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Basically if it becomes a rock, how long until it reenters and burns up?

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This really depends on your altitude first, and second your aerodynamic properties, the point in the solar cycle, and the mass of the object. The peak of a solar cycle increases drag on satellites as the upper atmosphere grows during that period of time. LEO varies dramatically, the altitude of the ISS is only stable for at most maybe a year without any kind of boost, while the first US satellite, launched into LEO, is still there after nearly 70 years.

The primary determination of lifetime is the altitude of the periapsis, although the apoapsis has an affect as well. While there are a number of variables, I found a paper discussing in great detail all of this, and it also has the following chart that gives a range of orbital lifetimes based on the orbital altitude.

Orbital lifetime

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  • $\begingroup$ What are the units on the horizontal axis? km? $\endgroup$ – SF. Feb 4 '16 at 13:12
  • $\begingroup$ Yes, although looking at it, I'mnot quite sure how realistic it is. Still... $\endgroup$ – PearsonArtPhoto Feb 4 '16 at 13:34
  • $\begingroup$ A lot will depend on apoapsis too. A highly eccentric, fairly low periapsis satellite will take lots and lots of passes lowering the apoapsis before periapsis begins decaying considerably, and the passes will be short and occupy very little time in its lifetime. $\endgroup$ – SF. Feb 4 '16 at 13:39
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It depends entirely on the orbit and the "aerodynamic" properties of the satellite. For example, the ISS is often quoted as descending between 70 to 100 metres per day and needs frequent boosts. (As geoffc has pointed out, it is an exceptional case due to the large area it covers.)

Another interesting case was GOCE. This earth observation satellite was designed to operate in low orbit, as low as 229km. According to wikipedia, its engine ran out of fuel on 21 October 2013, and it re-entered on 11 November 2013. (Between those two, a 155 km perigee was reported around 9 November though the exact timing of this is not necessarily precise.)

On the other hand, there are lots of old things still in orbit - some even operating, see this question

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    $\begingroup$ And the ISS is literally the worst case, being the biggest thing in orbit (right?), and having tons of frontal area for air resistance. Also depends on how high its initial orbit. Lesser affect the higher up you are, still within the bounds of 'LEO'. $\endgroup$ – geoffc Feb 2 '16 at 14:59
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    $\begingroup$ ISS isn't the worst case, but it is close. A paint fleck from the ISS is worse than the ISS actually. $\endgroup$ – PearsonArtPhoto Feb 2 '16 at 15:08
  • $\begingroup$ In general big objects decay slower than small ones because to a first approximation area scales with the square of dimension while mass scales with the cube of dimension. $\endgroup$ – Peter Green Sep 15 '17 at 0:19

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