Why do objects accelerate due to gravity?
It depends on the context. If you are talking first semester physics or something like that, then the acceleration is due to the force of gravity according to Newton's law: a = F/m. If you are talking more sophisticated as in general relativity, then objects accelerate because spacetime moves past them. The surface of the Earth accelerates upwards at a rate of about 10 m/s<sup>2</sup> with respect to spacetime.
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