# Geocentric systems

The following coordinate systems at the centre of the Earth.

## 1. Systems based on the Earth's rotation axis

#### 1.1 Geographic (GEO)

This system has its Z axis parallel to the Earth's rotation axis (positive to the North) and its X axis towards the intersection of the Equator and the Greenwich Meridian. Thus it is convenient for specifying the location of ground stations and ground-based experiments as these are fixed quantities in the GEO system.

A note of warning. When GEO coordinates are expressed in spherical form, the latitude component is identical what is termed geocentric latitude by astronomers and geographers. However, note that this is different to the system of geodetic latitude used in normal map-making. The geodetic latitude at any location is the angle between the equatorial plane and the local normal to the Earth's surface. In general that normal is NOT parallel to a radius vector because the shape of the Earth is an oblate spheroid and not a sphere.

#### 1.2 Geocentric equatorial inertial (GEI)

This system has its Z axis parallel to the Earth's rotation axis (positive to the North) and its X axis towards the First Point of Aries (the direction in space defined by the intersection between the Earth's equatorial plane and the plane of its orbit around the Sun (the plane of the ecliptic). This system is (to first order) fixed with respect to the distant stars. It is convenient for specifying the orbits (and hence location) of Earth-orbiting spacecraft as one can specify a Keplerian orbit in this frame.

However note that the GEI system is subject to second order change with time owing to the various slow motions of the Earth's rotation axis with respect to the fixed stars. Thus for GEI coordinates one must specify the date (normally termed the epoch) to which the coordinate system applies. For space physics work one should use the epoch-of-date GEI system, i.e. the system applying at the same time as the data were taken. (Thus the rotation axis in GEI is identical with the GEO rotation axis.) On these pages the unqualified acronym GEI refers to the epoch-of-date system. See Hapgood (1995) for a more detailed discussion of this issue.

#### 1.3 Geocentric equatorial inertial for epoch J2000.0 (GEI2000)

Spacecraft orbits and locations are often made available in geocentric equatorial inertial coordinates for a fixed epoch, e.g. the standard astronomical epoch known as J2000.0, which is 12:00 UT on 1 January 2000. We treat this as a separate coordinate system (with the qualified acronym GEI2000) and specify how to transform from this to other systems.

## 2. Systems based on the Earth-Sun line

#### 2.1 Geocentric solar ecliptic (GSE)

This system has its X axis towards the Sun and its Z axis perpendicular to the plane of the Earth's orbit around the Sun (positive North). This system is fixed with respect to the Earth-Sun line. It is convenient for specifying magnetospheric boundaries. It has also been widely adopted as the system for representing vector quantities in space physics databases.

#### 2.2 Geocentric solar magnetospheric (GSM)

This system has its X axis towards the Sun and its Z axis is the projection of the Earth's magnetic dipole axis (positive North) on to the plane perpendicular to the X axis. The direction of the geomagnetic field near the nose of the magnetosphere is well-ordered by this system. Thus it is considered the best system to use when studying the effects of interplanetary magnetic field components (e.g. Bz) on magnetospheric and ionospheric phenomena.

## 3. Systems based on the dipole axis of the Earth's magnetic field

#### 3.1 Solar magnetic (SM)

This system has its Z axis parallel to the Earth's magnetic dipole axis (positive North) and its Y axis perpendicular to the plane containing the dipole axis and the Earth-Sun line (positive in direction opposite to the Earth's orbital motion). The direction of the geomagnetic field in the outer magnetosphere is well-ordered by this system. It is the preferred system for defining magnetic local time in the outer magnetosphere.

#### 3.2 Geomagnetic (MAG)

This system has its Z axis parallel to the Earth's magnetic dipole axis (positive North) and its Y axis is the intersection between the Earth's equator and the geographic meridian 90 degrees east of the meridan containing the dipole axis.

Last updated 17 July 1997 by Mike Hapgood (Email: M.Hapgood@rl.ac.uk)