Spectral Structure of the Solar Inertial Motion from 12999 BC to 16998 AD

The solar inertial motion (SIM) reflects the dynamics of the planetary system around the Sun. To study and accurately model the frequency domain of the SIM is of great importance as any function of the orbits as a whole is expected to be spectrally coherent with it. This study proposes a comprehensive spectral model for accurately reconstructing the SIM frequencies using the orbital periodicities of the Jovian planets. Specifically, we utilize high-precision records of the SIM (from 12999 BC to 16998 AD) obtained from the latest JPL ephemeris 4les DE440 and DE441 to estimate the temporal sequences of the periods and lengths of the SIM orbital cycles. The 30,000 yr-long SIM records are used to evaluate SIM periodograms with the highest spectral resolution currently available. The obtained sharp spectra enabled the validation of our spectral model constructed using the orbital near-commensurabilities of Jupiter, Saturn, Uranus, and Neptune.We provide a brief overview of the primary mathematical properties of the proposed model and, in particular, we demonstrate that it can be conveniently represented and managed through the adoption of a vectorial formulation, which allows for the rapid calculation of each SIM periodicity. This formulation employs the synodic periods of each planet pair as constructors, in addition to the orbital period of a single planet (e.g., Jupiter alone). Thus, we demonstrate that the proposed spectral model accurately identi4es the speci4c planetary origin of each frequency of the SIM, which are numerous, and illustrate that they are clustered around speci4c frequency values. Finally, we also show that these SIM frequency clusters are well centered around periods given by the harmonic model Pn ≈ 179/(n − 1) yr (where n>= 2 is the cluster order) up to at least the 20th harmonic and discuss the significance of some of the long millennial SIM periodicities.