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Trapped Radiation ENvironment model Development

Frequently Asked Questions

[ Question | Answer | Illustration | See Also ]

Question

    G.05 - Which 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 structure /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).

    When geodetic coordinates are used, geographic position are given relatively 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. Vrho, Vtheta, Vphi 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

    Vrho = Vx sin theta cos phi + Vy sin theta sin phi + Vz cos theta
    Vtheta = Vx cos theta cos phi + Vy cos theta sin phi - Vz sin theta
    Vphi = -Vx sin phi + Vy 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 only 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.

    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 10+3m
    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

    None

See also

    UC160, general constants