# Coordinate systems

In space physics, it is extremely important to know where the measurements have been made. This is not as trivial a question as one might think, since it is not enough to know the location with respect to the Earth and/or the Sun in some arbitrary coordinate system. One may have to consider things like differences between the solar equatorial plane and the Earth's orbital plane, the changing direction of Earth's spin axis during the year, and the magnetic dipole orientation. Sometimes the reference of the coordinates may be something more exotic than planetary bodies: for example, magnetopause provides the possibility to use boundary normal coordinates. Especially when one has to make comparisons between measurements from different places in space and from ground, the coordinate transformation routines are valuable.

There are several geocentric coordinate systems in use, the most obvious and best known being the geographic system. Some of them are listed below with some heliocentric systems:

Geocentric systems

Geocentric equatorial inertial

GEI

X=First point of Aries
Z=Geographic North Pole

Geographic

GEO

X=Intersection of Greenwich meridian and geographic equator
Z=Geographic North Pole

Geocentric solar ecliptic

GSE

X=Earth-Sun line
Z=Ecliptic North Pole

Geocentric solar magnetospheric

GSM

X=Earth-Sun line
Z=Projection of dipole axis on GSE YZ plane

Solar magnetic

SM

Y=Perpendicular to plane containing Earth-Sun line and dipole axis. Positive sense is opposite to Earth's orbital motion
Z=Dipole axis

Geomagnetic

MAG

Y=Intersection between geographic equator and the geographic meridian 90 degrees east of the meridian containing the dipole axis
Z=Dipole axis

Heliocentric systems

Heliocentric Aries ecliptic

HAE

X=First point of Aries
Z=Ecliptic North Pole

Heliocentric Earth ecliptic

HEE

X=Sun-Earth line
Z=Ecliptic North Pole

Heliocentric Earth equatorial

HEEQ

X=Intersection between solar equator and solar central meridian as seen from Earth
Z=North Pole of solar rotation axis

Also a system called Corrected GeoMagnetic (CGM) coordinates exists (see here for more details and online calculation service!). There exist also an Altitude Adjusted Corrected Geomagnetic coordinates (AACGGM) system and an Apex magnetic coordinate system (Richmond, 1995).

Boundary normal coordinates are defined relative to some natural boundary such as the magnetopause or the bow shock. They allow the data to be ordered in a way which is related to that boundary. Two of the axes lie in a plane tangential to the boundary, and one axis is normal to this boundary. For more information see, e.g., Kawano and Higuchi (1996).

A good description how to make transformations between the different coordinate systems can be found in a paper by Hapgood (1992). Similar routines are also included in the famous Tsyganenko magnetic field models.

### References

• Hapgood, M. A., Space physics coordinate transformations: A user guide, Planetary and Space Science, 40, 711-717, 1992.
• Kawano, H. and T. Higuchi, A generalization of the minimum variance analysis method,Ann. Geophysicae, 14, 1019-1024, 1996.
• Richmond, A. D., Ionospheric electrodynamics using magnetic apex coordinates,J. Geomag. Geoelectr., 47, 191, 1995.
• No labels