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I am familiar with all different orbits but I struggle with the new launch injection method in GTO.

What are the differences between sub-synchronous and super-synchronous transfer orbits compared to a traditional GTO?

I have read that SpaceX and Proton are offering such tailored services; what are the benefits for the payload?

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Supersynchronous orbits are sometimes used because of a more efficient inclination change at high apogee compared to a typical Hohmann transfer orbit to GEO (aka GTO) with apogee at GEO altitude, before a GEO satellite is placed into its allocated orbital slot. This would be useful for launches from high latitude launch sites. Technically, the GEO disposal or graveyard orbit is also a supersynchronous orbit, since it has a longer orbital period than a synchronous orbit.

Subsynchronous orbits can be any transfer orbits to GEO that don't achieve apogee with a single Hohmann transfer impulse to GTO to later circularize the orbit with another, such as transfer orbits that slowly increase apogee with multiple perigee burns, using the Oberth effect to their advantage. This might be especially useful to all electric geostationary satellites that use highly mass efficient but low thrust propulsion. They can also be used as intermediate orbits for deactivated but not decommissioned GEO satellites, or during change of allocated orbital slot with a so-called orbit phasing maneuver.

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I think Tildalwave's answer captures the essence. Here are some peripheral points specifically on the super-synchronous part:

  1. Its worth clarifying that such an injection requires a minimum of two manoeuvres to get to GEO, the first to raise the perigee/remove the inclination and the second to drop the apogee. The idea is that the extra cost of the apogee reduction is more than offset by the saving on the inclination change.

  2. As a historical point, its not such a new method. My first memory of it was in connection with the Orion 1 / Telstar 11 launch in 1994, though it could easily have been applied earlier.

  3. The common applied terminology "super-synchronous" in this context may seem confusing. By injection into an orbit with an apogee higher than GEO this new transfer orbit is called a "super-synchronous transfer orbit". However it does not itself have to have an orbital period greater than 24 hours, it earns the "super-synchronous" label simply from having an apogee radius greater than GEO. The term is slightly inconsistent with other orbit names because neither the transfer orbit itself nor the final destination are super-synchronous, just the intermediate point along the way.

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    $\begingroup$ Good points. Regarding the third one, it should then be noted that GTO as a transfer orbit also isn't geosynchronous, it only aims at an apogee at a geosynchronous altitude. I think that in that regard, naming could be consistent if we also used transfer in names of all transfer "orbits" (I personally think they should be "trajectories" to additionally avoid confusion). So sub/super-synchronous transfer orbit doesn't have to have semi-major axis smaller/larger than synchronous orbits, but it does have a sub/super-synchronous apoapsis. Does this make sense? $\endgroup$ – TildalWave Jan 20 '16 at 21:25
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    $\begingroup$ To me yes, though in fact I nearly tied myself in knots trying to come up with a straight explanation in my answer. $\endgroup$ – Puffin Jan 20 '16 at 21:29
  • $\begingroup$ A payload might prefer to initially be in a lower or higher than geosynchronous orbit because they are going to move it from the initial longitude anyway. So they drift while performing initial on-orbit checkout. $\endgroup$ – Matt Jessick Jan 21 '16 at 2:20

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