A dynamical study on the origin of the Moon

The process of the formation of the Moon still yields many open questions. The generally accepted scenario proposes a giant impact of a Mars-sized body onto the proto-Earth between 70 to 100 million years after the formation of the terrestrial planets. According to popular theories the Moon formed from the debris disk generated by this giant impact. The goal of our dynamical studies is to find the initial orbit of the Mars-sized impactor (Theia) by investigating the regarding probability of a collision with Earth. Due to previous studies it is assumed that Theia formed between Earth and Mars at the same time as the other terrestrial planets did. Then the planet has to stay on a stable orbit for tens of millions of years till it may collide with the Earth leaving the rest of the inner solar system almost unaffected. In order to investigate the most probable origin of Theia we did n-body simulations starting a Mars-sized object with semi-major axis between 1.085 AU to 1.119 AU at low inclination altering the mean anomaly for each starting position from 0-360 deg. Additionally, simulations with an initial position of Theia inside the orbit of Earth (semi-major axis between 0.875 AU and 0.940 AU) were carried out. In total up to 10000 scenarios were calculated. The used model consists of an inner solar system with Venus, Earth and Mars at their known positions and the additional Theia as well as Jupiter and Saturn at their present orbits. The system was calculated up to 100 million years finding three possible outcomes namely collision with Earth, ejection or stability for the whole calculation period for Theia. Our results place the possible origin of Theia at 1.17 AU where most collisions happen after more than 70 million years. Additionally, the results of the dynamical n-body studies provide important data of the impact such as impact velocity and impact angle which will serve as basis for further detailed investigation of the impact itself by SPH (Smooth Particle Hydrodynamics) computations.