Moon orbits around Earth and space station orbit around the Earth, can a space station have some objects orbit around it?
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No, low Earth orbit satellites can't have their own satellites.
From Wikipedia: https://en.wikipedia.org/wiki/Hill_sphere#Further_examples
An astronaut could not orbit the Space Shuttle (with mass of 104 tonnes), where the orbit is 300 km above the Earth, since the Hill sphere of the shuttle is only 120 cm in radius, much smaller than the shuttle itself. A sphere of this size and mass would be denser than lead. In fact, in any low Earth orbit, a spherical body must be more dense than lead in order to fit inside its own Hill sphere, or else it will be incapable of supporting an orbit. A spherical geostationary satellite however would only need to be more than 6% of the density of water to support satellites of its own.
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$\begingroup$ Formation flying is a definite possibility, though. $\endgroup$ Oct 9, 2015 at 9:44
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2$\begingroup$ If this helps, radius of the ISS' Hill sphere at its current semi-major axis and mass is ~ 1.9 m. If it orbited at GEO altitude, this would increase to 11.8 m, which still isn't enough to find a stable orbital inclination around it (essentially around Node 1 orthogonal to station's velocity vector) that doesn't intersect its truss. $\endgroup$ Oct 9, 2015 at 23:29