There is a large set of papers and monographs which consider the restricted three-body problem and apply the results to the orbits of satellites or spacecrafts in the Earth–Moon system. These studies ignore the impact of the Sun on these orbits. This approximation is justified for satellites in close Earth orbit. However, for satellites whose orbit is around the Sun, the Earth and the Moon or one of the Lagrange points the impact of the Sun’s presence cannot be ignored and one has to consider a four-body problem. In this paper, we derive the general equations of motion for satellites in a system that consists of a central body (Sun), first and second primaries and a satellite. These equations can be used for mission planning in general. Obvious practical example of such a system consists of the Earth and the Moon as the first and second primaries. These equations are then used in this paper to illustrate the impact of the central body on the motion of satellites around the two primaries.

有大量论文和专着考虑了受限三体问题，并将其结果应用于地月系统中卫星或航天器的轨道。这些研究忽略了太阳对这些轨道的影响。这种近似适用于近地轨道上的卫星。然而，对于轨道围绕太阳、地球和月球或拉格朗日点之一的卫星，太阳存在的影响不容忽视，必须考虑四体问题。在本文中，我们推导出了一个系统中卫星的一般运动方程，该系统由一个中心体（太阳）、第一和第二主星以及一颗卫星组成。这些方程一般可用于任务规划。这种系统的明显实际例子包括地球和月球作为第一和第二初选。