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In the Warhammer 40k universe, there are planets where the population hasn't developed so far and are left in the feudal stage, (or the technology has degenerated so much it is back to the point).

Around one of those feudal planets is a Tempest Class Frigate where some mystical (non essential for the question) circumstances has removed the crew, so it has just continued the orbit.

How much time will it take before the planet gravity pulls the hulk in to the atmosphere?

For all intents and purposes, assume the planet is as near Earth-like as possible and the orbit matches the MIR Space Station [Orbital inclination: 51.6 degrees, Perigee: 354 km, Apogee: 374 km].

Answers with the final result, with the means to carry out calculations are considered, but answers with both the result and formulas are favoured.

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This question asks for hard science. All answers to this question should be backed up by equations, empirical evidence, scientific papers, other citations, etc. Answers that do not satisfy this requirement might be removed. See the tag description for more information.

  • $\begingroup$ Not doing the math for you. Also, there was mention of sunspot activity, implying that there are factors that change. Mir orbited between 184 and 262 miles in altitude but was deorbited in a controlled fashion. Skylab on the other hand had its orbit decay. One of the boosters that put it into an approximately 260 mile orbit (it was eccentric) took a little less than 2 years to deorbit. I hope that helps. $\endgroup$ – ozone Nov 1 '15 at 13:34
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    $\begingroup$ Its not gravity that causes the satelite to deorbit. If gravity was the only force to contend with the hulk would stay on orbit forever. Satelites in LEO deorbits due to athmospheric drag. $\endgroup$ – Taemyr Nov 1 '15 at 14:07
  • $\begingroup$ The ISS, which is much larger and less aerodynamic than MIR needs aprox 1.4m/s in additional deltaV every so often to remain in orbit. When the Space Shuttle did the boost it required @ 200kg of fuel to be burned to add the extra velocity. Sadly, since the reboots are done at irregular intervals, it is difficult to make any clear calculations. Since most large satellites are deorbited under control, it is also hard to say from experience how long it would take, but I suspect that a large vessel would deorbit in about 2 years without reboosting. $\endgroup$ – Thucydides Nov 2 '15 at 1:43
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Things in orbit don't de-orbit because of gravity; in fact, gravity is half the reason things are IN orbit (the other half being the fact that they're going really really fast).

In ideal conditions, your ship's orbit would never change. There are two non-ideal things which will change the orbit over time:

  • Non-spherical earth: this will cause the orbital parameters to change, though I have been unable to find a good source of the math to tell me how. AFAIK though these effects are relatively minor.

  • Atmospheric drag (yes, there's atmosphere still up there): half the reason things are in orbit (and part of the definition of their orbit) is their speed. Drag will slow them down, thereby changing their orbit. Drag is effectively the same as a light retrograde burn, and retrograde burns is one of the most effective ways to lower your orbit - so effectively you're continuously lowering your orbit. How long it takes for this to effectively de-orbit your barge depends on a lot of factors, including how aerodynamic the ship is.

I found one interesting site:

http://orbitaldebris.jsc.nasa.gov/faqs.html

12). How long will orbital debris remain in Earth orbit? The higher the altitude, the longer the orbital debris will typically remain in Earth orbit. Debris left in orbits below 600 km normally fall back to Earth within several years. At altitudes of 800 km, the time for orbital decay is often measured in decades. Above 1,000 km, orbital debris will normally continue circling the Earth for a century or more.

So, without orbit maintenance, it would be reasonable to assume a few years before decay.

Another note:

However, interstellar spacecraft must have mastered the ability to transfer energy with them efficiently for space travel (i.e. they'd never work with today's rocket technology) so engine power is effectively a non-issue in planetary orbit. Also, if the ship is not designed for re-entry, then it must have craft that is - presumably also with the same level of engine efficiency. A ship like this might instead be in geosynchronous orbit instead of LEO because it can be very beneficial to continue seeing the part of the world you cared about to begin with (or to continue being in contact with the landing craft you sent down). The primary reason things nowadays are in LEO is because it would just too uneconomical with our current rocket technology to not do so.

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