Dipole model of the Earth's magnetic field (MLAT), or geomagnetic latitude, formula_10 is measured northwards from the equator (analogous to geographic latitude) and is related to formula_9 by formula_12. In this case, the radial and azimuthal components of the magnetic field (the latter still in the formula_9 direction, measured from the axis of the north pole) are given by formula_14 formula_15 formula_16 where formula_17 in this case has units of Earth radii (formula_18). Invariant latitude is a parameter that describes where a particular magnetic field line touches the surface of the Earth. It is given by formula_19 or formula_20 where formula_21 is the invariant latitude and formula_22
Latitude package Maxima and expresses the coefficients in terms of both eccentricity and flattening. The series method is not applicable to the isometric latitude and one must use the conformal latitude in an intermediate step. The following plot shows the difference between the geodetic latitude and the auxiliary latitudes other than the isometric latitude (which diverges to infinity at the poles) for the case of the WGS84 ellipsoid. In every case the auxiliary latitude is the less (in magnitude) than the geodetic latitude. The differences shown on the plot are in arc minutes. The horizontal resolution of the plot fails to