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Originally Posted by Phage
My understanding of gravity is this: If you have two masses they will orbit around each other. If one of the masses is larger, the smaller object will orbit it much more than the larger object orbits the smaller (but it still does a little bit). Planets can be detected around distant stars by watching for this "wobble".
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You're right. I was talking about an approximation (or a limit if you want to think of it that way). For example, engineers don't have to consider the mass of a satellite when figuring out what speed is needed to make it orbit the earth (of course the mass does matter when figuring out how to get the satellite up there at the proper speed). The effect of the satellite's mass on the earth is completely negligible.
The mass of the earth is about 1/300,000 that of the sun, so the wobble that it induces in the sun is exceedingly small. The orbit of the earth would not change significantly if its mass were half or double its real value.
More formally, if a given distribution of matter is somehow fixed in place, the motions of extra particles that interact only through gravity will be independent of their mass (in the limit that such particles have zero radius). This sounds like a ridiculously idealized statement, but most astrophysical situations satisfy it to a very high degree of approximation.