A Motivating Exploration on Lunar Craters and Low-Energy Dynamics in the Earth -- Moon System

TL;DR

This paper investigates lunar crater distribution by analyzing low-energy trajectories in the Earth-Moon system using dynamical systems theory, considering gravitational effects of the Sun, and exploring impact regions and origins.

Contribution

It introduces a novel approach using invariant manifolds and the Circular and Bicircular Restricted Three- and Four-Body Problems to model impact distributions on the Moon.

Findings

Low-energy impact trajectories can explain crater distribution patterns.

High-energy impacts contribute to low-energy ejecta impacting the lunar surface.

Impact regions are influenced by gravitational effects of the Sun and the Earth-Moon dynamics.

Abstract

It is known that most of the craters on the surface of the Moon were created by the collision of minor bodies of the Solar System. Main Belt Asteroids, which can approach the terrestrial planets as a consequence of different types of resonance, are actually the main responsible for this phenomenon. Our aim is to investigate the impact distributions on the lunar surface that low-energy dynamics can provide. As a first approximation, we exploit the hyberbolic invariant manifolds associated with the central invariant manifold around the equilibrium point L_2 of the Earth - Moon system within the framework of the Circular Restricted Three - Body Problem. Taking transit trajectories at several energy levels, we look for orbits intersecting the surface of the Moon and we attempt to define a relationship between longitude and latitude of arrival and lunar craters density. Then, we add the gravitational effect of the Sun by considering the Bicircular Restricted Four - Body Problem. As further exploration, we assume an uniform density of impact on the lunar surface, looking for the regions in the Earth - Moon neighbourhood these colliding trajectories have to come from. It turns out that low-energy ejecta originated from high-energy impacts are also responsible of the phenomenon we are considering.