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I'm not so sure it will eventually fall into the sun. As it's moving through a vacuum, only gravity is acting upon it. Therefore, what else will cause this "closed system" to change?
Unless we consider the fact that space is not really a vacuum (a true vacuum) and that there are other, very very small, forces that come into play. Remember, even light has an effect upon matter. As such, there is also a constant force (albeit an almost neglible force) "pushing" it away from the sun.
Mr Mephisto
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