00:01
All right, so let's say we have a satellite in orbit around earth, and we're told that at a particular point in this orbit, let's say this point we'll call this a, we're told it has a velocity of, let's see, let's get it right, 7 .1 kilometers per second, and it's at a distance, we'll call this ra of 1 .2 times 10 to the 7th meter.
00:26
So this is the orbital radius, not the distance from the surface of earth.
00:31
And the satellite itself has a mass of 2 ,000 kilograms.
00:36
And so the first part of this question, part a, asked, what's the total mechanical energy of the satellite at this point? so the total energy is going to be, of course, the kinetic energy plus the potential energy.
00:47
So we'll have one half mva squared minus, because the potential energy is negative, g times the mass of earth times the massive satellite over our a.
01:02
So if we plug in all of our numbers there, so it should give us a value of about negative 1 .609 times 10 to the 10th joules.
01:17
Now, the fact that it's negative shouldn't really trouble you because it's a bound state.
01:21
So any object in orbit really has like a negative energy, a negative total energy.
01:26
So anyway, if we continue, we want to know what's the angular momentum at this point.
01:32
So the angular momentum is just going to be the mass times the velocity times the radius in magnitude.
01:38
So 2 ,000 kilograms times 7 .1 times 10 to the 3rd meters per second times 1 .2 times 10 to the 7 meters...