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I am a general physics student, I had a question in my text-book and according to it two students having gravitational attraction between them = ($6.67\cdot10^-8\ \mathrm{Nm}^2/\mathrm{kg}^2$) is not worth worrying about.

My question is Why? How much force between two objects is worth anything?

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up vote 4 down vote accepted

In this case it is not the size of the force, but where it stands in relaion to the other forces acting on the same two students. They are subject to:

  • the gravitational attraction of the Earth
  • the normal force from the floor or chair
  • the reaction of the things around them due to thier movements both voluntary and involuntary
  • tiny pushes due to circulation of the air in the room
  • the residual graviation (called tide) from the Sun and the Moon
  • if they are in motion relative the ground the non-inertial centrifugal and coriolis pseudo-forces
  • if it is winter they may developed a static charge and be subject to electrostatic forces from those
  • if they have magnets about thier person's (silly magic jewery, magnetic jewery clasps, in cell phone holsters, etc) there are magnetostatic forces
  • Possibly the radiation pressure from sunlight (I haven't actually figured this one to see if it is comperable to thier mutual graviation attraction or not...)

all of which are bigger than gravitation attraction between them, so until we are taking all those other things into account we don't need to worry ourselves about their mutual gravitational attraction, because it's effects will be dominated by other things.

The general rule is that you order things by the size of their effect and only keep some number of the big ones. How many depends on why you want to know. It is very common to only need two or three leading effects, but for, say plotting the orbit of a space probe past the jovian planets you may need dozens (the gravity from lots and lots of different planets and moons plus of course the sun).

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0.0000000667 seems very little force of attraction between anything but incase of the electron and protons in an hydrogen atom having a gravitational force of 6.62x10^-47 it much less than that, but still our electrons repel that floor or chairs electrons and hence we hover, Means it is enough force to repel as compared to the mass of object like proton but very little quantity as compared to two students :) –  devWaleed Jan 6 '13 at 18:52
Gravitation is not responsible for the behavior of solids which, which is rather more complicated but just for figuring the difference in strength you can use the electrostatic forces between to atoms. –  dmckee Jan 6 '13 at 18:54
@dmckee You could even add other celestial bodies as more important than nearby people. Jupiter in opposition is dozens of times stronger than a person at 1 meter. –  Chris White Jan 7 '13 at 0:06
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