  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.
