Coming at them from practical applications is one approach. I've used spherical harmonics to model earth centric "surfaces" and fields - magnetics and gravity,

Coming at them from practical applications is one approach. I've used spherical harmonics to model earth centric "surfaces" and fields - magnetics and gravity, etc. You might think of them as a stacked sine and cosine waves (like a fourier transform breaking a continuous function into sin and cosine components) on a directional vector radiating outwards from the centre point of sphere. https://geomag.bgs.ac.uk/research/modelling/IGRF.html https://geomag.bgs.ac.uk/research/modelling/IGRF.html https://en.wikipedia.org/wiki/International_Geomagnetic_Reference_Field https://en.wikipedia.org/wiki/International_Geomagnetic_Refe... https://en.wikipedia.org/wiki/World_Magnetic_Model https://en.wikipedia.org/wiki/World_Magnetic_Model