On the shoulders of Laplace

F. Lopes (1) , J. L. Le Mouël (1) , V. Courtillot (1) , D. Gibert (2)

1 IPGP (UMR_7154) - Institut de Physique du Globe de Paris
2 LGL-TPE - Laboratoire de Géologie de Lyon - Terre, Planètes, Environnement

In 1799, Laplace derived the system of differential equations (now called Liouville-Euler) that fully describes the motions of the rotation axis of any celestial body. Laplace showed that only the gravitational forces and kinetic moments from other celestial bodies influence the rotation of any one of them. The equations involve three Euler angles that specify the motions of a body's rotation axis; they can be reduced to a system of two equations for the inclination and time derivative of the declination of the rotation axis. Laplace showed the existence of a forced annual oscillation and the so-called free Chandler wobble. Most current theories retain only two Euler angles and invoke an elastic Earth to match observations. We analyze the much longer time series of polar motion (coordinates m₁ and m₂ of the rotation pole at the Earth's surface) now available, in order to further explore phenomena that Laplace could not investigate, given the dearth of data in his time. We use singular spectral analysis (SSA) to extract components of the time series. The first three components (trend or Markowitz drift, forced annual oscillation and free Chandler oscillation) account for 73% of the variance of polar motion. Under the current theory, their modulation is thought to be a response to reorganization of oceanic and atmospheric masses. However, the periods of the first six SSA components of polar motion have been encountered in previous studies of sunspots and in the ephemerids of Jovian planets. We also analyze the derivatives of the envelopes of the three SSA components of polar motion. Again, most of these components have periods and modulations that correspond to the ephemeris (periods and combinations of commensurable periods) of Jovian planets. Examples include 171.5 yr (the Jose cycle linked to Neptune), 90 yr (the Gleissberg cycle linked to Uranus), 40 yr (a commensurable period linked to the Jovian planets), 22 yr, 11 yr (Jupiter, Sun), 60 yr, 30 yr (Saturn). Fig. 3 can be considered as the central result of the paper. It shows that the sum of forces of the four Jovian planets matches in a striking way the polar motion reconstructed with SSA components (the Markowitz trend removed). All our results argue that significant parts of Earth's polar motion are a consequence (rather than a cause) of the evolution of planetary ephemerids. The Sun's activity and many geophysical indices show the same signatures, including many climate indices. Two different mechanisms (causal chains) are likely at work: a direct one from the Jovian Planets to Earth, another from planetary motions to the solar dynamo; variations in solar activity would in turn influence meteorological and climatic phenomena. Given the remarkable coincidence between the quasi-periods of many of these phenomena, it is reasonable to assume that both causal chains are simultaneously at work. In that sense, it is not surprising to find the signatures of the Schwabe, Hale and Gleissberg cycles in many terrestrial phenomena, reflecting the characteristic periods of the combined motions of the Jovian planets.

Mots clés: Laplace Treatise of Celestial Mechanics; Liouville-Euler partial differential equations; Orbital kinetic moments of planets; Planetary influence on Sun and Earth; Two causal chains; Pairing commensurable planets; Singular spectrum analysis

Domaines: Planète et Univers [physics]

F. Lopes, J. L. Le Mouël, V. Courtillot, D. Gibert. On the shoulders of Laplace. Physics of the Earth and Planetary Interiors, 2021, 316, pp. 434-438. ⟨10.1016/j.pepi.2021.106693⟩. ⟨insu-03590033⟩