Improved Satellite in Orbit Collision Threat Prediction Method based on Integral Method

An improved collision probability calculation method is proposed to address the potential collision threat posed by external threat objects or internal members of star clusters to the Earth orbit satellite constellation. In the modeling of orbital dynamics of satellites in orbit, J2 perturbations caused by non-spherical resistance of the Earth and atmospheric resistance perturbations were considered. Regarding the probability density function integration method for calculating the probability of satellite collision, due to insufficient consideration of the cumulative effect of velocity errors on time, this method considers the actual velocity and relative velocity of the target satellite and the space threat object, establishes a dimensionless function with both as input parameters, and uses this function to improve the original method. The simulation results show that the collision probability of this method reaches a peak of 0.543% in real collision instances, exceeding the threshold for maneuver avoidance. As a result, there is a significant increase in collision probability in high-speed scenarios, with good improvement after the speed exceeds the set threshold.