Calculating Gravitational Attraction

Most people recognize that the gravitational force attracts them towards the Earth and keeps them stuck on the planet. But the gravitational force does so much more than that; it attracts any object with mass towards any other object with mass.

So, for example, this table is attracted gravitationally to the chair, and the chair is attracted to the table. This is a beautiful symmetric idea because it means that every object you can see around you is attracted to you gravitationally, and you are attracted to it. The reason we don't notice that attraction is because the force is so small.

So today, I'd like to show you how to calculate the size of the force of attraction between any two masses. In this example, we'll call this mass one and this object mass two. The force is proportional to mass one, so the larger mass one is, the bigger the force is. The force is also proportional to mass two; the bigger that mass is, the bigger the force is.

Now, the force is what we call inversely proportional to the distance between them squared. So if the distance between their centers is called r, then the further apart they are, the smaller this force is, and that makes sense. Now, to make this a true equality, we need to add Big G, the universal gravitational constant. This is just a number, a constant of the universe, which tells us how strong the gravitational force is. This number G is 6.67 * 10^-11 Newton m² per kilogram².

As you can see, it's a pretty small number, so the force is going to be relatively small. So let's do an example. Let's calculate the force of attraction between me and, say, João.

"Hello, this is my twin brother."

"Hi everybody!"

So the force F is going to be equal to the gravitational constant 6.67 * 10^-11 times my mass, which is 70 kg, times João's mass, which is 70 kg.

"Oh no, I thought you were putting on a little weight!"

"No, hey, 70 kg."

And divide by the distance between us, which is what, do you say, about 1.5 m?

"Don't forget to square it!"

"I wasn't going to forget!"

Okay, so this works out to be 1.45 * 10^-7 Newtons. There is a tenth of a millionth of a Newton attracting me and João. And that's not all, dude. Now, a Newton is the amount of force...