The Phys.org article Physicists provide first model of moon's rotational dynamics, accounting for the solid inner core describes the September 2018 paper by Christopher Stys and Mathieu Dumberry The Cassini State of the Moon's Inner Core.

The plain language summary of the paper is as follows:

It is well known that the reason we see only one face of the Moon is because the period of its revolution around Earth is equal to the period of Moon's rotation around itself. Yet the full description of the Moon's rotation is a bit more complex. The Lunar spin axis is inclined by 1.54° in space, and its direction is precessing, like a spinning top, at a period of 18.6 years. This precession is caused by the precession of the plane of the Lunar orbit at the same period, an arrangement known as a Cassini state, named after the seventeenth century Italian astronomer. Like the Earth, the Moon is suspected to have a metallic iron core, its outer region being fluid but the central part being solid. In this work, we calculate the tilt of the spin axis of this solid inner core so that it obeys a Cassini state. We show that this angle can be large, 17° with respect to the mantle for one specific model but that it is also very sensitive to the specific size and mass of the solid and fluid parts of the Lunar core which are not well known.

Further searching leads to Wikipedia's article Cassini's laws, "...a compact description of the motion of the Moon. They were established in 1693 by Giovanni Domenico Cassini, a prominent scientist of his time."

  1. The Moon has a 1:1 spin–orbit resonance. This means that the rotation–orbit ratio of the Moon is such that the same side of it always faces the Earth.
  2. The Moon's rotational axis maintains a constant angle of inclination from the ecliptic plane. The Moon's rotational axis precesses so as to trace out a cone that intersects the ecliptic plane as a circle.
  3. A plane formed from a normal to the ecliptic plane and a normal to the Moon's orbital plane will contain the Moon's rotational axis.

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Now that I have found out that the Moon's rotational axis is inclined by about 1.54 degrees with respect to its orbital plane, I can finally understand all of the motion in the Moon's disk during its orbit around the earth as described in the question Who does these mesmerizing simulations of the phases of the Moon? And how? and shown below.

Question: How did Cassini measure the "Cassini state" of the Moon? What did the data look like? Did he make detailed drawings, or measurements of certain features on the moon, perhaps near the terminator or limb?

A sample of the raw data or an image of his notes would also be wonderful to see if something is available.

Animation used in EarthSky.org:

EDIT: As pointed out here by the GIF's creator, the original image is actually in Wikipedia.

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Animation from Wikipedia:

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