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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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Typically "gravitational force" is defined as $$ F = G\frac{Mm}{r^2} $$ Dividing both sides by $m$ we get $$ \frac{F}{m} = G\frac{M}{r^2} $$ $\frac{F}{m}$ is acceleration and a gravitational field will accelerate any "free to fall" object within that field at the acceleration of that field irrespective of the mass of the object. Gravitation is not a force but an acceleration

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