Question

The earth attracts an apple towards itself, the apple also attracts the earth towards itself with the same force. Why then does the apple falls towards the earth, but the earth does not move towards the apple?

Answer 1

Yes, the apple attracts the earth with the same force as the earth attracts the apple with, around 1 newton.

But the earth does not move towards the apple

because there is not enough force to move an object that massive.

The more mass something has, the more force will be required to move it

For example, you require more muscular force to lift a weight of 10kg than 5kg.

So for an object that massive, 1 N is extremely little amount of force for it to move.