The envelope of ballistic trajectories and elliptic orbits

Eugene I. Butikov
2015 American Journal of Physics  
Simple geometric derivations are given for the shape of the "safety domain" boundary for the family of Keplerian orbits of equal energy in a central gravitational field and for projectile trajectories in a uniform field. Examples of practical uses of the envelope of the family of orbits are discussed and illustrated by computer simulations. This material is appropriate for physics teachers and undergraduate students studying classical mechanics and orbital motions.
doi:10.1119/1.4928176 fatcat:p6d2dmbkgrfetbv4cu5skxp74e