Reflections on the Hohmann Transfer

Authors: A. Miele; M. Ciarcià; J. Mathwig

Source: Journal of Optimization Theory and Applications, Volume 123, Number 2, November 2004 , pp. 233-253(21)

Publisher: Springer

Buy & download fulltext article:

Price: $47.00 plus tax (Refund Policy)

Abstract:

Walter Hohmann was a civil engineer who studied orbital maneuvers in his spare time. In 1925, he published an important book (Ref. 1) containing his main result, namely, that the most economical transfer from a circular orbit to another circular orbit is achieved via an elliptical trajectory bitangent to the terminal orbits. With the advent of the space program some three decades later, the Hohmann transfer maneuver became the most fundamental maneuver in space.

In this work, we present a complete study of the Hohmann transfer maneuver. After revisiting its known properties, we present a number of supplementary properties which are essential to the qualitative understanding of the maneuver. Also, we present a simple analytical proof of the optimality of the Hohmann transfer and complement it with a numerical study via the sequential gradient-restoration algorithm. Finally, as an application, we present a numerical study of the transfer of a spacecraft from the Earth orbit around the Sun to another planetary orbit around the Sun for both the case of an ascending transfer (orbits of Mars, Jupiter, Saturn, Uranus, Neptune, and Pluto) and the case of a descending transfer (orbits of Mercury and Venus).

Keywords: Flight mechanics; Astrodynamics; Celestial mechanics; Hohmann transfer maneuver; Orbital transfer; Ascending transfer; Descending transfer

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s10957-004-5147-z

Affiliations: 1: Aero-Astronautics Group, Rice University, Texas, USA

Publication date: 2004-11-01