Closed-Form Solutions for Near-Circular Arcs with Quadratic Drag

Abstract

This paper considers the restricted two-body problem in the presence of drag that varies with a power of the magnitude of the velocity. In general, the orbit equation for this problem is an integrodifferential equation. For extreme cases in which the motion is mostly tangential and the drag varies with the square of the magnitude of the velocity, a new transformation of the orbit equation results in an ordinary differential equation. For a model atmosphere in which the density varies inversely as the square of the distance from the center of attraction, we provide closed-form solutions to this differential equation. This extends previous work in which the density of the model atmosphere varies inversely with the distance from the center of attraction.