00:04
We have a diagram with point masses.
00:11
They're equal, capital m.
00:24
The distances here are a.
00:30
And then we have a point p, and we want to calculate the gravitational field at a distance r away.
00:52
So, first thing that i want to observe, is that the y component of the gravitational fields are going to cancel each other out.
01:09
The upper mass is going to pull upwards, and the lower mass is going to pull downwards, and they're going to exactly cancel each other out.
01:21
So if we look at, let me try that again, if we look at the accelerations here, in that direction.
01:39
Again, the vertical components cancel each other out.
01:42
So we're going to have horizontal component and horizontal component, where this is 90 degrees here.
01:56
The gravitational acceleration is g capital m over the distance squared.
02:22
But the distance which is here, is going to be the square root of a squared plus r squared.
02:45
So now we can write it as d squared equals a squared plus r squared, so it's going to be gm over a squared plus r squared.
02:59
All right, so that's going to be our acceleration.
03:03
Now, it's going to have a direction.
03:07
To it.
03:14
So the component in the horizontal direction is just going to be a part of the acceleration toward the upper point, for example.
03:42
And so that component, if we take r over d, which would be r over the square root of a squared plus r squared, that's going to be the fraction of the force that is in the horizontal direction.
04:17
So we also notice that there are two of them.
04:23
There's the upper one and the lower one.
04:26
So we have two of the accelerations, but we only want the portion that is in the direction, in the horizontal direction.
04:51
And i'm going to write i here to indicate horizontal direction...