Design of distant retrograde orbits based on a higher order analytical solutiont

Abstract

Because the distant retrograde orbits dynamics inherently depends on special functions, approximate analytical solutions in the literature are commonly constrained to providing rough approximations of the qualitative behavior. We rely on perturbation methods and succeed in computing a higher order analytical solution that extends the range of applicability of previous solutions to the problem of relative, quasi-satellite orbits with large librations. Besides, the analytical solution provides two design parameters that are effectively used in the computation of periodic, distant retrograde orbits without constraining to the typical 1:1 resonance.

Transfers around Phobos via bifurcated retrograde orbits: Applications to Martian Moons eXploration mission

“…In this research, we have utilized pseudo-arclength continuation [39] and shooting methods for calculating families of QSO as shown in the left subplot of Figure 3. Other alternative analytical approaches to compute QSOs include works of Kogan [40], Lidov [41,42], and Lara [43,44]. The current mission design of MMX envisages the utilization of different altitude planar QSOs in order to characterize the gravitational field before landing on Phobos.…”