Polar orbits around the newly formed Earth-Moon binary system

TL;DR

This study investigates the stability of polar orbits around the Earth-Moon system, revealing they were stable shortly after the Moon's formation but are currently unstable, with implications for planetary and exoplanetary systems.

Contribution

It provides the first analysis of polar orbit stability in the Earth-Moon system over its formation history and current state.

Findings

No stable polar orbits at current semi-major axis

Polar orbits were stable when the Moon's semi-major axis was about 10 R_⊕

Implications for the evolution of Earth-Moon and exoplanet-moon systems

Abstract

We examine the dynamics and stability of circumbinary particles orbiting around the Earth-Moon binary system. The moon formed close to the Earth (semi-major axis $a_{EM}\approx 3\, R_\oplus$) and expanded through tides to its current day semi-major axis ($a_{ EM}= 60\, R_\oplus$). Circumbinary orbits that are polar or highly inclined to the Earth-Moon orbit are subject to two competing effects: (i) nodal precession about the Earth-Moon eccentricity vector and (ii) Kozai-Lidov oscillations of eccentricity and inclination driven by the Sun. While we find that there are no stable polar orbits around the Earth-Moon orbit with the current day semi-major axis, polar orbits were stable immediately after the formation of the Moon, at the time when there was a lot of debris around the system, up to when the semi-major axis reached about $a_{ EM}\approx 10\, R_\oplus$. We discuss implications of polar orbits on the evolution of the Earth-Moon system and the possibility of polar orbiting moons around exoplanet-moon binaries.