Assuming Newtonian gravity (which should suffice) for an object launched from the surface of the Earth we get the equation

from energy conservation, where v0 is the initial (launch) speed, M is the mass of the Earth, R is the radius of the Earth, G is the Universal Gravitation constant, m is the mass of the object, and y is the height above the Earth. (Note:

) Or we could use Newton's 2nd:

(Positive downward.)

Neither equation is trivial to solve for y(t). I can't find my notes on how I did it, but I seem to recall solving the energy equation for y(t) at some point in the past. However, I don't recall getting any great inspiration from it either.

-Dan

The more I stare at the energy equation, the more I doubt I solved it. I may have solved a first or second approximation where y is small.