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gravity vs inertia

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As it's stated in Newton's law of gravitation, every object with mass attracts all other object with a force which causes acceleration. So basically there are infinite number of forces in our universe which affect our planet as well. My question is, can an inertifal frame (which has the net force of zero) exist in these condition, and does inertia itself play a role in determining acceleration due to gravity. If we have two objects many many miles aparat, and one has a much greater mass, will the heavier object still accelerate relative to the lighter one.

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