Garmaine Staff asked 2 years ago

Answers to What are the “Moon L, B, C” angles shown in this solar eclipse simulation? explain that L and B (or "l" and "b") are the "selenographic coordinates of the Moon's apparent center" (latitude and longitude respectively) as seen from Earth. While those two define the sub-Earth point, C is then used to determine the angle that the Moon's axis is rotated around that line it defines relative to Earth's axis in some way.

This answer to Ephemeris for lunar body-centered body-fixed coordinates? describes two Python methods in the Skyfield package that provide either the latitude and longitude parameters (L, B) or a 3×3 rotation matrix.

Question: How can one use those results to then calculate the L, B, C parameters? I'm assuming that the 3×3 rotation matrix contains what's needed but I'm not sure how to do the conversion.

above: Screen shot from NASA Goddard video Tracing the 2017 Solar Eclipse, below: screen shot from Taylor et al. 2011 (also NAO Technical Note No. 74 2010 August, Computation of the Quantities Describing the Lunar Librations in The Astronomical Almanac) borrowed from this answer.

Figure 1: The selenocentric sphere: showing the lunar orbit and the relationships between the subEarth point M, the mean lunar equator and the ecliptic. S is the descending node of the lunar equator on the ecliptic.