# Is the Earth's gravitational force limited by the mass of the second object?

Basically, why is the force exerted by the earth on a feather different than the force exerted by the earth on a brick? The brick has more mass, but why does that impact the force the earth exerts on the brick relative to the feather? I would intuitively think that the gravitational force the earth would exert on any object to be constant.

Since $$F = ma$$ and the objects would be near the earth's surface

$$F= \frac{Gm_1m_2}{r^2}$$

which becomes $$a=g$$

So, $$F=mg$$

So, since the mass of the brick is greater than that of the feather, the force the earth can exert on the brick increases? Is the earth's "pulling power" limited by the mass of the second object in any scenario, meaning that the earth exerts a limited force on the brick and the brick would also exert that same force on the earth?

Also, is it for this reason that the force between the objects is the same, given by Newton's third law? Intuitively, the earth is so massive and its distortion on spacetime should be constant, so to me the only reason why the force between an object and the earth (or any large mass) would change is due to the change in mass of the second object.

Would Gravitational field strength have anything to do with this? In my book, it says that gravitational field strength is the force of attrition per unit of mass. So does that confirm that the earth can only exert a certain force on an object depending on that objects mass??

• the earth can only exert a certain force on an object depending on that objects mass? Forget “can”; think “does”. Mar 25, 2021 at 0:36

You are close to the reason due to Newton's third law. Forces are interactions. The interaction between two objects with mass depends on the mass of both objects. If it only depended on one of the objects and not the other, then how would we (or the universe) choose which object's mass matters (pun always intended)? We always say colloquially "the pull of the Earth" just because that's how it feels to us; a much more massive object pulling on us and everything around us. But in reality it's an interaction: the force exists between the objects, both "pulling on" each other.

The concept you seem to prefer more is the idea of the gravitational field rather than the gravitational force. The gravitational field of the Earth is indeed only dependent on the mass of the Earth and has nothing to do with any interactions between the Earth and other masses.