 I think you've all heard of Newton's story where apparently he was sleeping under a tree in his backyard and then got hit by an apple and then concluded that apples fall always straight down and therefore gravity is always straight down. You probably have also calculated the force of gravity as f equals mg. So fg equals mg where you have used a value of 9.8 Newton's per kilogram or meters per second square, that's the same unit, to calculate the force of gravity on any object on the surface of the planet earth. Hopefully you have learned that this law fg is mg, it's actually limited to the surface of the planet, well more or less. If we go higher up in the air, if we go further away from the surface of the earth, what will happen is simply that g, the value, is not going to be 9.8 anymore, Newton's per kilogram, it will go slowly down, the further we go away from the earth. But now what made this to Newton actually also concluded when he was hit by the apple is that the same force that makes the apple fall down is also what keeps the earth on the path around the sun, that keeps the moon on the path around the earth. It's the attraction between objects on a small scale like the apple that is falling down being attracted by the earth or a big scale, two stars that are really really far away from each other. So in the case of two stars, how do we calculate this? So let's say I have a star, really big one here of mass capital N, and then I have a small star here, small N, and they're going to be attracted to each other. So the small star is attracted by the big star, so we have a force on the small star by the big one, and the big one is attracted by the small one, a force on the big one by the small one. We already know according to Newton's third law of motion that the two forces must be the same, but now the question is how do we calculate this? If I use fg equals mg, which m do I use? The first or the second one, which g do I use? It's more complicated, but there is a universal law of gravity that tells us what this force exactly is, and it goes to following. We use a new constant that we call capital G, that depends on the mass of the first object times the mass of the second object, and then divide it by the distance squared, so the distance being from the center of one object to the center of the other object, and that is what we call the universal law of gravity. And what is capital G? Capital G is one of these universal constants. It turns out that capital G is 6.67 times 10 to the minus 11 Newton square meters per kilogram square. If you look at the units here, we have kilograms once or twice, so we have two times the kilograms, so one kilogram here, one kilogram here, divided by the square meter, and what we end up having is Newton's. So let's have a second look at this. So we concluded that on Earth, actually to be on the surface of the planet, to be exact, fg is mg, and then in the universal case, for everywhere we have fg is capital G, which is 6.67 times 10 to minus 11 Newton square meters per kilogram square times the mass of the first object, times the mass of the other object, over the distance between the centers of the object squared. Now this is a perfect example of where we have a law that seems to work sufficiently good in one context, which is if we are on the surface of the planet. That doesn't mean this law is wrong, it's just that it's limited to being on the surface of the planet. On the other hand, we have the universal law, which as the name suggests, is supposed to be universal, meaning if we use it for the surface of the planet, it should also work. So let's see what happens if we calculate the force of gravity on an object, let's say an object of mass, m, that's on the planet Earth, on the surface, so at the distance r from the center of the Earth. Now if we plug this in, we should get the same thing as we used just fg equals mg. So what I'm actually going to be doing is I'm going to assume the mass of the Earth is m, and if you look at our equation here, we have force of gravity is g times m, so in this case the mass of the Earth times the big m over r squared. So all of this, this first part, capital G times mass of the Earth in this case over r raised to the Earth square, should be equal to g, 9.8 and the spectrogram square. So my hypothesis here, and we're going to test it, is that g, g is equal to capital G times mass of the Earth over the radius of the Earth squared. So let's look up some numbers, so we're going to have equal 6.67 times 10 to minus 11 newton square meters over kilogram squared times the mass of the Earth is 5.97 times 10 to the 24 kilograms and then divide it by the radius squared, the radius of the Earth turns out to be 6.37 times 10 to the 6 meters squared square meters. So here we had kilograms of screen, but it should work. So I have, if you just look at the units, looking at the units you have the square meter that's canceled here and we have the kilograms of the Earth which is canceled here, oh here made a mistake, here it is squared so the square falls away, so I will get the unit newtons per kilogram and if you are plugging the numbers on my calculator what I get is just give me a second. So what I got is a value of 9.8134 newtons per kilogram, so which is exactly proving that if you're on the surface of the planet the universal law of gravity becomes the law of gravity as we knew it from high school.