Assuming Newtonian gravity (which should suffice) for an object launched from the surface of the Earth we get the equationOriginally Posted by ThePerfectHacker
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:
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.
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.