Question

When you drop a ball you find that the ball accelerates towards the Earth due to the mutual gravitational force experienced. By Newton’s third law, the Earth also should experience an equal and opposite force. Why do we not see the Earth accelerating towards the ball?

Answer 1

Consider 1 kg ball; the force experienced due to the gravity of the Earth is equal to mg, which is equal to 9.8 N. The Earth also experiences a force of -9.8 N. If we put, F = ma and consider the mass of the Earth as 6$\times$${10}^{24}$ kg. Finding the acceleration of the Earth as, a = $\frac{F}{m}$ which is equal to $\frac{9.8}{6\times {10}^{24}}$ = 1.6$\times$${10}^{-24}$ $\frac{m}{{sec}^2}$.This is too small to be noticeable.