Initial Orbit Determination of Periodic Orbits in the Earth–Moon System With Ground-Based Optical Observations

This research investigates the initial orbit determination for missions in periodic orbits within the Earth–Moon system, observed optically from the ground. The proposed methodology requires estimates for three slant ranges at the time of three optical observations and uses the solution of two third-body-perturbed Lambert problems to find the trajectory that fits the observations in the circular restricted three-body problem (CR3BP). We study three different ways to provide the estimates for the slant ranges: an Earth-centered Gauss method, a Moon-centered Gauss method, and a tailored CR3BP admissible region. The solution of the third-body-perturbed Lambert problem, referred to here as the CR3BP Lambert solver, is achieved through a high-order correction of a classical Lambert solution. Extensive test cases for different families of periodic orbits show that estimates from the Moon-centered Gauss method perform better than those from the Earth-centered method. However, in both cases, the Keplerian assumption of Gauss' method can lead to large initial errors and divergence. When the admissible region approach is employed, a higher convergence rate is achieved, but up to four convergent solutions can be obtained, among which the correct one needs to be identified.