Orbital mechanics question for an author.

[strollen]

A friend of mine is writing a Clancy-like thriller with International Space Station as one of the settings. He has this question about orbital mechanics.

An untethered astronaut pushes off from the International Space Station.

My understanding is that rather than just float away, he will go into a new orbit, and that orbit will intersect the orbit of the ISS on the other side of the Earth.

The reference I read (and can't find again) said that this happens if the push off is to one side of the ISS and not toward or away from Earth. But I'd guess that it would be the same for any direction. That is, push down toward Earth, and he/she would to into an elliptical orbit that would intersect the original orbit.

Does that sound right?

I don't think the astronaut would intersect but I'm not sure.

[andrewas]

Any orbit obtained in a single push will intersect the ISS's orbit, but the ISS might not be there when the astronaut hits the intersection.

If the push is normal or antinormal, then the astronaut will hit ISS in half an orbit. An EVA suit should be good for the 45 minutes this will take, so the character should be able to re-board the station.

Prograde or retrograde will change the astronauts orbital period, so if he pushes backwards he will drop below and overtake the ISS, drawing further ahead of it with every orbit. There may be a solution where the astronaut hits ISS as hit overtakes it, but the initial push would have to be tiny for that to happen.

Not sure on radial thrust, but I think the period does change so the astronaut isn't getting home any time soon.

Note that in any real situation, the push off won't be perfectly aligned with one of these axis. So while you can get back to the ISS in 45 minutes by pushing off in the normal direction, the inevitable prograde or retrograde component will be enough to cause you to miss the ISS.

[Frida Space]

If you want to have a visual representation of the mechanics involved you could try it in KSP

[Dartguy]

Any orbit obtained in a single push will intersect the ISS's orbit, but the ISS might not be there when the astronaut hits the intersection.

If the push is normal or antinormal, then the astronaut will hit ISS in half an orbit. An EVA suit should be good for the 45 minutes this will take, so the character should be able to re-board the station.

Prograde or retrograde will change the astronauts orbital period, so if he pushes backwards he will drop below and overtake the ISS, drawing further ahead of it with every orbit. There may be a solution where the astronaut hits ISS as hit overtakes it, but the initial push would have to be tiny for that to happen.

Not sure on radial thrust, but I think the period does change so the astronaut isn't getting home any time soon.

Note that in any real situation, the push off won't be perfectly aligned with one of these axis. So while you can get back to the ISS in 45 minutes by pushing off in the normal direction, the inevitable prograde or retrograde component will be enough to cause you to miss the ISS.

That all makes sense, but the push up or down would have to be absolutely straight up or down to actually hit the station 9000 miles away on the other side of the planet. It would be such a shame to see the station move away by a few feet further every pass until you run out of air. But what a spectacular view!