# How is force of gravity between two objects equal?

I am not sure if my question seems bit naive. I get this feeling that i don't really the concept of force in itself , hence why I ask the foregoing question in the title. I know the formula to calculate force of gravity between two objects. I know how the force in the numerator of the formula is result of multiplication of mass of both objects , but I get confused as to why the force of gravity exerted by two objects over a distance has to be equal, especially when one object is really small (like a gas molecule, a ball, pen etc...) compared to the other (like planet earth, stars etc...). Like how can a small entity like gas molecule exert same force of gravity that earth exerts on it? I think my problem is that I think of force as a function of mass, more massive an object, more potential to exert force externally to other objects, and more potential to bear force exerted onto it without fracturing. So if earth can apply equal force on a smaller object, how can the smaller object withstand that force? If anyone could give a intuitive explanation to this, I would greatly appreciate it.

• Are you referring to objects in contact with each other such as an object on Earth's surface, or are you referring to objects at some distance from each other? May 18, 2021 at 18:07
• @AdrianHoward I am talking about objects that are at some distance from each other. May 18, 2021 at 19:29

This isn't just true of gravity per se. It's true of all forces, due to Newton's Third Law.

One of my favorite questions to ask of my intro physics students is the following:

In a collision between a freight train and a car, does the freight train exert more force on the car, or does the car exert more force on the freight train?

The answer, of course, is that by Newton's Third Law these two quantities must be equal. The effects of that force on each object are, of course, different; this is because the acceleration of each object depends on not just the force on it but also its mass. Specifically, we have $$a = F/m$$; and so for a given amount of force, the object of lower mass will accelerate more.

The same is true of the gravitational interaction between a pencil and the Earth. The force exerted on the pencil by the Earth must be the same as the force exerted on the Earth by the pencil. But the pencil is much much less massive than the Earth, so it accelerates much more than the Earth does once it is free to move.

• Hi Michael. Thanks for your response. I think the issue I have is that I conflate mass with force. More mass object has, more force it can exert on other object and more enforce it can withstand when force is applied to it. Given this misconception I suppose, I have a trouble reasoning how a particular like gas or pen withstand the force applied by something massive like Earth and also how they can get the force value to exert force on a massive object like Earth? May 18, 2021 at 18:03
• @newbeing Gravity is very weak on a per mass basis. Your arms can overcome the force applied by the ENTIRE Earth. And pens are held together by the far stronger electromagnetic force. I don't understand your confusion tbh. What is there to reason about something applying a small force on something large? Small is is not zero. May 18, 2021 at 20:18

Newton's third law requires it. In other words, momentum conservation requires it. Matter would self accelerate if it wasn't the case.

Newton's 3rd Law is really a statement about symmetry. There are no special objects in the Newtonian Universe that can apply force without feeling the reaction. If there were there would be all sorts of consequences. E.g. momentum wouldn't be conserved.

Your intuition with Gravity fails to appreciate how small the force of gravity is when a molecule or similar interacts gravitationally with the earth. The forces are tiny but still enough to affect the molecule, but the effect on the earth is so miniscule that it is not measurable.