Spheroids

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The previous discussion of direct geometric map projections assumes that the Earth is a sphere, and for many maps this is satisfactory. However, due to rotation of the Earth around its axis, the planet bulges slightly at the equator. This flattening of the sphere makes it an oblate spheroid, which is an ellipse rotated around its shorter axis.

Ellipse Diagram

cartography_ellipse_diagram

An ellipse is defined by its semi-major (long) and semi-minor (short) axes.

The amount of flattening of the Earth is expressed as the ratio:

cartography_flattening_earth_equation

Where:

a = equatorial radius (semi-major axis)

b = polar radius (semi-minor axis)

Most map projections use eccentricity rather than flattening. The relationship is:

cartography_eccentricity_equation

Where:

e2 = eccentricity

The flattening of the Earth is about 1 part in 300, and becomes significant in map accuracy at a scale of 1:100,000 or larger.

Calculation of a map projection requires definition of the spheroid (or ellipsoid) in terms of the length of axes and eccentricity squared (or radius of the reference sphere). Several principal spheroids are in use by one or more countries. Differences are due primarily to calculation of the spheroid for a particular region of the Earth’s surface. Only recently have satellite tracking data provided spheroid determinations for the entire Earth. However, these spheroids may not give the best fit for a particular region. In North America, the spheroid in use is the Clarke 1866 for NAD27 and GRS 1980 for NAD83 (State Plane).

If other regions are to be mapped, different projections should be used. Upon choosing a desired projection type, you have the option to choose a spheroid. The Projection Chooser contains all the supported spheroids. The following lists some of the commonly used spheroids.

  • Airy
  • Australian National
  • Bessel
  • Clarke 1866
  • Clarke 1880
  • Everest
  • GRS 1980
  • Helmert
  • Hough
  • International 1909
  • Krasovsky
  • Mercury 1960
  • Modified Airy
  • Modified Everest
  • Modified Mercury 1968
  • New International 1967
  • Southeast Asia
  • Sphere of Nominal Radius of Earth
  • Sphere of Radius 6370977m
  • Walbeck
  • WGS 66
  • WGS 72
  • WGS 84

SHARED Tip The spheroids listed above are the most commonly used. There are many other spheroids available, and they are listed in Projection Chooser. These additional spheroids are not documented in this Guide. You can add your own map projections and spheroids to ERDAS IMAGINE.

The semi-major and semi-minor axes of supported spheroids are listed in tables Earth Spheroids for use in ERDAS IMAGINE and Non-Earth Spheroids for use in ERDAS IMAGINE, as well as the principal uses of these spheroids.

Earth Spheroids for use in ERDAS IMAGINE

Spheroid

Semi-Major Axis

Semi-Minor Axis

Use

165

6378165.0

6356783.0

Global

Airy (1940)

6377563.0

6356256.91

England

Airy Modified (1849)

Ireland

Australian National (1965)

6378160.0

6356774.719

Australia

Bessel (1841)

6377397.155

6356078.96284

Central Europe, Chile, and Indonesia

Bessell (Namibia)

6377483.865

6356165.383

Namibia

Clarke 1858

6378293.0

6356619.0

Global

Clarke 1866

6378206.4

6356583.8

North America and the Philippines

Clarke 1880

6378249.145

6356514.86955

France and Africa

Clarke 1880 IGN

6378249.2

6356515.0

Global

Everest (1830)

6377276.3452

6356075.4133

India, Burma, and Pakistan

Everest (1956)

6377301.243

6356100.2284

India, Nepal

Everest (1969)

6377295.664

6356094.6679

Global

Everest (Malaysia & Singapore)

6377304.063

6356103.038993

Global

Everest (Pakistan)

6377309.613

6356108.570542

Pakistan

Everest (Sabah & Sarawak)

6377298.556

6356097.5503

Brunei, East Malaysia

Fischer (1960)

6378166.0

6356784.2836

Global

Fischer (1968)

6378150.0

6356768.3372

Global

GRS 1980 (Geodetic Reference System)

6378137.0

6356752.31414

Adopted in North America for 1983 Earth-centered coordinate system (satellite)

Hayford

6378388.0

6356911.946128

Global

Helmert

6378200.0

6356818.16962789092

Egypt

Hough

6378270.0

6356794.343479

As International 1909 above, with modification of ellipse axes

IAU 1965

6378160.0

6356775.0

Global

Indonesian 1974

6378160.0

6356774.504086

Global

International 1909 (= Hayford)

6378388.0

6356911.94613

Remaining parts of the world not listed here

IUGG 1967

6378160.0

6356774.516

Hungary

Krasovsky (1940)

6378245.0

6356863.0188

Former Soviet Union and some East European countries

Mercury 1960

6378166.0

6356794.283666

Early satellite, rarely used

Modified Airy

6377341.89

6356036.143

As Airy above, more recent version

Modified Everest

6377304.063

6356103.039

As Everest above, more recent version

Modified Mercury 1968

6378150.0

6356768.337303

As Mercury 1960 above, more recent calculation

Modified Fischer (1960)

6378155.0

6356773.3205

Singapore

New International 1967

6378157.5

6356772.2

As International 1909 below, more recent calculation

SGS 85 (Soviet Geodetic System 1985)

6378136.0

6356751.3016

Soviet Union

South American (1969)

6378160.0

6356774.7192

South America

Southeast Asia

6378155.0

6356773.3205

As named

Sphere

6371000.0

6371000.0

Global

Sphere of Nominal Radius of Earth

6370997.0

6370997.0

A perfect sphere

Sphere of Radius 6370997 m

6370997.0

6370997.0

A perfect sphere with the same surface area as the Clarke 1866 spheroid

Walbeck (1819)

6376896.0

6355834.8467

Soviet Union, up to 1910

WGS 60 (World Geodetic System 1960)

6378165.0

6356783.287

Global

WGS 66 (World Geodetic System 1966)

6378145.0

6356759.769356

As WGS 72 above, older version

WGS 72 (World Geodetic System 1972)

6378135.0

6356750.519915

NASA (satellite)

WGS 84 (World Geodetic System 1984)

6378137.0

6356752.31424517929

As WGS 72, more recent calculation

Non-Earth Spheroids

Spheroid models can be applied to planetary bodies other than the Earth, such as the Moon, Venus, Mars, various asteroids, and other planets in our Solar System. Spheroids for these planetary bodies have a defined semi-major axis and a semi-minor axis, measured in meters, corresponding to Earth spheroids.

See the "Ellipse Diagram" at the top of this topic for an illustration of the axes defined in an ellipse.

The semi-major and semi-minor axes of the supported extraterrestrial spheroids are listed in the following table.

Non-Earth Spheroids for use in ERDAS IMAGINE

Spheroid

Semi-Major Axis

Semi-Minor Axis

Moon

1738100.0

1736000.0

Mercury

2439700.0

2439700.0

Venus

6051800.0

6051800.0

Mars

3396200.0

3376200.0

Jupiter

71492000.0

66854000.0

Saturn

60268000.0

54364000.0

Uranus

25559000.0

24973000.0

Neptune

24764000.0

24341000.0

Pluto

1195000.0

1195000.0