First, let's write down formulas for quantities that we will need lateron (Heiskanen and Moritz, 1967). First the relationship between Earth flattening parameter , semi-major and semi-minor axes and :
or | (1) | ||
(2) | |||
(linear eccentricity) | (3) | ||
(first numerical eccentricity) | (4) | ||
(second numerical eccentricity) | (5) | ||
(an abbreviation) | (6) | ||
(gravity acc. at equator) | (7) | ||
(gravity acc. at poles) | (8) | ||
(Cartesian coordinates | (9) | ||
relative to center | (10) | ||
of Earth) | (11) |