Editing Hohmann transfer orbit (section)

=== Low-thrust transfer ===
{{main|Low thrust relative orbital transfer}}
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|change in velocity (delta-''v'')]] that is greater than the two-impulse transfer orbit<ref name="MIT_16.522">MIT, ''16.522: Space Propulsion'', Session 6, "[https://ocw.mit.edu/courses/aeronautics-and-astronautics/16-522-space-propulsion-spring-2015/lecture-notes/MIT16_522S15_Lecture6.pdf Analytical Approximations for Low Thrust Maneuvers]", Spring 2015 (retrieved 26 July 2017)
</ref> and takes longer to complete.

Engines such as [[ion thruster]]s 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.<ref name="MIT_16.522" /> 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 [[Electrically powered spacecraft propulsion|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.<ref>{{Cite book | last = Spitzer | first = Arnon | title = Optimal Transfer Orbit Trajectory using Electric Propulsion | publisher = [[USPTO]] | date = 1997 | url = https://patents.google.com/patent/US5595360}}</ref>