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## Main Question or Discussion Point

I recently saw the equation [tex] v= \sqrt{2 \int_{r_1}^{r_2} \frac{GM}{r}} [/tex] (G=gravitational constant, M=larger mass, r=radius). I know it has to do with the velocity of an object attracted by a larger object's gravity, which is pulling it a distance [tex] r_2-r_1 [/tex] taking into account the change in force of gravity. My question is: does this equation represent the instantaneous velocity at r1 or the average velocity? Also, how can this equation be changed to include the force of gravity of the smaller object on the larger one?