Approximate Formulas for Time in Nearly Circular Orbits with Drag

Abstract

In this paper we seek approximate closed-form solutions for the flight time in terms of the true anomaly for a satellite in a high near-circular orbit that decays as a result of atmospheric drag. Solutions of this problem are attempted based on three models that approximate the atmospheric density. For the first model and in certain special cases of the other two models, solutions are found that compare favorably with numerical simulations.

Two-Body Problem with Drag and High Tangential Speeds

“…In accordance with previous work [5][6][7][8][9] we consider only motion where j _ Rj jR _ j as in the case of arcs that are nearly circular. This simplifies the formula for the instantaneous specific angular momentum…”

“…Later results in this area are represented by the works of Hoots and France [2], King-Hele [3] and more recently Vallado [4]. Recently Humi and Carter [5][6][7][8][9] have approximated the equations of motion for the very important class of problems in which the radial speeds are relatively small in comparison with the tangential speeds, and have found solutions under these assumptions. The present paper completes this approach attempting to unify and extend some of these results.…”