- #1
nhmllr
- 185
- 1
So I looked at a neat derivation for what the minimun escape velocity is, and It was pretty clever. Because this is conserved:
KE + PE = 1/2 *mv^2 + -GMm/r
You can find what the velocity would have to be to get to infinity with zero velocity
1/2 *mvesc^2 + -GMm/r = 1/2 *m(0)^2 + -GMm/(infinity) = 0
1/2 *[STRIKE]m[/STRIKE]vesc^2 = GM[STRIKE]m[/STRIKE]/r
vesc = sqrt(2GM/r)
However, there is no "angle" term included in this. Does this mean that it can travel at this velocity at any angle and it will escape? What if the velocity vector is pointed right at the thing it's orbiting?
Thanks
KE + PE = 1/2 *mv^2 + -GMm/r
You can find what the velocity would have to be to get to infinity with zero velocity
1/2 *mvesc^2 + -GMm/r = 1/2 *m(0)^2 + -GMm/(infinity) = 0
1/2 *[STRIKE]m[/STRIKE]vesc^2 = GM[STRIKE]m[/STRIKE]/r
vesc = sqrt(2GM/r)
However, there is no "angle" term included in this. Does this mean that it can travel at this velocity at any angle and it will escape? What if the velocity vector is pointed right at the thing it's orbiting?
Thanks