- #1
kairama15
- 31
- 0
Hello, I am trying to find a function x(t) that describes a particle falling into a gravitational well from a certain distance. So, for example, I am trying to figure out the differential equation: F = m*(dx^2/dt^2) = -GMm/x^2.
Or simply, dx^2/dt^2=-GM/x^2
or even more simply,
x''(t)=-k/x^2 where k is a constant.
Does anyone know how to solve this or if it is even possible? I cannot find any resources online for this problem, but I feel like such a simple differential equation would have been attempted or successfully solved by now...
Or is there an easier way to solve this problem - finding x(t) in the gravitational well.
Thanks for any help!
Or simply, dx^2/dt^2=-GM/x^2
or even more simply,
x''(t)=-k/x^2 where k is a constant.
Does anyone know how to solve this or if it is even possible? I cannot find any resources online for this problem, but I feel like such a simple differential equation would have been attempted or successfully solved by now...
Or is there an easier way to solve this problem - finding x(t) in the gravitational well.
Thanks for any help!