Formula for the Chandler Period (Free Wobble of Planetary Bodies)

If the rotational equilibrium of a planetary body is disturbed, the rotation pole responds with a cyclical motion. When viewed from space, it is expressed as a wobble of the planet around its rotation axis and the duration of one cycle is referred to as the Chandler period. Because planets are not rigid, the wobble period differs from the  Euler period by the factor (1-k_X/k_f), where k_X/k_f is a ratio of two Love numbers. Here, we perform numerical simulations in which viscoelastic deformation of the planet and the Liouville equation hence polar motion are self-consistently coupled. We show that k_X is not the Love number at the frequency of the Chandler wobble itself, as is commonly assumed, but rather that it is close to k_e, the elastic Love number. This result is important when the Chandler periods of Earth and Mars are interpreted, because the measured frequency is related to the internal rheological structure in a different way than previously thought.

Details of this work are provided in the manuscript by Patočka and Walterová (2025).

 

References:

Patočka and Walterová (2025): “Formula for the Chandler Period (Free Wobble of Planetary Bodies)”, submitted to GRL, preprint in ESSOAr: 10.22541/essoar.172901323.38157149/v1