1. The problem statement, all variables and given/known data Most physics problems that involve a falling body assume constant acceleration. How does one account for the changing acceleration if a body is dropped from a very high altitude? 2. Relevant equations With constant acceleration, d = (1/2)at^2 or t = sqrt(2d/a) but a is not really constant so How is this solved. 3. The attempt at a solution My first thought was to do a piece wise solution. Start at a given altitude, assume a small time, say one second and calculate the distance traveled. Then calculate the acceleration based on the new distance between bodies and continue. Is there a closed form solutio?