@uhoh I see! I have just been updating my Earth gravity potential model to use GGM05C instead of GGM03S, so have been able to get back into looking into the details of what normalization I'm using.

To be precise, I'm using the normalization described here download.csr.utexas.edu/pub/grace/GGM05/GGM05_Notes.pdf , which seems to match the same used in this IERS note iers.org/SharedDocs/Publikationen/EN/IERS/Publications/tn/… (described in page 1)

The GGM0X models seem to use this normalization of the Legendre polynomials together with what they call "fully normalized" coefficients (as can be inferred by the fact that, in the header of their files, e.g. GGM05C.ICGEM.gz from download.csr.utexas.edu/pub/grace/GGM05 , they state "norm fully_normalized"

This document by the same authors of the CERES dataset www-geodyn.mit.edu/konopliv_dawn_ssr11.pdf states, by the end of the page that has Fig. 6, that the coefficients are chosen such that the integral of the squared harmonics equals the surface of a unit sphere (4pi), so I'm assuming that the same normalization for Legendre functions used with the GGM0X models should be used with this dataset ...?

@Rafa This is absolutely wonderful! It will take me some time and coffee to digest, but I'll let you know where it takes me. thank you!

Cool telescope optics question, but also involves "fairing packing"