Gravity's effects in Tetraspace?

[Vaev]

Hi all, this is my first post here. I've kind of been lurking here for a little while and read the orignial alkaline pages. I was somewhat curious on how gravity would work in the 4th dimension..

[wendy]

Gravity works in four dimensions in the same way it works anywhere else. You get this mass, and let it go, and it falls to the ground.

For objects on the surface of the planet, one can safely assume g is constant, eg 32.175 ft/s/s. For planet-sized objects, one treats it as a radiant field: that is, (field strength * surface of sphere of radius R) = constant, proportional to the mass of the planet = GM

G is pretty much constant over dimensions, that is 1/(density)/(time)**2. I usually set G = 1/c in size, to get numbers to come out.

Because the radiant field does not lead to stable orbits in dimensions other than 3, one needs to fake stability to get any sort of life to get going. After all, life takes many years to mature, and you don't want the planet falling into earth real soon now, do we?

[jinydu]

A simple generalization of Newton's Law of Gravitation using Gauss' Law indicates that in four dimensions, the gravitational force experienced by a mass m2 due to the prescence of another mass m1 is:

F = - (Gm1m2)/r^3 n-hat

where G is some universal constant, r is the distance between the masses and n-hat is a unit vector pointing from m1 to m2.

The electric field due to a mass M is:

g = - (GM)/r^3 n-hat

and the potential due to a mass M is:

V = - (GM)/2r^2 n-hat