 In this video, we'll look at the form of the equation of Newton's Law of Universal Gravitation, which was discovered by Newton through observation. Newton's Law of Universal Gravitation is the underlying foundation for many of the concepts that we'll address in this course. You might have learned about gravity as F equals mg, but that equation is only accurate for objects on the Earth's surface, like apples. It's pretty impressive to think that Newton managed to explain both the motion of apples falling on the Earth and the motion of stars and planets in the sky with the concept of gravity through a single equation. Up until that point, nobody had any reason to believe that the two were related. So can we come up with any ideas of what variables may be involved in Newton's Law of Universal Gravitation? Given that we do now know that gravity is the force responsible for how apples fall and how we move around the stars in the sky, what can we intuit about the form of the equation for Newton's Law of Universal Gravitation? Well, let's consider a time long, long ago when dinosaurs roamed the Earth. And let's consider an asteroid is speeding through space and its path would take it very, very close to Earth. How do we think that gravity would affect this asteroid? And therefore, what do we think might be involved in this equation for gravity? Firstly, we know that gravity attracts mass, and so we may expect that we would see the asteroid experiencing an attractive force toward the Earth. If the asteroid had continued on its previous path, then it could have sailed right by, but gravitational force tends to pull the object toward the Earth in addition to its previous path. Now, the force on the object is based on that object having mass. The asteroid's mass is attracted to the Earth's mass, and therefore the mass of both objects must play a role in determining the force due to gravity. Taking this a step further, we know from Newton's Third Law that for every force there is an equal force in the opposite direction. So if the asteroid is attracted to the Earth, then the Earth must be attracted to the asteroid, as there's no reason the Earth should be different to the asteroid in our example. We could guess that the Earth must experience the same gravitational force, and that the mass of both objects must be represented equally in our equation. So the mass of both objects must be important. But wait! If we think that mass is important, then what about that huge, huge mass at the centre of our solar system? Why doesn't the asteroid ignore the Earth and get pulled towards the Sun instead? The reason the Sun may play a lesser role in determining the force acting on the asteroid is its distance, so it can get that the closer two objects are, the stronger the gravitational force between them. The Sun is so much bigger than the Earth that the distance must be very important. Finally, for the direction of the force, we've inferred that the force must act on both objects, and also, due to the attractive nature of gravity, that the forces must be pointing toward each other. So does the equation for Newton's Law of Universal Gravitation actually match these predictions? As it turns out, it is pretty close. The gravitational force acting on two objects is equal to the mass of each of the objects multiplied together and divided by the square of the distance between the objects. But it is also multiplied by another constant, which is known as the universal constant of gravitation. So Newton's Law of Universal Gravitation is as follows. The gravitational force is equal to the mass of the first object times the mass of the second object. Now, we'll divide by distance, because increasing the distance tends to decrease the effect of gravity. So the equation is divided by the squared distance between the objects, and finally, it is multiplied by a constant value known as Big G, which is the universal constant of gravitation. Big G is, as far as we know, a fundamental value of our universe. As for the direction of the force, the force on both of the objects, the Earth and the asteroid in our example, point toward the other object due to their mutual attraction. Note that the force on both of the objects is equal in magnitude, though it points in the opposite direction. So, what does Big G equal in our equation? It turns out from experimental observations that Big G is equal to 6.67 times 10 to the minus 11 Newton meters squared over kilograms squared. We now have the final form of Newton's Law of Universal Gravitation, which describes two objects' mutual attraction due to gravity, and is dependent on only three parameters, each of the two objects' masses and the distance between the objects. So what did Newton think of his realization? After Newton had theorized his Law of Universal Gravitation, he wrote the following, that one body may act upon another at a distance through a vacuum, or, in other words, a force between two objects due to gravity, which we know acts on masses at a distance without requiring any medium such as air to transfer the force, is to me so great an absurdity that no man could ever fall into it. So Newton's quote is referring to gravity, which Newton calls absurd. If you consider the mechanical forces that you've previously learned about and that Newton would have encountered, there is always a mechanical force at work that physically and directly pushes or pulls on another object. For gravity, this direct mechanical link is missing. We tend to take understanding gravity for granted nowadays, but if you think of it from Newton's perspective, you can begin to see how great the leap this realization was for his time.