Editing Geostationary transfer orbit

{{Short description|Transfer orbit used to reach geosynchronous or geostationary orbit}}
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In space mission design, a '''geostationary transfer orbit''' ('''GTO''') or '''geosynchronous transfer orbit''' is a highly [[Elliptic orbit|elliptical]] type of [[geocentric orbit]], usually with a [[perigee]] as low as [[low Earth orbit]] (LEO) and an [[apogee]] as high as [[geostationary orbit]] (GEO). [[Satellite|Satellites]] that are destined for [[geosynchronous orbit]] (GSO) or GEO are often put into a GTO as an intermediate step for reaching their final orbit.<ref name="smad2ed">
Larson, Wiley J. and James R. Wertz, eds. Space Mission Design and Analysis, 2nd Edition. Published jointly by Microcosm, Inc. (Torrance, CA) and Kluwer Academic Publishers (Dordrecht/Boston/London). 1991.</ref> Manufacturers of launch vehicles often advertise the amount of payload the vehicle can put into GTO.<ref name=":0" />

==Background==

Geostationary and geosynchronous orbits are very desirable for many [[Communications satellite|communication]] and [[Earth observation satellite|Earth observation satellites]]. However, the [[delta-v]], and therefore financial, cost to send a spacecraft to such orbits is very high due to their high orbital radius. A GTO is an intermediary orbit used to make this process more efficient. Satellite operators often use a high-thrust, low-efficiency [[launch vehicle]] to put their satellite into GTO, and then, after detaching the launch vehicle, use low-thrust, high-efficiency thrusters onboard the satellite itself to circularize its orbit (to GEO). This mission architecture is useful because it minimizes the mass that the spacecraft must push to GEO, allows for maximally efficient circularization burns taking advantage of the [[Oberth effect]], and allows the spent launch vehicle to [[deorbit]] primarily through [[aerobraking]] due to its low perigee, minimizing its [[Space debris|orbital lifetime]]. 

==Technical description==

GTO is a [[highly elliptical orbit|highly elliptical Earth orbit]] with an [[apogee]] (the point in the orbit of the moon or a satellite at which it is furthest from the earth) of {{convert|42164|km|mi|abbr=on}},<ref>
{{cite book |title=Fundamentals of Astrodynamics and Applications |last=Vallado |first=David A. |year=2007 |publisher=Microcosm Press |location=Hawthorne, CA  |pages=31 }}
</ref> or a height of {{convert|35786|km|mi|abbr=on}} above sea level, which corresponds to the geostationary altitude. The period of a standard geosynchronous transfer orbit is about 10.5 hours.<ref>{{cite book|author=Mark R. Chartrand|title=Satellite Communications for the Nonspecialist|url=https://books.google.com/books?id=MM0d2cMUWbEC&pg=PA164|year=2004|publisher=SPIE Press|isbn=978-0-8194-5185-9|page=164}}</ref> The [[argument of perigee]] is such that apogee occurs on or near the equator. Perigee can be anywhere above the atmosphere, but is usually restricted to a few hundred kilometers above the Earth's surface to reduce launcher delta-V (<math>\Delta V</math>) requirements and to [[Orbital decay|limit the orbital lifetime of the spent booster]] so as to curtail space junk.

If using low-thrust engines such as [[electrical propulsion]] to get from the transfer orbit to geostationary orbit, the transfer orbit can be [[Supersynchronous orbit|supersynchronous]] (having an apogee above the final geosynchronous orbit). However, this method 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><ref>{{Cite book | last = Koppel | first = Christophe R.| title = Method and a system for putting a space vehicle into orbit, using thrusters of high specific impulse | publisher = USPTO | date = 1997 | url = https://patents.google.com/patent/US6213432}}</ref>
The typical launch vehicle injects the satellite to a supersynchronous orbit having the apogee above 42,164&nbsp;km. The satellite's low-thrust engines are thrusted continuously around the geostationary transfer orbits. The thrust direction and magnitude are usually determined to optimize the transfer time and/or duration while satisfying the mission constraints. The out-of-plane component of thrust is used to reduce the initial inclination set by the initial transfer orbit, while the in-plane component simultaneously raises the perigee and lowers the apogee of the intermediate geostationary transfer orbit. In case of using the Hohmann transfer orbit, only a few days are required to reach the geosynchronous orbit. By using low-thrust engines or electrical propulsion, months are required until the satellite reaches its final orbit.

The [[orbital inclination]] of a GTO is the angle between the orbit plane and the Earth's [[equator|equatorial plane]]. It is determined by the [[latitude]] of the launch site and the launch [[azimuth]] (direction). The inclination and eccentricity must both be reduced to zero to obtain a geostationary orbit. If only the [[Orbital eccentricity|eccentricity]] of the orbit is reduced to zero, the result may be a geosynchronous orbit but will not be geostationary. Because the <math>\Delta V</math> required for a plane change is proportional to the instantaneous velocity, the inclination and eccentricity are usually changed together in a single maneuver at apogee, where velocity is lowest.

The required <math>\Delta V</math> for an inclination change at either the ascending or descending [[orbital node|node]] of the orbit is calculated as follows:<ref name="Curtis, H.D. 2010 pp. 356-357">Curtis, H. D. (2010) [[Orbital Mechanics for Engineering Students]], 2nd Ed. Elsevier, Burlington, MA, pp. 356–357.</ref>
:<math>\Delta V = 2 V \sin \frac{\Delta i}{2}.</math>

For a typical GTO with a [[semi-major axis]] of 24,582&nbsp;km, [[perigee]] velocity is 9.88&nbsp;km/s and [[apogee]] velocity is 1.64&nbsp;km/s, clearly making the inclination change far less costly at apogee. In practice, the inclination change is combined with the orbital circularization (or "[[apogee kick]]") burn to reduce the total <math>\Delta V</math> for the two maneuvers. The combined <math>\Delta V</math> is the vector sum of the inclination change <math>\Delta V</math> and the circularization <math>\Delta V</math>, and as the sum of the lengths of two sides of a triangle will always exceed the remaining side's length, total <math>\Delta V</math> in a combined maneuver will always be less than in two maneuvers. The combined <math>\Delta V</math> can be calculated as follows:<ref name="Curtis, H.D. 2010 pp. 356-357"/>
:<math>\Delta V = \sqrt{ V_{t,a}^2 + V_\text{GEO}^2 - 2 V_{t,a} V_\text{GEO} \cos \Delta i},</math>

where <math>V_{t,a}</math> is the velocity magnitude at the apogee of the transfer orbit and <math>V_\text{GEO}</math> is the velocity in GEO.

==Other considerations==

Even at apogee, the fuel needed to reduce inclination to zero can be significant, giving equatorial launch sites a substantial advantage over those at higher latitudes. [[Russia]]'s [[Baikonur Cosmodrome]] in [[Kazakhstan]] is at 46° north latitude. [[Kennedy Space Center]] in the [[United States]] is at 28.5° north. [[China]]'s [[Wenchang Space Launch Site|Wenchang]] is at 19.5° north. [[India]]'s [[Satish Dhawan Space Centre|SDSC]] is at 13.7° north. [[Guiana Space Centre]], the European [[Ariane (rocket family)|Ariane]] and European-operated Russian [[Soyuz (rocket family)|Soyuz]] launch facility, is at [[5th parallel north|5° north]]. The "indefinitely suspended" [[Sea Launch]] launched from a floating platform directly on the equator in the [[Pacific Ocean]].

[[Expendable launch system|Expendable]] launchers generally reach GTO directly, but a spacecraft already in a low Earth orbit ([[Low Earth orbit|LEO]]) can enter GTO by firing a [[rocket]] along its orbital direction to increase its velocity. This was done when geostationary spacecraft were launched from the [[Space Shuttle]]; a "perigee kick motor" attached to the spacecraft ignited after the shuttle had released it and withdrawn to a safe distance.

Although some launchers can take their payloads all the way to geostationary orbit, most end their missions by releasing their payloads into GTO. The spacecraft and its operator are then responsible for the maneuver into the final geostationary orbit.  The 5-hour coast to first apogee can be longer than the battery lifetime of the launcher or spacecraft, and the maneuver is sometimes performed at a later apogee or split among multiple apogees. The solar power available on the spacecraft supports the mission after launcher separation. Also, many launchers now carry several satellites in each launch to reduce overall costs, and this practice simplifies the mission when the payloads may be destined for different orbital positions.

Because of this practice, launcher capacity is usually quoted as spacecraft mass to GTO, and this number will be higher than the payload that could be delivered directly into GEO.

For example, the capacity (adapter and spacecraft mass) of the [[Delta IV Heavy]] is 14,200&nbsp;kg to GTO, or 6,750&nbsp;kg directly to geostationary orbit.<ref name=":0">United Launch Alliance, ''Delta IV Launch Services User's Guide'' June 2013, p. 2-10, Figure 2-9; {{cite web|url=http://www.ulalaunch.com/site/docs/product_cards/guides/Delta%20IV%20Users%20Guide%20June%202013.pdf |title=Archived copy |access-date=2013-10-14 |url-status=dead |archive-url=https://web.archive.org/web/20131014123330/http://www.ulalaunch.com/site/docs/product_cards/guides/Delta%20IV%20Users%20Guide%20June%202013.pdf |archive-date=2013-10-14 }} accessed 2013 July 27.</ref>

If the maneuver from GTO to GEO is to be performed with a single impulse, as with a single solid-rocket motor, apogee must occur at an equatorial crossing and at synchronous orbit altitude. This implies an argument of perigee of either 0° or 180°. Because the argument of perigee is slowly perturbed by the [[Flattening|oblateness]] of the Earth, it is usually biased at launch so that it reaches the desired value at the appropriate time (for example, this is usually the sixth apogee on [[Ariane 5]] launches<ref>ArianeSpace, ''Ariane 5 User's Manual'' Issue 5 Revision 1, 2011 July, p. 2-13, {{cite web |url=http://www.arianespace.com/wp-content/uploads/2015/09/Ariane5_users_manual_Issue5_July2011.pdf |title=Archived copy |access-date=2016-03-08 |url-status=dead |archive-url=https://web.archive.org/web/20160309022120/http://www.arianespace.com/wp-content/uploads/2015/09/Ariane5_users_manual_Issue5_July2011.pdf |archive-date=2016-03-09 }} accessed 8 March 2016.</ref>). If the GTO inclination is zero, as with [[Sea Launch]], then this does not apply. (It also would not apply to an impractical GTO inclined at 63.4°; see [[Molniya orbit]].)

The preceding discussion has primarily focused on the case where the transfer between LEO and GEO is done with a single intermediate transfer orbit.  More complicated trajectories are sometimes used. For example, the [[Proton-M]] uses a set of three intermediate orbits, requiring five upper-stage rocket firings, to place a satellite into GEO from the high-inclination site of [[Baikonur Cosmodrome]], in [[Kazakhstan]].<ref>International Launch Services, [http://www.ilslaunch.com/sites/default/files/pdf/Proton%20Mission%20Planner%27s%20Guide%20Revision%207%20%28LKEB-9812-1990%29.pdf ''Proton Mission Planner's Guide''] Rev. 7 2009 November, p. 2-13, Figure 2.3.2-1, accessed 2013 July 27.</ref>  Because of Baikonur's high latitude and range safety considerations that block launches directly east, it requires less delta-v to transfer satellites to GEO by using a [[Supersynchronous orbit|supersynchronous transfer orbit]] where the apogee (and the maneuver to reduce the transfer orbit inclination) are at a higher altitude than 35,786&nbsp;km, the geosynchronous altitude.  Proton even offers to perform a supersynchronous apogee maneuver up to 15 hours after launch.<ref>International Launch Services, [http://www.ilslaunch.com/sites/default/files/pdf/Proton%20Mission%20Planner%27s%20Guide%20Revision%207%20%28LKEB-9812-1990%29.pdf ''Proton Mission Planner's Guide''] Rev. 7 2009 November, accessed 2013 July 27 Appendix F.4.2, page F-8.</ref>

The geostationary orbit is a special type of orbit around the Earth in which a satellite orbits the planet at the same rate as the Earth's rotation. This means that the satellite appears to remain stationary relative to a fixed point on the Earth's surface. The geostationary orbit is located at an altitude of approximately 35,786 kilometers (22,236 miles) above the Earth's equator.

==See also==
{{Portal|Spaceflight}}
* [[Astrodynamics]]
* [[Low Earth orbit]]
* [[List of orbits]]
* [[Aeronautics ]]

== References ==
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{{orbits}}

[[Category:Astrodynamics]]
[[Category:Earth orbits]]