00:03
All right.
00:04
So it looks like you have quite a few questions regarding this satellite in orbit and that it's beginning to lose its energy as it orbits and beginning to fall towards the planet.
00:17
So i'm going to get these set up for you and then hopefully that'll make sense, see that you'll be able to finish this homework assignment up.
00:25
So the first question a is, well, what's the velocity? well, this is the equation for orbital velocity.
00:31
Notice that the mass, the planet is what matters, not the mass of the satellite here.
00:38
So no matter what the mass of the satellite is, the velocity to maintain an orbit is always going to be found using the mass of the planet that it's going around.
00:49
So if we set this one up, we're going to have v as equal to b is equal to square root of 6 .67 times 10 to negative 11.
01:04
That's what capital g is stands for.
01:08
The mass of the earth, i looked that up on the internet, it's 5 .97, let me write correctly here, 9722 times 10 to the 24th, and that's in kilograms.
01:28
And this is all going to be divided by the radius of the orbit.
01:32
So they gave us two radii.
01:35
They gave us the, well, they gave us the heights or altitude of the satellite.
01:40
They didn't give us the radius of earth.
01:42
So i looked that up.
01:44
So you do have to add in the radius of the earth in these problems.
01:49
Because if you don't, you're not orbiting around from the center of the planet.
01:54
You're orbiting around the surface.
01:57
And so you would crash into the planet on half of orbit.
02:02
But so you've got to add that in.
02:08
And i've changed everything into meters because if we're going to do these problems where we're looking at jewels, we need to be in the standard units to get this to work out.
02:21
So everything needs to be in kilograms and meters and seconds for jewels to be our unit of measurement for change in energy.
02:30
So there's all the numbers for v.
02:32
That's the orbital speed.
02:36
The orbital period, i put that equation up here, too.
02:40
It's just 2 pi times the square root of.
02:43
This time it's the whole radius to the third power now.
02:55
So remember, we've got to add the radius of the earth in there.
03:00
And then we're going to divide that by 6 .67 times 10 to the negative 11th.
03:09
And the mass of the earth, which is 5 .9722 times 10 to the 24.
03:24
So there's the setups for the first two, a and b.
03:30
Just have to plug those into the calculator now.
03:33
So now we get to the more challenging stuff.
03:37
We've got this change in energy happening at a rate of 1 .1 times 10 to the 5th, jules, every rotation.
03:47
And it's a negative number because the changes is decreasing the mechanical energy.
03:53
So there's a non -conservative force occurring on this satellite.
03:59
Most of the time, that's due to a, we didn't get enough speed going to maintain the orbit, so it's gradually losing it.
04:11
There's not an air resistance out there, but there's a, the orbit is just nuts.
04:17
At the exact speed necessary to maintain that orbit forever.
04:22
I like the moon.
04:23
The moon is basically, they're going the same speed all the time.
04:29
It's slightly off, but very, very slightly.
04:32
So it's hard to get the exact value that you need to stay in orbit.
04:38
All right, so delta m .e is negative 1 .1 times to the fifth.
04:44
You need to multiply that by 1537.
04:47
So what i'm going to do is i'm going to find the total mechanical energy loss.
04:52
So if i do negative 1 .1 times 10 to the fifth, and i multiply that by 1537, that'll tell me how much total energy was lost.
05:03
So that's the first step to this.
05:09
Now, if that's the total energy loss, we need to figure.
05:17
They want us to figure out the altitude and speed and period of this system as this is.
05:24
Occurring and then they want us to find out the total force that's been that's being applied as well as if momentum is conserved so quite a quite a different group of questions here so let i'm just i'm going to answer the easier ones first so momentum is not the angular momentum is not could serve for the satellite but for the system it is so i'm gonna i'm answering that one first and then that and then the force that's causing it to slow down we we can that it's actually caused by the gravitation of earth but let's see here so we could say that the force times the distance traveled is equal to the change in energy so that that's the definition of work as work is f times d or the change in energy.
06:56
So if i could say here i would do like, so the force is going to be equal to, well, one revolution, so negative 1 .1 times 10 to the fifth divided by the circumference of the orbit.
07:19
So you just do 2 pi r there.
07:24
So that would be how you would solve those two.
07:27
Those are kind of the easier ones.
07:30
I think the toughest one here is going to be the altitude.
07:33
I'm trying to think here of what's the easiest way to do that...