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This is a supplemental answer for now because while we know that a two body orbit can be reduced to a one body orbit around a central potential, doing that here will be a little distracting and I think the result for the one body in central potential looks cleaner. See also answers to Can the radial oscillations of an elliptical orbit be solved using a ...

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The distance from the focus of attraction of an orbit can be expressed as a function of the true anomaly (angle) given by $r(\theta)=a\frac{1-e^2}{1+ecos(\theta)}$, where $a$ is the semi-major axis and $e$ is the eccentricity.

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Using Spice data files, the Skyfield library for Python can now report lunar libration as the sub-longitude and sub-latitude of the point on the Moon facing the Earth. To take an example from its documentation: from skyfield.api import PlanetaryConstants, load ts = load.timescale(builtin=True) t = ts.utc(2019, 12, 20, 11, 5) eph = load('de421.bsp') earth, ...

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