Gauss' Law For Gravity - Integral Form

Integral Form

The integral form of Gauss's law for gravity states:

where

(also written ) denotes a surface integral over a closed surface,

∂V is any closed surface (the boundary of a closed volume V),

dA is a vector, whose magnitude is the area of an infinitesimal piece of the surface ∂V, and whose direction is the outward-pointing surface normal (see surface integral for more details),

g is the gravitational field,

G is the universal gravitational constant, and

M is the total mass enclosed within the surface ∂V.

The left-hand side of this equation is called the flux of the gravitational field. Note that it is always negative (or zero), and never positive. This can be contrasted with Gauss's law for electricity, where the flux can be either positive or negative. The difference is because charge can be either positive or negative, while mass can only be positive.