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:
“Painting myself for others, I have painted my inward self with colors clearer than my original ones. I have no more made my book than my book has made me—a book consubstantial with its author, concerned with my own self, an integral part of my life; not concerned with some third-hand, extraneous purpose, like all other books.”
—Michel de Montaigne (1533–1592)
“In full view of his television audience, he preached a new religion—or a new form of Christianity—based on faith in financial miracles and in a Heaven here on earth with a water slide and luxury hotels. It was a religion of celebrity and showmanship and fun, which made a mockery of all puritanical standards and all canons of good taste. Its standard was excess, and its doctrines were tolerance and freedom from accountability.”
—New Yorker (April 23, 1990)