Mitigation of the Effects of Eclipse Boundary Crossings on the Numerical Integration of Orbit Trajectories Using an Encke Type Correction Algorithm

The proper application of a shadow model during the integration of orbit trajectories requires that the solar radiation pressure be sampled adequately during transitions between lighting conditions. An integration scheme is presented in which the lighting condition is held constant across steps of a primary integrator. If the lighting condition changes during that step, then an Encke-like integration is performed to correct the state at the end of the primary integration step. The effectiveness of this technique is presented for a set of Low Earth Orbits utilizing various combinations of the equations of motion and numerical integration methods.