[ubernostrum]

So, orbits are weird. As in, "burning your engines in space almost never does what you'd intuitively expect based on a lifetime on Earth with things like cars and planes" weird.

In order to get geostationary, you need to get to a circular orbit at an altitude of 35,786km above Earth's surface. Trying to do that all in one burn is, I guess, theoretically possible but is going to waste an absurd amount of fuel.

The reason for this is that changing altitude in orbit = changing your speed. Specifically, you have two points you care about: your apogee (highest altitude) and your perigee (lowest altitude). To raise your apogee in the most efficient manner, you accelerate prograde (in the direction of your orbit), at perigee. To raise perigee in the most efficient manner, you accelerate prograde at apogee. Or, more simply: what you do at a certain point in your orbit will end up affecting what happens at the point in your orbit that's precisely opposite the point where you did something.

So the most efficient way to get up there is to use a transfer orbit. First you get into a lower, "parking" orbit (which doesn't take as much fuel as going all the way up in one go). Then at perigee you burn to raise your apogee out to the altitude you want. Then you cruise to apogee, and burn again to raise your perigee, resulting in a circular orbit.

Here's a detailed article on that:

https://en.wikipedia.org/wiki/Hohmann_transfer_orbit

Except it never goes quite that simply in the real world, so you actually end up doing more than two engine burns, but under ideal theoretical circumstances, you'd do it in two.

[JshWright]

This is made even more complicated by the fact that SpaceX isn't launching from the equator, which means the satellite will need to change its orbital inclination. Inclination changes are less expensive the 'higher' up you are, so SES8 is in an orbit with an apogee almost twice as high as its eventual orbit. This allows it to use less fuel to correct the inclination.

I haven't read up on the burn plans, but it's possible that the mission is technically using a bi-elliptic transfer[1], rather than a straight hohmann transfer (warning: I learned my orbital mechanics from the Kerbal Space Academy).

[1] http://en.wikipedia.org/wiki/Bi-elliptic_transfer

[exDM69]

Bi-elliptic transfer sounds like a plausible explanation but my math gives it a bigger delta-v requirement than a straightforward Hohmann transfer.

Bi-elliptic transfer: (2.713240 + 0.908982 + 0.485255) = 4.107477 km/s Hohmann transfer: (2.335977 + 1.431307) = 3.7672853 km/s

This alone does not explain why they did so. But this is all assuming that the trajectory is planar. If there was a plane change coupled with the second burn at high apogee, it could explain it.

[ubernostrum]

If there is a plane change involved (as apparently there is), then getting further out before executing the plane change involves less delta-v; performing a plane-change maneuver at apogee is by far the most efficient way.

[sandGorgon]

Is this the same way that the Indian mars mission reached its "transfer altitude"?

[Pinckney]

They did a few things differently. Because their thrust was relatively limited, they made several short burns at perigee to raise their apogee in successive stages. Essentially, it was more efficient to fire their engine several times very close to perigee in 5-10 minute bursts, than make one long 30 minute burn.

Secondly, there was never any stage where they circularized their orbit, as one would do with a Hohmann. Rather, they kept burning at perigee until they escaped earth. Picture a an ellipse growing more and more eccentric until it becomes open at one end.

Also note that they never burned at apogee. The point wasn't to raise apogee so they could escape at apogee, but to increase velocity at perigee until they could reach escape velocity with a 20 minute burn on their last orbit.

http://www.isro.org/mars/mission-profile.aspx