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It might seem obvious but i can't imagine how is gravitational pull is different from acceleration due to gravity?

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Gravitational pull is the cause - the force. Acceleration is the consequence of this cause, assuming that the gravitational force is not cancelled by another force.

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The term "gravitational pull" is probably meant to convey force, which is related to but distinct from acceleration. Under a common assumption of constant mass (which may be false in general, e.g., a rocket), F = ma by Newton's second law, so you don't lose much except conceptual precision in very simple situations... but such conceptual difference can become rather important.

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