# Lunisolar Forcing of the Chandler Wobble

In Chapter 13 of the book, we have a description of the mechanism forcing the Chandler Wobble in the Earth’s rotation. Even though there is not yet a research consensus on the mechanism, the prescribed lunisolar forcing seemed plausible enough that we included a detailed analysis in the text.  Recently we have found a recent reference to a supporting argument to our conjecture, which is presented below …

The paper by Barkin et al is brief yet includes enough information that one can likely reproduce their results.  Keeping track of the ascending node of the lunar orbit (see figure below), the idea is that due to the gravitational tidal forces from the moon and sun, there is enough of a cyclic reinforcement to result in a rotation perturbation, i.e. a wobble. In other words, the inertial moments of the deformable Earth enable enough of a reinforcing torque under the centrifugal forces caused by the Earth’s rotation and the gravitational field of the Moon to maintain the measured wobbling frequency.

The important trace in the following figure from Barkin is the cycle in RED which shows the ~433 day wobble period, which we claimed was related directly to the 27.2122 day nodel (or draconic) nodal cycle. From the paper, they come tantalizingly close to the same conclusion:

Figure 1 gives a decomposition of the Earth pole oscillation process into components for the coordinate yp. The resultant oscillation is presented at the top; this is followed by the Chandler, annual components, and the residual. A clearly distinguishable variation of the amplitude with a frequency that is twice the frequency of the precessional motion of the lunar orbit (twice the revolution frequency of the node of the lunar orbit) can be noted in the Chandler component of the oscillation process.

What they are referring to is the one-half the 18.6 year repeat envelope due to the interference between one-half the 27.2122 day nodal (draconic) cycle and a weaker influence of one-half the 27.3216 day synodic (tropical) cycle. The raw IERS measurements are the interference between the annual wobble with the Chandler wobble (with a ~6.4 year beat pattern) while the factored Chandler wobble will show the interference between half the nodal cycle and a semi-annual impulse (the faster cycles of 433 days) along with the 9.3 year envelope.

The following figure is a model fit to a simulated Chandler wobble pattern applying only an interference between the draconic, tropical, and annual cycles (note that the book provides more detail). Unfortunately, it’s still not clear in the Barkin paper that they definitely ascribe the 433 day wobble cycle to the reinforcing constructive interference between half the draconic cycle and a semi-annual equatorial-crossing impulse. That is the mechanism that has proved elusive to geophysicists through the years, even though the match is exact:

365.242 / (365.242/(27.2122/2) – 26) = 433 days

The transitive argument  that needs to be accepted is that a 9.3 year perturbation cycle can only exist (and be measurable) if and only if the 433 day cycle is perturbed by a related tidal mechanism. In other words, the 9.3 cycle requires the 433 day cycle be derived by a similar mechanism.

## 3 thoughts on “Lunisolar Forcing of the Chandler Wobble”

1. geoenergymath

Calculation of the CW period: from
Hu, H.X.S., W. van der Wal, and L.L.A. Vermeersen. “Rotational Dynamics of Tidally Deformed Planetary Bodies and Validity of Fluid Limit and Quasi-Fluid Approximation.” Icarus 321 (March 2019): 583–92. https://doi.org/10.1016/j.icarus.2018.08.013.

This is probably what they (Barkin et al) also use to fit the CW period — Ω plus 3 unknowns consisting of A,B,C, instead of the one fixed and known period corresponding to the Draconic cycle.

also this
https://arxiv.org/pdf/1901.10066.pdf has a detailed analysis using the same triaxial (A,B,C) resonance view
Guo, Zhiliang, and Wenbin Shen. “Formulation of a Triaxial Three-Layered Earth Rotation: I. Theory and Rotational Normal Mode Solutions.” ArXiv Preprint ArXiv:1901.10066, 2019.

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2. geoenergymath