Simulation-based collision detection

Thirty (30) years ago, I learned in school how to calculate the intersection of two spheres in 3D space. Today, I needed this to avoid the collision of flying objects in a Tecnomatix Plant Simulation model.

Simple engineering mathematics: Can you calculate the collision circle between two spheres moving in a 3D coordinate system? Plant Simulation can perform vector calculations based on arrays. You can download this Plant Simulation model file (.spp) in the Plant Simulation Community Forum > here.