On the shoulders of Laplace

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