A numerical investigation of planetesimal collision trajectories with a Moon accumulating in Earth orbit

In the scenario of lunar origin in which the Moon is assumed to have accreted most of its mass while in orbit about the Earth, ismals on the accrea knowledge of the relative impact rates of heliocentric planetting Earth and Moon is essential for any attempt to establish dynamical constraints on lunar origin. Numerical integrations of the regularized equations of motion for four bodies (Sun, Earth, Moon, planetismal) were done. A planetismal impact trajectory was calculated by assuming that the planetismal has hit the surface of the Moon at an assumed location, traveling in an assumed direction, and with an assumed impact speed. Next, the equations of motion were numerically integrated backward in time in order to determine from where the planetismal has come. In this way those volumes in heliocentric orbital element space which contribute trajectories that directly impact the Moon.