A compound acceleration problem

After too much beating my head against the wall on this problem, I've decided to ask for help. Unfortunately, this is not homework, first off, I'd be much younger, but mostly because if it were, then either the answer would be in the textbook, or it would be in one of the hundreds of references I've examined. This has to do with a free-falling object. All the sources I find treat the calculus of gravity as if it were a continuous, unvarying field, and almost always assume s = 32f/s^2. Position, velocity and acceleration are all handled just fine as long as the acceleration remains absolutely constant.



I would like to define formulas to calculate velocity, distance, acceleration and rate of change of acceleration over time as a free-falling object approaches a large mass. The rate of change of acceleration is the sticking point. As the falling object approaches the large mass, the acceleration should increase in relation to the square of the distance. So, the acceleration is in fact not constant as so many papers, articles and text books like to claim.



So, with a known central mass, and a starting distance for a stationary particle, how do I determine the instantaneous distance, velocity and rate of acceleration at any given time? By 'stationary' I intend to mean with respect to the much larger mass. And I say 'much larger' because I don't want to deal with how much the large mass moves toward the tiny particle.



Any help would be appreciated.

via JREF Forum http://forums.randi.org/showthread.php?t=270461&goto=newpost