Two-body problem with variable mass: A new approach

Hadjidemetriou, John D.

doi:10.1016/0019-1035(63)90072-1

Cited by 168 publications

(124 citation statements)

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“…Consequently, with help from the vis-viva equation, the equations of motion in orbital elements may be derived (Omarov 1962;Hadjidemetriou 1963;Veras et al 2011). In the 'adiabatic' case, where the averaged equations of motion, denoted by brackets, can be used (within a few hundred au; see Veras et al 2011),…”

Section: E F F E C T O F S T E L L a R M A S S L O S S O N M O O N Smentioning

confidence: 99%

Liberating exomoons in white dwarf planetary systems

Payne¹,

Veras²,

Holman³

et al. 2016

Mon. Not. R. Astron. Soc.

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Previous studies indicate that more than a quarter of all white dwarf (WD) atmospheres are polluted by remnant planetary material, with some WDs being observed to accrete the mass of Pluto in 10 6 yr. The short sinking time-scale for the pollutants indicates that the material must be frequently replenished. Moons may contribute decisively to this pollution process if they are liberated from their parent planets during the post-main-sequence evolution of the planetary systems. Here, we demonstrate that gravitational scattering events amongst planets in WD systems easily trigger moon ejection. Repeated close encounters within tenths of planetary Hill radii are highly destructive to even the most massive, close-in moons. Consequently, scattering increases both the frequency of perturbing agents in WD systems, as well as the available mass of polluting material in those systems, thereby enhancing opportunities for collision and fragmentation and providing more dynamical pathways for smaller bodies to reach the WD. Moreover, during intense scattering, planets themselves have pericentres with respect to the WD of only a fraction of an astronomical unit, causing extreme Hill-sphere contraction, and the liberation of moons into WD-grazing orbits. Many of our results are directly applicable to exomoons orbiting planets around main-sequence stars.

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Section: E F F E C T O F S T E L L a R M A S S L O S S O N M O O N Smentioning

confidence: 99%

Liberating exomoons in white dwarf planetary systems

Payne¹,

Veras²,

Holman³

et al. 2016

Mon. Not. R. Astron. Soc.

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“…Hadjidemetriou in [14] uses a tangential perturbing acceleration proportional to the test particle's velocity v,…”

Section: Discussion Of Other Approaches and Numerical Calculationsmentioning

confidence: 99%

“…Other phenomena which may, in principle, show connections with the problem treated here are the secular decrease of the semimajor axes of the LAGEOS satellites, amounting to 1.1 mm d −1 , [8] and the increase of the lunar orbit's eccentricity of 0.9 × 10 −11 yr −1 [9]. Many treatments of the mass loss-driven orbital dynamics in the framework of the Newtonian mechanics, based on different approaches and laws of variation of the central body's mass, can be found in literature; see, for example, [2,4,[10][11][12][13][14][15][16][17][18] and references therein. However, they are sometimes rather confused and involved, giving unclear results concerning the behavior of the Keplerian orbital elements and the true orbit.…”

Section: Introductionmentioning

confidence: 99%

Classical and Relativistic Orbital Motions around a Mass-Varying Body

Iorio

2010

SRX Physics

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I work out the Newtonian and general relativistic effects due to an isotropic mass lossṀ/M of a body on the orbital motion of a test particle around it; the present analysis is also valid for a variationĠ/G of the Newtonian constant of gravitation. Concerning the Newtonian case, I use the Gauss equations for the variation of the elements and obtain negative secular rates for the osculating semimajor axis a, the eccentricity e, and the mean anomaly M, while the argument of pericenter ω does not experience secular precession; the longitude of the ascending node Ω and the inclination i remain unchanged as well. The true orbit, instead, expands, as shown by a numerical integration of the equations of motion with MATHEMATICA; in fact, this is in agreement with the seemingly counter-intuitive decreasing of a and e because they refer to the osculating Keplerian ellipses which approximate the trajectory at each instant. A comparison with the results obtained with different approaches by other researchers is made. General relativity induces positive secular rates of the semimajor axis and the eccentricity completely negligible in the present and future evolution of the solar system.

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“…The greatly increased stellar luminosity, particularly at the AGB tip, can cause significant evaporation of planetary atmospheres [19]. The expulsion of material from the star on the AGB causes the expansion of planetary orbits [12], while drag from the expelled material can cause the orbits of planetesimals to shrink [4]. The reduction of a e-mail: alex.mustill@uam.es This is an Open Access article distributed under the terms of the Creative Commons Attribution License 2.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.…”

Section: Introductionmentioning

confidence: 99%

White dwarf planets

Mustill

Villaver

Veras

et al. 2013

EPJ Web of Conferences

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Abstract. The recognition that planets may survive the late stages of stellar evolution, and the prospects for finding them around White Dwarfs, are growing. We discuss two aspects governing planetary survival through stellar evolution to the White Dwarf stage. First we discuss the case of a single planet, and its survival under the effects of stellar mass loss, radius expansion, and tidal orbital decay as the star evolves along the Asymptotic Giant Branch. We show that, for stars initially of 1 − 5 M , any planets within about 1 − 5 AU will be engulfed, this distance depending on the stellar and planet masses and the planet's eccentricity. Planets engulfed by the star's envelope are unlikely to survive. Hence, planets surviving the Asymptotic Giant Branch phase will probably be found beyond ∼ 2 AU for a 1 M progenitor and ∼ 10 AU for a 5 M progenitor. We then discuss the evolution of two-planet systems around evolving stars. As stars lose mass, planet-planet interactions become stronger, and many systems stable on the Main Sequence become destabilised following evolution of the primary. The outcome of such instabilities is typically the ejection of one planet, with the survivor being left on an eccentric orbit. These eccentric planets could in turn be responsible for feeding planetesimals into the neighbourhood of White Dwarfs, causing observed pollution and circumstellar discs.

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Two-body problem with variable mass: A new approach

Cited by 168 publications

References 3 publications

Liberating exomoons in white dwarf planetary systems

Liberating exomoons in white dwarf planetary systems

Classical and Relativistic Orbital Motions around a Mass-Varying Body

White dwarf planets

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