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.
Read more about this topic: Gauss' Law For Gravity
Famous quotes containing the words integral and/or form:
“Make the most of your regrets; never smother your sorrow, but tend and cherish it till it come to have a separate and integral interest. To regret deeply is to live afresh.”
—Henry David Thoreau (1817–1862)
“The old idea that the joke was not good enough for the company has been superseded by the new aristocratic idea that the company was not worthy of the joke. They have introduced an almost insane individualism into that one form of intercourse which is specially and uproariously communal. They have made even levities into secrets. They have made laughter lonelier than tears.”
—Gilbert Keith Chesterton (1874–1936)