Keeping a spacecraft on a vertical circular collinear lagrange point orbit

A propulsively managed stationkeeping strategy for a spacecraft orbiting a collinear equilibrium point in a threebody system is introduced. A nominal circular solution with nonuniform speed, which is derived from the Jacobi integral equation, employing elliptic integral theory, is used in a plane perpendicular to the line joining the two primaries. Thrust control inputs, which are found to be nonlinear functions of time, are used to negate the instability of the nominal orbit. Analytical relationships for control requirements are developed. Orbit parameters are analyzed and chosen so that the cost of maintaining the nominal orbit is minimized. Resulting thrust requirements are assessed for feasibility with respect to existing propulsion capabilities. Significant freedoms are found to exist for tailoring thrust demands. If proven feasible, the thrust managed orbit could find applications in communications, in situ space measurements, observation platforms, forecasting-warning systems, and loitering. An in situ magnetosphere sampling mission based on a lunar synchronized geopolar orbit is proposed and analyzed using the new results.