A team of astronauts is running low on fuel in space and the

A team of astronauts is running low on fuel in space and they need to reach the transfer orbit that extends from Planet X (where they are currently orbiting) to Planet Y (where they wantto be orbiting). Assuming the orbits of the planets, as well as the transfer orbit, are all elliptical, where (in their orbit) and in what direction (radially, tangentially, both, etc.) would it be most ecient for the team to re their engines? Why?

Solution

Hohmann orbits involve an elliptical transfer maneuver, but both the initial and final orbits are circular.The total energy is independent of the eccentricity.

Thus, a Hohmann transfer between two elliptical orbits is not possible. The most efficient burn for greater orbital energy always occurs at perigee, but that will only increase the eccentricity of the orbit. More complicated corrections are required to translate from one elliptical orbit to another.

One approach we could take is a Hohmann intermediary orbit, but it\'s not necessarily the most efficient. In this, you\'d perform the second half of a Hohmann maneuver to make circular your first orbit (towards apogee or towards perigee - whichever direction you need to go depending on if your second orbit is larger or smaller than the first). Secondly, you\'d use a standard Hohmann transfer maneuver to establish a circular orbit with a radius equivalent to the periapsis or apoapsis of the destination elliptical orbit (which one again depends on if it\'s larger or smaller). Third, you\'d conduct the first half of a Hohmann transfer orbit to re-establish the correct eccentricity.

Technically, it\'s like conducting a total two Hohmann transfer orbits. If the destination ellipse is non-intersecting (that is, either fully inside or outside the original ellipse), this is indeed the most efficient maneuver. But if it\'s intersection, it\'ll be less efficient.