Is the moon pulling the earth towards it ?

We said earth has gravity. We also said sun has bigger gravity pull. Does the moon have one too? If so is it pulling us in? You know, Newton, when he had his famous eureka moment, sitting under the apple tree and watching an apple fall ( you know the rest ) he said, even the apple has gravity and exerts a pull on the earth! To understand this better, we need to dig a little deeper into gravity and the factors influencing it.

Let's start with wikipedia's definition of gravity. It is a natural phenomena by which all physical bodies attract each other. Well, there is our answer. Moon being a physical body, is pulling the earth too. But how much is the pull? Didn't Newton think of it ever ? Sure, he did. And has thought of it enough to come up with a theory and a formula for it (Hail Newton )

F = K *m1 * m2 / r2

(Read it as, m one times m two divided by r squared. K being some constant)

Please don't get intimidated. All that he means is, gravitational force depends on the mass of the two concerned bodies and is inversely proportional to the square of the distances between them. That means, more the mass of the objects involved, more the force. And lesser the distance inbetween them, more the force (kinda)

Let's try and apply this formula to both the Earth and the Moon. Lets say m1 is the Earth and m2 is the Moon and r is the distance inbetween them. Sounds simple. But wait, hey , if I subsitute their values I end up getting one value for f, or force. Does that mean the force exerted by the Earth on the moon is the same as the force exerted by the moon on the Earth? In that case, why dint the Earth go around the moon? Or even better question, equal and opposite forces, why didn't they cancel out each other. Hmm... bit of a puzzler isn't it?

It actually isn't that much of a puzzler if you already knew Mr.Force quite well ! Let's go to wikipedia again, this time for definition of force.
It is something that tends to change the motion of an object. Can be described by intuitive concepts such as push or pull. 

Let's handle the second question first, Equal and opposite forces should cancel each other, true. But when ? When they act on the same object. Here the forces act on different objects, that is, the Earth's gravity acts on the moon and the moon's gravity acts on the Earth. So two different objects. Cancellation is out of the question now isn't it?

The first question now. The same magnitude of force acts on both these huge bodies. Looks like how they react to it depend on them. That's it. That's the answer.Do you see it? The Earth being so huge, requires more force to make it move. The moon being comparatively smaller, is easier to be influenced, as in, the amount of force exerted by the Earth is sufficient to move the moon, but the same amount of force exerted by the moon is not sufficient to move the Earth, or atleast so we see! Let's just say the Earth is stronger than the moon.

Looking at it with the Force formula

F= m* a

(Force equals mass into acceleration )

This equation also says the same. Given the same force, the body with the bigger mass moves lesser than the body with a smaller mass. How much they move and do they move at all, will all come to you if you put in the numbers there, but hey, I always shy away from big number calculations. All I need is an understanding and I'm content.

So.. the moon does try attracting our Earth with the same force. But our Earth says, no Mr.Moon(/Ms.Moon), I want you to come to me!