Update: 20th October 2005

The Keys of Atlantis

A Study of Ancient Unified Numerical and Metrological Systems

by Peter Wakefield Sault

Copyright Peter Wakefield Sault 2003-2005
All rights reserved worldwide

The Keys of Atlantis

Appendix D.

Geodesic and Lunar Data

The Earth

The shape of the Earth is an oblate spheroid, which for most practical purposes can be approximated as an ellipsoid. Due to the Earth's spin it is wider across the Equator than across the Poles, the difference in diameters amounting to some 27 miles.

Equatorial Radius, a IAU, 1976 6,378,140m
Geod. Ref. Sys., 1980 6,378,137m
Merit, 1983 6,378,136m
Flattening Factor, f=(a-b)/a IAU,1976; Merit 298.257-1
G.R.S., 1980 298.257222-1
Polar Radius, b=a(1-f) 6,356,752m

Figure D-1. Variables for Great Circle Approximations

The first step in approximating a great circle circumference is to ascertain the minor radius, R. The major radius (a) is always the equatorial radius of the Earth. That great circle tilted 0 is the Equator itself (EW, coloured red in Figure D-1) and is here treated as though it were a true circle. As the angle of tilt increases, the minor radius - which is that from the centre of the Earth to the vertex of the great circle - decreases. The length of the radius is calculated by taking it as an intermediate radius of a meridian (EVN, coloured green in Figure D-1), an ellipse which passes through the North and South Poles and whose major and minor radii are known, being the equatorial (a) and polar (b) radii respectively, using the following formula, where q is the angle of tilt to the Equator (i.e. the dihedral angle between the plane of the equator and that of the tilted great circle):-

The circumference P of the tilted great circle (VW, coloured blue in Figure D-1) is then calculated by substituting R into Ramanujan's second approximation (which, for ellipses comparable in size and eccentricity to great circles of the earth, is accurate to within a Bohr radius):-

The Moon

Ignoring topographical features, the Moon is an almost perfect sphere. It has a very slight bulge, amounting to no more than a few metres, in the side which faces the Earth. This bulge, which dates from the solidification of the Moon before the features which we see resulting from meteoric bombardment appeared, is sufficient to keep the same side facing towards the Earth at all times. It is a curious accident that the apparent angular diameter of the Moon as viewed from the Earth, about , is almost identical to that of the Sun, allowing the Solar Corona to be viewed at the periphery of the Lunar disk during total eclipses of the Sun.

The Moon's mean radius, k, is expressed in units of Earth's equatorial radius.

k IAU, 1982 0.2725076
Mean Lunar Radius, ka 1,738,090.5m

The Moon's orbit about the Earth is an ellipse of eccentricity 0.0549 inclined at 58' to the Ecliptic, the plane of the Earth's orbit. The points where the Moon's orbit crosses the Ecliptic are the nodes, which move westward, taking 18.6 years to go all the way round the Earth. The point where the Moon is nearest the Earth, the perigee, moves eastward, taking 8.8 years for a complete circuit. The movement of the Moon against the stars is, therefore, quite complicated and variable. Nevertheless, the Moon remains within the zodiacal band along the Ecliptic.

The highest latitude where the Moon ever passes directly overhead is 2835', comprising the sum of the inclinations of the terrestrial Equator and the orbit of the Moon, 2327' and 58' respectively, to the Ecliptic.

The Keys of Atlantis

Copyright Peter Wakefield Sault 2003-2005
All rights reserved worldwide

Music: Nikolai RIMSKY-KORSAKOV (1844-1908), Scheherezade, Op.35 (symphonic suite), The Sea and Sinbad's Ship.
MIDI realization J.Nishio