# How did Newton answer this question? (mutual gravitational attraction)

## Main Question or Discussion Point

I didn't study physics in college nor any other science major, but I love physics and read a lot about it. Still I find troubling contradictions in my understanding of Newton's interpretation of gravity.

For starters, how can the force of gravity be directly proportional to the two masses? If two bodies with equal masses are trying to pull each other this will cause them to repel each not attract each other, because each mass is exerting a force of gravity in a direction opposite to the direction of the gravity of the other mass, making the outcome of the two equal opposite forces = zero!

I imagine them like two people pulling each other with the same force, this obviously wont cause the two bodies to move closer to each other, like two kids with equal mass playing tug of war. Therefore, if a planet was close to Earth, according to Newton, they will both move closer to each other, but according to the people pulling each other, they will never touch each other!

What are you guys think? Is this a flaw in Newton's theory, or am I missing something?

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berkeman
Mentor
I didn't study physics in college nor any other science major, but I love physics and read a lot about it. Still I find troubling contradictions in my understanding of Newton's interpretation of gravity.

For starters, how can the force of gravity be directly proportional to the two masses? If two bodies with equal masses are trying to pull each other this will cause them to repel each not attract each other, because each mass is exerting a force of gravity in a direction opposite to the direction of the gravity of the other mass, making the outcome of the two equal opposite forces = zero!

I imagine them like two people pulling each other with the same force, this obviously wont cause the two bodies to move closer to each other, like two kids with equal mass playing tug of war. Therefore, if a planet was close to Earth, according to Newton, they will both move closer to each other, but according to the people pulling each other, they will never touch each other!

What are you guys think? Is this a flaw in Newton's theory, or am I missing something?
Um, no. Put the 2 kids on frictionless ice and let them pull on the rope. The attractive force pulls them together. Two masses in space do the same thing via gravity.

Nugatory
Mentor
this obviously wont cause the two bodies to move closer to each other, like two kids with equal mass playing tug of war. Therefore, if a planet was close to Earth, according to Newton, they will both move closer to each other, but according to the people pulling each other, they will never touch each other!
Call the two bodies A and B. A's gravitational field produces a force on B that pulls B towards A; meanwhile B's gravitational field produces a force on A that pulls A towards B. That's about as attractive as can be.

The tug of war game is different because both kids have also dug their heels into the ground and are using their legs to resist the force of the rope pulling them towards one another. As Berkeman says... Put them on frictionless ice and the rope would pull them towards one another while their feet skitter and slide across the ice.

Call the two bodies A and B. A's gravitational field produces a force on B that pulls B towards A; meanwhile B's gravitational field produces a force on A that pulls A towards B. That's about as attractive as can be.

The tug of war game is different because both kids have also dug their heels into the ground and are using their legs to resist the force of the rope pulling them towards one another. As Berkeman says... Put them on frictionless ice and the rope would pull them towards one another while their feet skitter and slide across the ice.
Um, no. Put the 2 kids on frictionless ice and let them pull on the rope. The attractive force pulls them together. Two masses in space do the same thing via gravity.
thank you both for bothering to reply, but I really don't think that what you said is true, and you can try it. let two people tie the rope around their bellies and start pulling each other opposite ways, if their pull (force of gravity) is equal they will not move at all!

Nugatory
Mentor
thank you both for bothering to reply, but I really don't think that what you said is true, and you can try it. let two people tie the rope around their bellies and start pulling each other opposite ways, if their pull (force of gravity) is equal they will not move at all!
Look at what I said about A's force on B and B's force on A again.... A is reaching out to arms' length, grabbing the rope at the end of his reach, and then tugging it towards his belly to produce the same effect as his gravity pulling on B.

When the two people tie a rope around their bellies and start pulling each other opposite ways, take them A and B,then it is in NO way related to gravity,as A isn't actually trying to pull B,but rather trying to move away from him and so is B trying to move away from A,but they can't because of the attached rope.Now,for the answer to the previous question,take it as A pulling B's shoulder and B pulling A's shoulder(they will kind of hug).So ,two objects of equal masses apply equal force(pull) on each other and accelerate equally.Moreover,they would meet at the center of the distance between them.

A.T.
I find troubling contradictions in my understanding of Newton's interpretation of gravity.
It seems more like your confusion stems from misunderstanding of Newton's Laws of Motion:
http://en.wikipedia.org/wiki/Newton's_laws_of_motion
Try to understand those first, and how they apply to systems of multiple interacting bodies.

For starters, how can the force of gravity be directly proportional to the two masses? If two bodies with equal masses are trying to pull each other this will cause them to repel each not attract each other, because each mass is exerting a force of gravity in a direction opposite to the direction of the gravity of the other mass, making the outcome of the two equal opposite forces = zero!
I have no idea how you came with repulsion, if the sum of forces is zero. Zero total force, on the system of both bodies, merely means that the common center of mass of that system doesn't accelerate. But that doesn't prevent them from accelerating towards each other.

Dale
Mentor
thank you both for bothering to reply, but I really don't think that what you said is true, and you can try it. let two people tie the rope around their bellies and start pulling each other opposite ways, if their pull (force of gravity) is equal they will not move at all!
berkeman and Nugatory are both 100% correct. Your tug of war analogy fails because the people are interacting with the ground as well as the rope. Think of two astronauts tethered with a rope in deep space so that you eliminate all other forces. If they pull on the rope then they will both move towards their mutual center of mass. Since you cannot push with a rope, that will be the only type of motion possible in this scenario.

FactChecker
Gold Member
Two people playing tug of war are trying to pull themselves away from the other. They are trying to drag the other side along, but their force is to move away from the other. If one side let go as a surprise, the other would fall backward. That is the opposite of gravity. If they were gravity, they would run toward each other, the rope would go limp, and they would crash into each other. That is why you are reaching the opposite conclusion.

Two people playing tug of war are trying to pull themselves away from the other. They are trying to drag the other side along, but their force is to move away from the other. If one side let go as a surprise, the other would fall backward. That is the opposite of gravity. If they were gravity, they would run toward each other, the rope would go limp, and they would crash into each other. That is why you are reaching the opposite conclusion.
Exactly! This is what I'm trying to say, thus we have two scenarios:

1- If you imagine the force of gravity as a force that makes each mass pull the other mass towards it, then the analogy of the tug of war game should apply accurately, the sum of the two opposing equal forces is zero.

2- If you imagine the force of gravity as a force that makes each mass pushes itself towards the other mass, then they would collide in the common center.

Nugatory and Paradox101 made it clear that each mass stretches its "arm of gravity" to the other mass and pulls. We can create a similar scenario: Two people having two ropes will tie one end around the body of the other person and hold the other end of the rope with their hands, then they will start pulling standing on Berkeman's frictionless ice, they will never collide! In fact they wont move one inch closer to each other!

We can create another similar scenario: let's fix small wheels under the shoes of the two people -to make the effect of friction negligible-, and then each one will hold the neck of the other and start pulling with the exact same force at the exact same time. Again, it's impossible for them to "hug each other"! It's true that each mass is being pulled towards the other, but let's not forget that each mass is pulling the other with the same force, making each mass experiencing two opposing equal forces!

The two masses will come closer to each other in only one scenario, that is if the force of gravity is a force the moves the mass itself to the other mass, as in two lovers running to hug each other. But that's not the case in Newton's understanding of gravity.

You can't have the cake and eat it too, the result of two masses exerting a pulling force on each other is the opposite of the result of two masses pushing themselves to each other. Experiment, when possible, is the best judge on any theoretical dispute, and I believe we can experiment those ideas on ice, roller shoes or cars and see if two equal masses stretching their gravitational hands or ropes on each other will collide as Newton said or not.

I hope I made myself clear..

It seems more like your confusion stems from misunderstanding of Newton's Laws of Motion:
http://en.wikipedia.org/wiki/Newton's_laws_of_motion
Try to understand those first, and how they apply to systems of multiple interacting bodies.

I have no idea how you came with repulsion, if the sum of forces is zero. Zero total force, on the system of both bodies, merely means that the common center of mass of that system doesn't accelerate. But that doesn't prevent them from accelerating towards each other.
I actually read that wikipedia page a lot more than you think, and read way more resources on that subject, yet still couldn't find a clear answer. I wish you clarify it for me if you know more than I do.

And you are right I might've not been accurate when I used the word "repulsion", I meant to say that the force of attraction one mass exerts on the other will be canceled by the force of the other equal mass. The common center you refer to is true when the two bodies are self-pushing each other toward each other or being pushed together by outer forces. But if that system only contains the forces of the two equal masses then I can't imagine them to collide for the reasons I illustrated on the previous reply.

jbriggs444
Homework Helper
2019 Award
Nugatory and Paradox101 made it clear that each mass stretches its "arm of gravity" to the other mass and pulls. We can create a similar scenario: Two people having two ropes will tie one end around the body of the other person and hold the other end of the rope with their hands, then they will start pulling standing on Berkeman's frictionless ice, they will never collide! In fact they wont move one inch closer to each other!
In fact they will. Both ropes will be under tension. Both will be pulling each person in the direction of the other. Each person will be subject to two forces, both in the same direction. Each person will move toward the other.

Dale
Mentor
1- If you imagine the force of gravity as a force that makes each mass pull the other mass towards it, then the analogy of the tug of war game should apply accurately, the sum of the two opposing equal forces is zero.
This is a common misunderstanding of Newtons third law, but it is simply a misunderstanding. The third law forces act on different objects, they do not sum to zero. There is one and only one force on each object, and that force is unbalanced, so each object accelerates.

On object 2 there is a gravitational/rope force pulling towards object 1. The third law pair to that force is the equal and opposite gravitational/rope force acting on object 1 and pulling it towards object 2. There are no other forces, therefore each object experiences an unbalanced force and accelerates towards the other.

FactChecker
Gold Member
Exactly! This is what I'm trying to say, thus we have two scenarios:

1- If you imagine the force of gravity as a force that makes each mass pull the other mass towards it, then the analogy of the tug of war game should apply accurately, .
No. I meant just the opposite. Your force through your legs is trying to pull you AWAY from the other side. The only thing that is stopping you is that you hang onto the rope and the other side holds you back. But the force stopping you is the other side's force, not yours. If they let go, the force through your legs would pull you away. That is the opposite of gravitational force.

A.T.