Geostationary transfer orbit
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A geosynchronous transfer orbit or geostationary transfer orbit (GTO) is a Hohmann transfer orbit used to reach geosynchronous or geostationary orbit using high thrust chemical engines.[1] It is a highly elliptical Earth orbit with an apogee of 42,164 km (26,000 mi),[2] or 35,786 km (22,000 mi) above sea level, which corresponds to the geostationary (GEO) altitude. 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 (V) requirements and to limit the orbital lifetime of the spent booster so as to curtail space junk. In case of using low thrust engines or electrical propulsion, the geostationary transfer orbit requires the initial orbit to be supersynchronous to the final geosynchronous orbit. This method however takes much longer to achieve due to the low thrust injected into the orbit.[3] 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 outer plane direction. The outer plane direction removes the initial inclination set by the initial transfer orbit while the inner plane direction 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 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 is a geosynchronous orbit. Because the V required for a plane change is proportional to the instantaneous velocity, the inclination and eccentricity are usually changed together in a single manoeuvre at apogee where velocity is lowest.
1 Technical description
2 Other considerations
Technical description[edit]
The required V for an inclination change at either the ascending or descending node of the orbit is calculated as follows:[4]
For a typical GTO with a semimajor 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 V for the two maneuvers. The combined V is the vector sum of the inclination change V and the circularization V, and as the sum of the lengths two sides of a triangle will always exceed the remaining side's length, total V in a combined maneuver will always be less than in two maneuvers. The combined V can be calculated as follows:[4]
where is the velocity magnitude at the apogee of the transfer orbit and is the velocity in GEO.
Other considerations[edit]
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 degrees north latitude. Kennedy Space Center is at 28.5 degrees north. Guiana Space Centre, the Ariane launch facility, is at 5 degrees north. Sea Launch launches from a floating platform