Capture of interplanetary bodies in geocentric orbits and early lunar evolution

Abstract

During the accretion of planets such as Earth, which are formed by collisional accretion of plan-etesimals, the probability of capture of interplanetary bodies in planetocentric orbits is calculated following the approach of Hills (1973) and the π -body simulation, using simplectic integration method. The simulation, taking an input mass equal to about 50% of the present mass of the inner planets, distributed over a large number of planetoids, starting at 4 M γ after the formation of solar system, yielded four inner planets within a period of 30 M γ. None of these seed bodies, out of which the planets formed, remained at this time and almost 40% mass was transferred beyond 100 AU. Based on these calculations, we conclude that ≈ 1.4 times the mass of the present inner planets was needed to accumulate them. The probability of capture of planetoids in geocentric orbits is found to be negligible. The result emphasizes the computational difficulty in 'probability of capture' of planetesimals around the Earth before the giant impact. This conclusion, however, is in contradiction to the recent observations of asteroids being frequently captured in transient orbits around the Earth, even when the current population of such interplanetary bodies is smaller by several orders of magnitude compared to the planetary accumulation era.