Spheroid

This option is used to define the parameters for a spheroid (or ellipsoid - see Spheroids, Ellipsoids and the Geoid below) and to display the details of all spheroids currently defined in the Definitions library.

Spheroids, Ellipsoids and the Geoid

Spheroid and Ellipsoid are terms used to describe the idealised geometrical shape of the Earth for mathematical purposes. Many geodesists, geophysicists, cartographers and other scientists use these terms interchangeably although usually preferring the use of one term above the other. Meanwhile others emphatically insist that there are important differences between them that should not be diminished.

However the shape of the Earth is much more complex than either of these terms represent, hence the term Geoid describes the physical shape of the Earth as being a surface of equal gravitational potential along which the direction of the gravitational attraction is always perpendicular to it. The geoid coincides exactly with the mean sea level surface of the Earth (if it were at rest) but undulates as affected by gravitational anomalies and concentrations due to continental land masses, mountains, valleys and depressions, both on the land and under the sea.

Within the Geoida software application and this Help documentation the user may find either of the terms Spheroid or Ellipsoid used and should consider them as synonymous. The following comments and definitions of the terms Spheroid, Ellipsoid and Geoid from different sources may be of interest.

The distinction is made between a spheroid and an ellipsoid because these terms are often used interchangeably in geodesy texts. According to the Oxford English Dictionary (OED, 1989), a spheroid is:

"Spheroid - A body approaching in shape to a sphere, especially one formed by the revolution of an ellipse about one of its axes"

whereas an ellipsoid is (ibid.):

"Ellipsoid - A solid of which all the plane sections through one of the axes are ellipses, and all other sections are ellipses or circles. Formerly in narrower sense: A solid generated by the revolution of an ellipse about one of its axes; now called ellipsoid of revolution"

Evidently, there is some ambiguity in the exact name which should be used to describe this approximation of the figure of the earth. In accordance with the revised (Oxford English Dictionary) definition of the ellipsoid, the term spheroid is deemed more appropriate in this instance, and will be used hereafter.

'An updated explanation of the Geocentric Datum of Australia (GDA) and its effects upon future mapping' - Dr Will E. Featherstone MAIC, School of Spatial Sciences, Curtin University of Technology, Circa 1995
http://www.cage.curtin.edu.au/~will/datum.html

Spheroid, Ellipsoid, and Geoid

Spheroid is a solid generated by rotating an ellipse about either the major or minor axis

Ellipsoid is a solid for which all plane sections through one axis are ellipses and through the other are ellipses or circles. If any two of the three axes of that ellipsoid are equal, the figure becomes a spheroid (ellipsoid of revolution). If all three are equal, it becomes a sphere.

Geoid is the equipotential gravity surface of the earth at mean sea level. At any point it is perpendicular to the direction of gravity.

'Introduction to Geodesy: The history and concepts of modern geodesy' - Smith, James R., John Wiley & Sons, 1997. http://elearning.algonquincollege.com/coursemat/viljoed/gis8746/concepts/geodesy/spheroid.htm

More complicated figures

The possibility that the Earth's equator is an ellipse rather than a circle and therefore that the ellipsoid is triaxial has been a matter of scientific controversy for many years. Modern technological developments have furnished new and rapid methods for data collection and since the launch of Sputnik 1, orbital data have been used to investigate the theory of ellipticity.

A second theory, more complicated than triaxiality, proposed that observed long periodic orbital variations of the first Earth satellites indicate an additional depression at the south pole accompanied by a bulge of the same degree at the north pole. It is also contended that the northern middle latitudes were slightly flattened and the southern middle latitudes bulged in a similar amount. This concept suggested a slightly pear-shaped Earth and was the subject of much public discussion. Modern geodesy tends to retain the ellipsoid of revolution and treat triaxiality and pear shape as a part of the geoid figure: they are represented by the spherical harmonic coefficients C₂₂, S₂₂ and C₃₀, respectively, corresponding to degree and order numbers 2.2 for the triaxiality and 3.0 for the pear shape.

WAPedia: 'Figure of the Earth'
http://wapedia.mobi/en/Figure_of_the_Earth