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Yes, but as the sun burns it loses mass, mostly as solar wind, and if you were to take that same sphere with a g factor of 1 and shrunk it down to a infinitly small radius, then you would have a singularity, however a very small one with a small event horizon, but a singularity with an increased g force. And if you expand the sun out enough it becomes nothing but, tada, a cloud of gas with a negligible gravitational pull. Gravity may not be solely determined by density, but density is a factor.
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Apathy: The best outlook this side of I don't give a damn.
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