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

[vivinisaac]

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 doesn't sound right bcuz i thought if we stand anyware on the flat surface
we wud experience the same gravitational force

 

[jtbell]

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.

 

[genneth]

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.

 

[Loren Booda]

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.

 

[rcgldr]

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 infinite large plane would be constant, no matter where you were.

 

[Loren Booda]

What material geometry would create a logarithmic, ln|r|, dependence for a gravitational field?

 

[rbj]

If the rectangular slab were infinite in extent and the lone mass-energy present, its field would indeed be perfectly perpendicular from its surface.

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.