Abstract: Collision probability represents the risk of collision between two spacecrafts during the encountering phase. Collision probability calculation is the basis of designing the collision avoidance maneuver strategy. If the relative velocity between two spacecrafts is large and the encountering time is short, the relative motion is approximately linear. Under this assumption, the problem of solving the threedimensional probability density is reduced to a twodimensional problem. Numerical integral methods are usually used to calculate the collision probability. An analytical solution based on probability integral is derived, which can reduce the amount of computation while the decreased accuracy is not so much. A case study is presented to validate the given method.

Key words: collision probability, spacecraft, probability integral