A geosynchronous transfer orbit or geostationary transfer orbit (GTO) is a Hohmann transfer
orbit—an elliptical orbit used to transfer between two circular orbits of different radii
in the same plane—used to reach geosynchronous or geostationary orbit using high-thrust chemical
engines.Geosynchronous orbits (GSO) are useful for various civilian and military purposes,
but demand a great deal of delta-v to attain. Since, for station-keeping, satellites intended
for this orbit typically carry highly efficient but low-thrust engines, total mass delivered
to GSO is generally maximized if the launch vehicle provides only the delta-v required
to be at high thrust, i.e., to escape Earth's atmosphere and overcome gravitational losses,
and the satellite provides the delta-v required to turn the resulting intermediate orbit,
which is the GTO, into the useful GSO.
== Technical description == GTO is a highly elliptical Earth orbit with
an apogee of 42,164 km (26,199 mi), or 35,786 km (22,236 mi) above sea level, which corresponds
to the geostationary altitude. The period of a standard geosynchronous transfer orbit
is about 10.5 hours. 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 (
Δ V
) requirements and to 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 (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.
The typical launch vehicle injects the satellite to a supersynchronous orbit having the apogee
above 42,164 km. The satellite's low-thrust engines are thrusted continuously around the
geostationary transfer orbits in an inertial direction. This inertial direction is set
to be in the velocity vector at apogee but with an out-of-plane component. The out-of-plane
component removes the initial inclination set by the initial transfer orbit, while the
in-plane component raises simultaneously 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 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 eccentricity of the orbit is reduced to zero, the result may be a geosynchronous
orbit but will not be geostationary. Because the
Δ V
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
Δ V
for an inclination change at either the ascending
or descending node of the orbit is calculated as follows:
Δ V
= 2
V sin
⁡
Δ i
2
.
{\displaystyle \Delta V=2V\sin {\frac {2}}.}
For a typical GTO with a semi-major axis of 24,582 km, perigee velocity is 9.88 km/s and
apogee velocity is 1.64 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
Δ V
for the two maneuvers. The combined
Δ V
is the vector sum of the inclination change
Δ V
and the circularization
Δ V
, and as the sum of the lengths of two sides
of a triangle will always exceed the remaining side's length, total
Δ V
in a combined maneuver will always be less
than in two maneuvers. The combined
Δ V
can be calculated as follows:
Δ V
=
V
t ,
a
2
+
V
GEO
2
− 2
V
t ,
a
V
GEO
cos ⁡
Δ i
,
{\displaystyle \Delta V={\sqrt {V_{t,a}^{2}+V_{\text{GEO}}^{2}-2V_{t,a}V_{\text{GEO}}\cos \Delta i}},}
where
V
t ,
a
{\displaystyle V_{t,a}} is the velocity magnitude at the apogee of
the transfer orbit and
V
GEO
{\displaystyle V_{\text{GEO}}} 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. Baikonur Cosmodrome in Kazakhstan is at 46° north latitude. Kennedy
Space Center is at 28.5° north. Guiana Space Centre, the Ariane launch facility, is at
5° north. Sea Launch launches from a floating platform directly on the equator in the Pacific
Ocean. Expendable launchers generally reach GTO directly,
but a spacecraft already in a 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 kg to GTO, or 6,750 kg directly to geostationary
orbit.If the manoeuvre 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 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). 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.
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
transfer orbit where the apogee (and the maneuver to reduce the transfer orbit inclination)
are at a higher altitude than 35,786 km, the geosynchronous altitude. Proton even offers
to perform a supersynchronous apogee maneuver up to 15 hours after launch.
== See also ==
Astrodynamics Low Earth orbit
List of orbits