What Happens to Acceleration When Two Equal Masses Attract Each Other?

[Nissan]

I was thinking about Newton's law of gravity:
F = Gm1m2/r^2.
with this law we can see that the acceleration of on object in Earth is (G*mass of the earth) which is 9.8N.
what happens if we cosider in our equation abody which his mass is equvalnce to the mass of the earth?
each object will give the other an acceleration of 9.8N, does it mean's that the total acceleration would be 19.6N? does that mean's that we attract the Earth as well in a fixed acceleration?

 

[Danger]

does that mean's that we attract the Earth as well in a fixed acceleration?

Look at the equation again. (m2...)

 

[dextercioby]

I was thinking about Newton's law of gravity:
F = Gm1m2/r^2.
with this law we can see that the acceleration of on object in Earth is (G*mass of the earth) which is 9.8N.
what happens if we cosider in our equation abody which his mass is equvalnce to the mass of the earth?
each object will give the other an acceleration of 9.8N, does it mean's that the total acceleration would be 19.6N? does that mean's that we attract the Earth as well in a fixed acceleration?

Your post is simply incomprehensible. The acceleration is not measured in N (Newtons), but in \mbox{m s}^{-2}.

Daniel.

 

[Danger]

Good catch, Dexter. I've never used Newtons for anything, so I didn't know what that N meant.
(Seriously... I never heard of a Newton until I got onto PF. I still don't know what it is. Everything that I've ever done was in Watts, Foot-pounds, psi, etc..)

 

[HallsofIvy]

In addition, there is no such thing as "total acceleration". If two objects were the same mass and at a distance such that the acceleration was 9.8 meters per second squared, the each would be attracted toward the other at 9.8 meters per second squared. You could then calculate that the distance between them was decreasing at a rate that was increasing at 19.6 meters per second squared but that would not be an "acceleration" of any object.

To answer your last question: yes, we attract the Earth at a fixed acceleration. Since "we" attract the Earth with the same force as that the Earth applies to the object, but the Earth is much more massive than "we" are, that fixed acceleration is unmeasurably small.

This applies, of course, only to objects in free fall. If I am standing on the earth, the Earth and I attract each other with the same force, but there is no acceleration.