Earth exerts a force on an object equal to the objects weight. the object exerts a force on earth

I think the answer is it equal zero?

F = G * Mass earth * Mass object /radius of earth^2

The earth pulls the object exactly as hard toward the center of the earth as the object pulls earth toward the object.
Neither accelerates as a result because if the object is on earth it is pushing down on the surface and the earth surface is pushing up on the object.

No, the answer is not zero. According to Newton's third law of motion, for every action, there is an equal and opposite reaction. So, while the Earth exerts a force on an object equal to its weight, the object also exerts a force on the Earth. The force that the object exerts on the Earth is called the "reaction force" and is equal in magnitude but opposite in direction to the force that the Earth exerts on the object.

To understand how the object exerts a force on the Earth, you need to consider that forces are always interactions between two objects. When you exert a force on an object, such as pushing or pulling it, you are actually applying a force on that object and it is also applying an equal and opposite force on you. Similarly, the force of gravity that pulls objects towards the Earth is also an interaction between the object and the Earth.

In the case of an object's weight, it is the force of gravity pulling the object towards the center of the Earth. This force is the same magnitude as the force that the object exerts on the Earth, but in the opposite direction. So, the object exerts a force on the Earth just as the Earth exerts a force on the object, and these forces are equal but act in opposite directions.

To summarize, when an object experiences the force of gravity due to the Earth, the Earth also experiences a reaction force of equal magnitude but in the opposite direction from the object. Therefore, the force that the object exerts on the Earth is not zero.