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. Why doesn’t the Earth move?

Answer 1

Explanation:

When an object falls freely under the influence of gravity, the net force exerted on it by the Earth is "mg". According to third law of Newton, the force exerted from one object to another have equal and opposite direction.

Let m and m' are the mass of object and earth respectively. Using third law of motion,

$F_{12}=-F_{21}$

We can ignore the mass of the object as the mass of earth is much more as compared to object. So, the acceleration of the earth toward the object is very less for other considerations.

Hence, the earth doesn't move due to its larger mass as compared to the object.

Answer 2

Answer:

We can see that the acceleration of the earth is inversely proportional to M,  and knowing that M is around 6x10²⁴ kg, the acceleration of the earth will be around 10⁻²⁵ m/s², practically zero. That is why, earth does not move significantly.

Explanation:

When an object falls freely under the influence of gravity, by second Newton's law, the force acting on the object will be:

$F_{OBJ}=m_{OBJ}\cdot a$

where a is the acceleration due to the gravitational attraction force.

The acceleration a in this case is g (gravity) which is around 9.81 m/s².  

Now, applying Newton’s third law we will have:

$F_{OBJ}=-F_{EARTH}$

Using the Newton's second law again,

$m_{OBJ}\cdot g=-M_{EARTH}\cdot a$

and we can calculate the acceleration of the earth.

$a=-\frac{m_{OBJ}\cdot g}{M_{EARTH}}$

We can see that the acceleration of the earth is inversely proportional to M,  and knowing that M is around 6x10²⁴ kg, the acceleration of the earth will be around 10⁻²⁵ m/s², practically zero. That is why the earth does not move significantly.

I hope it helps you!