An oscillation with a period of about 2100-2500 years, the Hallstatt cycle, is found in cosmogenic radioisotopes (C-14 and Be-10) and in paleoclimate records throughout the Holocene. Herein we demonstrate the astronomical origin of this cycle. Namely, this oscillation is coherent to the major stable resonance involving the four Jovian planets - Jupiter, Saturn, Uranus and Neptune - whose period is p=2318 yr. The Hallstatt cycle could derive from the rhythmic variation of the circularity of the solar system disk assuming that this dynamics could eventually modulate the solar wind and, consequently, the incoming cosmic ray flux and/or the interplanetary/cosmic dust concentration around the Earth-Moon system. The orbit of the planetary mass center (PMC) relative to the Sun is used as a proxy. We analyzed how the instantaneous eccentricity vector of this virtual orbit varies from 13,000 B. C. to 17,000 A. D.. We found that it undergoes kind of pulsations as it clearly presents rhythmic contraction and expansion patterns with a 2318 yr period together with a number of already known faster oscillations associated to the planetary orbital stable resonances. We found that a fast expansion of the Sun-PMC orbit followed by a slow contraction appears to prevent cosmic rays to enter within the system inner region while a slow expansion followed by a fast contraction favors it. Similarly, the same dynamics could modulate the amount of interplanetary/cosmic dust falling on Earth. These would then cause both the radionucleotide production and climate change by means of a cloud/albedo modulation. Other stable orbital resonance frequencies (e.g. at periods of 20 yr, 45 yr, 60 yr, 85 yr, 159-171-185 yr, etc.) are found in radionucleotide, solar, aurora and climate records, as determined in the scientific literature. Thus, the result supports a planetary theory of solar and/or climate variation.
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