Satellite splat II: an inelastic collision with a surface-launched projectile and the maximum orbital radius for planetary impact

Abstract

Starting with conservation of energy and angular momentum, we derive a convenient method for determining the periapsis distance of an orbiting object, by expressing its velocity components in terms of the local circular speed. This relation is used to extend the results of our previous paper, examining the effects of an adhesive inelastic collision between a projectile launched from the surface of a planet (of radius R) and an equal-mass satellite in a circular orbit of radius rs. We show that there is a maximum orbital radius rs ≈ 18.9R beyond which such a collision cannot cause the satellite to impact the planet. The difficulty of bringing down a satellite in a high orbit with a surface-launched projectile provides a useful topic for a discussion of orbital angular momentum and energy. The material is suitable for an undergraduate intermediate mechanics course.