIC 10990452, each of which is shown to have an eccentricity exceeding 0.5. Radial velocity curves are also derived from the Kepler photometric data. We demonstrate that the results are in good agreement with those obtained by another technique based on the analysis of the pulsation phases.
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.
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
2016-06-01
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 degrees per year, 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)
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.
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)
Deleflie, Florent; Rossi, Alessandro; Portmann, Christophe; Métris, Gilles; Barlier, François
2011-03-01
This paper aims at investigating the stability over 150 years of a very large number of trajectories in the Medium Earth Orbit (MEO) region, near the orbits devoted to radionavigation such as the Global Navigation Satellite Systems (GNSS like GPS, Glonass, Galileo, COMPASS).The stability is characterized by the long term evolution of the eccentricity, and a stable orbit will be defined by initial conditions not inducing through gravitational perturbations a high difference between the perigee and apogee altitudes over a 150 years (for keeping as low as possible the collision risk with operational orbits).The initial conditions of motion used for our tests cover a wide range of semi-major axes and inclinations, regularly sampled, so as to describe as exhaustively as possible the gravitational perturbations acting on the space debris population in these regions.In this study, we pay particular attention to the dynamical properties which can make the orbits eccentricity becoming very large, due to effects induced by the non-spherical shape of the Earth, and the luni-solar attraction, with an amplitude governed by the satellite inclination, as well. We show that even if apogee and perigee variations must be limited to less than 300 km (corresponding to a maximum allowed eccentricity growth of 0.01), there are some cases where the eccentricity growth can rise up to the order of 0.7 over a few decades.The paper is organized such as follows. We begin with the general and historical background of the study. We then give some detail about the semi-analytical modelling than we will propagate with about 36,000 various initial conditions over 150 years. These simulations are based on a parallelized code which works on a “Grid” with about 60,000 CPUs available, ensuring reasonable integration times. First interpretations are then addressed, from an analytical point of view, searching for combinations of angles and initial conditions inducing very long periodic terms in the
Mars orbits with daily repeating ground traces
NASA Technical Reports Server (NTRS)
Noreen, Gary K.; Kerridge, Stuart; Diehl, Roger; neelon, Joseph; Ely, Todd; Turner, Andrew
2003-01-01
This paper derives orbits at Mars with ground traces that repeat at the same times every solar day (sol). A relay orbiter in such an orbit would pass over insitu probes at the same times every sol, ensuring consistent coverage and simplifying mission design and operations. 42 orbits in five classes are characteried: 14 cicular equatorial prograde orbits; 14 circular equatorial retrograde orbits; 11 circular sun synchrounous orbits; 2 eccentroc equatorial orbits; 1 eccentric critcally inclined orbit. the paper reports on the performance of a relay orbiter in some of the orbits.
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
NASA Astrophysics Data System (ADS)
Bini, Donato; Damour, Thibault; Geralico, Andrea
2016-05-01
We raise the analytical knowledge of the eccentricity expansion of the Detweiler-Barack-Sago redshift invariant in a Schwarzschild spacetime up to the 9.5th post-Newtonian order (included) for the e2 and e4 contributions, and up to the 4th post-Newtonian order for the higher eccentricity contributions through e20 . We convert this information into an analytical knowledge of the effective-one-body radial potentials d ¯ (u ) , ρ (u ) and q (u ) through the 9.5th post-Newtonian order. We find that our analytical results are compatible with current corresponding numerical self-force data.
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.
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)
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
NASA Astrophysics Data System (ADS)
Delva, P.; Hees, A.; Bertone, S.; Richard, E.; Wolf, P.
2015-12-01
The Einstein Equivalence Principle (EEP) is one of the foundations of the theory of General Relativity and several alternative theories of gravitation predict violations of the EEP. Experimental constraints on this fundamental principle of nature are therefore of paramount importance. The EEP can be split into three sub-principles: the universality of free fall (UFF), the local Lorentz invariance (LLI) and the local position invariance (LPI). In this paper we propose to use stable clocks in eccentric orbits to perform a test of the gravitational redshift, a consequence of the LPI. The best test to date was performed with the Gravity Probe A (GP-A) experiment in 1976 with an uncertainty of 1.4× {10}-4. Our proposal considers the opportunity of using Galileo satellites 5 and 6 to improve on the GP-A test uncertainty. We show that considering realistic noise and systematic effects, and thanks to a highly eccentric orbit, it is possible to improve on the GP-A limit to an uncertainty around (3-4)× {10}-5 after one year of integration of Galileo 5 and 6 data.
NASA Astrophysics Data System (ADS)
Veillet, Christian
2001-07-01
The discovery that the Trans Neptunian Object {TNO} 1998 WW31 has a satellite was announced on IAU Circular 7610 {16th April 2001}. 1998 WW31 has been observed on three HST orbits, thanks to an allocation of DD time. The combination of all the ground based obse rvations and these three high precision HST positions allowed a first determination of the motion of the faint component with resp ect to the primary body. Instead of the circular orbit assumed before the HST observations, we found a highly eccentric orbit whose eccentricity, 0.7, is poorly constrained by the observations, mainly made far from the pericenter. Some models could even accommod ate an eccentricity as high as 0.9. These results will be presented a the AAS DPS meeting on Nov 27 and a paper is being submitted to Nature. A normal proposal has been made for the next cycle, but we now know that the companion will pass at the pericenter betw een January and March of 2002, and the next occurrence will be only in September 2003 {+/- a couple of months with the current uncer tainties}. With a separation of the two components at pericenter close to 0.15", there is no way it can be observed from the ground with any sufficient accuracy. Hubble's unparalleled resolution will enable us to assess the ellipticity of the orbit in a definite way, providing an important constraint to the models proposed for the creation of such a binary system. It is our intent, as soon as our Nature paper is published, to implement an outreach site showing the evolution of our knowledge of the system with the acqu isition of new data from HST and from the ground, as a "case study" demonstrating the "prediction-correction" scheme widely used in science, with the advantage of simple basic physics {Keplerian motion, simple assumptions on physical characteristics like density o r albedo} easily accessible to young students, but still bringing important conclusions on the nature of the objects themselves.
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)
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)
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.
Eccentricity and argument of perigee control for orbits with repeat ground tracks
NASA Technical Reports Server (NTRS)
Vincent, Mark A.
1992-01-01
In order to gain an understanding into the problem of eccentricity (e) and argument of perigee (omega) control for TOPEX/Poseidon, the two cases where the highest latitude crossing time and one of the equator crossings are held constant are investigated. Variations in e and omega cause a significant effect on the satellite's ground-track repeatability. Maintaining e and omega near their frozen values will minimize this variation. Analytical expressions are found to express this relationship while keeping an arbitrary point of the ground track fixed. The initial offset of the ground track from its nominal path determines the subsequent evolution of e and omega about their frozen values. This long-term behavior is numerically determined using an earth gravitational field including the first 17 zonal harmonics. The numerical results are plotted together with the analytical constraints to see if the later values of e and omega cause unacceptable deviation in the ground track.
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."
Chaos in the test particle eccentric Kozai-Lidov mechanism
Li, Gongjie; Naoz, Smadar; Holman, Matt; Loeb, Abraham
2014-08-20
The Kozai-Lidov mechanism can be applied to a vast variety of astrophysical systems involving hierarchical three-body systems. Here, we study the Kozai-Lidov mechanism systematically in the test particle limit at the octupole level of approximation. We investigate the chaotic and quasi-periodic orbital evolution by studying the surfaces of section and the Lyapunov exponents. We find that the resonances introduced by the octupole level of approximation cause orbits to flip from prograde to retrograde and back as well as cause significant eccentricity excitation, and chaotic behavior occurs when the mutual inclination between the inner and the outer binary is high. We characterize the parameter space that allows large amplitude oscillations in eccentricity and inclination.
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.
Large retrograde Centaurs: visitors from the Oort cloud?
NASA Astrophysics Data System (ADS)
de la Fuente Marcos, C.; de la Fuente Marcos, R.
2014-08-01
Among all the asteroid dynamical groups, Centaurs have the highest fraction of objects moving in retrograde orbits. The distribution in absolute magnitude, H, of known retrograde Centaurs with semi-major axes in the range 6-34 AU exhibits a remarkable trend: 10 % have H<10 mag, the rest have H>12 mag. The largest objects, namely (342842) 2008 YB3, 2011 MM4 and 2013 LU28, move in almost polar, very eccentric paths; their nodal points are currently located near perihelion and aphelion. In the group of retrograde Centaurs, they are obvious outliers both in terms of dynamics and size. Here, we show that these objects are also trapped in retrograde resonances that make them unstable. Asteroid 2013 LU28, the largest, is a candidate transient co-orbital to Uranus and it may be a recent visitor from the trans-Neptunian region. Asteroids 342842 and 2011 MM4 are temporarily submitted to various high-order retrograde resonances with the Jovian planets but 342842 may be ejected towards the trans-Neptunian region within the next few hundred kyr. Asteroid 2011 MM4 is far more stable. Our analysis shows that the large retrograde Centaurs form an heterogeneous group that may include objects from various sources. Asteroid 2011 MM4 could be a visitor from the Oort cloud but an origin in a relatively stable closer reservoir cannot be ruled out. Minor bodies like 2011 MM4 may represent the remnants of the primordial planetesimals and signal the size threshold for catastrophic collisions in the early Solar System.
Crepp, Justin R.; Johnson, John Asher; Hillenbrand, Lynne A.; Hinkley, Sasha; Carpenter, John M.; Fischer, Debra A.; Brewer, John M.; Howard, Andrew W.; Marcy, Geoffrey W.; Isaacson, Howard; Wright, Jason T.; Boyajian, Tabetha; Von Braun, Kaspar
2012-06-01
The companion to the G0V star HR7672 directly imaged by Liu et al. has moved measurably along its orbit since the discovery epoch, making it possible to determine its dynamical properties. Originally targeted with adaptive optics because it showed a long-term radial velocity (RV) acceleration (trend), we have monitored this star with precise Doppler measurements and have now established a 24 year time baseline. The RV variations show significant curvature (change in the acceleration) including an inflection point. We have also obtained a recent image of HR7672B with NIRC2 at Keck. The astrometry also shows curvature. In this paper, we use jointly fitted Doppler and astrometric models to calculate the three-dimensional orbit and dynamical mass of the companion. The mass of the host star is determined using a direct radius measurement from CHARA interferometry in combination with high-resolution spectroscopic modeling. We find that HR7672B has a highly eccentric, e = 0.50{sup +0.01}{sub -0.01}, near edge-on, i = 97.3{sup +0.4}{sub -0.5} deg, orbit with semimajor axis, a = 18.3{sup +0.4}{sub -0.5} AU. The mass of the companion is m = 68.7{sup +2.4}{sub -3.1} M{sub J} . HR7672B thus resides near the substellar boundary, just below the hydrogen-fusing limit. These measurements of the companion mass are independent of its brightness and spectrum and establish HR7672B as a rare and precious 'benchmark' brown dwarf with a well-determined mass, age, and metallicity essential for testing theoretical evolutionary models and synthetic spectral models. Indeed, we find that such models under-predict its luminosity by a factor of Almost-Equal-To 2. HR 7672B is presently the only L, T, or Y dwarf known to produce an RV trend around a solar-type star.
INFERRING THE ECCENTRICITY DISTRIBUTION
Hogg, David W.; Bovy, Jo; Myers, Adam D.
2010-12-20
Standard maximum-likelihood estimators for binary-star and exoplanet eccentricities are biased high, in the sense that the estimated eccentricity tends to be larger than the true eccentricity. As with most non-trivial observables, a simple histogram of estimated eccentricities is not a good estimate of the true eccentricity distribution. Here, we develop and test a hierarchical probabilistic method for performing the relevant meta-analysis, that is, inferring the true eccentricity distribution, taking as input the likelihood functions for the individual star eccentricities, or samplings of the posterior probability distributions for the eccentricities (under a given, uninformative prior). The method is a simple implementation of a hierarchical Bayesian model; it can also be seen as a kind of heteroscedastic deconvolution. It can be applied to any quantity measured with finite precision-other orbital parameters, or indeed any astronomical measurements of any kind, including magnitudes, distances, or photometric redshifts-so long as the measurements have been communicated as a likelihood function or a posterior sampling.
Inferring the Eccentricity Distribution
NASA Astrophysics Data System (ADS)
Hogg, David W.; Myers, Adam D.; Bovy, Jo
2010-12-01
Standard maximum-likelihood estimators for binary-star and exoplanet eccentricities are biased high, in the sense that the estimated eccentricity tends to be larger than the true eccentricity. As with most non-trivial observables, a simple histogram of estimated eccentricities is not a good estimate of the true eccentricity distribution. Here, we develop and test a hierarchical probabilistic method for performing the relevant meta-analysis, that is, inferring the true eccentricity distribution, taking as input the likelihood functions for the individual star eccentricities, or samplings of the posterior probability distributions for the eccentricities (under a given, uninformative prior). The method is a simple implementation of a hierarchical Bayesian model; it can also be seen as a kind of heteroscedastic deconvolution. It can be applied to any quantity measured with finite precision—other orbital parameters, or indeed any astronomical measurements of any kind, including magnitudes, distances, or photometric redshifts—so long as the measurements have been communicated as a likelihood function or a posterior sampling.
NASA Astrophysics Data System (ADS)
Harakawa, Hiroki; Sato, Bun'ei; Omiya, Masashi; Fischer, Debra A.; Hori, Yasunori; Ida, Shigeru; Kambe, Eiji; Yoshida, Michitoshi; Izumiura, Hideyuki; Koyano, Hisashi; Nagayama, Shogo; Shimizu, Yasuhiro; Okada, Norio; Okita, Kiichi; Sakamoto, Akihiro; Yamamuro, Tomoyasu
2015-06-01
We report detections of new exoplanets from a radial-velocity (RV) survey of metal-rich FGK stars by using three telescopes. By optimizing our RV analysis method to long time-baseline observations, we have succeeded in detecting five new Jovian planets around three metal-rich stars, HD 1605, HD 1666, and HD 67087, with masses of 1.3 {{M}⊙ }, 1.5 {{M}⊙ }, and 1.4 {{M}⊙ }, respectively. A K1 subgiant star, HD 1605 hosts two planetary companions with minimum masses of {{M}p}sin i=0.96{{M}Jup} and 3.5{{M}Jup} in circular orbits with the planets’ periods P=577.9 and 2111 days, respectively. HD 1605 shows a significant linear trend in RVs. Such a system consisting of Jovian planets in circular orbits has rarely been found and thus HD 1605 should be an important example of a multi-planetary system that is likely unperturbed by planet-planet interactions. HD 1666 is an F7 main-sequence star that hosts an eccentric and massive planet of {{M}p}sin i=6.4{{M}Jup} in an orbit with {{a}p}=0.94 AU and eccentricity e=0.63. Such an eccentric and massive planet can be explained as a result of planet-planet interactions among Jovian planets. While we have found large residuals of rms=35.6 m {{s}-1}, the periodogram analysis does not support any additional periodicities. Finally, HD 67087 hosts two planets of {{M}p}sin i=3.1{{M}Jup} and 4.9{{M}Jup} in orbits with P=352.2 and 2374 days, and e=0.17 and 0.76, respectively. Although the current RVs do not lead to accurate determinations of its orbit and mass, HD 67087 c can be one of the most eccentric planets ever discovered in multiple systems.
NASA Astrophysics Data System (ADS)
Chen, Yuan-Yuan; Ma, Yuehua; Zheng, Jiaqing
2016-02-01
We explore planetary migration scenarios for formation of high inclination Neptune Trojans (NTs) and how they are affected by the planetary migration of Neptune and Uranus. If Neptune and Uranus's eccentricity and inclination were damped during planetary migration, then their eccentricities and inclinations were higher prior and during 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 explaining the origin of NTs that is particularly effective if Uranus and Neptune experienced eccentricity and inclination damping during planetary migration.
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.
Retrograde ejaculation occurs when semen enters the bladder instead of going out through the urethra during ejaculation. ... bladder (bladder neck) does not close. This causes semen to go backwards into the bladder rather than ...
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)
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)
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.
... 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 . ...
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.
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.
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
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
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.
Phase Curves of Eccentric Exoplanets
NASA Astrophysics Data System (ADS)
Lewis, Nikole K.; de Wit, Julien; Laughlin, Gregory P.; Knutson, Heather
2016-01-01
Nearly 15% of the known exoplanet population have significantly eccentric orbits (e > 0.25). Systems with planets on highly eccentric orbits provide natural laboratories to test theories of orbital evolution, tidal forcing, and atmospheric response. The two best studied eccentric exoplanets are HAT-P-2b (e~0.5) and HD 80606 b (e~0.9). Both of these eccentric planets have full or partial orbit phase curve observations taken with the 3.6, 4.5, and 8.0 micron channels of the Spitzer IRAC instrument. These phase-curve observations of HAT-P-2b and HD 80606 b have given us important insights into atmospheric radiative timescales, planetary rotation rates and orbital evolution, and planet-star tidal interactions. Here I will overview the key results from the Spitzer observational campaigns for HAT-P-2b and HD 80606 b and look toward the future of phase curve observations of eccentric exoplanets in the era of JWST.
MECHANISM FOR EXCITING PLANETARY INCLINATION AND ECCENTRICITY THROUGH A RESIDUAL GAS DISK
Chen Yuanyuan; Liu Huigen; Zhao Gang; Zhou Jilin E-mail: zhoujl@nju.edu.cn
2013-05-20
According to the theory of Kozai resonance, the initial mutual inclination between a small body and a massive planet in an outer circular orbit is as high as {approx}39. Degree-Sign 2 for pumping the eccentricity of the inner small body. Here we show that with the presence of a residual gas disk outside two planetary orbits, the inclination can be reduced to as low as a few degrees. The presence of the disk changes the nodal precession rates and directions of the planet orbits. At the place where the two planets achieve the same nodal processing rate, vertical secular resonance (VSR) occurs so that the mutual inclination of the two planets will be excited, which might further trigger the Kozai resonance between the two planets. However, in order to pump an inner Jupiter-like planet, the conditions required for the disk and the outer planet are relatively strict. We develop a set of evolution equations, which can fit the N-body simulation quite well but can be integrated within a much shorter time. By scanning the parameter spaces using the evolution equations, we find that a massive planet (10 M{sub J} ) at 30 AU with an inclination of 6 Degree-Sign to a massive disk (50 M{sub J} ) can finally enter the Kozai resonance with an inner Jupiter around the snowline. An inclination of 20 Degree-Sign of the outer planet to the disk is required for flipping the inner one to a retrograde orbit. In multiple planet systems, the mechanism can happen between two nonadjacent planets or can inspire a chain reaction among more than two planets. This mechanism could be the source of the observed giant planets in moderate eccentric and inclined orbits, or hot Jupiters in close-in, retrograde orbits after tidal damping.
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.
Coorbital motion in the co-planar RTBP: family of Quasi-satellite periodic orbits
NASA Astrophysics Data System (ADS)
Pousse, A.; Robutel, P.; Vienne, A.
2015-10-01
In the framework of the Restricted Three-body Problem (RTBP), we consider a primary whose mass is equal to one, a secondary on circular or eccentric motion with a mass # and a massless third body. The three bodies are in coplanar motion and in co-orbital resonance. We actually know three classes of regular coorbital motions: in rotating frame with the secondary, the tadpole orbits (TP) librate around Lagrangian equilibria L4 or L5; the horseshoe orbits (HS) encompass the three equilibrium points L3, L4 and L5; the quasi-satellite orbits (QS) are remote retrograde satellite around the secondary, but outside of its Hill sphere. Contrarily to TP orbits which emerge from a fixed point in rotating frame, QS orbits emanate from a oneparameter family of periodic orbits, denoted family-f by Henon (1969). In the averaged problem, this family can be understood as a family of fixed points. However, the eccentricity of these orbits can reach high values. Consequently a development in eccentricity will not be efficient. Using the method developed by Nesvorny et al. (2002) which is valid for every values of eccentricity, we study the QS periodic orbits family with a numerical averaging. In the circular case, I will present the validity domain of the average approximation and a particular orbit. Then, I will highlight an unexpected result for very high eccentricity on families of periodic orbits that originate from L3, L4 and L5. Finally, I will sketch out an analytic method adapted to QS motion and exhibit associated results in the eccentric case.
Hydrodynamic instability in eccentric astrophysical discs
NASA Astrophysics Data System (ADS)
Barker, A. J.; Ogilvie, G. I.
2014-12-01
Eccentric Keplerian discs are believed to be unstable to three-dimensional hydrodynamical instabilities driven by the time-dependence of fluid properties around an orbit. These instabilities could lead to small-scale turbulence, and ultimately modify the global disc properties. We use a local model of an eccentric disc, derived in a companion paper, to compute the non-linear vertical (`breathing mode') oscillations of the disc. We then analyse their linear stability to locally axisymmetric disturbances for any disc eccentricity and eccentricity gradient using a numerical Floquet method. In the limit of small departures from a circular reference orbit, the instability of an isothermal disc is explained analytically. We also study analytically the small-scale instability of an eccentric neutrally stratified polytropic disc with any polytropic index using a Wentzel-Kramers-Brillouin (WKB) approximation. We find that eccentric discs are generically unstable to the parametric excitation of small-scale inertial waves. The non-linear evolution of these instabilities should be studied in numerical simulations, where we expect them to lead to a decay of the disc eccentricity and eccentricity gradient as well as to induce additional transport and mixing. Our results highlight that it is essential to consider the three-dimensional structure of eccentric discs, and their resulting vertical oscillatory flows, in order to correctly capture their evolution.
Ureteral retrograde brush biopsy
Biopsy - brush - urinary tract; Retrograde ureteral brush biopsy cytology; Cytology - ureteral retrograde brush biopsy ... to be biopsied is rubbed with the brush. Biopsy forceps may be used instead to collect a ...
ECCENTRIC EVOLUTION OF SUPERMASSIVE BLACK HOLE BINARIES
Iwasawa, Masaki; An, Sangyong; Matsubayashi, Tatsushi; Funato, Yoko; Makino, Junichiro
2011-04-10
In recent numerical simulations, it has been found that the eccentricity of supermassive black hole (SMBH)-intermediate black hole (IMBH) binaries grows toward unity through interactions with the stellar background. This increase of eccentricity reduces the merging timescale of the binary through the gravitational radiation to a value well below the Hubble time. It also gives a theoretical explanation of the existence of eccentric binaries such as that in OJ287. In self-consistent N-body simulations, this increase of eccentricity is always observed. On the other hand, the result of the scattering experiment between SMBH binaries and field stars indicated that the eccentricity dose not change significantly. This discrepancy leaves the high eccentricity of the SMBH binaries in N-body simulations unexplained. Here, we present a stellar-dynamical mechanism that drives the increase of the eccentricity of an SMBH binary with a large mass ratio. There are two key processes involved. The first one is the Kozai mechanism under a non-axisymmetric potential, which effectively randomizes the angular momenta of surrounding stars. The other is the selective ejection of stars with prograde orbits. Through these two mechanisms, field stars extract the orbital angular momentum of the SMBH binary. Our proposed mechanism causes the increase in the eccentricity of most of SMBH binaries, resulting in the rapid merger through gravitational wave radiation. Our result has given a definite solution to the 'last-parsec problem'.
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.
Mohamed, Jumshad B; Shivakumar, B; Sudarsan, Sabitha; Arun, K V; Kumar, T S S
2010-01-01
Retrograde peri-implantitis constitutes an important cause for implant failure. Retrograde peri-implantitis may sometimes prove difficult to identify and hence institution of early treatment may not be possible. This paper presents a report of four cases of (the implant placed developing to) retrograde peri-implantitis. Three of these implants were successfully restored to their fully functional state while one was lost due to extensive damage. The paper highlights the importance of recognizing the etiopathogenic mechanisms, preoperative assessment, and a strong postoperative maintenance protocol to avoid retrograde peri-implant inflammation. PMID:20922082
Perturbed motion at small eccentricities
NASA Astrophysics Data System (ADS)
Emel'yanov, N. V.
2015-09-01
In the study of the motion of planets and moons, it is often necessary to have a simple approximate analytical motion model, which takes into account major perturbations and preserves almost the same accuracy at long time intervals. A precessing ellipse model is used for this purpose. In this paper, it is shown that for small eccentricities this model of the perturbed orbit does not correspond to body motion characteristics. There is perturbed circular motion with a constant zero mean anomaly. The corresponding solution satisfies the Lagrange equations with respect to Keplerian orbital elements. There are two families of solutions with libration and circulation changes in the mean anomaly close to this particular solution. The paper shows how the eccentricity and mean anomaly change in these solutions. Simple analytical models of the motion of the four closest moons of Jupiter consistent with available ephemerides are proposed, which in turn are obtained by the numerical integration of motion equations and are refined by observations.
Analysis of the Radio Astronomy Explorer lunar orbit mission.
NASA Technical Reports Server (NTRS)
Groves, R. T.
1972-01-01
The second Radio Astronomy Explorer spacecraft (RAE-B) is planned to be inserted into lunar orbit in 1973. The transfer trajectory design, lunar orbit selection and launch opportunities are developed in relation to the spacecraft mass properties, propulsion capability and the scientific, environmental and engineering constraints. Alternative midcourse guidance and lunar orbit trim strategies are analyzed and compared. A means of achieving a launch window without varying launch azimuth and park orbit coast time is described. The resulting mission design is characterized by near-minimum energy lunar transfer trajectories and low eccentricity, retrograde critical inclination lunar orbits. Acceptable launch periods are shown to exist for six consecutive months and for two to four consecutive days per month.
The origin of the eccentricities of the rings of Uranus
NASA Technical Reports Server (NTRS)
Goldreich, P.; Tremaine, S.
1981-01-01
The effect of gravitational perturbations from a nearby satellite on the eccentricity e of a narrow particulate ring is considered. The perturbations near a resonance in an eccentric ring may be divided into corotation and Lindblad terms. For small e, the corotation terms damp e, whereas the Lindblad terms excite e. In the absence of saturation the corotation terms win by a small margin, and e damps. However, if the perturbations open gaps at the strongest resonances, then the Lindblad terms win, and e grows. This result offers an explanation for the existence of both circular and eccentric rings around Uranus. It is also shown that eccentricity changes induced by circular rings on eccentric satellite orbits are similar to those induced by satellites with circular orbits on eccentric rings.
On the detectability of eccentric binary pulsars
NASA Astrophysics Data System (ADS)
Bagchi, Manjari; Lorimer, Duncan R.; Wolfe, Spencer
2013-06-01
By generalizing earlier work of Johnston and Kulkarni, we present a detailed description of the reduction in the signal-to-noise ratio for observations of binary pulsars. We present analytical expressions, and provide software, to calculate the sensitivity reduction for orbits of arbitrary eccentricity. We find that this reduction can be quite significant, especially in the case of a massive companion like another neutron star or a black hole. On the other hand, the reduction is less for highly eccentric orbits. We also demonstrate that this loss of sensitivity can be recovered by employing `acceleration search' or `acceleration-jerk search' algorithms.
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.
Orbital Evolution of Asteroids
NASA Astrophysics Data System (ADS)
Dermott, S. F.; Kehoe, T. J. J.
2011-10-01
The synthetic orbital frequencies and eccentricities of main belt asteroids computed by Knezevic and Milani [2] show evidence that the structure of the asteroid belt has been determined by a dense of web of high-order resonances. By examining the orbital frequency distribution at high resolution, we discover a correlation between asteroid number density, mean orbital eccentricity and Lyapunov Characteristic Exponent. In particular, the orbital eccentricities of asteroids trapped in resonance tend to be higher than those of non-resonant asteroids and we argue that this is observational evidence for orbital evolution due to chaotic diffusion.
Eccentricity boost of stars around shrinking massive black hole binaries
NASA Astrophysics Data System (ADS)
Iwasa, Mao; Seto, Naoki
2016-06-01
Based on a simple geometrical approach, we analyze the evolution of the Kozai-Lidov mechanism for stars around shrinking massive black hole binaries on circular orbits. We find that, due to a peculiar bifurcation pattern induced by the Newtonian potential of stellar clusters, the orbit of stars could become highly eccentric. This transition occurs abruptly for stars with small initial eccentricities. The approach presented in this paper may be useful for studying the Kozai-Lidov mechanism in various astrophysical contexts.
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.
Habitable Climates: The Influence of Eccentricity
NASA Astrophysics Data System (ADS)
Dressing, Courtney D.; Spiegel, David S.; Scharf, Caleb A.; Menou, Kristen; Raymond, Sean N.
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 2)-1/2, one might expect the greatest habitable semimajor axis (for fixed atmospheric composition) to scale as (1 - e 2)-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 habitable conditions.
Eccentricity versus Mass for Low-Mass Secondaries and Planets
NASA Astrophysics Data System (ADS)
Mazeh, Tsevi; Mayor, Michel; Latham, David W.
1997-03-01
Spectroscopic orbits have been reported for six unseen companions orbiting solar-type stars with minimum possible masses in the range 0.5-10 Jupiter masses. The four least massive companions, around 51 Peg, 47 UMa, 55 Cnc, and τ Boo, have nearly circular orbits, while the two most massive companions, around HD 114762 and 70 Vir, have eccentricities of 0.35 and 0.40. We compare the orbital eccentricities of these six planet candidates with the eccentricities of the planets in the solar system, of the three planets found around the pulsar PSR B1957+12, and of the low-mass secondaries in a subsample of the spectroscopic binaries from the Carney-Latham proper-motion survey. The distribution of eccentricities for the combined samples displays a striking pattern: the companions with masses smaller than about 5 Jupiter masses have circular orbits, while the more massive companions have eccentric orbits. We outline four possible scenarios that might have produced this pattern of eccentricity versus mass.
Emerging Trends in Retrograde Signaling.
Suvarna, Yashasvi; Maity, Nivedita; Shivamurthy, M C
2016-05-01
Retrograde signaling is defined as the signaling events leading from the plastids to the nucleus in plants and across the chemical synapse, from the postsynaptic neuron to the presynaptic neuron in animals. The discovery of various retrograde messengers has opened many avenues and clouds of thoughts as to the role of retrograde signaling. They have been implicated particularly in long-term potentiation (LTP) and synaptic plasticity. But the basic assumptions about retrograde signaling have not been studied upon for many years. This review focuses on established facts and hypothesis put forward in retrograde signaling. PMID:26081150
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)
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).
Eccentric motion of spinning compact binaries
NASA Astrophysics Data System (ADS)
Tessmer, Manuel; Schäfer, Gerhard
2014-05-01
The equations of motion for spinning compact binaries on eccentric orbits are treated perturbatively in powers of a fractional mass-difference ordering parameter. The solution is valid through first order in the mass-difference parameter. A canonical point transformation removes the leading-order terms of the spin-orbit Hamiltonian which induce a wiggling precession of the orbital angular momentum around the conserved total angular momentum, a precession which disappears in the case of equal masses or one single spin. Action-angle variables are applied that make a canonical perturbation theory easily treatable.
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.
Low Eccentricity Earth Satellite KAM Tori
NASA Astrophysics Data System (ADS)
Wiesel, William E.
2015-09-01
The accuracy of a new theory of Earth satellite motion is assessed across inclination and orbital altitude. This theory is based on periodic orbits in the zonal potential, with a Floquet solution for nearby motion, augmented by perturbation solutions for other perturbing forces. It is completely numerical and well adapted to the rich computational environments of today. Its root mean square error is generally in the tens of meters over a one day data arc, for eccentricities less than e = 0.1. The perturbation methods fail near geopotential resonances, but the theory has been adapted to handle the vicinity of a resonance without significant loss of accuracy. The geometric structure of the solution is also explored, and it is shown that most orbits in the full geopotential are static structures that rotate with the Earth's rotation. Geopotential KAM tori shrink down to a two dimensional surface as the analog of zero eccentricity orbits. A first attempt is made at visualizing the torus over the Earth's surface. Precision calculation of low eccentricity KAM tori may lead to much decreased stationkeeping costs for Walker constellations.
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
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
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.
Transit Timing Variations for Inclined and Retrograde Exoplanetary Systems
NASA Astrophysics Data System (ADS)
Payne, Matthew J.; Ford, Eric B.; Veras, Dimitri
2010-03-01
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° < i < 170°, only reducing in amplitude for i>170°. Systems in higher order MMRs (e.g., 5:1) increase in TTV amplitude as inclinations increase toward 45°, becoming approximately constant for 45° < i < 135°, and then declining for i>135°. Planets away from resonance slowly decrease in TTV amplitude as inclinations increase from 0° to 180°, 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° < i <= 180°), 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.
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
Gravitational waves from spinning eccentric binaries
NASA Astrophysics Data System (ADS)
Csizmadia, Péter; Debreczeni, Gergely; Rácz, István; Vasúth, Mátyás
2012-12-01
This paper is to introduce a new software called CBwaves which provides a fast and accurate computational tool to determine the gravitational waveforms yielded by generic spinning binaries of neutron stars and/or black holes on eccentric orbits. This is done within the post-Newtonian (PN) framework by integrating the equations of motion and the spin precession equations, while the radiation field is determined by a simultaneous evaluation of the analytic waveforms. In applying CBwaves various physically interesting scenarios have been investigated. In particular, we have studied the appropriateness of the adiabatic approximation, and justified that the energy balance relation is indeed insensitive to the specific form of the applied radiation reaction term. By studying eccentric binary systems, it is demonstrated that circular template banks are very ineffective in identifying binaries even if they possess tiny residual orbital eccentricity, thus confirming a similar result obtained by Brown and Zimmerman (2010 Phys. Rev. D 81 024007). In addition, by investigating the validity of the energy balance relation we show that, contrary to the general expectations, the PN approximation should not be applied once the PN parameter gets beyond the critical value ˜0.08 - 0.1. Finally, by studying the early phase of the gravitational waves emitted by strongly eccentric binary systems—which could be formed e.g. in various many-body interactions in the galactic halo—we have found that they possess very specific characteristics which may be used to identify these type of binary systems. This paper is dedicated to the memory of our colleague and friend Péter Csizmadia a young physicist, computer expert and one of the best Hungarian mountaineers who disappeared in China’s Sichuan near the Ren Zhong Feng peak of the Himalayas on 23 Oct. 2009. We started to develop CBwaves jointly with Péter a couple of months before he left for China.
Growth of eccentric modes in disc-planet interactions
NASA Astrophysics Data System (ADS)
Teyssandier, Jean; Ogilvie, Gordon I.
2016-05-01
We formulate a set of linear equations that describe the behaviour of small eccentricities in a protoplanetary system consisting of a gaseous disc and a planet. Eccentricity propagates through the disc by means of pressure and self-gravity, and is exchanged with the planet via secular interactions. Excitation and damping of eccentricity can occur through Lindblad and corotation resonances, as well as viscosity. We compute normal modes of the coupled disc-planet system in the case of short-period giant planets orbiting inside an inner cavity, possibly carved by the stellar magnetosphere. Three-dimensional effects allow for a mode to be trapped in the inner parts of the disc. This mode can easily grow within the disc's lifetime. An eccentric mode dominated by the planet can also grow, although less rapidly. We compute the structure and growth rates of these modes and their dependence on the assumed properties of the disc.
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
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.
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.
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.
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.
Eccentric binaries. Tidal flows and periastron events
NASA Astrophysics Data System (ADS)
Moreno, E.; Koenigsberger, G.; Harrington, D. M.
2011-04-01
Context. A number of binary systems present evidence of enhanced activity around periastron passage, suggesting a connection between tidal interactions and these periastron effects. Aims: The aim of this investigation is to study the time-dependent response of a star's surface as it is perturbed by a binary companion. Here we focus on the tidal shear energy dissipation. Methods: We derive a mathematical expression for computing the rate of dissipation, Ė, of the kinetic energy by the viscous flows that are driven by tidal interactions on the surface layer of a binary star. The method is tested by comparing the results from a grid of model calculations with the analytical predictions of Hut (1981, A&A, 99, 126) and the synchronization timescales of Zahn (1977, A&A, 57, 383; 2008, EAS Pub. Ser., 29, 67). Results: Our results for the dependence of the average (over orbital cycle) energy dissipation, Ėave, on orbital separation are consistent with those of Hut (1981) for model binaries with an orbital separation at periastron rper/R1 ≳ 8, where R1 is the stellar radius. The model also reproduces the predicted pseudo-synchronization angular velocity for moderate eccentricities (e ≤ 0.3). In addition, for circular orbits our approach yields the same scaling of synchronization timescales with orbital separation as given by Zahn (1977, 2008) for convective envelopes. The computations give the distribution of Ė over the stellar surface, and show that it is generally concentrated at the equatorial latitude, with maxima generally located around four clearly defined longitudes, corresponding to the fastest azimuthal velocity perturbations. Maximum amplitudes occur around periastron passage or slightly thereafter for supersynchronously rotating stars. In very eccentric binaries, the distribution of Ė over the surface changes significantly as a function of orbital phase, with small spatial structures appearing after periastron. An exploratory calculation for a highly
The eccentricity effect: target eccentricity affects performance on conjunction searches.
Carrasco, M; Evert, D L; Chang, I; Katz, S M
1995-11-01
The serial pattern found for conjunction visual-search tasks has been attributed to covert attentional shifts, even though the possible contributions of target location have not been considered. To investigate the effect of target location on orientation x color conjunction searches, the target's duration and its position in the display were manipulated. The display was present either until observers responded (Experiment 1), for 104 msec (Experiment 2), or for 62 msec (Experiment 3). Target eccentricity critically affected performance: A pronounced eccentricity effect was very similar for all three experiments; as eccentricity increased, reaction times and errors increased gradually. Furthermore, the set-size effect became more pronounced as target eccentricity increased, and the extent of the eccentricity effect increased for larger set sizes. In addition, according to stepwise regressions, target eccentricity as well as its interaction with set size were good predictors of performance. We suggest that these findings could be explained by spatial-resolution and lateral-inhibition factors. The serial self-terminating hypothesis for orientation x color conjunction searches was evaluated and rejected. We compared the eccentricity effect as well as the extent of the orientation asymmetry in these three conjunction experiments with those found in feature experiments (Carrasco & Katz, 1992). The roles of eye movements, spatial resolution, and covert attention in the eccentricity effect, as well as their implications, are discussed. PMID:8539099
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.
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
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.
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.
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.
Chemical Timescales in the Atmospheres of Highly Eccentric Exoplanets
NASA Astrophysics Data System (ADS)
Visscher, Channon
2012-10-01
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 relatively higher CO abundances at periapse to relatively higher CH4 abundances at apoapse. Here we examine chemical timescales for CO<->CH4 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<->CH4 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<->CH4 chemistry at faster vertical mixing rates, whereas orbit-induced thermal quenching may play a significant role at slower mixing rates. 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 CH4 on hydrogen-dominated exoplanets. Observations of CO and CH4 on highly eccentric exoplanets may yield important clues to the chemical and dynamical properties of their atmospheres.
Relativistic apsidal motion in eccentric eclipsing binaries
NASA Astrophysics Data System (ADS)
Wolf, M.; Claret, A.; Kotková, L.; Kučáková, H.; Kocián, R.; Brát, L.; Svoboda, P.; Šmelcer, L.
2010-01-01
Context. The study of apsidal motion in detached eclipsing binary systems is known to be an important source of information about stellar internal structure as well as the possibility of verifying of General Relativity outside the Solar System. Aims: As part of the long-term Ondřejov and Ostrava observational projects, we aim to measure precise times of minima for eccentric eclipsing binaries, needed for the accurate determination of apsidal motion, providing a suitable test of the effects of General Relativity. Methods: About seventy new times of minimum light recorded with photoelectric or CCD photometers were obtained for ten eccentric-orbit eclipsing binaries with significant relativistic apsidal motion. Their O-C diagrams were analysed using all reliable timings found in the literature, and new or improved elements of apsidal motion were obtained. Results: We confirm very long periods of apsidal motion for all systems. For BF Dra and V1094 Tau, we present the first apsidal-motion solution. The relativistic effects are dominant, representing up to 100% of the total observable apsidal-motion rate in several systems. The theoretical and observed values of the internal structure constant k 2 were compared for systems with lower relativistic contribution. Using the light-time effect solution, we predict a faint third component for V1094 Tau orbiting with a short period of about 8 years. Partly based on photoelectric observations secured at the Hvar Observatory, Faculty of Geodesy, Zagreb, Croatia, in October 2008.
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.
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.
The highly eccentric detached eclipsing binaries in ACVS and MACC
NASA Astrophysics Data System (ADS)
Shivvers, Isaac; Bloom, Joshua S.; Richards, Joseph W.
2014-06-01
Next-generation synoptic photometric surveys will yield unprecedented (for the astronomical community) volumes of data and the processes of discovery and rare-object identification are, by necessity, becoming more autonomous. Such autonomous searches can be used to find objects of interest applicable to a wide range of outstanding problems in astronomy, and in this paper we present the methods and results of a largely autonomous search for highly eccentric detached eclipsing binary systems in the Machine-learned All-Sky Automated Survey Classification Catalog. 106 detached eclipsing binaries with eccentricities of e ≳ 0.1 are presented, most of which are identified here for the first time. We also present new radial-velocity curves and absolute parameters for six of those systems with the long-term goal of increasing the number of highly eccentric systems with orbital solutions, thereby facilitating further studies of the tidal circularization process in binary stars.
AN ORBIT FIT FOR THE GRILLMAIR DIONATOS COLD STELLAR STREAM
Willett, Benjamin A.; Newberg, Heidi Jo; Zhang Haotong; Yanny, Brian; Beers, Timothy C. E-mail: beers@pa.msu.edu
2009-05-20
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 deg. 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 deg. 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.
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)
Nagasawa, M.; Lin, D. N. C.; Ida, S.
2003-04-01
Most extrasolar planets are observed to have eccentricities much larger than those in the solar system. Some of these planets have sibling planets, with comparable masses, orbiting around the same host stars. In these multiple planetary systems, eccentricity is modulated by the planets' mutual secular interaction as a consequence of angular momentum exchange between them. For mature planets, the eigenfrequencies of this modulation are determined by their mass and semimajor axis ratios. However, prior to the disk depletion, self-gravity of the planets' nascent disks dominates the precession eigenfrequencies. We examine here the initial evolution of young planets' eccentricity due to the apsidal libration or circulation induced by both the secular interaction between them and the self-gravity of their nascent disks. We show that as the latter effect declines adiabatically with disk depletion, the modulation amplitude of the planets' relative phase of periapsis is approximately invariant despite the time-asymmetrical exchange of angular momentum between planets. However, as the young planets' orbits pass through a state of secular resonance, their mean eccentricities undergo systematic quantitative changes. For applications, we analyze the eccentricity evolution of planets around υ Andromedae and HD 168443 during the epoch of protostellar disk depletion. We find that the disk depletion can change the planets' eccentricity ratio. However, the relatively large amplitude of the planets' eccentricity cannot be excited if all the planets had small initial eccentricities.
Resonant Post-Newtonian Eccentricity Excitation in Hierarchical Three-body Systems
NASA Astrophysics Data System (ADS)
Naoz, Smadar; Kocsis, Bence; Loeb, Abraham; Yunes, Nicolás
2013-08-01
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.
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.
Structuring eccentric-narrow planetary rings
NASA Astrophysics Data System (ADS)
Papaloizou, J. C. B.; Melita, M. D.
2005-06-01
A simple and general description of the dynamics of a narrow-eccentric ring is presented. We view an eccentric ring which precesses uniformly at a slow rate as exhibiting a global m=1 mode, which can be seen as originating from a standing wave superposed on an axisymmetric background. We adopt a continuum description using the language of fluid dynamics which gives equivalent results for the secular dynamics of thin rings as the well-known description in terms of a set of discrete elliptical streamlines formulated by Goldreich and Tremaine (1979, Astron. J. 84, 1638-1641). We use this to discuss the nonlinear mode interactions that appear in the ring through the excitation of higher m modes because of the coupling of the m=1 mode with an external satellite potential, showing that they that can lead to the excitation of the m=1 mode through a feedback process. In addition to the external perturbations by neighboring satellites, our model includes effects due to inelastic inter-particle collisions. Two main conditions for the ring to be able to maintain a steady m=1 normal mode are obtained. One can be expressed as an integral condition for the normal mode pattern to precess uniformly, which requires the correct balance between the differential precession induced by the oblateness of the central planet, self-gravity and collisional effects is the continuum form of that obtained from the N streamline model of Goldreich and Tremaine (1979, Astron. J. 84, 1638-1641). The other condition, not before examined in detail, is for the steady maintenance of the nonzero radial action that the ring contains because of its finite normal mode. This requires a balance between injection due to eccentric resonances arising from external satellites and additional collisional damping associated with the presence of the m=1 mode. We estimate that such a balance can occur in the ɛ-ring of Uranus, given its currently observed physical and orbital parameters.
Retrograde signaling: Organelles go networking.
Kleine, Tatjana; Leister, Dario
2016-08-01
The term retrograde signaling refers to the fact that chloroplasts and mitochondria utilize specific signaling molecules to convey information on their developmental and physiological states to the nucleus and modulate the expression of nuclear genes accordingly. Signals emanating from plastids have been associated with two main networks: 'Biogenic control' is active during early stages of chloroplast development, while 'operational' control functions in response to environmental fluctuations. Early work focused on the former and its major players, the GUN proteins. However, our view of retrograde signaling has since been extended and revised. Elements of several 'operational' signaling circuits have come to light, including metabolites, signaling cascades in the cytosol and transcription factors. Here, we review recent advances in the identification and characterization of retrograde signaling components. We place particular emphasis on the strategies employed to define signaling components, spanning the entire spectrum of genetic screens, metabolite profiling and bioinformatics. This article is part of a Special Issue entitled 'EBEC 2016: 19th European Bioenergetics Conference, Riva del Garda, Italy, July 2-6, 2016', edited by Prof. Paolo Bernardi. PMID:26997501
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
Apsidal motion in five eccentric eclipsing binaries
NASA Astrophysics Data System (ADS)
Wolf, M.; Zasche, P.; Kučáková, H.; Lehký, M.; Svoboda, P.; Šmelcer, L.; Zejda, M.
2013-01-01
Aims: As part of the long-term Ondřejov and Ostrava observational projects, we aim to measure the precise times of minimum light for eccentric eclipsing binaries, needed for accurate determination of apsidal motion. Over fifty new times of minimum light recorded with CCD photometers were obtained for five early-type and eccentric-orbit eclipsing binaries: V785 Cas (P = 2.d70, e = 0.09), V821 Cas (1.d77, 0.14), V796 Cyg (1.d48, 0.07), V398 Lac (5.d41, 0.23), and V871 Per (3.d02, 0.24). Methods: O-C diagrams of binaries were analysed using all reliable timings found in the literature, and new elements of apsidal motion were obtained. Results: We derived for the first time or improved the relatively short periods of apsidal motion of about 83, 140, 33, 440, and 70 years for V785 Cas, V821 Cas, V796 Cyg, V398 Lac, and V871 Per, respectively. The internal structure constants, log k2, for V821 Cas and V398 Lac are then found to be -2.70 and -2.35, under the assumption that the component stars rotate pseudosynchronously. The relativistic effects are weak, up to 7% of the total apsidal motion rate.
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.
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
2008-06-01
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(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. PMID:18483399
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.
Light curve solutions and out-of-eclipse variabilities of six eccentric Kepler binaries
NASA Astrophysics Data System (ADS)
Kjurkchieva, D.; Vasileva, D.; Dimitrov, D.
2016-04-01
As a result from light curve solutions of six eccentric Kepler binaries we determined their orbital elements and stellar parameters. We established linear dependence of their eccentricities on the orbital periods. Besides eclipses all targets reveal out-of-eclipse light variabilities modulated on different time scales. KIC 11409698, KIC 5284133 and KIC 8316503, the targets with the biggest eccentricities in our sample, exhibit tidally induced light brightening (hump) around the periastron phase. Just they reveal considerable reflection effect due to the big temperature difference of their components (above 2200 K). The detected humps confirmed the theoretical dependence of the hump amplitude on the eccentricity and mass ratio. KIC 12557713 and KIC 7691527 show photospheric activity caused by two diametrically opposite cool spots on the lateral sides of their primary components (flip-flop effect). We found flares in the Kepler data of KIC 7691527 that is another appearance of the activity of this target.
Proposed search for the detection of gravitational waves from eccentric binary black holes
NASA Astrophysics Data System (ADS)
Tiwari, V.; Klimenko, S.; Christensen, N.; Huerta, E. A.; Mohapatra, S. R. P.; Gopakumar, A.; Haney, M.; Ajith, P.; McWilliams, S. T.; Vedovato, G.; Drago, M.; Salemi, F.; Prodi, G. A.; Lazzaro, C.; Tiwari, S.; Mitselmakher, G.; Da Silva, F.
2016-02-01
Most compact binary systems are expected to circularize before the frequency of emitted gravitational waves (GWs) enters the sensitivity band of the ground based interferometric detectors. However, several mechanisms have been proposed for the formation of binary systems, which retain eccentricity throughout their lifetimes. Since no matched-filtering algorithm has been developed to extract continuous GW signals from compact binaries on orbits with low to moderate values of eccentricity, and available algorithms to detect binaries on quasicircular orbits are suboptimal to recover these events, in this paper we propose a search method for detection of gravitational waves produced from the coalescences of eccentric binary black holes (eBBH). We study the search sensitivity and the false alarm rates on a segment of data from the second joint science run of LIGO and Virgo detectors, and discuss the implications of the eccentric binary search for the advanced GW detectors.
Spin Complicates Eccentric BH-NS Mergers
NASA Astrophysics Data System (ADS)
Kohler, Susanna
2015-08-01
When a neutron star (NS) has a glancing encounter with a black hole (BH), its spin has a significant effect on the outcome, according to new simulations run by William East of Stanford University and his collaborators. Spotting an Eccentric Merger. In a traditional BH-NS merger, the two objects orbit each other quasi-circularly as they spiral in. But there's another kind of merger that's possible in high-density environments like galactic nuclei or globular clusters: a dynamical capture merger, in which a NS and BH pass each other just close enough that the gravity of the black hole "catches" the NS, leading the two objects to merge with very eccentric orbits. During an eccentric merger, the NS can be torn apart -- at which point some fraction of the tidally-disrupted material will escape the system, while some fraction instead accretes back onto the BH. Knowing these fractions is important for being able to model the expected electromagnetic signatures for the merger: the unbound material can power transients like kilonovae, whereas the accreting material may be the cause of short gamma-ray bursts. The amount of material available for events like these would change their observable strengths. Testing the Effects of Spin. To see whether NS spin has an impact on the behavior of the merger, East and collaborators use a general-relativistic hydrodynamic code to simulate the glancing encounter of a BH and a NS with dimensionless spin between a=0 (non-spinning) and a=0.756 (rotation period of 1 ms). They also vary the separation of the first encounter. The group finds that changing the NS's spin can change a number of outcomes of the merger. To start with, it can affect whether the NS is captured by the BH, or if the encounter is glancing and then both objects carry on their merry way. And if the NS is trapped by the BH and torn apart, then the higher the NS's spin, the more matter outside of the BH ends up unbound, instead of getting trapped into an accretion disk
Silsbee, Kedron; Rafikov, Roman R.
2015-01-10
Detections of planets in eccentric, close (separations of ∼20 AU) binary systems such as α Cen or γ Cep provide an important test of planet formation theories. Gravitational perturbations from the companion are expected to excite high planetesimal eccentricities, resulting in destruction rather than growth of objects with sizes of up to several hundred kilometers in collisions of similar-sized bodies. It was recently suggested that the gravity of a massive axisymmetric gaseous disk in which planetesimals are embedded drives rapid precession of their orbits, suppressing eccentricity excitation. However, disks in binaries are themselves expected to be eccentric, leading to additional planetesimal excitation. Here we develop a secular theory of eccentricity evolution for planetesimals perturbed by the gravity of an elliptical protoplanetary disk (neglecting gas drag) and the companion. For the first time, we derive an expression for the disturbing function due to an eccentric disk, which can be used for a variety of other astrophysical problems. We obtain explicit analytical solutions for planetesimal eccentricity evolution neglecting gas drag and delineate four different regimes of dynamical excitation. We show that in systems with massive (≳ 10{sup –2} M {sub ☉}) disks, planetesimal eccentricity is usually determined by the gravity of the eccentric disk alone, and is comparable to the disk eccentricity. As a result, the latter imposes a lower limit on collisional velocities of solids, making their growth problematic. In the absence of gas drag, this fragmentation barrier can be alleviated if the gaseous disk rapidly precesses or if its own self-gravity is efficient at lowering disk eccentricity.
Detectability of eccentric compact binary coalescences with advanced gravitational-wave detectors
NASA Astrophysics Data System (ADS)
Coughlin, M.; Meyers, P.; Thrane, E.; Luo, J.; Christensen, N.
2015-03-01
Compact binary coalescences are a promising source of gravitational waves for second-generation interferometric gravitational-wave detectors such as advanced LIGO and advanced Virgo. While most binaries are expected to possess circular orbits, some may be eccentric, for example, if they are formed through dynamical capture. Eccentric orbits can create difficulty for matched filtering searches due to the challenges of creating effective template banks to detect these signals. In previous work, we showed how seedless clustering can be used to detect low-mass (Mtotal≤10 M⊙) compact binary coalescences for both spinning and eccentric systems, assuming a circular post-Newtonian expansion. Here, we describe a parametrization that is designed to maximize sensitivity to low-eccentricity (0 ≤ɛ ≤0.6 ) systems, derived from the analytic equations. We show that this parametrization provides a robust and computationally efficient method for detecting eccentric low-mass compact binaries. Based on these results, we conclude that advanced detectors will have a chance of detecting eccentric binaries if optimistic models prove true. However, a null observation is unlikely to firmly rule out models of eccentric binary populations.
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.
An Eccentric-Disk Model for the Nucleus of M31
NASA Astrophysics Data System (ADS)
Tremaine, Scott
1995-08-01
The nucleus of M31 may be a thick eccentric disk, composed of stars traveling on nearly Keplerian orbits around a black hole or other dark compact object. This hypothesis reproduces most of the features seen in HST photometry of the center of M31; in particular the bright off-center source P1 is the apoapsis region of the disk. An eccentric disk can also explain the rotation curve and asymmetric dispersion profile revealed by ground-based observations. The central object must be smaller than ~1 pc so that the potential felt by the disk is nearly Keplerian. The disk eccentricity may be excited by dynamical friction from the bulge.
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.
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.
Chemical Timescales in the Atmospheres of Highly Eccentric Exoplanets
NASA Astrophysics Data System (ADS)
Visscher, Channon
2012-09-01
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 CH4 abundances at apoapse. Here, we examine chemical timescales for CO\\rightleftarrowsCH4 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\\rightleftarrowsCH4 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\\rightleftarrowsCH4 chemistry at faster vertical mixing rates (Kzz > 107 cm2 s-1), whereas orbit-induced thermal quenching may play a significant role at slower mixing rates (Kzz < 107 cm2 s-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 CH4 on hydrogen-dominated exoplanets. Observations of CO and CH4 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
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.
Eccentric-Disk Models for the Nucleus of M31
NASA Astrophysics Data System (ADS)
Peiris, Hiranya V.; Tremaine, Scott
2003-12-01
We construct dynamical models of the ``double'' nucleus of M31 in which the nucleus consists of an eccentric disk of stars orbiting a central black hole. The principal approximation in these models is that the disk stars travel in a Keplerian potential; i.e., we neglect the mass of the disk relative to the black hole. We consider both ``aligned'' models, in which the eccentric disk lies in the plane of the large-scale M31 disk, and ``nonaligned'' models, in which the orientation of the eccentric disk is fitted to the data. Both types of model can reproduce the double structure and overall morphology seen in Hubble Space Telescope photometry. In comparison with the best available ground-based spectroscopy, the models reproduce the asymmetric rotation curve, the peak height of the dispersion profile, and the qualitative behavior of the Gauss-Hermite coefficients h3 and h4. Aligned models fail to reproduce the observation that the surface brightness at P1 is higher than at P2 and yield significantly poorer fits to the kinematics; thus, we favor nonaligned models. Eccentric-disk models fitted to ground-based spectroscopy are used to predict the kinematics observed at much higher resolution by the Space Telescope Imaging Spectrograph on the Hubble Space Telescope, and we find generally satisfactory agreement.
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
PHOTOMETRIC PHASE VARIATIONS OF LONG-PERIOD ECCENTRIC PLANETS
Kane, Stephen R.; Gelino, Dawn M.
2010-11-20
The field of exoplanetary science has diversified rapidly over recent years as the field has progressed from exoplanet detection to exoplanet characterization. For those planets known to transit, the primary transit and secondary eclipse observations have a high yield of information regarding planetary structure and atmospheres. The current restriction of these information sources to short-period planets may be abated in part through refinement of orbital parameters. This allows precision targeting of transit windows and phase variations which constrain the dynamics of the orbit and the geometric albedo of the atmosphere. Here, we describe the expected phase function variations at optical wavelengths for long-period planets, particularly those in the high-eccentricity regime and multiple systems in resonant and non-coplanar orbits. We apply this to the known exoplanets and discuss detection prospects and how observations of these signatures may be optimized by refining the orbital parameters.
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.
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
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. PMID:9641913
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.
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.
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.
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. PMID:26271519
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.
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)
Comparisons of eccentric binary black hole simulations with post-Newtonian models
NASA Astrophysics Data System (ADS)
Hinder, Ian; Herrmann, Frank; Laguna, Pablo; Shoemaker, Deirdre
2010-07-01
We present the first comparison between numerical relativity (NR) simulations of an eccentric binary black hole system with corresponding post-Newtonian (PN) results. We evolve an equal-mass, nonspinning configuration with an initial eccentricity e≈0.1 for 21 gravitational wave cycles before merger, and find agreement in the gravitational wave phase with an adiabatic eccentric PN model with 2 PN radiation reaction within 0.1 radians for 10 cycles. The NR and PN phase difference grows to 0.7 radians by 5 cycles before merger. We find that these results can be obtained by expanding the eccentric PN expressions in terms of the frequency-related variable x=(ωM)2/3 with M the total mass of the binary. When using instead the mean motion n=2π/P, where P is the orbital period, the comparison leads to significant disagreements with NR.
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.
Determining phase relations of proxy data using the eccentricity-precession pattern
NASA Astrophysics Data System (ADS)
Zeeden, C.; Rivera, T. A.
2012-04-01
The phase relation between proxy data and orbital forcing is not always obvious; a link to both precession/insolation maxima or -minima can often be reasoned for. We present a novel approach to extract the phase relation using solely eccentricity-precession pattern from high quality proxy data. We determine the position of consecutive eccentricity maxima as precisely as possible from a stratigraphic record using both eccentricity filters and the amplitude modulation of precession. This way we obtain both the position of these eccentricity maxima as well as the sedimentation rate between successive maxima with error margins. Combining these results with the precession pattern in the geological record, we can determine whether precession-related patterns relate to precession (or insolation) minima or maxima. This approach relies on high quality geological data, the assumption of a direct eccentricity and precession response to orbital forcing, and a well defined orbital solution, but avoids the assumption of an instantaneous response to obliquity. For data with filtered components showing a good fit with the proxy data, this approach yields good results. Using high quality proxy data (color, magnetic susceptibility), we are able to determine the phase relation for equatorial Atlantic Miocene successions of ODP Leg 154. The research leading to these results has received funding from the [European Community's] Seventh Framework Programme ([FP7/2007-2013] under grant agreement n° [215458]. This research used data provided by IODP. Funding for this research was provided by NWO.
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.
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.
Neptune's story. [Triton's orbit perturbation
NASA Technical Reports Server (NTRS)
Goldreich, P.; Murray, N.; Longaretti, P. Y.; Banfield, D.
1989-01-01
It is conjectured that Triton was captured from a heliocentric orbit as the result of a collision with what was then one of Neptune's regular satellites. The immediate post-capture orbit was highly eccentric. Dissipation due to tides raised by Neptune in Triton caused Triton's orbit to evolve to its present state in less than one billion years. For much of this time Triton was almost entirely molten. While its orbit was evolving, Triton cannibalized most of the regular satellites of Neptune and also perturbed Nereid, thus accounting for that satellite's highly eccentric and inclined orbit. The only regular satellites of Neptune that survived were those that formed well within 5 Neptune radii, and they move on inclined orbits as the result of chaotic perturbations forced by Triton.
Spectral signatures of disk eccentricity in young binary systems. I. Circumprimary case
NASA Astrophysics Data System (ADS)
Regály, Zs.; Sándor, Zs.; Dullemond, C. P.; Kiss, L. L.
2011-04-01
Context. Star formation occurs via fragmentation of molecular clouds, which means that the majority of stars born are members of binary systems. There is growing evidence that planets might form in circumprimary disks of medium-separation (≲50 AU) binaries. The tidal forces caused by the secondary generally act to distort the originally circular circumprimary disk to an eccentric one. Since the disk eccentricity might play a major role in planet formation, it is of great importance to understand how it evolves. Aims: We investigate disk eccentricity evolution to reveal its dependence on the physical parameters of the binary system and the protoplanetary disk. To infer the disk eccentricity from high-resolution near-IR spectroscopy, we calculate the fundamental band (4.7 μm) emission lines of the CO molecule emerging from the atmosphere of the eccentric disk. Methods: We model circumprimary disk evolution under the gravitational perturbation of the orbiting secondary using a 2D grid-based hydrodynamical code, assuming α-type viscosity. The hydrodynamical results are combined with our semianalytical spectral code to calculate the CO molecular line profiles. Our thermal disk model is based on the double-layer disk model approximation. We assume LTE and canonical dust and gas properties for the circumprimary disk. Results: We find that the orbital velocity distribution of the gas parcels differs significantly from the circular Keplerian fashion. The line profiles are double-peaked and asymmetric in shape. The magnitude of asymmetry is insensitive to the binary mass ratio, the magnitude of viscosity (α), and the disk mass. In contrast, the disk eccentricity, thus the magnitude of the line profile asymmetry, is influenced significantly by the binary eccentricity and the disk geometrical thickness. Conclusions: We demonstrate that the disk eccentricity profile in the planet-forming region can be determined by fitting the high-resolution CO line profile asymmetry
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.
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
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.
Concentrating solar cookers with eccentric axis
Wang Xiping; Sha Yong Ling; Hou Shugin; Liu Zude
1992-12-31
This paper describes the design, development and use of a concentrating solar cooker with eccentric axis in China. For the same power, the older circular parabolic cookers are large in volume and less convenient to operate than the cooker with eccentric axis. Calculations are presented for the design of the cooker and for obtaining an accurate test of its efficiency.
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.
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
in all directions (p<0.05). Finally, we found that hyper-g centrifugation significantly decreased gaze holding ability in the vertical plane. The main findings of this study are as follows: (1) vertical gaze-holding is less stable than horizontal, (2) gaze-holding to upward targets is less stable than to downward targets, (3) tilt affects gaze holding, and (4) hyper-g affects gaze holding. This difference between horizontal and vertical gaze-holding may be ascribed to separate components of the velocity-to-position neural integrator for eye movements, and to differences in orbital mechanics. The differences between upward and downward gaze-holding may be ascribed to an inherent vertical imbalance in the vestibular system. Because whole body tilt and hyper-g affects gaze-holding, it is implied that the otolith organs have direct connections to the neural integrator and further studies of astronaut gaze-holding are warranted. Our statistical method for representing the range of normal eccentric gaze stability can be readily applied to normals who maybe exposed to environments which may modify the central integrator and require monitoring, and to evaluate patients with gaze-evoked nystagmus by comparing to the above established normative criteria.
PLANETARY MIGRATION AND ECCENTRICITY AND INCLINATION RESONANCES IN EXTRASOLAR PLANETARY SYSTEMS
Lee, Man Hoi; Thommes, Edward W. E-mail: ethommes@physics.uoguelph.ca
2009-09-10
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 {sub 2} {approx}> 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 {sub 1}/m {sub 2} {approx}> 0.2, it is possible to evolve into this family by fast migration only for m {sub 1}/m {sub 2} {approx}> 2. Thommes and Lissauer have found that a capture into the 4:2 inclination resonances is possible only for m {sub 1}/m {sub 2} {approx}< 2. We show that this capture is also possible for m {sub 1}/m {sub 2} {approx}> 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 {sub 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.