Air Force Institute of Technology Wright-Patterson Air Force Base
Orbital altitudes congested with spacecraft and debris combined with recent collisions have all but negated the Big Sky Theory. As the sheer number of orbital objects to track grows unbounded so does interest in prediction methods that are rapid and minimally computational. Claimed as the other solvable solution, the recently completed solution too orbital motion about the earth, based on Vintis method and including the major effects of the equatorial bulge, opens up the prospect of much more accurate analytical models for space situational awareness. A preliminary examination of this solution is presented. A numerical state transition matrix is found using Lagrange partial derivatives to implement a nonlinear least squares fitting routine. Orbit fits using only the solvable solution for non-circular, non-equatorial trajectories less than 60 degrees inclination are on the order of a few hundred meters with projected, average error growth of less than a kilometer per day which is similar to the expected performance of the Air Forces method. Also, a classical perturbations approach to incorporate the dissipative effects of air drag using Hamiltonian action and angle formulation is developed. Predicted drag effects re 97.5 correct after one day and 87 correct after five days when compared to an integrated truth. Results are validated by performing a similar method on the two body problem.