Effect of solar perturbation on motion near the collinear earth-moonlibration points.

Abstract

The perturbative acceleration of the sun disrupts the equilibrium of the five Lagrange libration points in the earth-moon system by introducing a nonhomogeneous forcing function in the equations of motion. Analytic expressions for this forcing function, including the indirect effect of the sun on the moon, are derived. It is shown that the perturbation at the collinear points is of second-order only, in the ratio of the moon's distance to the sun's distance. For the LI and Lz points the magnitude of the perturbative acceleration is about 2 X 10~ meters/sec. To verify this result, actual trajectories were computed by numerical integration for a body starting from rest at the LI and L% points using a four-body model. Sun and moon positions were obtained from an ephemeris tape. Initial velocities were chosen so as to suppress the divergent motion resulting from the unstable nature of the collinear points. The motion was in good agreement with that predicted by the analysis of the solar perturbation. It is concluded that the stationkeeping propulsion required to maintain a vehicle near LI or L% is nearly independent of the solar perturbation and therefore depends primarily upon the accuracy of the navigation and guidance systems.