Is Earth's gravitational pull equal to an object's falling force?

[fbsthreads]

if an object is falling to earth, is the equal and opposite force to gravity (Newtons 3rd law) the pull of the Earth towards the object?

 

[TALewis]

Absolutely. If the Earth pulls on you with a force of 700 N, then you pull right back on the Earth with 700 N as well. It's just not so apparent because the Earth is so massive that the extra 700 N doesn't move the Earth much at all.

 

[fbsthreads]

but to emit 700N wouldn't i have to do this by emitting gravitons?

 

[ahrkron]

Yes. It is a similar situation to that you have when two charges are interacting. Both emit and absorb photons, and their momenta are affected accordingly.

 

[TALewis]

Newton's law of gravitation is given as

$$F = G\frac{m_1m_2}{r^2}$$

where F is the gravitational force between two bodies, G is the universal gravitational constant, m1 and m2 are the masses of the two bodies being considered, and r is the distance between the centers of mass of the two bodies.

However this gravitational force is manifest, by gravitons or gravity waves or space-time curvature or whatever (I am not knowledgeable about such things), you attract the Earth and the Earth attracts you by virtue of your mutual mass. The mechanism for your attracting the Earth is the same by which you are attracted to it.

This is true for all mass in the universe: Every object with mass is attracted to every other mass. Your pencil is attracted to your calculator. Your TV is attracted to your remote. Your cat is attracted to your refrigerator. It doesn't matter what the object is: if it has mass, it produces a gravitational field that influences other masses.

We don't see all of these small gravity forces between objects because gravity is such a very WEAK force. It takes an object as massive as a planet for us to notice its gravity.

 

[KingNothing]

This is why I never liked and still do not like when my physics teacher says that "gravitational acceleration is independent of mass"...It just bugs me.

 

[sharpstones]

well yes, saying "gravitational acceleration is independent of mass" is of course an incorrect statement, but it's because your teacher is using it to loosely. In an intro to physics setting unless you are talking about the motion of planets you almost always talk of g as being = 9.8 m/s^2 because the mass of whatever you are talking about is usually a lot smaller then the mass of the earth. In this case the mass of whatever you are analyzing becomes negligible and you do not have to worry about it.

 

[TALewis]

The value of Earth's gravitational acceleration can be found from Newton's law of gravitation by simply leaving out the small mass from the equation:

$$g=G\frac{M}{r^2}$$

Here M is the mass of the Earth.