Relative Speeds of Interacting Astronomical Bodies

Simultaneous conservation of linear momentum and of mechanical energy can be used to calculate the relative speed of an isolated pair of astronomical bodies as a function of the distance separating them. An exact treatment is straightforward and has application to such contemporary topics as the launch velocities of rockets, and collisions between an asteroid and the Earth. In contrast, when these topics are discussed in introductory physics courses, an infinite-Earth-mass approximation is typically invoked. In addition to being unphysical, this denies students an opportunity for a richer exploration of the conservation laws of mechanics.