But this law of universal gravitation wasn't quite enough, because

that only tells you how much an object is being pulled.

But what you also need to know is that how the object is influenced by the pull.

And that is given in terms of this another famous equation called F equals ma.

Which you might have actually studied in high school physics class.

So, in this equation, m stands for mass.

And, and this idea is called inertial mass.

Namely that if you are given a force, and

if the mass is bigger, you get less acceleration.

So a stands for acceleration.

Namely, that the mass is a measure of how

difficult it is to change the motion of an object.

And that I think is plainly clear just by comparing these two objects.

So, suppose you provide the same push on a tank and on a little kid on this tricycle.

And with the same push, you can hardly move this tank at all.

Right?

Because it's so massive.

But with the same little push that little poor kid may fall down.

So you can really change the, the course of his motion.

So, which one is easier to move is really determined by how massive the object is.

Heavier it is, it is very difficult to change the course of the motion.

So, m in F equal ma really stands for how

difficult it is to change the motion of an object.

So, as you see in this animation the sun is not at

the center, because the orbit is an ellipse, not a complete circle.

And as the planet moves around the Sun, it

gets pulled more strongly when it's closer, but gets

pulled less forcefully when it's farther away, so that

changes the course of motion at the same time.

But the most important thing about this is that

by combining the two equations we talked about.

F equals ma,

that tells you how the motion gets affected by the pull.

And how big the pull is, and that's the Universal Theory of Gravitation.

If you put these two equations together, you

can fully explain this elliptical orbit of individual planets.

And to work that out with Algebra, it's a little

complicated, I'm not going to actually show that, precisely my lecture.

But you're welcome to solve one of the

problem sets where you can verify that this elliptical

motion really comes out from these two equations.

So, by combining these two equations, F equals ma and F goes like the GM over r

squared, that's the inverse square law of gravity, then you

can fully understand these elliptical motions of individual planets.

And therefore, you'll fully understand the origin of four seasons.

So that's the way a physical theory is supposed to give

you a deep understanding of what's going on in our universe.

And it actually, happens at incredible speed.

If you measure how fast the earth revolves around the

sun, it's at the speed of 30 kilometers per second.

You might feel dizzy about this.

It's incredibly fast, but nonetheless we're not throwing away from

the earth, because again we're bound tightly by the gravity of

the earth towards the earth, and we're not we don't have

to worry about this, its fallingoutside from, from the planet.