My understanding is that when tidal locking of a body first happens it transitions from a state where the average rotation period is faster than the orbital period to a state where they are the same on average.

This leaves it "rocking" back and forth as seen from the other body by almost ±180° initially, but the same kind of damping that initiated this state will continue to reduce this motion until the body is nearly "locked" to the other.

That's for a circular orbit. For an elliptical orbit there are still (at least small) gravitational torques that change throughout an orbital period, and when the inclination of the body's orbit relative to the larger body is non-zero and the axis of the orbiting body is inclined relative to its orbit, the torques become more complex.

Question: Is it possible to roughly express how much of our Moon's apparent libration amplitude seen from the Geocenter is due to:

  1. strictly to the Moon's eccentricity of about 0.0549 and assuming a constant rate of rotation? (for illustration purposes; from here and this I estimate about 6.3 degrees)
  2. other geometrical effects like inclination and tilt?
  3. residual or induced "rocking" i.e. deviations from a steady, "monthly" rotation around its own axis?

If these categories are awkward feel free to break it down differently. I'm assuming that one or two are much larger than the others, and each can at least be roughly quantified.

Related to lunar libration motion quantification:

To give some idea of what libration looks like here are two GIFs of our Moon's libration from Who does these mesmerizing simulations of the phases of the Moon? And how?


Sources: above and below


  • 2
    $\begingroup$ companion question: How “locked” are Pluto and Charon? How much does each librate as seen from the other? $\endgroup$
    – uhoh
    Jul 15, 2020 at 2:39
  • 1
    $\begingroup$ I think everything you want in answered in Astronomical Algorithms Ch 53 "Ephemeris for Physical Observations of the Moon". "Optical Librations" are the effects caused by the eccentricity of the moon's orbit, "Physical Librations" are the effects caused by the moon's variation in rotation, and the "Position Angle" are the observed effects due to the moon's orbit's inclination. $\endgroup$ May 30, 2022 at 19:42


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