In Soviet literature, such as Pionery Raketnoi Tekhniki, the term Hohmann-Vetchinkin transfer orbit is sometimes used, citing the presentation of the elliptical transfer concept by mathematician Vladimir Vetchinkin in public lectures on interplanetary travel given 1921-1925.
The Hohmann transfer orbit is one half of an elliptic orbit that touches both the orbit that one wishes to leave (labeled 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 so that it will follow the elliptical orbit; this adds energy to the spacecraft's orbit. When the spacecraft has reached its destination orbit, its orbital speed (i.e., orbital energy) must be increased again in order to make its new orbit circular; the engine is fired again to accelerate it to the required velocity.
The Hohmann transfer orbit is theoretically based on impulsive velocity changes to create the circular orbits, therefore a spacecraft using a Hohmann transfer orbit will typically use high thrust engines to minimize the amount of extra fuel required to compensate for the non-impulsive maneuver. Low thrust engines can perform an approximation of a Hohmann transfer orbit, by creating a gradual enlargement of the initial circular orbit through carefully timed engine firings. This requires a delta-v that is up to 141% greater than the 2 impulse transfer orbit (see also below), and takes longer to complete.
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, decelerating the spacecraft and causing it to drop into the lower-energy elliptical transfer orbit. The engine is then fired again in the lower orbit to decelerate the spacecraft into a circular orbit.
Although the Hohmann transfer orbit is almost always the most economical way to get from one circular orbit to another (in the same plane), there are situations in which a bi-elliptic transfer is even more economical: particularly when the semi-major axis of the final orbit is more than about 12 times greater than that of the initial orbit.
Solving this equation for velocity results in the Vis-viva equation,
Therefore the delta-v required for the Hohmann transfer can be computed as follows:
Whether moving into a higher or lower orbit, by Kepler's third law, the time taken to transfer between the orbits is:
(one half of the orbital period for the whole ellipse)
In the smaller circular orbit the speed is 7.73 km/s, in the larger one 3.07 km/s. In the elliptical orbit in between the speed varies from 10.15 km/s at the perigee to 1.61 km/s at the apogee.
Compare with the delta-v for an escape orbit: 10.93 − 7.73 = 3.20 km/s. Applying a delta-v at the LEO of only 0.78 km/s more would give the rocket the escape speed, while at the geostationary orbit a delta-v of 1.46 km/s is needed for reaching the sub-escape speed of this circular orbit. This illustrates that at large speeds the same delta-v provides more specific orbital energy, and, as explained in gravity drag, energy increase is maximized if one spends the delta-v as soon as possible, rather than spending some, being decelerated by gravity, and then spending some more (of course, the objective of a Hohmann transfer orbit is different).
Such a low-thrust maneuver requires more delta-v than a 2-burn Hohmann transfer maneuver, requiring more fuel (for a given engine design). However, if only low-thrust maneuvers are required on a mission, then continuously firing a very high-efficiency, low-thrust spacecraft propulsion engines might be able to generate this higher delta-v using less fuel and a smaller engine than a high-thrust engine using a "more efficient" Hohmann transfer maneuver.
A Hohmann transfer orbit will take a spacecraft from low Earth orbit (LEO) to geosynchronous orbit (GEO) in just over five hours (geostationary transfer orbit), from LEO to the Moon (lunar transfer orbit, LTO) in about 5 days and from the Earth to Mars in about 214 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 increase speed in-flight.
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