where ([phi], [lambda]) is (colatitude
, longitude), [omega] is the frequency ([[omega].sub.i] = 2[pi]/[T.sub.i], where [T.sub.i] is the period), and t is time.
where r = 1 m is the radius of the middle surface S, 0 [less than or equal to] [[gamma].sub.1] [less than or equal to] 2[pi] is longitude, and 0 [less than or equal to] [y.sub.2] [less than or equal to] [pi]/2 is colatitude
. The thickness of the middle surface S is 2[epsilon] where [epsilon] is the semithickness.
where [lambda] and [theta] are longitude and colatitude
, respectively, a is the Earth's radius (6,371.2 km), r is geocentric distance, [P.sup.m.sub.n] (cos [theta]) is Schmidt quasinormalized associated Legendre function of order n and degree m, and [g.sup.m.sub.n] and [h.sup.m.sub.n] are spherical harmonic coefficients of geomagnetic potential.
The Earth's gravity acceleration g can be expressed as function of the geographic colatitude
angle [theta] and height h, applying, if necessary, the free air correction (FAC) which accounts for altitudes above sea level, by the International Gravity Formula (IGF) 1967 6]:
[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].sub.d].
where [[bar.C].sub.nm], [[bar.S].sub.nm] are fully normalized spherical harmonic coefficients, of degree n and order m; GM = 398 600.4415 [km.sup.3] [s.sup.-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 378136.3 m is the EGM96 equatorial radius (Lemoine et al.
The rock face has a slope of about 58 |degrees~, near to the colatitude
of the site.
As shown in figure 1, the sides are named as follows: (a) Polar Distance, the angular distance between the Pole and the position on earth directly below the star (90 |degrees~ altitude) called the Geographical Position (G.P.), 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.