00:01
All right, so we're told we have a satellite orbiting at a certain distance from earth.
00:05
Let's just pretend this is a satellite or something.
00:08
And it's at a height above the surface.
00:13
We're told of 1 .07 times 10 to the 7 meters.
00:19
And so we want to find the gravitational force acting on the satellite.
00:24
First off, so let's call this part a.
00:26
And the masses involved would be the mass of the satellite, which are totaled us 639 kilograms.
00:35
The mass of earth is, sorry, we'll write this about 5 .98 times 10 to the 24th kilograms, and the radius of earth will go with the number they give 6 .38 times 10 to the 6th meters.
00:52
So the gravitational force then is going to be newton's constant times the mass of earth, times the mass of the satellite, divided by r plus h squared, because that's the distance from the satellite to like the center of mass of earth.
01:11
And so if we plug in our numbers, this is going to be 6 .67 times 10 to the negative 11 cubic meters per kilogram per second squared times 5 .98 times 10 to the 24th kilograms times 639 kilograms then all divided by the total distance which is about 1 .708 times 10 to the 7 meters squared and that gives us a force of about 842 newtons or sorry not 840 i was misreading that 874 .2 .2.
01:53
So that's our force at that distance.
01:56
Part b then asks us to calculate the satellite's speed.
02:01
So the orbital velocity at that height is just going to be the square root of g times the mass of earth over the distance from the center of earth.
02:09
So that's r plus h...