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Working on a project of sorts and I can't wrap my head around this at all., have a question regarding leaving the ISS orbit. If, let us say as an example, an astronaut jumped out of a capsule which was traveling towards the ISS, and that astronaut missed the ISS and kept going. Would he:

  1. Enter his own orbit at a different inclination? and would he come in contact with the ISS eventually again? Or chances of that would be slim?
  2. Would he keep going into outer space?

I know it may sound odd, but any help with this would be appreciated.

EDIT! I can't thank you all enough, all this information is amazing. Hopefully, I'll update you soon with the reasoning for my query.

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The capsule and the ISS are both in orbit around the Earth; almost the same orbit, if the capsule and ISS are within sight of each other, and the relative speed between the two is modest. If the astronaut carefully lets go of the capsule without pushing away, he will remain in exactly the same orbit as the capsule.

Jumping away from the capsule imparts a small change in speed and thus a small alteration in orbit, so now all three elements (capsule, ISS, and astronaut) are in very similar orbits. Whether the astronaut returns to the vicinity of the spacecraft or the ISS later depends on which direction he jumps.

The astronaut will not keep going into outer space unless he can impart about 3500 m/s of forward velocity change with his "jump" -- the difference between velocity in low orbit and Earth escape velocity.

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  • $\begingroup$ Ok that helps a lot. I'm trying to visualize it in my head as well. In my project, the capsule is moving faster than the ISS, so I'm also assuming that the difference in speed at which the astronaut jumps out and is traveling at and let's say when he misses the ISS, is large enough that it would cause him to have a different inclination there for never coming in contact with the station again. In my project he never makes it back I'm just trying to figure out if there would be a way for him to meet up with the ISS again, I'm hoping not. lol $\endgroup$
    – Heliosc7
    Nov 24, 2020 at 0:46
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    $\begingroup$ If the capsule is closing with the ISS from behind, it's moving faster, and thus has a slightly higher apogee and slightly longer orbital period; if the astronaut jumps sideways, the astronaut's inclination will be different from the ISS inclination as well. The combination of those two features means it will be a long time before the astronaut meets the ISS again. $\endgroup$
    – Russell Borogove
    Nov 24, 2020 at 0:53
  • $\begingroup$ Perfect, thank you so much!! $\endgroup$
    – Heliosc7
    Nov 24, 2020 at 1:00
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    $\begingroup$ If it matters, if not rescued before then, atmospheric drag will cause the astronaut's body to reenter the Earth's atmosphere and burn up in something like a year or two. (It varies significantly with not-completely predictable solar activity, so you can't predict the reentry time far in advance.) $\endgroup$
    – Russell Borogove
    Nov 24, 2020 at 1:05
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    $\begingroup$ That's pretty opaque IMO. Without adding a lot of definitions, it's meaningless to me. I'll summarize the significance of the 3000, er, 3500 m/s without a formal derivation instead. $\endgroup$
    – Russell Borogove
    Nov 25, 2020 at 0:23

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