Gravitational Effects of a Hollow Spherical Shell

[johnhuntsman]

Just a quick question concerning the concept mentioned in the title to make some clarification. Does an object have to be located at the center of the hollowed out space in a spherical shell (with uniformly distributed mass) for the net gravitational force to be zero? In other words, at the would be center of mass if the shell weren't hollow and had its mass evenly distriuted.

Could a particle be a distance r from the center of a hollowed out space in a spherical shell with uniformly distributed mass and still be weightless? Or would being closer to one side of the shell give it weight (i.e., net force due to gravity not equal to 0)?

 

[haruspex]

Just a quick question concerning the concept mentioned in the title to make some clarification. Does an object have to be located at the center of the hollowed out space in a spherical shell (with uniformly distributed mass) for the net gravitational force to be zero? In other words, at the would be center of mass if the shell weren't hollow and had its mass evenly distriuted.

No. It is a remarkable fact that in three dimensions (only) the inverse square law results in there being no field anywhere inside a uniform spherical shell (whether we're talking gravity or charge).
It is similarly remarkable that outside the shell the field is exactly as though the mass/charge were all concentrated at the centre of the shell. This does not happen for other shapes.

 

[johnhuntsman]

Alrightt. Thanks : D