Temporary Capture of Asteroids by an Eccentric Planet

Abstract

We have investigated the probability of temporary capture of asteroids in eccentric orbits by a planet in a circular or an eccentric orbit through analytical and numerical calculations. We found that in the limit of the circular orbit, the capture probability is $\sim 0.1\%$ of encounters to the planet's Hill sphere, independent of planetary mass and semimajor axis. In general, the temporary capture becomes more difficult as the planet's eccentricity ($e_{\mathrm{p}}$) increases. We found that the capture probability is almost independent of $e_{\mathrm{p}}$ until a critical value ($e_{\mathrm{p}}^{\mathrm{c}}$) that is given by $\simeq$ 5 times the Hill radius scaled by the planet's semimajor axis. For $e_{\mathrm{p}}>e_{\mathrm{p}}^{\mathrm{c}}$, the probability decreases approximately in proportion to $e_{\mathrm{p}}^{-1}$. The current orbital eccentricity of Mars is several times larger than $e_{\mathrm{p}}^{\mathrm{c}}$. However, since the range of secular change in Martian eccentricity overlaps $e_{\mathrm{p}}^{\mathrm{c}}$, the capture of minor bodies by the past Mars is not ruled out.

Accepted for publication in AJ, 14 pages and 6 figures

References in corpus (3)

• Irregular Satellites of the Planets: Products of Capture in the Early Solar System
• Formation of Phobos and Deimos via a Giant Impact
• Temporary Capture of Asteroids by a Planet: Dependence of Prograde/Retrograde Capture on Asteroids' Semimajor Axes

Cited by in corpus (6)

• Speeding past planets? Asteroids radiatively propelled by giant branch Yarkovsky effects
• On the Jacobi capture origin of binaries with applications to the Earth-Moon system and black holes in galactic nuclei
• The white dwarf planet WD J0914+1914 b: barricading potential rocky pollutants?
• A halo of trapped interstellar matter surrounding the solar system
• Origin of Mars's moons by disruptive partial capture of an asteroid
• Primitive asteroids in the main belt, Cybele, and Hilda populations from Gaia DR3