Hohmann transfer orbit

In astronautics and aerospace engineering, the Hohmann transfer orbit is an orbital path that moves a spacecraft from one point to another using a very low amount of energy. It was named after Walter Hohmann, the German scientist who published it in 1925. (See also interplanetary travel.) A Hohmann transfer orbit will take a spacecraft from Low Earth Orbit (LEO) to geosynchronous orbit (GEO) in just over three hours, from LEO to the Moon in about 5 days and from the Earth to Mars in about 260 days. However, Hohmann transfers are very slow for trips to more distant points, so when visiting the outer planets it is common to use a gravitational slingshot to modify a faster path into a Hohmann orbit in-flight.

Hohmann transfer orbits rely on the relationship between the velocity of an object in orbit and the altitude of that orbit - the faster an object is moving, the higher the orbit will be. The idea in its most basic form, then, is to construct an orbit that touches both the orbit that one wishes to leave (labelled 1 on diagram) and the orbit that one wishes to reach (3 on diagram). The transfer (2 on diagram) is initiated by firing the spacecraft's engine in order to accelerate it into a higher and more elliptical orbit. When the spacecraft has reached its destination orbit, the engine is fired again to further accelerate it, this time to a speed that will match the intended final orbit.

When used to move a spacecraft from orbiting one planet to orbiting another, the situation becomes somewhat more complex. For example, consider a spacecraft travelling from the Earth to Mars. At the beginning of its journey, the spacecraft will already have a certain velocity associated with its Earth orbit - this is velocity that will not need to be found when the spacecraft enters the transfer orbit (around the Sun). At the other end, the spacecraft will need a certain velocity to orbit Mars, which will actually be less than the velocity needed to continue orbiting the Sun in the transfer orbit, let alone attempting to orbit the Sun in an Mars-like orbit. Therefore, the spacecraft will have to decelerate and allow Mars' gravity to capture it. Therefore, relatively small amounts of thrust at either end of the trip are all that are needed to arrange the transfer. Note, however, that the alignment of the two planets in their orbits is crucial - the destination planet and the spacecraft must arrive at the same point in their respective orbits around the Sun at the same time.

Hohmann transfer orbits also work to bring a spacecraft from a higher orbit into a lower one - in this case, the spacecraft's engine is fired in the opposite direction to its current path, causing it to drop into the elliptical transfer orbit, and fired again in the lower orbit to brake it to the correct speed for that lower orbit.

Whether moving into a higher or lower orbit, the time taken to transfer between the orbits is:

where

t = transfer time

r₁ = radius of initial orbit

r₂ = radius of final orbit

Gm = gravitational parameter (3.986 x 10⁵ km³/s² for Earth, 1.327 x 10¹¹ km³/s² for the Sun)

In 1997, a set of orbits known as the Interplanetary Superhighway was published, providing even lower-energy (though much slower) paths between different orbits than Hohmann transfer orbits.