00:01
So we have a planet that has a radius of 3 .24 times 10 to the 6 meters, and we know that the escape velocity on that planet is 7 .65 times 10 to the 3rd meters per second.
00:11
And ultimately, we want to find what the acceleration due to gravity on that planet is.
00:18
So to start, we know that the acceleration for gravity on any planet should be gravitational constant times the mass of the planet, times the radius squared.
00:29
So we know the gravitational constant and we're given the radius, so the only thing we don't have here is the mass.
00:36
So hopefully then using this information we'll define what the mass of the planet is.
00:41
So let's think about the escape velocity.
00:44
We know that the escape velocity for a planet should be the square root of two times the gravitational constant times the mass of the planet over the radius of the planet.
00:57
So it looks like we could solve for the mass of the planet here.
01:01
So we'll square both sides.
01:03
So v squared equals 2gm over r.
01:08
And then we can solve for the mass, and that should be v squared r over 2g...