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Author Topic: What arrangement of matter results in a uniform gravitational field globally aro  (Read 1213 times)

lean bean

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What arrangement of matter results in a uniform gravitational field globally around that arrangement?
By uniform gravitational field I mean… same acceleration at each point in field.

The Earth and other single sources of gravitation have tidal forces in their fields.
You cannot have a global frame about the Earth that avoids tidal effects, although you can have ‘flat’ spacetime in small areas of the field, as long as that area is small enough to avoid tidal effects. 

My question is…
Can anyone give an example of an arrangement of matter which results in a uniform gravitational field globally around,that is, outside that arrangement ?
 My self, I can’t think of such an arrangement off the top of my head.  :)


 

Offline Pmb

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If you confine matter to a finite region of space then there will be tidal forces outside the distribution regardless of how its distributed. At large distances then all approximate a point and thats the same field as a spherical body of uniform mass density.

However, you can have an infinite sheet of mass of uniform mass density. That generates a uniform gravitationl field. Also if you cut out a spherical cavity inside a spherical body of uniform mass density, the center of the cavity being non-coinciding with the center of the body, then there will be a uniform gravitational field inside the cavity. For proof see

http://home.comcast.net/~peter.m.brown/gr/grav_cavity.htm
 

Offline lightarrow

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However, you can have an infinite sheet of mass of uniform mass density. That generates a uniform gravitationl field.
As "subset" of this case, I would add a spherical distribution of matter with very large radius R: out of it the field is approximately uniform (as much as the maximum distance d between two points is low with respect to R).
 

lean bean

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If you confine matter to a finite region of space then there will be tidal forces outside the distribution regardless of how its distributed. At large distances then all approximate a point and thats the same field as a spherical body of uniform mass density.
Explained like that it's so Obvious... I do get hiccups in my thinking sometimes.
 That cavity page is interesting.
Thanks both :)


 

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