00:01
So in this problem, we're going to look at newton's law of gravitation, and we have planets and coordinates, so we should start with our axis, kind of x and y, by convention.
00:12
And we have our planet over here, negative 8 times 10 to 11 meters in the x.
00:18
Now the exponents are kind of copy weirdly, so these are what i think they are.
00:23
Of course, changing the numbers doesn't change the process much.
00:29
We're saying this is in meters and then 10 to the 24 kilograms mass for our planet.
00:39
And then for our star, saying it's at 9 times 10 to 11 and 10 to the 11 meters, 6 times 10 to the 30 kilograms.
00:57
And so the force between these is going to be based on newton's law of gravitation, where the force by gravity is equal to g, the gravitational constant.
01:05
The mass of the first object, the mass of the second, divide by the radius between them squared.
01:12
And so we can draw a vector between these two places, and this is some radius, of course it's a vector, and we can find its length by looking at components.
01:24
And so we have here some change in x and some change in y.
01:36
And so we can find the radius by taking the square root of delta x squared, plus delta y squared.
01:46
And when we evaluate this, well, delta x here is going to be the second position minus the first, and so it's where we end up minus where we start.
02:03
So we started at 9 times 10 to 11 meters.
02:06
We can factor out that exponent though.
02:09
So 9 minus, and then we started at negative 8, so minus negative 8.
02:14
And this is times the 10 to 11 and all of that i think that is one too many nope that that was the right number of parentheses there we square that and then we add the delta y so we started at 10 to the 11 meters so that's one because we going to factor out that exponent again we subtract the starting position which was a 5 times 10 to the 11 wrap everything in the bracket so both are squared and so we see the radius between these two planets is 17 .46 times 10 to the 11 meters.
02:57
Leave the improper sign to differentiation just so we can easily see the relation.
03:02
So that's basically all the calculation we need to do to plug in to find the force of gravitation.
03:09
We need a gravitational constant though, we can look that up to be 6 .674 times 10 to the negative 11.
03:20
And that's in newton's per meter squared kilogram square...