On the probability of the collision of a Mars-sized planet with the Earth to form the Moon

TL;DR

This study uses n-body simulations to estimate the probability and characteristics of a Mars-sized body colliding with Earth shortly after planetary formation, providing insights into the Moon's origin.

Contribution

It offers a purely dynamical analysis of collision probabilities involving a hypothetical Mars-sized impactor in early Earth-like planetary systems.

Findings

Most probable impactor origin at ~1.16 AU

Collision velocities and angles estimated from simulations

Supports further detailed impact modeling

Abstract

The problem of the formation of the Moon is still not explained satisfactorily. While it is a generally accepted scenario that the last giant impact on Earth between some 50 to 100 million years after the starting of the formation of the terrestrial planets formed our natural satellite, there are still many open questions like the isotopic composition which is identical for these two bodies. In our investigation we will not deal with these problems of chemical composition but rather undertake a purely dynamical study to find out the probability of a Mars-sized body to collide with the Earth shortly after the formation of the Earth-like planets. For that we assume an additional massive body between Venus and Earth, respectively Earth and Mars which formed there at the same time as the other terrestrial planets. We have undertaken massive n-body integrations of such a planetary system with 4 inner planets (we excluded Mercury but assumed one additional body as mentioned before) for up to tens of millions of years. Our results led to a statistical estimation of the collision velocities as well as the collision angles which will then serve as the basis of further investigation with detailed SPH computations. We find a most probable origin of the Earth impactor at a semi-major axis of approx. 1.16 AU.