A Numerical Implementation of Spherical Object Collision Probability

Abstract

Collision probability analysis for spherical objects exhibiting linear relative motion is accomplished by combining covariances and physical object dimensions at the point of closest approach. The resulting covariance ellipsoid and hardbody can be projected onto the plane perpendicular to relative velocity when the relative motion is assumed linear. Collision potential is determined from the object footprint on the projected, two-dimensional, co-variance ellipse. The resulting double integral can be reduced to a single integral by various methods. This work addresses the numerical computation of this single integral using Simpson’s one-third rule to achieve at least two significant figures of accuracy over a wide range of parameters.