### spherical harmonics

(harmonic functions on the surface of a sphere)

**Spherical harmonics** are functions on the surface
of a sphere which fulfill the same role as the
sine function providing harmonics for periodic
functions. **Laplace spherical harmonics**
effectively divide the sphere into portions,
portioning the sphere by number of meridian divisions
and number of latitude divisions. The **mode**
of the harmonic is designated by two numbers,
l and m, l being a natural number indicating the number of latitude divisions,
and m being a natural number indicating the number of meridian divisions,
there being no more meridian divisions than
latitude divisions. For example, for l=1, m=1,
the sphere is divided along an equator and
a meridian, resulting in four portions.

Spherical harmonics are used in seismology
(including asteroseismology), and are
of interest in the theory of
core collapse supernovae.
They are also used in characterizing the
distribution of the cosmic microwave background variations
around the celestial sphere.
They can be used in characterizing weather
around a world.
Also, they are used as a technique in
the solution of differential equations.

(*mathematics*)
http://en.wikipedia.org/wiki/Spherical_harmonics

**Referenced by:**

Goddard gravity model (GGM)

J_{2}

multipole expansion

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