A study of distant retrograde orbits in the neighborhood of the moon

Abstract

In this work, we have numerically investigated a region of retrograde orbits around the Moon in the light of the four-body Sun-Earth-Moon-particle problem. In this context, the gravitation effects of the Sun was taken into account, and the Earth and the Moon assumed their realistic orbital parameters. From this study we identified initial conditions for lunar Distant Retrograde Orbits (DROs) that remain bounded after propagating a conservative quantity of 20 years. By comparing our results with the results obtained in the Circular Restricted Three Body Problem (CRTBP) we see a substantial loss of particles, the region of stability diminished to 4% the original size encountered for the CRTBP. This set of lunar DROs has initial velocities around 0.5 (y-axis) and initial values of x around 0.8 in the rotating Earth-Moon frame. Regarding their initial lunar orbital elements, their eccentricities follows the equation e = 2.25963x10-6 a + 0.23845 (standard error of 1%), while their initial semi-major axis values are between 110,000 and 185,000 Km.