Analytical Study of Tangent Orbit and Conditions for Its Solution Existence Academic Article uri icon


  • This paper presents an analytical study of the two-body tangent orbit technique by providing solution-existence conditions. The flight-direction angle is used to describe and solve this problem. Closed-form solutions are obtained for three classic problems: specified arrival flight-direction angle, specified departure flight-direction angle, and cotangent transfers. Not all of the problems admit solutions; thus, closed-form conditions for solution existence are provided by imposing a positive semilatus rectum constraint and a negative transfer-orbit energy (elliptic orbit transfer) constraint. The final solution-existence condition is then provided in terms of the true anomaly range for initial or final orbit. The singularity problem of 180 deg orbit transfer is also analyzed. Several examples are provided to verify the proposed analytical methods. Copyright 2011 by Gang Zhang, Di Zhou, Daniele Mortari, and Troy A. Henderson. Published by the American Institute of Aeronautics and Astronautics, Inc.

published proceedings


author list (cited authors)

  • Zhang, G., Zhou, D. i., Mortari, D., & Henderson, T. A.

citation count

  • 24

complete list of authors

  • Zhang, Gang||Zhou, Di||Mortari, Daniele||Henderson, Troy A

publication date

  • January 2012