# Would a satellite in retrograde orbit have a different speed than it would in prograde?

I understand that more power is required to launch a satellite into retrograde orbit, but once it's up there how much does the orbit differ from the more usual West to East? Would you still use $v\approx\sqrt{\frac{GM}{r}}$ to find the speed or are there more things to consider, such as the drag in LEO.

I'm assuming a simplified circular orbit.

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This is a good question, but you didn't mention to what precision you'd like any effects discussed? Since you mention atmospheric drag in LEO, I imagine you'd want answers to be fairly precise? I calculate for ISS altitude change in speed of atmosphere of ± 0.27 km/s which is at ISS speed (7.71 km/s) ± 0.355% change in its decay rate, so ~ + 0.7% faster orbital decay (from about 2 km/month) if it was orbiting retrograde. But there might be other things to consider, such as tidal perturbations that I don't have any numbers for. – TildalWave Mar 31 '14 at 15:53
BTW speed itself doesn't change prograde to retrograde, since it defines your orbital altitude, but the decay rate (and with it precession, or simplifying - eccentricity) would, if your orbit has something more to work against than merely orbit around a single, perfectly homogeneous gravitational field alone (and no system is perfect, so there's always something, like tidal perturbations, gravity anomalies, atmospheric/exospheric drag, insolation intervals, magnetosphere, solar winds,... at play). – TildalWave Mar 31 '14 at 16:04