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GeodesyData
✖
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

open allclose all

Basic Examples  (4)Summary of the most common use cases

Semiaxes of Clarke1866:

In[1]:=1
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-qtr8w9
Out[1]=1

Semimajor axis and inverse flattening of GRS80:

In[1]:=1
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-oshwng
Out[1]=1

Eccentricity of the GRS80 reference ellipsoid:

In[1]:=1
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-lfm2oz
Out[1]=1

The parameters required to transform from ITRF00 to NAD83CORS96:

In[1]:=1
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-ifgwjw
Out[1]=1

Scope  (17)Survey of the scope of standard use cases

Names and Classes  (3)

List of all available named datums and reference ellipsoids:

In[1]:=1
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-3ufd8z
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-rg5zjb
Out[2]=2

Standard name of a datum in the Wolfram Language:

In[1]:=1
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-xgk74v
Out[1]=1

English name of a datum:

In[2]:=2
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-03p1lj
Out[2]=2

Alternate names:

In[3]:=3
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-lp88lh
Out[3]=3

List of available classes:

In[1]:=1
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-0xefux
Out[1]=1

List of available named datums:

In[2]:=2
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-8r0pvr
Out[2]=2

List of available reference ellipsoids:

In[3]:=3
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-ord6bt
Out[3]=3

List of direct datum transformations with available data:

In[4]:=4
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-up9wb4
Out[4]=4

Graph of those direct transformations:

In[5]:=5
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-z52xtw
Out[5]=5

Properties and Values for Reference Ellipsoids  (8)

List of available properties:

In[1]:=1
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-3v5h4v
Out[1]=1

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

In[1]:=1
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-vc335a
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-y4xh7e
Out[2]=2

Or by the semimajor axis a and the inverse flattening :

In[3]:=3
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-6y6y8i
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-g0jsr9
Out[4]=4

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

In[1]:=1
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-n5klo0
Out[1]=1

The second eccentricity :

In[2]:=2
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-ijlmuz
Out[2]=2

The flattening :

In[3]:=3
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-etgc0a
Out[3]=3

Or its inverse :

In[4]:=4
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-rmz4c3
Out[4]=4

Specify an arbitrary oblate ellipsoid by giving the semiaxis lengths:

In[1]:=1
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-lldma9
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-iz0ega
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-0svb7q
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-s4nn83
Out[4]=4

Specify the semimajor axis and the inverse flattening:

In[5]:=5
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-26semm
Out[5]=5
In[6]:=6
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-kqb72x
Out[6]=6
In[7]:=7
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-lecdvl
Out[7]=7
In[8]:=8
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-2cwodo
Out[8]=8

The Earth is nearly spherical:

In[1]:=1
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-owgfnh
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-d0ygp6
Out[2]=2

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

In[3]:=3
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-gopqqc
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-rsuu4q
Out[4]=4
In[5]:=5
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-o0q2ss
Out[5]=5
In[6]:=6
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-3mbll6
Out[6]=6

With symbolic input:

In[7]:=7
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-n5rvgz
Out[7]=7
In[8]:=8
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-skge1p
Out[8]=8
In[9]:=9
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-6eatzt
Out[9]=9
In[10]:=10
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-lixw8e
Out[10]=10

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

In[1]:=1
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-dbv99z
Out[1]=1

Latitude can also be given as a Quantity angle:

In[2]:=2
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-roswek
Out[2]=2

Curvature radius of the normal section perpendicular to the meridian:

In[3]:=3
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-ugftc
Out[3]=3

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

In[4]:=4
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-cj6v1w
Out[4]=4

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

In[5]:=5
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-qp8762
Out[5]=5

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

In[1]:=1
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-q8tthe
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-9qt5y2
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-uk1k3r
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-0dwxl0
Out[4]=4
In[5]:=5
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-tgv4ty
Out[5]=5
In[6]:=6
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-by5n4m
Out[6]=6
In[7]:=7
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-kky02q
Out[7]=7
In[8]:=8
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-cq0j3w
Out[8]=8
In[9]:=9
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-f6hgbj
Out[9]=9
In[10]:=10
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-cely56
Out[10]=10
In[11]:=11
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-tdt9t
Out[11]=11
In[12]:=12
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-uhd8mc
Out[12]=12

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

In[1]:=1
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-7o51ix
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-dtpb7u
Out[2]=2

Distance is not proportional to difference in geodetic latitude:

In[3]:=3
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-i91kd
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-yyhatx
Out[4]=4

Properties and Values for Datums and Datum Transformations  (6)

Each datum has an associated reference ellipsoid:

In[1]:=1
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-i1ayjn
Out[1]=1

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

In[2]:=2
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-q2q42a
Out[2]=2

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

In[1]:=1
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-0734cu
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-qrp7od
Out[2]=2

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

In[1]:=1
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-si27nl
Out[1]=1

A transformation between datums is represented as a pair:

In[1]:=1
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-07cinj
Out[1]=1

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

In[1]:=1
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-0406e1
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-2ost4h
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-jplq7g
Out[3]=3

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

In[1]:=1
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-2nzwel
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-rhz6pr
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-zro6vz
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-8up1r6
Out[4]=4

These are their variations per year:

In[5]:=5
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-b8u1ff
Out[5]=5
In[6]:=6
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-2je9se
Out[6]=6
In[7]:=7
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-tnnxlk
Out[7]=7

Applications  (1)Sample problems that can be solved with this function

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

In[1]:=1
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-8zx5cp
Out[1]=1

Transform it to the "WGS72" datum:

In[2]:=2
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-kq00os
Out[2]=2

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

In[3]:=3
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-46f9lp
Out[3]=3

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

In[4]:=4
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-qb1aw1
Out[4]=4

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

In[5]:=5
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-so5fbg
Out[5]=5

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

In[6]:=6
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-679vpz
Out[6]=6
In[7]:=7
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-hp2hw6
Out[7]=7

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

In[8]:=8
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-jqrsk9
Out[8]=8

Properties & Relations  (2)Properties of the function, and connections to other functions

Distance computations along meridians can also be performed with GeoDistance:

In[1]:=1
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-zqgh1d
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-lry3y0
Out[2]=2

The result is independent of longitude:

In[3]:=3
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-8uszfb
Out[3]=3

Meridians are normal sections of zero azimuth:

In[1]:=1
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-rruw05
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-spkmxn
Out[2]=2

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

In[3]:=3
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-319i1j
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0fq7vd0ouu8ma-qo8782
Out[4]=4
Wolfram Research (2008), GeodesyData, Wolfram Language function, https://reference.wolfram.com/language/ref/GeodesyData.html (updated 2020).
✖
Wolfram Research (2008), GeodesyData, Wolfram Language function, https://reference.wolfram.com/language/ref/GeodesyData.html (updated 2020).

Text

Wolfram Research (2008), GeodesyData, Wolfram Language function, https://reference.wolfram.com/language/ref/GeodesyData.html (updated 2020).

✖
Wolfram Research (2008), GeodesyData, Wolfram Language function, https://reference.wolfram.com/language/ref/GeodesyData.html (updated 2020).

CMS

Wolfram Language. 2008. "GeodesyData." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2020. https://reference.wolfram.com/language/ref/GeodesyData.html.

✖
Wolfram Language. 2008. "GeodesyData." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2020. https://reference.wolfram.com/language/ref/GeodesyData.html.

APA

Wolfram Language. (2008). GeodesyData. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GeodesyData.html

✖
Wolfram Language. (2008). GeodesyData. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GeodesyData.html

BibTeX

@misc{reference.wolfram_2025_geodesydata, author="Wolfram Research", title="{GeodesyData}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/GeodesyData.html}", note=[Accessed: 07-May-2025 ]}

✖
@misc{reference.wolfram_2025_geodesydata, author="Wolfram Research", title="{GeodesyData}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/GeodesyData.html}", note=[Accessed: 07-May-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_geodesydata, organization={Wolfram Research}, title={GeodesyData}, year={2020}, url={https://reference.wolfram.com/language/ref/GeodesyData.html}, note=[Accessed: 07-May-2025 ]}

✖
@online{reference.wolfram_2025_geodesydata, organization={Wolfram Research}, title={GeodesyData}, year={2020}, url={https://reference.wolfram.com/language/ref/GeodesyData.html}, note=[Accessed: 07-May-2025 ]}