Geostationary transfer orbit

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. 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. 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 {displaystyle Delta 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 {displaystyle Delta 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 {displaystyle Delta V} for an inclination change at either the ascending or descending node of the orbit is calculated as follows: 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 {displaystyle Delta V} for the two maneuvers. The combined Δ V {displaystyle Delta V} is the vector sum of the inclination change Δ V {displaystyle Delta V} and the circularization Δ V {displaystyle Delta 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 {displaystyle Delta V} in a combined maneuver will always be less than in two maneuvers. The combined Δ V {displaystyle Delta V} can be calculated as follows: where V t , a {displaystyle V_{t,a}} is the velocity magnitude at the apogee of the transfer orbit and V GEO {displaystyle V_{ ext{GEO}}} is the velocity in GEO. 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.