Calculations of dipole axis, dipole poles, and dipole tilt angle

Example of how to calculate dipole tilt angle:

>>> print dipole_tilt(datetime(1927, 6, 10, 12, 00), epoch = 1927)
[ 26.79107107]

One can also give several times as input, and the tilt angle will be calculated for each of them. Since the calculations are entirely based on array calculations, this is quite fast.

>>> print dipole_tilt([datetime(1927, 6, 10, 12, 00), datetime(1927, 6, 10, 10, 00)], epoch = 1927)
[ 26.79107107  20.89550663]

The epoch keyword is the year (with fraction) for which the dipole axis is calculated. This is done from IGRF coefficients, using linear interpolation between models. Setting the epoch is optional, and the default value is 2015. One can provide either one value for the epoch, or one value for each input. The latter may be a little slow, and is usually overkill unless the dates are very far apart:

>>> print dipole_tilt([datetime(1927, 6, 10, 12, 00), datetime(2015, 6, 10, 12, 00)], epoch = (1927, 2015))
[ 26.79107107,  25.58815326]

Calculation of dipole axis, dipole poles, dipole tilt angle, and subsolar point is described in Laundal, K.M. & Richmond, A.D. Space Sci Rev (2017) 206: 27. https://doi.org/10.1007/s11214-016-0275-y

(Note that there seems to be a mistake in equation 14 of that paper, showing a formula for for the centered dipole longitude in the northern hemisphere. That formula will give the pole longitude in the southern hemisphere instead)

numpy, pandas