Invariant latitude

The dipole model of the Earth's magnetic field is a first order approximation of the rather complex true Earth's magnetic field. Due to effects of the interplanetary magnetic field, and the solar wind, the dipole model is particularly inaccurate at high L-shells (e.g., above L=3), but may be a good approximation for lower L-shells. For more precise work, or for any work at higher L-shells, a more accurate model that incorporates solar effects, such as the Tsyganenko magnetic field model, is recommended.

The following equations describe the dipole magnetic field.

First, define ${\displaystyle B_{0}}$ as the mean value of the magnetic field at the magnetic equator on the Earth's surface. Typically ${\displaystyle B_{0}=3.12\times 10^{-5}\ {\textrm {T}}}$.

Then, the radial and azimuthal fields can be described as

${\displaystyle B_{r}=-2B_{0}\left({\frac {R_{E}}{r}}\right)^{3}\cos \theta }$

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