Third-Body Perturbation Effects on Satellite Formations

The effects of third-body perturbations on satellite formations are investigated using differential orbital elements to describe the relative motion. Absolute and differential effects of the lunar perturbation on satellite formations are derived analytically based on the simplified model of the circular restricted three-body problem. This analytical description includes averaged long-term effects on the orbital elements, including the full transformation between the osculating elements and the lunar-averaged elements, which is absent from previous research. A simplified Earth-Moon system model is used, but the results are applicable to any formation reference orbit about the Earth. Simulations are performed to determine the effects of the lunar perturbation on example formations in upper MEO, highly eccentric orbits by using the formation design criteria of Phases I and II of the NASA Magnetospheric Multiscale mission. The changes in angular differential orbital elements ( δ ω , δ Ω, and δ M 0 ) and in science return quality due to this perturbation are compared to changes due to J 2 . The method is then expanded to include the inclination of the Moon’s orbit and results are compared to simulation using the NASA General Mission Analysis Tool.