00:01
Okay, hello.
00:03
So let's think of this situation here.
00:06
You have a mass, mass u equals 767 kilograms, and you place yourself between the moon and the earth.
00:19
So that's the earth.
00:24
Then there's you, a little you, and then there's a moon, the moon.
00:30
The moon.
00:31
Okay.
00:32
So the question here is, how far away in kilometers from the surface of the earth from the surface of the earth must you be so that the net force on you is zero meaning when there are two objects right or when there are objects they exert a gravitational force on each other so this system has three objects the earth you and the moon so all of you exert a force on each other.
01:13
So now let's look at you as the main object.
01:18
And let's simplify this drawing here.
01:21
So this is you.
01:23
This is the earth and that is the moon.
01:26
So the earth exert a force of fg on you.
01:33
Right? and then the moon exerts another force of fg on you.
01:38
Fg on you.
01:40
And so where should you be from the surface of the earth so that these two force they are equal? so how do we even quantify that in terms of a physical equation? so i want you to remember that f of g equals the gravitational constant of m1, m2, divided by the separation of the two objects squared.
02:19
Okay, so since we know that, oh, these two forces has to be equal, so we can find the gravitational force of each of them, and then we set them equal to each other.
02:35
Let's get started.
02:38
So we can start by saying that fg of earth to you is equal to the fg of the moon to you.
02:51
That means g m1, m2 divided by r squared of the earth to u equals g of m3 which is the mass of the moon and then m2 which is your mass because the moon is exerting force on you and we really don't have to care about the moon exerting the force on the earth because that doesn't really have anything to do with you divided by r of the moon to u being squared.
03:30
So we see that g is the same in both sides because it's a universal gravitational constant so we can drop it off.
03:39
That, ta -da.
03:41
All right, and we see that m2 is on both sides as well.
03:46
So we can cancel that out and cancel that out.
03:49
Now we're left with this simple, simple equation here.
03:53
Let me move the m2.
03:54
This up a little bit.
03:56
Okay, so we have m1 and m3.
04:00
So this is the mass of the earth and then the mass of the moon divided by the separation of you and the earth and you with the moon.
04:13
Okay, so the information that we're given here is that r from the center of the earth, the radius, well the separation of the center of the earth to the moon is this far away, which is equivalent to 385 -0 -000 -000 meters.
04:39
So every time you convert from kilometers to meters, you multiply it by a thousand.
04:45
All right, so this only tells you the distance between the two objects.
04:49
Now remember that you're in the center.
04:52
Okay, so how do we calculate that? so we know that this distance all the way here, it's going to be 385 0 0 0 0 0 meter, right? and so this is your distant from the earth.
05:19
And so this part right here from you to the moon, naturally it has to be 385000000 minus this part, which is x.
05:32
So when you add these two, the negative x and the positive x, they cancel out, you're gonna left with that one.
05:39
So we know that that's right.
05:40
Okay, so we're gonna substitute the distance from you and the center of the earth, r -e -y, with x.
05:49
So we have x squared.
05:51
Okay, now the distance from you to the moon is this one as we discuss.
05:57
So that's gonna be 385 -0 -0 -0 -0 -0 -0 minus x squared.
06:07
Remember, it has to be squared.
06:10
Okay, now what's the mass of the earth? it's given that the mass of the earth is 5 .97 times 10 to the power of 24...