Multi-Targets Visiting Orbit Design Based on Numerical Method

In this paper, for the two/three targets in the circle orbit with the same altitude, a numerical method is presented to design an orbit for a spacecraft to visit multiple targets without maneuvering. First, for the two targets' case, an equation is established by the relationship of the two angles that both are the function of the time, one of the angles is the angle between two targets' geocentric position vectors at two times, and another one is the spacecraft flight angle during the two times. The visit time can be solved by the assumption that one of the visit times is known in the equation, and the orbit element can be transferred from the position and velocity vector determined by the solved visit time. Then, for the three targets' case, the problem is decoupled into two cases of two targets, and there is a public target in each case. Based on the method for two targets, two different orbits can be obtained by determining the visit time of the public target. The difference between two orbits can be expressed by the difference in velocity vectors of the public target at different times. A sampling method is utilized to select two velocity vectors with relatively small differences as initial values, the Newton iteration method is used to obtain visit times with higher accuracy. Simulation results illustrate the effectiveness of the orbit design methods.