Hohmann transfer orbit

In astronautics and aerospace engineering, the Hohmann transfer orbit is a certain orbital path that moves a spacecraft from one point to another using a very low amount of energy. It was named after the German scientist who worked it out in 1925. (See also interplanetary travel.)

In the case of inter-orbit transfers, the most common example of a Hohmann transfer is the geostationary transfer orbit. In the case of Moon missions it is translunar injection. In a Moon mission, the craft first has to reach low Earth orbit (LEO). It then has to boost itself to an elliptical orbit, with the Earth at the one focus and the Moon at the other. Once it reaches the Moon it decelerates to achieve a Lunar orbit. Transfers between other bodies are similar.

The basic idea is to construct an orbit where the speed at apogee is close to the speed of the Earth in its orbit, and the speed at perigee is the speed of the point in question, the Moon, Mars, or even some other orbit around the Earth. Small amounts of thrust at either end of the trip are all that are needed to arrange the transfer. However, Hohmann transfers are also 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.

To achieve these transfers, a spacecraft has to execute a series of changes in velocity (Delta V's). The equation is as follows:

<math>DV = I_{sp} g \ln \frac{mr}{mr-mf}</math>

I_sp = specific impulse of the fuel (the number of seconds that 1 kg fuel can generate 10 Newtons)

g = the acceleration of gravity (9,81 m/s²)

mr = mass of the rocket and fuel

mf = mass of used fuel

A set of orbits known as the Interplanetary Superhighway has been recently discovered which is slower but even lower-energy than Hohmann transfer orbits.