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Orbital evolution of a planet with tidal dissipation in a restricted three-body system

Research in Astronomy and Astrophysics 2019年第9期19卷 79-96页

作者： Wen-Lei Wang Xue-Qing Xu Xin-Hao Liao Shanghai Astronomical Observatory Chinese Academy of SciencesShanghai200030China Key Laboratory of planetary Sciences Shanghai Astronomical ObservatoryChinese Academy of SciencesShanghai200030China University of Chinese Academy of Sciences Beijing100049China

The angle between planetary spin and the normal direction of an orbital plane is supposed to reveal a range of information about the associated planetary formation and evolution. Since the orbit’s eccentricity and inclination oscillate periodically in a hierarchical triple body and tidal friction makes the spin parallel to the normal orientation of the orbital plane with a short timescale in an isolated binary system, we focus on the comprehensive effect of third body perturbation and tidal mechanism on the angle. Firstly, we extend the Hut tidal model(1981) to the general spatial case, adopting the equilibrium tide and weak friction hypothesis with constant delay time, which is suitable for arbitrary eccentricity and any angle ? between the planetary spin and normal orientation of the orbital plane. Furthermore, under the constraint of angular momentum conservation, the equations of orbital and ratational motion are given. Secondly, considering the coupled effects of tidal dissipation and third body perturbation, and adopting the quadrupole approximation as the third body perturbation effect, a comprehensive model is established by this work. Finally, we find that the ultimate evolution depends on the timescales of the third body and tidal friction. When the timescale of the third body is much shorter than that of tidal friction, the angle ? will oscillate for a long time,even over the whole evolution;when the timescale of the third body is observably larger than that of the tidal friction, the system may enter stable states, with the angle ? decaying to zero ultimately, and some cases may have a stable inclination beyond the critical value of Lidov-Kozai resonance. In addition, these dynamical evolutions depend on the initial values of the orbital elements and may aid in understanding the characteristics of the orbits of exoplanets.

关键词： astrometry and celestial mechanics:celestial mechanics planet-star interactions planets and satellites:dynamical evolution and stability

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Is it plausible to expect a close encounter of the Earth with a yet undiscovered astronomical object in the next few years?

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Natural Science 2010年第11期2卷 1181-1188页

作者： Lorenzo Iorio 不详

We analytically and numerically investigate the possibility that a still undiscovered body X, moving along an unbound hyperbolic path from outside the solar system, may penetrate its inner regions in the next few years posing a threat to the Earth. By conservatively using as initial position of X the lower bounds on the present‐day distance of X dynamically inferred from the gravitational perturbations induced by it on the orbital motions of the planets of the solar system, both the analyses show that, in order to reach the Earth’s orbit in the next 2 yr, X should move at a highly unrealistic speed , whatever its mass is. For example, by assuming for it a solar ( M ) or brown dwarf mass ( ), now at not less than kau (1 kau=1000 astronomical units), v would be of the order of and of the speed of light c, respectively. By assuming larger present‐day distances for X, on the basis of the lacking of direct observational evidences of electromagnetic origin for it, its speed would be even higher. Instead, the fastest solitary massive objects known so far, like hypervelocity stars (HVSs) and supernova remnants (SRs), travel at , having acquired so huge velocities in some of the most violent astrophysical phenomena like interactions with supermassive galactic black holes and supernova explosions. It turns out that the orbit of the Earth would not be macroscopically altered by a close (0.2 au) passage of such an ultrafast body X in the next 2 yr. On the contrary, our planet would be hurled into the space if a Sun‐sized body X would encounter it by moving at . On the other hand, this would imply that such a X should be now at just 20-30 au, contrary to all direct observational and indirect dynamical evidences.

关键词： Gravitation Celestial Mechanics planet-star Interactions Methods: Analytical Method: Numerical

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