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For instance do the planets around the sun experience drag from the near vacuum of space? Or do the (hydrogen) atoms in interplanetary have a mean velocity near orbital speeds? And if so would (small) celestial objects orbiting the sun in the opposite direction (not sure if these would all me comets, or also might be asteroids) experience a significant drag?

When searching for whether if this question has been asked before I also found this question in which the best answer also mentions gravitational waves. Would combining drag and gravitational waves significantly increase the dissipation of the orbital energy, compared to just gravitational waves? And would this mean that every orbit would eventually collide?

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Hmmm... I think you didn't notice that orbital decay caused by gravitational waves is very very negligible that the planet is barely disturbed until the end of whole universe ;-) –  Waffle's Crazy Peanut Jul 8 '13 at 15:45
@CrazyBuddy, I mentioned it so someone might be able to compare it with the possible drag. –  fibonatic Jul 8 '13 at 15:53
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The solar wind is a significant component of non-orbiting particles in the solar system. It exerts a pressure on the order of nanopascals (at the radius of Earth; it gets stronger toward the Sun), which seems tiny but given that it acts constantly for millions of years is strong enough to slowly change the orbit of small bodies. Small bodies are more strongly affected because they typically have a larger cross-section to mass ratio. The effect on comets is particularly spectacular:

comet showing a gas and a dust tail

There are a couple of other sources of "friction" in vacuum. You mention gravitational waves in your question, and this effect is reasonably well covered in the answers to the question you linked. Another effect is dynamical friction. This one is a purely gravitational effect, so the term "friction" is a bit misleading. This illustration below sums up the effect nicely; as a massive body moves through a collection of other masses (could be a protoplanet moving through gas, a star moving through a field of other stars, a galaxy moving through a cluster of galaxies) it pulls some mass toward it, forming an overdense wake so that there is a net force opposing the motion.

dynamical friction illustration

The last effect I want to mention is radiation pressure (or photon pressure). Light actually exerts a slight pressure all on its own, which has an easily measurable effect on small solar system bodies, and is probably one of the best ways to try and save the Earth from a killer asteroid (forget nukes, use paint!). It's also the principle behind solar sails.

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But doesn't radiation pressure (and solar wind) from the sun scales proportionally to $r^{-2}$, just like gravity and therefore give the sun an effective lower gravitational parameter? –  fibonatic Jul 8 '13 at 15:51
Not sure what you mean by that - yes, both effects scale as $r^{-2}$, but the solar wind has a variable intensity depending on solar activity and photon pressure is subject to shadows - a solar sail sitting in the shadow of the Earth wouldn't work very well... so putting them in as a correction to the gravitational potential is at best a very crude approximation. –  Kyle Jul 8 '13 at 16:52
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