how can we guess that the acceleration due to gravity is.constant
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The acceleration due to gravity on Earth is not a constant, precisely because as you pointed out the gravitational force depends on a separation which is not constant.
Moreover, the Earth is not a perfect uniform sphere
it varies from one place to another place on the surface of the earth. It is flattened at the poles and bulged out at the equator.
but for answering questions we may take it as constant.
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