00:01
So for this problem, given the orbital period of a satellite going around the earth, we want to determine how far off the earth's surface it's sitting.
00:14
So in order to do this, we need an equation that relates the period of an orbit to the radius of that orbit.
00:24
And that's going to be kepler's law.
00:27
Kepler's third law, specifically this right here.
00:35
So this r in kepler's law here is the distance from the center of the object we're orbiting all the way out to the object that's orbiting.
00:47
So you can see from our drawing here that that's actually going to be the sum of r sub e, the radius of the earth, and r sub s, the distance from the surface to the orbiting object.
01:00
So what we should be able to do here is just substitute in for r and solve for r sub s, which is the distance that the satellite is sitting off the surface of the earth.
01:16
Everything else should be known.
01:18
We'll have to look up the mass of the earth and the radius of the earth, but these are all just constants.
01:23
So let's go ahead and substitute in 4 pi squared over gm's e times r sub e plus r sub s cubed.
01:51
I'm going to multiply both sides by gm over 4 pi squared.
01:58
So we should have g m sub e t squared over 4 pi squared equals r sub e plus r sub s cubed and then we'll take the cube root of both sides and subtract r sub e so what we left with r sub s equals all this stuff g m sub e t squared over 4 pi squared the 1 third power since we took the cube root minus r sub e okay so now i all we have to do is substitute in all our values here.
02:55
So remember the universal gravitational constant is about 6 .67 times 10 to the minus 11 meters cubed over kilogram second square...