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Acc to newtons gravitational theory f=GmM/r^2and the distance r is

  1. Sep 25, 2007 #1
    acc to newtons gravitational theory f=GmM/r^2
    and the distance r is taken from the centre of mass of the object
    so hypothetically if there was a flat rectangular planet gravity would be highest at the centre of the rectangular planet and if we stand away from the center gravitational pull should decrease
    is this true
    it doesnt sound right bcuz i thought if we stand anyware on the flat surface
    we wud experience the same gravitational force
  2. jcsd
  3. Sep 25, 2007 #2


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    Staff: Mentor

    That formula works for extended objects only when they have spherical symmetry. Otherwise you have to apply the formula to each point of the object, and integrate (using calculus) to find the net gravitational force.
  4. Sep 25, 2007 #3
    Near the surface of a large, flat slab, the field is approximately perpendicular to the slab. Only near the edges would you notice anything was different. So yes, it is stronger near the center, but for a fairly large flat slab you wouldn't notice.
  5. Sep 25, 2007 #4
    If the rectangular slab were infinite in extent and the lone mass-energy present, its field would indeed be perfectly perpendicular from its surface. (Try integrating Newton's gravitational law over surface mass density out to infinity in two dimensions.) Any observer, however, would distort the local field, thus inducing greater gravitational field density than when considering the normal field by itself.
  6. Sep 25, 2007 #5


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    Homework Helper

    Gravity from a point source is relative to 1/r^2. Gravity from an infinitely long line source would be relative to 1/r. Gravity from an infinte large plane would be constant, no matter where you were.
  7. Sep 26, 2007 #6
    What material geometry would create a logarithmic, ln|r|, dependence for a gravitational field?
  8. Sep 26, 2007 #7


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    not only that, but if the slab were an infinite plane, the graviatational field would be constant with distance from the plane or slab. no 1/r^2 or even 1/r attenuation of the field.
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