Notes on WGS 84

Ellipsoid flattening ratio 1/f = 298.257 223 563 where f is flattening.

Flattening f = 0.00 335 281 0665)

Flattening distance (a × f) is 21.38468575 kilometres so Polar radius b is (a - a × f) = 6356,752.314 m (minor semi-axis)

At a given Lat and Long (Parallel / Meridian)

Meridian radius: M = a (1 - e ²) (1 - e ² × sin ²(lat))^(-3/2)
where a is the semi-major axis (equator radius) ; and,
e is eccentricity, where e ² = 2f - f ², so e = 0.08181919

Parallel radius: v = a (1 - e ² sin ²(lat))^(-½) Radius depends upon the azimuth of the vertical plane, except at the poles.

Radius at given latitude (Distance from Earth centre to Point concerned) = 1/(Cos lat × (root ((1/a ²) + (Tan lat ²/b ²))))

Geodesic distance = a × integral between Lat A and Lat B ((W/X + Y/Z)^½)

Where:

W = (1 - e ²) ²
X = (1 - e ² × sin ²lat)³
Y = (Long B - Long A) ² × (1 - e ² × sin ²Lat)
Z = ((1 - e ²) × (Tan Lat B - Tan Lat A - e ²(Lat B - Lat A)) × Cos ²Lat)
and e = eccentricity (0.08181919 for WGS 84)

UTC is earth time and is adjusted by leap seconds to take into account the gradual slowing down of the earth's rotation.

GLONASS time datum is Moscow-based UTC and takes a minimum of 15 mins to reset when UTC leap seconds change. During this time the whole system is inoperative.

GPS time datum is system time which was originally UTC but in 1995 was 10 seconds different. No change is made to allow for leap seconds.

International Atomic Time is based on Caesium clocks, has no leap seconds, and in 1995 was 29 sec different to UTC.

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Last updated by John Leibacher on Sunday, November 5, 1995 at 17:53