Closed-Form Solution for Ballistic Vehicle Motion

A closed-form solution is developed for the motion of a ballistic vehicle entering the atmosphere over a flat nonrotating Earth. The Alien and Eggers approach of using an exponential atmosphere is retained; however, the vehicle drag coefficient is expressed as a function of velocity instead of being considered a constant. Use of the derived equations allows an analyst to solve directly for the vehicle velocity at any point along the trajectory, as well as for the maximum axial acceleration and the altitude at which it occurs.