DOI: 10.5281/zenodo.17619044
title: Dynamic Records of Solar Inertial Motion (SIM)

description: This page provides several data files related to the Sun’s inertial motion (SIM).

References [1,2] show that, over the period between Julian Days −3,027,183 (10 Jan −13,000) and +7,930,128 (7 Nov +16,999), the Sun’s inertial motion consists of a sequence of basic cycles, each containing a pericycle and an apocycle.

The data files were generated using programs based on the DE440 and DE441 ephemerides produced by the Solar System Dynamics Group at the Jet Propulsion Laboratory [3,4]. All times are expressed in Barycentric Dynamical Time (TDB). Descriptions of some fundamental calculation methods can be found in Ref.  [5] and [6].

Decimal values in the data are intentionally left with extra precision and may be rounded to the desired level as needed.



The file pericycles.txt contains Julian days, years, coordinates, and mutual distances for the entering and exiting points of all 1,510 pericycles within the period from 15 January −12,987 to 7 March 16,990. The data format is described in format_pecs.txt.

Within the same time range, the relative maxima and minima of both distance and velocity magnitude of the Sun with respect to the Solar System Barycenter (SSB) have been calculated. These values are provided in the files maxmind.txt and maxminv.txt, respectively. The format for both files is detailed in format_maxmin.txt.

The file cycle_paths.txt includes the start and end dates of pericycles, apocycles, and basic cycles, along with the approximate lengths of the paths (in kilometers) and the times taken to complete the three cycles. The path lengths were calculated by dividing the paths into small arcs, each traversed in a predetermined time interval, with the assumption of uniformly accelerated motion in each arc. The file format is provided in format_cp.txt.

The file path_maxmin.txt contains the minima, maxima, and average values for the path lengths and the times taken to complete the cycles.

The file rtr_motion.txt contains data on all 69 periods of the Sun’s retrograde motion found between 10 January −13,000 (Julian Day −3,027,183) and 9 December 16,999 (Julian Day 7,930,160). The format is detailed in format_rtr.txt.



Each of the following six zip files contains a text file with daily data calculated for the period from the year 1000 to 2800, along with a file describing the data format. The angular momenta are given per unit mass.

The data can be used to examine the behavior of the related functions over different periods and to plot their graphs.

We denote vectors using bold letters: position r, velocity v, acceleration a, jerk J = da/dt, angular momentum L about the Solar System Barycenter (SSB), and M about the center of curvature, the center c of the osculating spheres. The magnitudes of the vectors are represented by two vertical bars, | |.

· Distance |r|, magnitude of velocity |v| and of acceleration |a|: sim_dva.7z· Radius of curvature ρ = |v|³/|v×a|: sim_rd.7z· Magnitude |L| = |r×v| of the angular momentum about the SSB: sim_mt.7z· Magnitude |M| = ρ|v| of the angular momentum about the center of curvature: sim_md.7z· Torsion coefficient τ = v⋅(a×j)/|v×a|²: sim_tor.7z· Osculating spheres belonging to the curve evolute of trajectory,  center c = r+[ρ/(|v×a||v|)][(v×a)×v]+(ρ′/τ)[(v×a)/|v×a|] and radius Rs = [ρ²+(ρ′/τ)²]½: sim_ev.7zTo obtain the exact values, quantities assuming unit mass must be multiplied by the solar mass (in kilograms), and the corresponding units should then be adjusted by multiplying by kilograms.



References:

[1] Piovan, L., & Milani, F. (2006). Moto del Sole intorno al baricentro del sistema solare. Astronomia, 3 (May–June), 38–44.

[2] Scafetta, N., & Milani, F. (2025). Spectral Structure of the Solar Inertial Motion from 12999 BC to 16998 AD. Publications of the Astronomical Society of the Pacific (PASP), 137, 054402.

[3] Park, R. S., Folkner, W. M., Williams, J. G., & Boggs, D. M. (2021). The JPL Planetary and Lunar Ephemerides DE440 and DE441. Astronomical Journal, 161(3), 105.

[4] NASA Jet Propulsion Laboratory. Planetary Ephemerides (ASCII files). Retrieved from ftp://ssd.jpl.nasa.gov/pub/eph/planets/ascii

[5] Pimm, F. S., & Bjorn, T. (1969). Prediction of Smoothed Sunspot Numbers Using Dynamic Relations Between the Sun and Planets. NASA Technical Report N69-29781, Washington, D.C.

[6] Fuchs, D. (2013). Evolutes and Involutes of Spatial Curves. American Mathematical Monthly, 120(3), 217–231.

Original link: http://sunlab.altervista.org/