Is stable orbit of a small satellite around the ISS theoretically possible with minimal station keeping?
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$\begingroup$ related: Can dust be in orbit around a spacecraft which orbits the Earth or Moon? and Satellite of a satellite of a satellite $\endgroup$– uhohJan 8, 2021 at 12:59
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3$\begingroup$ No, it gets far bigger perturbations from the upper atmosphere. Essentially, the small satellite would be decelerated by the atmosphere far quicker than the ISS. The little gravity of the ISS could not compensate it. $\endgroup$– peterhJan 8, 2021 at 23:55
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4$\begingroup$ No this isn't a duplicate. The answer to the other question about "orbits the Earth or Moon" addresses radiation pressure but not atmospheric drag. This question is specifically about the unusually shaped and very low average density ISS at the precariously low altitude of 400 km. $\endgroup$– uhohJan 9, 2021 at 0:23
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$\begingroup$ Also you have a reopen vote about your own question, click "reopen". You already have 2, you need 5. $\endgroup$– peterhJan 9, 2021 at 23:00
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$\begingroup$ @peteth Thanks, But i am not able to view my question in reopen votes section. It is empty. $\endgroup$– AshvinJan 10, 2021 at 6:42
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2 Answers
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A first-order approximation to see whether an orbit could be stable is to calculate the radius of the Hill sphere of the parent:
$$R_H \approx a\sqrt[3]{\frac{m}{3M}}$$
With the mass or the ISS ($m$), the mass of the Earth ($M$), and the orbital radius of the ISS ($a$), we see that the region the ISS dominates gravitationally has a radius of less than 2 metres, that is, inside the station itself.
Orbiting the ISS is therefore almost completely the same thing stability-wise as orbiting the Earth, that is, we can just ignore the influence of the ISS.
The ISS needs regular station keeping to deal with atmospheric drag, and thus this ISS satellite would need the same. Possibly a bit more since it would have a larger surface-to-mass ratio since it's smaller.
answered Jan 8, 2021 at 12:07
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Good question, I had this answered my self a few years back by a video by Scott Manley, I did try my hand at explaining but I see now how wrong and random I was so here is the original video:
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$\begingroup$ Sorry for confusing you, I meant that you would need the ISS at Earth L1 for it's sphere of influence to be large enough so a stable orbit for the small satellite is plausible. To add on if you look at the shape of the ISS it would be impossible to orbit close for a long period of time because you would be thrown off by the irregular shape therefore you must crumple the ISS like tinfoil and turn it into a ball so orbit isn't just plausible, it's possible. Plus if you look at the Moon, you can't orbit close for a long period of time just because of the craters. $\endgroup$ Jan 9, 2021 at 2:01
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1$\begingroup$ I've just happened to noticed that you've rewritten your answer. It looks like my comments are no longer relevant so I'll delete them. In the future it doesn't hurt if you ping commenters that a revision has happened so they can do this. Thanks! $\endgroup$– uhohJan 12, 2021 at 0:47