 So we're going to start talking about gravitational fields, the idea that you can represent and understand the force of gravity with a set of rules called gravitational field theory. The first rule is that any object that has mass makes a gravitational field. So it's kind of fun to start talking about big things with lots of mass like planets and moons or like this big death star that kind of appeared about my house this morning. So let's take a look at these gravitational fields. Gravitational fields are made by any object that has mass. Fields can be represented by field lines which are vectors but they're kind of special vectors. The field lines always point towards the center of the object making the gravitational field but the field lines extend forever to infinity. In order to tell how strong the field is, we don't look at the length of the line like a normal vector, we look at how close together the lines are. The stronger the field, the closer together the lines will be. That means the field is a lot stronger here where the lines are closer together and it's weaker here, further away from the center of the object where the lines are further apart. This animation does a nice job of showing the gravitational field. Here we've got a little object, it's that green triangle, it's called a test object and it's feeling a gravitational field from the earth. Notice when it's closer to the earth, the gravitational field, that white line, is a lot larger. In this further way, the field is a lot smaller. Let's talk about how to calculate that gravitational field strength. So we're going to start off with the lowercase g, that's the symbol for gravitational field strength. It's got those absolute value signs around it, those vertical lines because this will only ever give us a positive value. It'll never tell us the direction of the gravitational field. We're going to calculate that gravitational field strength by multiplying together two numbers. We're going to start off by multiplying the universal gravitational constant, that's capital G. It's the same everywhere in the universe and for every problem we ever work on it will be 6.67 times 10 to the negative 11 Newton meters squared per kilogram squared. That unit is a total mouthful. We're going to multiply that by m, which is mass in kilograms of the object producing the gravity. So in our example, that would be like the death star. Then we're going to divide all of it by r squared. r is the separation from the center of the gravity producing object to wherever you're at feeling this gravitational field. Now of course the constant and the equation is on your data sheet. So if you need to look it up, there it is. But how do we take this idea for gravitational fields and turn it into something for force? Hey Newton! The first equation is just Newton's second law. Force equals mass times acceleration due to gravity. We're just putting in gravitational field strength for acceleration due to gravity. The mass here is the mass of the object feeling the gravitational field. So in this case it would be like me, not the death star. The second equation is called Newton's universal law of gravitation. Force of gravity is G, that's that universal gravitational constant again, times mass 1, which is the mass of the first object, times mass 2, which is mass of the other object, all divided by that r squared term again. Both of these equations have that 1 over r squared term and that means that they have an inverse square relationship. It means the further away you get from an object making a gravitational field, the weaker the field is. But if you get twice as far away, the field is 4 times weaker. And if you get 3 times further away, the field is 9 times weaker. If you make a graph of gravitational field or gravitational force against separation, you get this nice curved shape. This is the inverse square relationship in a graph. And again you can see how the force of gravity or the field of gravity gets 4 times weaker if you're twice as far away, 9 times weaker if you're 3 times further away, 16 times weaker if you're 4 times further away, etc etc. To get a little bit more practice with these calculations, check out this super old proportionality video where I go through a few examples using gravitational fields.