Mathematical Modeling of the Optimal Acceleration Angle to Avoid Collisions in Space

Abstract

In outer space, a spaceship experiences almost no external forces that can slow down its movement. Under these circumstances, crashing into other space objects becomes particularly threatening, as the spaceship must move, turn its thrusters, and accelerate in the opposite direction to avoid collision. However, the possible directions of the thrusters that achieve the goal of avoiding an object vary greatly. The goal of this research is to create a mathematical model using knowledge of physics and mathematics to find the optimal angle to accelerate at with a given initial velocity, distance to the object, and maximum acceleration, which will assist spaceships in steering away from objects in the safest way possible. Specifically, this means the angle at which the minimum distance between the spaceship and the object’s center is the furthest out of all angles. The mathematical model in the research creates two equations that provide the optimal angle for two separate situations between the given variables and confirm that velocity, distance, and acceleration all play a role in the final optimal angle. The model also provides two equations for the minimum distance that the spaceship will be from the object's center if it accelerates at that angle. This knowledge and model can be used in spaceships to not only avoid collisions against other objects in space but also to leave a restricted zone or a harmful area in space in the safest way possible, potentially saving the lives of passengers from fatal crashes and other threats.