In
geodesy, a map projection of the triaxial ellipsoid maps Earth or some other
astronomical body modeled as a
triaxial ellipsoid to the plane. Such a model is called the
reference ellipsoid. In most cases, reference ellipsoids are
spheroids
A spheroid, also known as an ellipsoid of revolution or rotational ellipsoid, is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid with two equal semi-diameters. A spheroid has circ ...
, and sometimes
spheres. Massive objects have sufficient gravity to overcome their own rigidity and usually have an oblate ellipsoid shape. However, minor moons or
small solar system bodies
A small Solar System body (SSSB) is an object in the Solar System that is neither a planet, a dwarf planet, nor a natural satellite. The term was first defined in 2006 by the International Astronomical Union (IAU) as follows: "All other objects, ...
are not under
hydrostatic equilibrium
In fluid mechanics, hydrostatic equilibrium (hydrostatic balance, hydrostasy) is the condition of a fluid or plastic solid at rest, which occurs when external forces, such as gravity, are balanced by a pressure-gradient force. In the planetary ...
. Usually such bodies have irregular shapes. Furthermore, some of
gravitationally rounded objects may have a tri-axial ellipsoid shape due to rapid rotation (such as
Haumea
, discoverer =
, discovered =
, earliest_precovery_date = March 22, 1955
, mpc_name = (136108) Haumea
, pronounced =
, adjectives = Haumean
, note = yes
, alt_names =
, named_after = Haumea
, mp_category =
, orbit_ref =
, epoc ...
) or unidirectional strong tidal forces (such as
Io).
Examples
A triaxial equivalent of the
Mercator projection was developed by
John P. Snyder
John Parr Snyder (12 April 1926 – 28 April 1997) was an American cartographer most known for his work on map projections for the United States Geological Survey (USGS). Educated at Purdue and MIT as a chemical engineer, he had a lifetime interest ...
.
Equidistant map projections of a triaxial ellipsoid were developed by Paweł Pędzich.
Conic Projections of a triaxial ellipsoid were developed by Maxim Nyrtsov.
Equal-area cylindrical and azimuthal projections of the triaxial ellipsoid were developed by Maxim Nyrtsov.
Jacobi conformal projections were described by
Carl Gustav Jacob Jacobi
Carl Gustav Jacob Jacobi (; ; 10 December 1804 – 18 February 1851) was a German mathematician who made fundamental contributions to elliptic functions, dynamics, differential equations, determinants, and number theory. His name is occasiona ...
.
See also
*
Geodesics on a triaxial ellipsoid
*
Map projection
In cartography, map projection is the term used to describe a broad set of transformations employed to represent the two-dimensional curved surface of a globe on a plane. In a map projection, coordinates, often expressed as latitude and longit ...
*
Reference ellipsoid
*
Jacobi ellipsoid
*
Latitude
In geography, latitude is a coordinate that specifies the north– south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from –90° at the south pole to 90° at the north pol ...
*
Ellipsoidal coordinates
Ellipsoidal coordinates are a three-dimensional orthogonal coordinate system (\lambda, \mu, \nu) that generalizes the two-dimensional elliptic coordinate system. Unlike most three-dimensional orthogonal coordinate systems that feature quadratic ...
*
Planetary coordinate system
References
{{Reflist
Map projections