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Do we consider the dwarf planet Ceres to be in the inner solar system or outer solar system (or possibly neither / in between). It is located within the asteroid belt, but is the asteroid belt part of the inner or outer solar system?

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Inner. The entire asteroid belt is in the Inner Solar System (now). The definition of "Inner" vs. "Outer" is non-arbitrary, based on the current "frost line", approx. 5 a.u. radius.

https://en.wikipedia.org/wiki/Frost_line_%28astrophysics%29

https://en.wikipedia.org/wiki/Solar_System#Inner_Solar_System

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    $\begingroup$ Small footnote. As the sun grows older and more luminous, the frost line moves outwards. The asteroid belt and Ceres likely formed outside the frost line, as that would explain why Ceres has so much ice under it's surface. $\endgroup$ – userLTK Feb 1 '16 at 23:56

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