European Space Agency

Royal Belgian Institute for Aeronomy

G.05 - What are the coordinates and units used ?

Answer

In the library, the geographic positions are expressed, as far as possible, in the Geocentric Equatorial (GEO) coordinate system in the form of longitude, colatitude and radial distance from the centre of the Earth (see zgeo). A convertor between geocentric and geodetic coordinates is provided in the library (subroutines um535() and um536()) as well as a convertor between GEO, Geocentric Equatorial Inertial (GEI), Geomagnetic (MAG), Solar Magnetic (SM) and Geocentric Solar Magnetospheric (GSM) coordinate systems (subroutines ut550() and ut555()).

See the Coordinate Systems definition table.

When geodetic coordinates (longitude, latitude and altitude) are used, geographic positions are given relative to the Earth’s geoid instead of a spherical approximation of the Earth’s surface. This coordinate system is generally associated to satellite ephemeris but is not well suited for mathematical computation. Different standard of World Geodetic System are currently in use. In the UNILIB library, the geodetic coordinates refer to the description of the Earth’s geoid by an axially symmetrical ellipsoid (the parameters of which are defined in common block uc160). The geodetic altitude is given by the distance from the ellipsoid surface, and the geodetic latitude is given by the angle between the equatorial plane and the line perpendicular to the ellipsoid surface which passes through the position. Be aware that in the library the same structure is used to represent geocentric and geodetic coordinates (see zgeo). Note also that the ellipsoid defined in the library does not correspond with the WGS84 standard (used by the Global Positioning System) nor the International 1924 standard.

The vector attached to a geographic position is stored with the help of spherical components (e.g. \(V_\rho\), \(V_\theta\), and \(V_\phi\) where the indices \(\rho\), \(\theta\) and \(\phi\) indicate the radial distance, the colatitude and the longitude in GEO, respectively). The spherical components are related to the cartesian components by the transformation

\(V_\rho = V_x sin(\theta)cos(\phi) + V_y sin(\theta)sin(\phi) + V_z cos(\theta)\)

\(V_\theta = V_x cos(\theta)cos(\phi) + V_y cos(\theta)sin(\phi) + V_z sin(\theta)\)

\(V_\phi = -V_x sin(\phi) + V_y cos(\phi)\)

One should note that the GEO spherical components and the Geocentric Inertial (GEI) spherical components of a vector are identical since both coordinate systems differ by a rotation arround the Z axis. The SI units are used to express the different physical quantities except for the quantities listed in the table below. Angles should be expressed in degrees.

constants

Quantity	Unit	Relation to SI
energy	MeV	1.602177×10-13 J
date	day	86400 s
dipole geomagnetic moment	Gauss RE3	2.58621×10-16 T m3
distance	km	103 m
Earth radius	RE	6,371,200 m
mass	amu	1.66054×10-27 kg
mass thickness	g cm-2	10 kg m-2
mass density	g cm -3	1000 kg m-3
number density	cm-3	10 6 m-3
magnetic flux density	Gauss	10-4 T
cross section	mbarn	10 -31 m2

Illustration

See Also

• uc160, general constants

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