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# Geostationary transfer orbit

A Geosynchronous Transfer Orbit or Geostationary Transfer Orbit (GTO) is a Hohmann transfer orbit around the Earth between a low Earth orbit (LEO) and a geosynchronous orbit (GEO). It is an ellipse where the perigee is a point on a LEO and the apogee has the same distance from the Earth as the GEO. The term Geostationary Transfer Orbit is more technically correct, but is not commonly used in the space industry.

Heavy Lift Launch Vehicles are the only rockets capable of moving heavier satellites into geostationary or geosynchronous orbits. The capability of achieving geostationary transfer orbit is critical to the placement of modern satellites.

After a typical launch the inclination of the LEO (the angle between the plane of the orbit and the plane of the equator) is determined by the latitude of the launch site and the direction of launch. The GTO typically inherits the same inclination. The inclination must be reduced to zero to obtain a geostationary orbit. Most of the delta-v ($Delta$V) for this inclination change is done at the GEO distance because that requires less energy than at LEO. This is because the required $Delta$V for a given inclination change $Delta i$ is directly proportional to orbit velocity $V$ which is lowest in its apogee. The required $Delta$V for an inclination change in either the ascending or descending Orbital node of the orbit is calculated as follows:

$Delta V = 2 V sin frac\left\{Delta i\right\}\left\{2\right\}$

For a typical GTO with a semimajor axis of 24,582 km, the perigee velocity of a GTO is 9.88 km/s while the apogee velocity is at 1.64 km/s. Therefore it is most efficient to change inclination at GEO. However, note that in actual operation, the inclination change is combined with the orbital circularization (or "apogee kick") burn, and considerably less $Delta$V is required than the above calculation would imply.

A launch vehicle can move from LEO to GTO by firing a rocket at a tangent to the LEO to increase its velocity perigee kick burn). Typically the upper stage of the vehicle has this function. The GTO then cycles between a perigee tangent to LEO and an apogee tangent to a geosynchronous orbit at the equator. At the point where the orbit intersects the desired orbit, the rocket can conduct an apogee-kick burn to insert itself into orbit, simultaneously correcting its inclination to achieve a geostationary position 35,792 kilometers (22,240 miles) over a specific spot on the equator. It is usually the satellite itself that performs the apogee kick burn into geostationary orbit. Therefore the capacity of a rocket which can launch various satellites is often quoted in terms of separated spacecraft mass to GTO rather than spacecraft mass to GEO. Alternatively the rocket may have the option to perform the boost for insertion into GEO itself. This saves the satellite's fuel, but considerably reduces the separated spacecraft mass capacity.

For example, the capacity (separated spacecraft mass) of the Delta IV Heavy:

• GTO 12 757 kg (185 km x 35,786 km at 27.0 deg inclination), theoretically more than any other currently available launch vehicle (has not flown with such a payload yet)
• GEO 6 276 kg

Insertion into geostationary orbit is typically performed at the orbital nodes (usually the ascending node). This is because most launch sites from which launches into a GTO are performed are located on the northern hemisphere.

The preceeding 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 four intermediate orbits, requiring five rocket firings, to place a satellite into GEO from the high-inclination site of Baikonur Cosmodrome, in Kazakhstan.

### Transfer Stage

In most cases, the spent upper stages of launch vehicles are left behind in the GTO (some are occasionally left in GEO, like the Proton Block DM). If the perigee of the GTO is chosen to be low enough to make atmospheric drag quickly decrease apogee altitude, the upper stage will be no collision threat to the satellites in the geostationary ring. Eventually, it will reenter the atmosphere of the Earth. Most upper stages that are used to bring payloads to a GTO are designed to meet this requirement.

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