ABSTRACT
Recently has grown the interest of placing natural or artificial objects in the neighbourhood of the Moon. We numerically investigate a region of retrograde orbits around the Moon associated with the C Family of periodic orbits and the quasi-periodic orbits that oscillate around them (Broucke 1968; Winter 2000). We have given continuity to Winter (2000) investigations by introducing a more realistic dynamical scenario, one based on the four-body Sun–Earth–Moon–particle problem. Our results showed that the region of stability diminished to approximately 4 ${{\ \rm per\ cent}}$, the original size encountered for the circular-restricted three-body problem (CRTBP), mainly due to the Sun’s gravitational perturbations. None the less, the size of the region continues to be significant and we were able to found distant retrograde orbits (DROs) around the Moon with eccentricity following e = 2.259 63 × 10−6a + 0.238 45 (standard error of 1 ${{\ \rm per\ cent}}$) and semimajor axis values of the initial osculating orbits, varying between 110 000 and 185 000 km, remaining stable for a time span of 104 lunar periods. This set of distant orbits from the Moon are characterized by a narrow range of acceptable initial positions (0.8–0.83) and velocities of ∼0.5, in the rotating Earth–Moon frame. The out of plane amplitude oscillations of $\pm 15\, 000$ km presented by these DROs are a natural outcome of the significant Moon’s inclination of 5.15°. Some results presented on this work can be useful for lunar missions, such as the ones that would require prolonged stays around the satellite and use stable distant orbits as ‘parking’ orbits, such as the advanced concepts of NASA’s Asteroid Redirect Mission, proposed a few years ago.
Initial Parameter Analysis about Resonant Orbits in Earth-Moon System
