GeodesyData

GeodesyData["name","property"]

gives the value of the specified property for a named geodetic datum or reference ellipsoid.

GeodesyData[{a,b},"property"]

gives the value of the property for the ellipsoid with semimajor axis a and semiminor axis b.

GeodesyData[obj,{"property",coords}]

gives the value of the property at the specified coordinates.

Details

  • GeodesyData[] gives a list of all available named geodetic datums and reference ellipsoids.
  • Geodetic datums are specified by standard names such as "NAD27" and "ITRF00".
  • Reference ellipsoids are given standard names such as "Clarke1866" and "GRS80".
  • GeodesyData["Datum"] gives the names of all available named geodetic datums; GeodesyData["ReferenceEllipsoid"] gives those of all available named reference ellipsoids.
  • GeodesyData["datum","ReferenceEllipsoid"] gives the name of the reference ellipsoid associated with the specified datum.
  • Basic geometrical properties include:
  • "EllipsoidParameters"ellipsoid parameters
    "InverseFlattening"inverse flattening of the ellipsoid
    "SemimajorAxis"length of the semimajor axis (equatorial radius)
    "SemiminorAxis"length of the semiminor axis (or polar radius)
  • Additional geometrical properties include:
  • "AngularEccentricity"angular eccentricity of the ellipsoid
    "AuthalicRadius"radius of a sphere of the same surface
    "Eccentricity"first eccentricity of the ellipsoid
    "Flattening"flattening of the ellipsoid
    "LinearEccentricity"linear eccentricity of the ellipsoid
    "MeanMassRadius"mean mass radius
    "MeanRadius"geometric mean radius
    "MeridianQuadrant"length of the meridian from the equator to the pole
    "SecondEccentricity"second eccentricity of the ellipsoid
    "SecondFlattening"second flattening of the ellipsoid
    "Semiaxes"semimajor and semiminor axes of the ellipsoid
    "ThirdEccentricity"third eccentricity of the ellipsoid
    "ThirdFlattening"third flattening of the ellipsoid
    "VolumetricRadius"radius of a sphere of equal volume
  • Coordinate-dependent properties include:
  • {"ConformalRadius",lat}conformal radius at latitude lat
    {"MeridionalArc",lat1,lat2}length of the meridian between latitudes lat1 and lat2
    {"MeridionalCurvatureRadius",lat}radius of curvature in the meridian at latitude lat
    {"PrimeVerticalCurvatureRadius",lat}radius of curvature in the prime vertical at latitude lat
    {"NormalSectionCurvatureRadius",lat,a}radius of curvature at latitude lat in the direction azimuth a
  • Properties converting from geodetic latitude to alternative forms of latitude include:
  • {"AuthalicLatitude",lat}latitude of an equivalent point on the authalic sphere
    {"ConformalLatitude",lat}conformal projection of a geodesic latitude lat
    {"GeocentricLatitude",lat}angle between the equatorial plane and a line from the center
    {"IsometricLatitude",lat}isometric latitude referred to lat
    {"RectifyingLatitude",lat}projection preserving distance between meridians
    {"ReducedLatitude",lat}parametric latitude of an equivalent point on a sphere
  • Properties converting from alternative forms of latitude to geodetic latitude include:
  • {"FromAuthalicLatitude",lat}latitude of an equivalent point on the authalic sphere
    {"FromConformalLatitude",lat}conformal projection of a geodesic latitude lat
    {"FromGeocentricLatitude",lat}angle between the equatorial plane and a line from the center
    {"FromIsometricLatitude",lat}isometric latitude referred to lat
    {"FromRectifyingLatitude",lat}projection preserving distance between meridians
    {"FromReducedLatitude",lat}parametric latitude of an equivalent point on a sphere
  • Other properties include:
  • "AlternateNames"alternate English names
    "StandardName"Wolfram Language standard name
    "Name"English name
    "Properties"available properties
  • Reference ellipsoids can be specified by semiaxes {a,b} or by semimajor axis and inverse flattening {a,{invf}}.
  • Input latitudes can be given as numbers in degrees or as Quantity angles. Semiaxis lengths in input can be given as numbers in meters or as Quantity lengths.
  • Angular results are given as Quantity angles in degrees. Distance results are given as Quantity lengths in meters.
  • GeodesyData gives symbolic results if the parameters of a reference ellipsoid are given symbolically.
  • GeodesyData[{datum1,datum2}] gives rules for the parameters used to transform datum1 to datum2.
  • GeodesyData[{datum1,datum2},"param"] gives the specified parameter for transforming from datum1 to datum2.
  • Transformation parameters for datums include:
  • "ParameterDefinitionYear"decimal year when parameter values were defined
    "Rotation"rotation angles in milliarcseconds
    "RotationDerivative"rate of change of rotation in milliarcseconds per year
    "Scale"transformation scale factor
    "ScaleDerivative"annual change of transformation scale factor
    "Translation"translation vector given in meters
    "TranslationDerivative"rate of change of translation vector in meters per year

Examples

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Basic Examples  (4)

Semiaxes of Clarke1866:

Semimajor axis and inverse flattening of GRS80:

Eccentricity of the GRS80 reference ellipsoid:

The parameters required to transform from ITRF00 to NAD83CORS96:

Scope  (17)

Names and Classes  (3)

List of all available named datums and reference ellipsoids:

Standard name of a datum in the Wolfram Language:

English name of a datum:

Alternate names:

List of available classes:

List of available named datums:

List of available reference ellipsoids:

List of direct datum transformations with available data:

Graph of those direct transformations:

Properties and Values for Reference Ellipsoids  (8)

List of available properties:

An ellipsoid of revolution is characterized by the semiaxes lengths {a,b} of a vertical section:

Or by the semimajor axis a and the inverse flattening :

The shape of an ellipse of semiaxes {a,b} can be described by the eccentricity :

The second eccentricity :

The flattening :

Or its inverse :

Specify an arbitrary oblate ellipsoid by giving the semiaxis lengths:

Specify the semimajor axis and the inverse flattening:

The Earth is nearly spherical:

Therefore, the various concepts of radius have similar values and are also similar to the semiaxes lengths:

With symbolic input:

On an ellipsoid, the curvature radius of a meridian varies with latitude, specified as a number in degrees:

Latitude can also be given as a Quantity angle:

Curvature radius of the normal section perpendicular to the meridian:

Curvature radius of a normal section of a given azimuth, measured clockwise from north:

Plot all possible values of the curvature radius of normal sections of the ellipsoid:

Convert from geodetic latitude to other types of latitude, and back to geodetic latitude:

Compute lengths along meridians. This is a quadrant (equator to pole):

Distance is not proportional to difference in geodetic latitude:

Properties and Values for Datums and Datum Transformations  (6)

Each datum has an associated reference ellipsoid:

Different datums may have the same reference ellipsoid but differ in position or orientation:

Most properties of a datum are just properties of its ellipsoid:

The WGS 84 datum has been updated but the ellipsoid parameters have been kept:

A transformation between datums is represented as a pair:

The relation between two datums is encoded in the seven parameters of a Helmert transformation:

The relation between some datums changes in time. These are the parameters at definition time:

These are their variations per year:

Applications  (1)

Perform a change of datum using GeoPositionXYZ. Take the {0,0} point in the "NAD27" datum:

Transform it to the "WGS72" datum:

In the new datum, the same point has different latitude and longitude values and nonzero height:

The origins of the datums are related by a translation, in meters:

There is also a change of length, in units of 10-8:

And a small rotation, encoded as a vector in milliarcseconds:

This is the seven-parameter Helmert transformation of the original coordinates:

Properties & Relations  (2)

Distance computations along meridians can also be performed with GeoDistance:

The result is independent of longitude:

Meridians are normal sections of zero azimuth:

The prime vertical curvature is that of the meridian-perpendicular normal section:

Introduced in 2008
 (7.0)
 |
Updated in 2014
 (10.0)
2020
 (12.1)