The Envelope of a Family of Elliptic Orbits and Ballistic Trajectories

Abstract

The paper presents a simple geometric derivation for the “safety domain” boundary for the family of Keplerian orbits of satellites or ballistic missiles, moving in a central field of gravity, and for the family of parabolic trajectories of projectiles in a uniform gravitational field launched from a common starting point at equal velocities. Examples of practical application of the envelope of a family of orbits for solving ballistics problems are discussed. These examples are illustrated by computer simulations.