theta] is referred to as the colatitude
and [empty set] is referred to as the azimuth (Fig.
To mathematically formulate the problem, we begin by defining the spherical harmonic spectral expansion of a function f([theta], [PHI]) with colatitude
coordinate [theta] [member of] [0, [pi]] and longitude coordinate [PHI] [member of] [0, 2[pi]] as follows:
In these coordinates, for d > 1 the major colatitude
is taken to be the last, [[alpha].
2] is an adopted gravity mass constant of the EGM96; (r, [theta], [lambda]) are geocentric radius, spherical colatitude
, and longitude of the computational point, respectively; a = 6 378136.
whose latitude remains constant as the star transits the sky from rising to setting; (b) the Colatitude
, the angular distance between the Pole and the observer's meridian position; and (c) the Coaltitude, the angular distance between the observer and the Geographical Position.
The corresponding pivotal section is a circle which depends only on k and on the colatitude
[theta] of the normal to the pivotal plane.
The orientation of the shapes is given by the colatitude
[theta] and the azimut [phi].
For a purely isotropic distribution of points on a sphere, the colatitudes
(corresponding to the angle [theta]) of the points have the density function [PHI]([theta])= 1/2 sin [theta] on [0, [pi]].