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As the space is a vacuum and there is no friction in space, Can we assume that, if we place an object in gravity in exactly the right distance from a planet with gravity and in the right acceleration, it will orbit indefinitely, or until another object with a gravitational force will interfere?

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Yes. What else did you think was going on? – Emilio Pisanty Apr 17 '13 at 10:56

Actually no, because even in a perfect vacuum the object will emit gravitational waves and slowly spiral into the planet.

However this is a somewhat pedantic answer since for all but very high masses orbiting very close to each other, the gravity wave radiation is so small that the orbit would be stable on timescales far longer than the age of the universe. However the effect has actually been measured. The two white dwarf stars in the J0651 system are so close that they orbit each other every 13 minutes. The decay of the orbit due to the emission of gravitational waves has been measured, and the two stars are expected to collide in about 2 million years.

But lest you be mislead, let me emphasise that for a system like the Earth orbiting the Sun or satellites orbiting the Earth the orbital decay due to gravitational wave emission is utterly negligable.

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+1: Nice... I didn't think that gravitational waves would be a big problem to this question :-) – Waffle's Crazy Peanut Apr 17 '13 at 12:07
For pedantic's sake, let us not forget tidal effects for extended sources ;) – DilithiumMatrix Apr 17 '13 at 15:20
Depending on the compositions of the bodies the tidal effec can work the opposite way, the moon is receding from the earth because of the tidal – anna v Apr 17 '13 at 15:45
@Jiminion: doesn't my second paragraph make it clear this is a somewhat theoretical issue? – John Rennie Feb 15 at 17:45
Yes. Sorry. I skimmed the first sentence and saw the 2 million years. – Jiminion Feb 15 at 19:25

Let's clearly say that your first one is basically an assumption. Space is not completely vacuum. It does have atoms and molecules. There are a lot of questions here that address this point. Once an orbit is set over a massive object, the orbit stays there forever unless the mass of the object is changed or it is perturbed by another massive body interacting gravitationally.

This is why the satellites (good), their debris (bad) stay on orbit around the earth (causing a head-ache to us) with their initially imparted orbital velocity

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I would also like to add, before some smarty-pants comes along and says 'duh, the moon' that the moon IS a satellite and so is already covered by this answer – RhysW Apr 17 '13 at 11:13
The fact that space is not completely vacuum is important for orbit decay especially in low earth orbits. For instance, the ISS has to orient its huge solar arrays such that the cross sectional area is small. Otherwise drag from the sparse atoms and molecules would cause its orbit to decay too fast. This drag is the reason that periodically they have to raise the orbit of the ISS. – OSE Apr 17 '13 at 15:15

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