Question

When an object falls freely under the influence of gravity, there is a net force mg exerted on it by the earth. Yet, by Newton’s third law, the object exerts an equal and opposite force on the earth. Does the earth move? Explain.

Short answer

The earth does not move because of its larger mass as compared to the mass of the object.

Step-by-step solution

Step 1. Newton’s third law

When an object falls freely under the influence of gravity, there is a net force $F_o=mg$exerted on it by the earth. According to Newton’s third law, the object should also exert an equal and opposite force on the earth.

Step 2. Application of Newton’s second law

According to Newton’s second law, the expression for the force on the earth can be written as

$F_E=M{a}_E.$

Here, $M$is the mass of the earth, and $a_E$is the acceleration of the earth.

From the third law of motion,

$\begin{array}{c}{F}_E=F_o\\ M{a}_E=mg\\ a_E=\frac{mg}{M}\end{array}$.

Step 3. Compare the masses of the earth and the object

As the mass of the earth is very large compared to the mass of the object, the acceleration of the earth becomes negligible, which is in the order of ${10}^{-25}g$. Hence, the object falls towards the earth, and the earth does not rise up towards the object.