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The shell bound by two concentric, similar, and aligned ellipsoids (a homoeoid) exters no gravitational force on a point inside of it. [7] Meanwhile, the shell bound by two concentric, confocal ellipsoids (a focaloid) has the property that the gravitational force outside of two concentric, confocal focaloids is the same. [8]
In physics, spherical multipole moments are the coefficients in a series expansion of a potential that varies inversely with the distance R to a source, i.e., as . Examples of such potentials are the electric potential, the magnetic potential and the gravitational potential.
The gravitational potential (V) at a location is the gravitational potential energy (U) at that location per unit mass: =, where m is the mass of the object. Potential energy is equal (in magnitude, but negative) to the work done by the gravitational field moving a body to its given position in space from infinity.
Siméon Denis Poisson. Poisson's equation is an elliptic partial differential equation of broad utility in theoretical physics.For example, the solution to Poisson's equation is the potential field caused by a given electric charge or mass density distribution; with the potential field known, one can then calculate the corresponding electrostatic or gravitational (force) field.
The quadrupole moment tensor Q is a rank-two tensor—3×3 matrix. There are several definitions, but it is normally stated in the traceless form (i.e. + + =).The quadrupole moment tensor has thus nine components, but because of transposition symmetry and zero-trace property, in this form only five of these are independent.
Thomson's problem is related to the 7th of the eighteen unsolved mathematics problems proposed by the mathematician Steve Smale — "Distribution of points on the 2-sphere". [2] The main difference is that in Smale's problem the function to minimise is not the electrostatic potential 1 r i j {\displaystyle 1 \over r_{ij}} but a logarithmic ...
a point charge; a uniformly distributed spherical shell of charge; any other charge distribution with spherical symmetry; The spherical Gaussian surface is chosen so that it is concentric with the charge distribution. As an example, consider a charged spherical shell S of negligible thickness, with a uniformly distributed charge Q and radius R.
For example, a hollow sphere does not produce any net gravity inside. The gravitational field inside is the same as if the hollow sphere were not there (i.e. the resultant field is that of all masses not including the sphere, which can be inside and outside the sphere).