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I get it that there will be a gravitational force between objects attracted towards gravity but can there be a gravitational force between two objects resting on horizontal plane? In other words, does an object experience gravitational force in all directions?

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What do You mean with "towards gravity"? This "horizontal plane" is equally strange. –  Georg Mar 10 '11 at 15:13
    
I mean downwards towards the earth surface. –  user2467 Mar 10 '11 at 15:23

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The question is confusing, but I think you might possibly mean the following: Are two objects resting on a horizontal table gravitationally attracted to each other? If that's your question, then the answer is yes. The gravitational attraction is very weak for "normal-sized" objects, though. You can use the rule $$ F={Gm_1m_2\over r^2} $$ to work it out. In this formula, $G=6.67\times 10^{-11}\,{\rm N\,m^2/kg^2}$, $m_1,m_2$ are the masses, and $r$ is the separation between their centers. (Strictly speaking this is only correct if the objects are spheres.)

Cavendish managed to measure this attraction back in the 1700s, in a truly amazing experiment.

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Yes, the question is really about 3 bodies in a Gravitational Field. We can take the masses as m1, m2 and M, where M is the larger planetary body on whose plane surface they both sit. Ted Bunn has just answered whilst I was composing this, so his answer contains the relevant Force formula between m1 and m2.

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Yes. They still feel the force due to the Earth's gravity on the tabletop. They also feel an upward force from the tabletop that counteracts the Earth's gravitational pull, and leaves them sitting stationary on the tabletop. This is why it's harder on your feet when you're carrying a lot of weight than it is when you are not--the ground has to push up on your feet more to cancel out the added gravitational pull on you.

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Can you tell me about the upward force on a object at rest? –  user2467 Mar 10 '11 at 21:04

If you consider the center of mass of each body to be a point, the gravitational force direction between them are the vectors connecting each center of mass.

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how do they experience force between each other when the gravity pulls them downwards? –  user2467 Mar 10 '11 at 15:25
    
@Michael ""If you consider the center of mass of each body to be a point, the gravitational force.."" Center of mass always is a point, but this is never a prerequisite for gravity! There is a big turmoil in user2123's thoughts, those have to be cleared first!-1 –  Georg Mar 10 '11 at 15:28
    
My awkward response (com as a point) addresses user 2123's question regarding the direction of gravitational force direction between two bodies. –  Michael Luciuk Mar 10 '11 at 16:07
    
Your answer is incorrect. The gravitational force between two bodies does not in general point in the same direction as the vector pointing between their centers of mass. –  Mark Eichenlaub Mar 10 '11 at 18:03
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Mark, please explain. The question related to two bodies resting on a horizontal plane. –  Michael Luciuk Mar 10 '11 at 20:32

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