Gravitational Acceleration by Calculus

[zking786]

While we are told that g = 9.81 m/s/s, this is only an approximation and isn't necessarily always true when we do precise calculations. Since, by the Universal Gravitation Laws, acceleration is determined by the mass of each object and the distance between the objects, we can't necessarily use a "fixed" gravitational acceleration of 9.81, since as we are free-falling gravity's acceleration changes as a function of distance. In fact, even mass changes as we accelerate. I've always wondered how we could compute the true free-fall for an object of mass m as it falls.

 

Any ideas?

[the tree]

Your awsners, and some nonsense by me, are in this thread.