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In orbital mechanics, the Hohmann transfer orbit (/ˈhmən/) is an elliptical orbit used to transfer between two circular orbits of different radii around a central body in the same plane. The Hohmann transfer often uses the lowest possible amount of propellant in traveling between these orbits, but bi-elliptic transfers can beat it in some cases.

The orbital maneuver to perform the Hohmann transfer uses two engine impulses, one to move a spacecraft onto the transfer orbit and a second to move off it. This maneuver was named after Walter Hohmann, the German scientist who published a description of it in his 1925 book Die Erreichbarkeit der Himmelskörper (The Attainability of Celestial Bodies).[1] Hohmann was influenced in part by the German science fiction author Kurd Lasswitz and his 1897 book Two Planets.

The elliptic transfer orbits between different bodies (planets, moons etc.) are often referred to as Hohmann transfer orbits. When used for traveling between celestial bodies, a Hohmann transfer orbit requires that the starting and destination points be at particular locations in their orbits relative to each other. Space missions using a Hohmann transfer must wait for this required alignment to occur, which opens a so-called launch window. For a space mission between Earth and Mars, for example, these launch windows occur every 26 months. A Hohmann transfer orbit also determines a fixed time required to travel between the starting and destination points; for an Earth-Mars journey this travel time is about 9 months. When transfer is performed between orbits close to celestial bodies with significant gravitation, much less delta-v is usually required, as Oberth effect may be employed for the burns.

They are also often used for these situations, but low-energy transfers which take into account the thrust limitations of real engines, and take advantage of the gravity wells of both planets can be more fuel efficient.[2][3][4]

The bi-elliptic transfer consists of two half-elliptic orbits. From the initial orbit, a first burn expends delta-v to boost the spacecraft into the first transfer orbit with an apoapsis at some point

To get to the Sun, it is actually not necessary to use a Δv of 24 km/s. One can use 8.8 km/s to go very far away from the Sun, then use a negligible Δv to bring the angular momentum to zero, and then fall into the Sun. This can be considered a sequence of two Hohmann transfers, one up and one down. Also, the table does not give the values that would apply when using the Moon for a gravity assist. There are also possibilities of using one planet, like Venus which is the easiest to get to, to assist getting to other planets or the Sun.

The bi-elliptic transfer consists of two half-elliptic orbits. From the initial orbit, a first burn expends delta-v to boost the spacecraft into the first transfer orbit with an apoapsis at some point away from the central body. At this point a second burn sends the spacecraft into the second elliptical orbit with periapsis at the radius of the final desired orbit, where a third burn is performed, injecting the spacecraft into the desired orbit.[9]

While they require one more engine burn than a Hohmann transfer and generally require a greater travel time, some bi-elliptic transfers require a lower amount of total delta-v than a Hohmann transfer when the ratio of final to initial semi-major axis is 11.94 or greater, depending on the intermediate semi-major axis chosen.[10]

The idea of the bi-elliptical transfer trajectory was first[citation needed] published by semi-major axis is 11.94 or greater, depending on the intermediate semi-major axis chosen.[10]

The idea of the bi-elliptical transfer trajectory was first[citation needed] published by Ary Sternfeld in 1934.[11]

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 change in velocity (delta-v) that is greater than the two-impulse transfer orbit[12] and takes longer to complete.

Engines such as ion thrusters are more difficult to analyze with the delta-v model. These engines offer a very low thrust and at the same time, much higher delta-v budget, much higher specific impulse, lower mass of fuel and engine. A 2-burn Hohmann transfer maneuver would be impractical with such a low thrust; the maneuver mainly optimizes the use of fuel, but in this situation there is relatively plenty of it.

If only

Engines such as ion thrusters are more difficult to analyze with the delta-v model. These engines offer a very low thrust and at the same time, much higher delta-v budget, much higher specific impulse, lower mass of fuel and engine. A 2-burn Hohmann transfer maneuver would be impractical with such a low thrust; the maneuver mainly optimizes the use of fuel, but in this situation there is relatively plenty of it.

If only low-thrust maneuvers are planned on a mission, then continuously firing a low-thrust, but very high-efficiency engine might generate a higher delta-v and at the same time use less propellant than a conventional chemical rocket engine.

Going from one circular orbit to another by gradually changing the radius simply requires the same delta-v as the difference between the two speeds.[12] Such maneuver requires more delta-v than a 2-burn Hohmann transfer maneuver, but does so with continuous low thrust rather than the short applications of high thrust.

The amount of propellant mass used measures the efficiency of the maneuver plus the hardware employed for it. The total delta-v used measures the efficiency of the maneuver only. For electric propulsion systems, which tend to be low-thrust, the high efficiency of the propulsive system usually compensates for the higher delta-V compared to the more efficient Hohmann maneuver.

Transfer orbits using electrical propulsion or low-thrust engines optimize the transfer time to reach the final orbit and not the delta-v as in the Hohmann transfer orbit. For geostationary orbit, the initial orbit is set to be supersynchronous and by thrusting continuously in the direction of the velocity at apogee, the transfer orbit transforms to a circular geosynchronous one. This method however takes much longer to achieve due to the low thrust injected into the orbit.[13]

In 1997, a set of orbits known as the Interplanetary Transport Network (ITN) was published, providing even lower propulsive delta-v (though much slower and longer) paths between different orbits than Hohmann transfer orbits.[14] The Interplanetary Transport Network is different in nature than Hohmann transfers because Hohmann transfers assume only one large body whereas the Interplanetary Transport Network does not. The Interplanetary Transport Network is able to achieve the use of less propulsive delta-v by employing gravity assist from the planets.[citation needed]

See also