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Ball falls to earth, and earth moves to ball?!!

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Sandeepan Dhar Choudhary asked:

“When the ball falls on the earth, the earth also moves up to meet it. But the motion of the earth is not noticeable. Explain why?”

Answer:

The force exerted by the ball on earth is same as the force exerted by the earth on the ball. The acceleration of the ball towards earth is approximately 10 m/s2.

The acceleration of earth towards the ball = force/mass of earth ≈ 10-23 m/s2

When the earth moves towards the ball with this acceleration, the time required to travel the distance will be very large. If we assume a distance of 1m, and from the equation

we get t ≈ 1012 seconds whereas the ball reaches the earth in 0.4 seconds

[warning]In a nut shell, we can say that we cannot notice the motion of earth towards the ball due to the extremely low value of acceleration of earth towards the ball.[/warning]

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