When an apple falls towards the earth, the earth moves up to meet the apple. Is this true?If yes, why is the earth's motion not noticeable?

According to Newton's third law, action and reaction are equal and opposite.

There is a gravitational force of attraction that acts between then falling apple and the earth. The magnitude of acceleration imparted by this force determines which of the bodies (the apple or the earth) will have a larger magnitude of acceleration.

Given that the acceleration imparted on the apple and the earth by the gravitational force F  is;

a = F/m

where m is the mass of the object.

We can easily see that the earth has a much larger mass than the apple hence the magnitude of acceleration imparted to the apple by this force is much larger the magnitude of acceleration imparted to the earth by the same force.

Hence, we can see the apple moving but not the earth.

For a definition of gravity see

link

Yes, this is true.

-- While the apple is falling, the same gravitational force acts on both the apple and the Earth.

-- The mass of the apple is somewhere in the neighborhood of 1/4 kg.

-- The mass of the Earth is about 5.972 x 10²⁴ kg.

-- Since the Earth has roughly 2.389 x 10²⁶ times as much mass as the apple has, the apple has roughly 2.389 x 10²⁶ greater acceleration than the Earth has, and moves roughly 2.389 x 10²⁶ times as far down as the Earth moves up, before they smack together.

-- That's why you don't notice the Earth's motion.

-- Also, you're standing on the Earth, moving up with it, toward the apple.  Maybe it would be different if you were sitting on the apple, riding it down to the ground, and you were able to notice the motion of the ground coming up to meet you at a speed that's 0.00000000000000000000000000419 of YOUR speed.  

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explanation:

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