Gravitational Force: Is There Only One?

[alexbib]

In a system with two masses M and m, separated by distance d, is there only one force GMm/d^2 pulling them together, or are there two forces, one exerted by M on m, and one exerted by m on M?

If there is only one force, then the relative acceleration of these two objects would only depend on the biggest mass. So a planet and a ping pong ball would fall together just as quickly as two planets separated by the same distance. That seems a bit weird.

 

[Jimmy]

The gravitational force between two massive objects is mutual. This obeys Newton's third law. You exert the same gravitational force on the entire Earth that the Earth exerts on you. Every particle in your body exerts a force on every particle of the Earth as every particle of the Earth exerts a force on your particles. The force you exert on the Earth doesn't cause much acceleration, however, since the Earth is so much more massive than you.

 

[alexbib]

yeah, but this is not what I am asking. Consider an observer on the earth, and me falling towards him. Would he see me accelerate at 9.8m/s/s, or a 9.8+the small acceleration I am causing the Earth to have? I know that this acceleration I am giving the Earth is negligible, but there is a difference. If two masses of 10kg exert a grav force of 100N on each other, will their relative acceleration(that is, the acceleration of mass a measured from a point of view on mass b) be 10m/s/s, or 20m/s/s?

 

[Jimmy]

Each object, at the moment in time when they are exerting 100 Newtons of force on each other, would each be accelerating toward each other at 10 m/s^2. The relative acceleration from the point of view of either mass would be 20 m/s^2.

 

[Jimmy]

For two 10 kg objects to exert that strong of force on each other, they would have to be very close and very dense. In fact, they would have to be approximately 8 micrometers apart.

$$R = \sqrt{\frac{G M m}{F}}$$

 

[alexbib]

bah, for point masses it's possible I only chose these numbers for simplicity, not for their realism

Thanks a lot for answering!

 

[Jimmy]

I understand. I didn't really notice until after I answered your last question. I was curious how close they would have to be.

Actually, I sould be thanking you for your choice of numbers. Made things quite easy.

 

[turin]

Gravity is a fictitious force, as I understand it. It is distinct from, say, the electrostatic force. In the case of the electrostatic force, the effect is that the two bodies actually "feel" the acceleration. In this way, the force is real. In the case of gravity, if two point masses are acting gravitationally on each other, then neither one feels anything (until they collide, of course). In this way, the force is fictitious. In the electrostatic case, the trajectories of the particles are curved relative to any intertial frame. In the gravitational case, the particles are moving along the closest things to straight lines that exist.

In the spirit of your question, in the case of electrostatic force:
a charged object induces a field in an intertial frame. This field causes an acceleration relative to this inertial frame. The acceleration itself is the same with respect to any inertial frame. So, even as Newton had suspected, the interaction is not q-q (charge directly interacting with charge), but it is q-F, and F-q (that is, charge interacting with field, and field interacting with charge).