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 point on the surrounding sphere (of radius ) which is the projection parallel to the Earth's axis of a point on the ellipsoid at latitude . It was introduced by Legendre and Bessel who solved problems for geodesics on the ellipsoid by transforming them to an equivalent problem for spherical geodesics by using this smaller latitude. Bessel's notation, , is also used in the current literature. The parametric latitude is related to the geodetic latitude by: The alternative name arises from the parameterization of the equation of the ellipse describing a meridian section. In terms of Cartesian coordinates , the