text: how to find the velocity of an object at the exact center of earth? i understand that since a = gm/r^2 (gravitational pull), and mass of a sphere = 4/3(pi)(r^2) (assuming constant density) that a = 4/3(pi)gr=gr/r-initial. but how would one then find the velocity at any point? you have the acceleration; just integrate to get the velocity!