On probabilistic modeling and feasibility of collision between a randomly moving meteor and satellite

The collision between a 3-Dimensional randomly moving meteor with the satellite is studied from a probability point of view. The satellite moves along slinky-turn-ellipse curve and starts its motion from a known point \( (X_{0} ,Y_{0} ,Z_{0} ) \). The meteor comes from a distant space with dynamic random movement. The main contribution of this paper is to find the conditions that make the expected value of the collision time is finite. In addition, we obtain two candidate utility functions namely the mean time to collision and the cumulative probability of collision. Also, we obtain the estimated distance between them at any time \( t \) by using Bayes estimation method. An example with numerical results is given to show the effectiveness of this method.