Question

when an Apple falls towards the earth moves to meet the apples.Is this true?If yes'why is the earth motion not noticeable?​

Answer 1

Oh, yes. It's definitely true.

The answer to your question is:

Because the Earth has something like (6 x 10²⁴) times as much mass as the apple has.

So when equal, opposite gravitational forces act on both of them, the apple's downward acceleration toward the Earth is something like (6 x 10²⁴) times as much as the Earth's upward acceleration toward the apple.

The apple doesn't spend too much time falling, before it hits the ground and both bodies stop moving toward each other. In that time, the apple travels something like (6 x 10²⁴) times farther than the Earth does.

So if the apple falls a mile down from the branch of the tree, then the Earth moves something like 0.000 000 000 000 000 000 011 inch up toward it.

THAT's why Earth's motion is not noticeable to us.

Answer 2

This is theoretically true, because of Newton's 3rd law. If A exerts a force F(A->B) on B, then B exerts an equal but opposite force F(B->A) on A.

But the mass of the Earth is ‘slightly’ bigger than the mass of the apple. So the forces may be equal — but the accellerations will not be. We know the accelleration the apple gets: g = 9.81 m/s2. So we can calculate the accelleration the Earth will get, assuming the mass of the apple is 0.2 kg and comparing that to the mass of the Earth: 6.10^24 kg. So Earth will get an accelleration of g /3.10^25. So when the apple moved 1 m to the Earth, the Earth has moved 3.10^-26 m to the apple. The size of a proton is estimated to be a bit less than 10^-15 m, so the distance the Earth would move to the apple fits tens of billions of times in one proton.

So: yes, theoretically the Earth moves to the apple. Practically no, not even considering the fact that all around the Earth all kinds of things will be falling at the same time.