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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.


Referenced by:
Goddard gravity model (GGM)
multipole expansion