So my google-fu is failing me so I'm hoping someone can help out here.

I've been reading up on chase orbits and how things like the Shuttle, dragon, etc all approach the ISS and I understand the process, what I cannot find are the formulas to work out the distance between the chase spacecraft and the ISS or the per orbit catch up rate.

Can anyone help me find it?

  • $\begingroup$ Can you be more specific? The distance can be calculated in the same way the distance between any two objects can be calculated. And what is the second parameter "per orbit catch up rate"? Units? $\endgroup$ Mar 7 '20 at 14:09
  • $\begingroup$ km, m it doesn't matter. I'm trying to work out how to time the rendezvous. SO, for example, if I'm closing at the rate of 100km per orbit and the ISS is 10,000km away I know it'll take 100 orbits. $\endgroup$ Mar 7 '20 at 15:16
  • $\begingroup$ So the unit on your "per orbit catch up rate" is "km per orbit"? $\endgroup$ Mar 7 '20 at 15:18
  • $\begingroup$ km per orbit would work for this question, yes. $\endgroup$ Mar 8 '20 at 0:13
  • $\begingroup$ slightly related: What is the “ISS's Keep Out Sphere” and what is its radius? $\endgroup$
    – uhoh
    Mar 8 '20 at 2:06

A circular orbit at 400 km height has a period of 1 hour, 32 minutes and 24 seconds. At 302 km it is 1:30:24, only two minutes faster.

If the chaser at 302 km was launched 20 seconds too late, it will need 1/6 of a full orbit to keep up to the target at 400 km, or 15 minutes and 4 seconds. But the target and the chaser are now above the same point on Earth only, the height difference is still 98 km.


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