When playing Kerbal Space Program, I realized that there is a difference between surface speed and orbital speed; this difference is quite variable, although the Kerbin's surface speed is only 175 m/s.

My question is: how do NASA or SpaceX calculate the orbital velocity? One of the many ways to do this is using the vis-viva equation, but the vis-viva equation needs the value of the semi-major-axis, so my question now is: how can you figure out the orbital velocity without knowing the semi-major axis?

  • $\begingroup$ It's a good question! I'd guess that they start with a gravity model of the body and a bunch of position measurements via some combination of self-reported positions (by telemetry) using GPS or other location-providing satellites like TDRS and by ground observations of positions and velocities, then adjusting/fitting simulated trajectories in order to best fit all of those observations. $\endgroup$ – uhoh Oct 31 '20 at 23:25
  • $\begingroup$ Thanks for the answer! But supposing if they didn't have satellites or all that technology, if we were talking about the launch of sputnik 1 for example. would there be any formula to calculate the orbital speed or the Semi Major Axis without depending on each other? $\endgroup$ – John Oct 31 '20 at 23:42
  • $\begingroup$ It's just a comment, I think someone will write a full answer. But in your question you write "My question is how NASA or SpaceX calculate the orbital velocity?" Sputnik had a radio transmitter that "beeped" and could be tracked by radio, and I'm sure several governments independently did exactly the same kind of thing that is done today. The difference is that back then we didn't have a good gravity model of the Earth, so the fitting procedures on the first few satellites ever launched gave us better gravity models! $\endgroup$ – uhoh Oct 31 '20 at 23:46
  • $\begingroup$ For more on that see Did Sputnik 1 tell us more than “beep”? What science was improved by information gained from its orbiting the Earth? and other things linked there. Also see 1959 Peanuts cartoon about the Fischer ellipsoid (Earth is “pear-shaped”)? and other things linked there. $\endgroup$ – uhoh Oct 31 '20 at 23:49
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    $\begingroup$ Thanks! And sorry for any confusion $\endgroup$ – John Nov 1 '20 at 0:01

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