Orbit Design and Analysis Challenges in Cislunar Space Caused By Lunisolar Perturbations

There is currently increased interest in flying spacecraft in cislunar space, which can roughly be defined as the volume between geostationary orbit and the orbit of the Moon. Satellites in this region are significantly affected by gravitational perturbations from both Moon and Sun, leading to complicated long-term orbital behavior. The authors have studied these effects as part of their work on the Magnetospheric Multiscale (MMS) mission: this has been flying four spacecraft in formation since launch in Mar. 2015 in an orbit with current apogee radius 28 Earth radii (~179,000 km), or halfway to the orbit of the Moon.

The Lidov-Kozai (L-K) mechanism describes the evolution of the orbit of a satellite that is significantly perturbed by the gravitational attraction of a third body. It has recently proved very useful in the study of systems of exoplanets, where the orbit of one planet can be affected significantly by the gravitational attraction of the others, even to the extent of being “flipped” to become retrograde. Lidov’s work was motivated by his work on Luna 3, launched on October 4, 1959, which flew in a highly elliptical Earth orbit past the Moon, took the first images of the far side, downlinked them on the way down to perigee, and then reentered in April 1960, after 11 orbits, as a result of lunisolar perturbations.

Interestingly, although development of the L-K equations was motivated by Luna 3, it has recently been recognized that the orbit of this spacecraft was not fully explained by this model. This paper will examine the conditions under which the L-K model applies well, and when it does not. The paper will present an exploration of this question that studied several classes of cislunar orbits: that of MMS; that of a high-apogee, high-eccentricity orbit such as for a lunar transfer, modeled on that of the Peregrine lander; a high orbit with lower eccentricity, modeled on that of the Chandrayaan-3 Propulsion Module when it was returned to Earth orbit; and high orbits in resonance with the Moon, so preventing close lunar gravity assists. For each orbit class, the behavior with different semi-major axes has been examined, to study at what geometry the Lidov-Kozai dynamics break down: these results will be presented in the paper.