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In one of the short stories of Stanislaw Lem the main character, Ijon Tichy, accidentally drops off a piece of pork out of his spaceship, and this pork becomes a satellite of the spaceship, causing the eclipse of one of the stars on regular basis.

While theoretically it is possible, under which circumstances something like that would be possible? Even if the mass of the spaceship would be very big, the object would have to leave it with very little relative speed, but how little should it be? And how dangerous such 'satellites' would be? They would be annoying, because they would disrupt observations a bit, but is there any other potential danger of such event?

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  • $\begingroup$ Isn't this another question of is this a topic space exploration vs physics? $\endgroup$ – John Riselvato Jul 17 '13 at 20:39
  • $\begingroup$ I asked a similar question on physics before, the objects are too small, for it to orbit it would have to be insanely close to it to the point that they are almost indistinguishable as seperate entities. The question i asked was related to bowling balls and dice in space. It was in chat though, not an actual question $\endgroup$ – user106 Jul 17 '13 at 21:40
  • $\begingroup$ Shame this question is off-topic - I find it rather interesting. I think the first part of the question (which breaks down to "is it possible for an object to establish an orbit around a spacecraft" is probably more well-suited on Physics. If the answer there is "yes", then the second question ("What dangers could such satellites pose to a spacecraft") might be more on-topic here. However, it should probably be more tailored to a specific real-life spacecraft or class of spacecrafts as I'm sure some can shrug off worse impacts than others. $\endgroup$ – Iszi Jul 17 '13 at 22:29
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For an object A to be gravitationally bound to another body B that is orbiting a larger body C itself, A must be inside body B's Hill sphere.

Now, the derivation of the radius of the Hill sphere does not take into account things like weirdly-shaped space stations with very complex gravitational fields, but rather it assumes perfectly spherically symmetric bodies B, C, and a massless A.

So the concept doesn't apply as-is, but let's use it anyway by making the assumption that all of the ISS is compressed into a small sphere of homogeneous density, as dense as its materials will allow. Taking this "idealized" ISS as an example, the following numbers apply:

  • mass: roughly 450,000 kg
  • altitude: between 435 km and 330 km.
  • with the mean radius of Earth 6371km, this implies
    • a semi-major axis of 6753.5 km
    • an orbital eccentricity of 0.0078

Then, using 5.972e24 kg for the mass of the Earth, the radius of the ISS' Hill sphere is about 2 metres.

The Hill sphere is a more complete definition of the sphere of influence, which is the region in space where the gravity of body B dominates over body C. For the ISS, the sphere of influence is about 15 cm.

So given these numbers, and knowing that it's true gravitational field is vastly more complex than just that little idealized sphere, it's pretty much impossible to orbit the ISS. As AlanSE noted, you can put things in apparent orbits, but these are normally only transient and will cease being close to the ISS after a few dozen of these "orbits". Another way to understand that is by looking at the three body problem, particularly at the derivation of the Lagrange points. The thing to note is that the Hill sphere is the region where there is orbital stability (in the phase space of the differential equations that is, not celestial orbits), meaning, body's that start just outside the Hill sphere will show diverging orbital behaviour, whereas bodies that start just inside the Hill sphere will show stable or converging orbits.

Things will change though if the ISS were placed in deep interalactic space, far away from any celestial body. In principle, perturbations from all those remote sources will be completely negligible, and the ISS would gravitationally dominate a vast region in space, making orbits about it possible. Don't expect these orbits to be fast though; I haven't run the numbers, but I expect anything thrown faster than a few mm/s will already be moving beyond ISS escape velocity. Also, don't expect these orbits to be anywhere near Keplerian; as I mentioned, the mass distribution of the ISS is nowhere near regular, and so the orbits about it will also deviate significantly from nice conic sections.

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In the conventional sense of a satellite this is wrong. For two very good reasons here.

  1. The space ship's GM term is so small that even the slightest movement will put the bacon outside its escape velocity
  2. Even if the space ship were HUGE, it becomes a Newton's cannonball problem, where it will travel back to exactly its release point

There is a very different kind of circular motion that can be observed, however. For the mathematical specifics you can find sufficient treatment here:

https://physics.stackexchange.com/questions/24816/what-exactly-is-the-microgravity-field-in-orbit

Basically, if your space ship is orbiting another body, like the Earth, then depending on how you release something, it may float in circles around your vessel. One way to see this is taking on complementary elliptical orbits. The spaceship achieves the high point of its orbit around Earth as the bacon achieves the low point of its orbit, and vice versa. It is a subtle detail of orbital mechanics that they can seem to dance around each other.

However, this is not a "true" orbit and the microgravity field of orbit has very unique properties. To begin with, two objects are not bound to each other - over time they can float apart with ever increasing distance. Objects can also swap back and fourth in just one direction as the orbits cross each other. They have videos of this on the ISS.

The Newton's cannonball problem would also apply. If you gave a nudge to a wrench from the ISS, it can make its way back to you within 90 minutes - the time taken for one orbit. The release motion to start it in an circular path around the ISS would require separating it first.

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