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The orbit of the centre of the Sun around the centre of mass of the solar system (in units of 10 )3 AU, astronomical unit = 149 á 10 6 km), for further details see Fig. 2. The dashed horizontal abscissa in the upper part of the ®gure represents the diameter of the Sun 

The orbit of the centre of the Sun around the centre of mass of the solar system (in units of 10 )3 AU, astronomical unit = 149 á 10 6 km), for further details see Fig. 2. The dashed horizontal abscissa in the upper part of the ®gure represents the diameter of the Sun 

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A solar activity cycle of about 2400 years has until now been of uncertain origin. Recent results indicate it is caused by solar inertial motion. First we describe the 178.7-year basic cycle of solar motion. The longer cycle, over an 8000 year interval, is found to average 2402.2 years. This corresponds to the Jupiter/Heliocentre/Barycentre alignme...

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... ®rst basic cycle of solar inertial motion, the cycle of 178.7 years, was found by Jose (1965) in a repetition of solar motion characteristics computed between 1653 and 2060, and most important the time derivative of the Sun's angular momentum was found. The cycle was con®rmed by Fairbridge and Shirley (1987) since 760 AD, and by Fairbridge and Sanders (1987) since 777 AD. Jakubcova and Pick (1987) veri®ed the 178.7 year cycle as the basic period of solar motion periodicities (see their Fig. 1). These periods have been found as its higher harmonics [also Fairbridge, 1997, e.g. 28´17828´28´178.7=5004.5 (252´JS252´252´JS; 24´20824´24´208.5 year VJU)] and mostly correspond to the orbital periods of the giant planets [i.e. the periods of 80±90 (U), 60, 45 (SN), 35 (SU), 30 (S), 13.8 (JU), 12.8 (JN), 11.9 (J), 10 ...
Context 2
... solar inertial motion (i.e., the motion of the Sun around the centre of mass of the solar system) is the central phenomenon of the solar system, caused by varying positions, predominantly, of the giant planets (Fairbridge and Sanders, 1987). The contribution by the inner planets is minute. The varying positions of the giant planets [Jupiter (J), Saturn (S), Uranus (U), Neptune (N)] force the Sun to move inside a circular area which has a diameter of 0.02 AU (astronomical unit) or 3 á 10 6 km, see Fig. 1. This is negligible in comparison with the size of the solar system, but it is very signi®cant with respect to the size of the Sun. The diameter of the area in which the Sun moves represents 4.4 solar radii. The Sun moves with a velocity between 9 and 16 m á s )1 , i.e. 30 and 60 km á h -1 . This solar motion is computable in advance, a great advantage that opens up the possibility of establishing predictive assessments of solar ...

Citations

... In both cases, a perfect match between theoretical and experimental oscillations exists. These same cycles also emerge in the solar inertial motion [110,[112][113][114]. The Bray-Hallstatt cycle of 2000-2500 years is observed in several solar [59,115,116] and climate records [6,117,118] as well. ...
... Several authors found evidence supporting the planetary hypothesis for the origin of the solar activity oscillations by comparing solar activity records with the inertial motion of the Sun around the barycenter of the solar system [6,12,112,114,[137][138][139]. The Sun's wobbling mechanism is sometimes criticized as having no effect on solar activity, because the center of the Sun is in free-fall movement with no significant forces stressing the star. ...
... Charvátová [112] first noted that solar wobbling presents alternating complicated ordered and disordered dynamics that are correlated with, for example, the Bray-Hallstat solar and climate oscillations. Scafetta et al. [6] noted that such ordered and disordered dynamics, being related to changes in the gravitational and magnetic properties of the heliosphere, could modulate the particle fluxes from outside and within the solar system. ...
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The complex dynamics of solar activity appear to be characterized by a number of oscillations ranging from monthly to multimillennial timescales, the most well-known of which being the 11-year Schwabe sunspot cycle. Solar oscillations are important because they also characterize the oscillations observed in Earth’s climate and can thus be used to explain and forecast climate changes. Thus, it is important to investigate the physical origin of solar oscillations. There appear to be two possibilities: either the oscillations in solar activity are exclusively controlled by internal solar dynamo mechanisms, or the solar dynamo is partially synchronized to planetary frequencies by planetary forcings. The latter concept has recently gained support from a growing amount of evidence. In this work, we provide an overview of the many empirical facts that would support a planetary hypothesis of the variability of solar activity and emphasize their importance for climate research. We show that the frequencies produced by the complex interactions of all of the planets are coherent with the major solar activity and climate cycles, from monthly to multimillennial timescales, including the well-known Schwabe 11-year solar cycle. We provide some persuasive theoretical and empirical support for the planetary hypothesis of solar and climate variability.
... 本文将小波谱和EEMD方法应用于疫病指数和太 阳黑子数, 以探索流行病和太阳活动变化之间的关系. IMF6的周期可能对应于由太阳惯性运动驱动的Hallstatt cycle(约2000~2400年) (Charvátová, 2000;Usoskin 等, 2016). 太阳极大期和极小期分别倾向于在Hallstatt ...
... In fact, the orbit of the Earth is still a nearly stable ellipse with the Sun at one of its foci, as first noted by Kepler, because the gravitational forces of the jovian planets attracting the Sun act also on the Earth and the other inner planets making them all to wobble almost in synchrony. Yet, the SIM model could still have a physical meaning as it describes the pulsing dynamics of the heliosphere relative to the outer galactic space, as first noted in Charvátová (2000) and later developed in Scafetta et al. (2016). For example, if, as hypothesize by Bertolucci et al. (2017), solar activity is triggered by some kind of matter streaming from the deep-space towards the Sun, then, relative to the our star, such an external flux would be expected to be modulated by the SIM motion. ...
Article
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Gravitational planetary lensing of slow-moving matter streaming towards the Sun was suggested to explain puzzling solar-flare occurrences and other unexplained solar-emission phenomena (Bertolucci et al. in Phys. Dark Universe17, 13, 2017). If it is actually so, the effect of gravitational lensing of this stream by heavy planets (Jupiter, Saturn, Uranus and Neptune) could be manifested in solar activity changes on longer time scales too where solar records present specific oscillations known in the literature as the cycles of Bray–Hallstatt (2100–2500 yr), Eddy (800–1200 yr), Suess–de Vries (200–250 yr), Jose (155–185 yr), Gleissberg (80–100 year), the 55–65 yr spectral cluster and others. It is herein hypothesized that these oscillations emerge from specific periodic planetary orbital configurations that generate particular waves in the force-fields of the heliosphere which could be able to synchronize solar activity. These harmonics are defined by a subset of orbital frequencies herein labeled as “orbital invariant inequalities” of the solar system that derive from the synodical periods among the Jovian planets. Thus, they are associated with the repeating pattern of planetary alignment relative to the Sun when tidal forcing, interplanetary magnetic couplings and planetary lensing effects could be enhanced. These frequencies are physically relevant also because they are invariant relative to any spinning system centered on the Sun and, therefore, they and their combinations should characterize the spectrum of any forcing able to externally synchronizing the internal dynamics of the solar dynamo. Herein the orbital invariant inequalities of the solar system are determined and are demonstrated to cluster around specific spectral bands that exactly correspond to the above spectrum of solar activity. In particular, the orbital invariant inequality model is shown to predict, both in frequency and phase, the Bray–Hallstatt cycle (2100–2500 yr) found in Δ14C\Delta ^{14}C and in climate records throughout the Holocene. The result suggests that some kind of planetary forcing is synchronizing solar internal dynamics.
... Following Jose's original work, there were several further attempts to link the Sun's motion around the CMSS with long-term variations in solar activity (Landscheidt, 1981(Landscheidt, , 1999Chárvátova, 1988Chárvátova, , 1990Chárvátova, , 2000Zaqarashvili, 1997;Javaraiah and Gokhale, 1995;Javaraiah, 2003;Juckett, 2000). However, each of these attempts was dismissed by Shirley (2006), based upon the argument that di↵erential forces within the Sun cannot be produced by the Sun's motion around the CMSS (hereafter referred to as the solar inertial motion or SIM), since the Sun is in a state of free-fall. ...
... Following Jose's original work, there were several further attempts to link the Sun's motion around the CMSS with long-term variations in solar activity (Landscheidt, 1981(Landscheidt, , 1999Chárvátova, 1988Chárvátova, , 1990Chárvátova, , 2000Zaqarashvili, 1997;Javaraiah and Gokhale, 1995;Javaraiah, 2003;Juckett, 2000). However, each of these attempts was dismissed by Shirley (2006), based upon the argument that di↵erential forces within the Sun cannot be produced by the Sun's motion around the CMSS (hereafter referred to as the solar inertial motion or SIM), since the Sun is in a state of free-fall. ...
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The Sun’s activity constantly varies in characteristic cyclic patterns. With new material and new analyses, we reinforce the old proposal that the driv- ing forces are to be found the planetary beat on the Sun and the Sun’s mo- tions around the center of mass. This is a Special Issue published on Pattern Recognition in Physics where various aspects of the Planetary–Solar–Terrestrial interaction are highlighted in 12 independent papers. The Special Issue ends with General Conclusions co-authored by 19 prominent specialists on solar- terrestrial interaction and terrestrial climate. They conclude that the driving factor of solar variability must emerge from gravitational and inertial effects on the Sun from the planets and their satellites. By this, an old hypothesis seems elevated into a firm theory, maybe even a new paradigm.
... Several authors have associated the SBM with climatic and solar activity series (Jose, 1965;Charvatova, 2000;Leal-Silva andVelasco Herrera, 2012 Scafetta, 2010;Cionco and Compagnucci, 2012;McCracken et al., 2014;Cionco and Abuin, 2016;Okhlopkov, 2016;Sun et al., 2017;McCrann et al., 2018). However, other authors criticize the statistical methods adopted and the significance of some of the results (Cameron and Schussler, 2013;Holm, 2014Holm, , 2015. ...
Article
Precipitation and temperature over Tucuman (26.8°S, 65.2°W), a province located in the Northwestern region of Argentina, is analyzed for the interval 1889–2018 in search of any plausible statistical associations with impacts and responses from solar variability. The aim of the study was to contribute data to the controversial issue of climate variations in response to both anthropogenic and natural forcings. The long-term behavior of Tucuman climatic series involves overall warming and augmented precipitation tendencies, possibly linked to the increasing greenhouse gases concentration or even other local man-made factors like increasing urbanization. In addition, we identified sporadic ~4 and ~8-year periodicities, and a ~20-year oscillation after the 1950–1960's. Based on the physical hint that bidecadal periodicities detected in climate parameters are probably not linked to the solar 11-year-like irradiance cycles, we expand our scope of investigations to include another effect which has been recently considered in the dynamics of large rivers as “the planetary hypothesis of the solar cycles”. This new hypothesis supposes that the barycentric dynamics of the Sun could be involved in modulations of the intrinsic solar magnetic and radiative output cycles and therefore Earth-bound climatic responses. Thus, we present a wide-ranging statistical analysis of correlation, cross spectrum, and coherence between Tucuman's climatic series and solar orbital parameters, including also the analysis of hemispheric mean temperatures. Our results show significant coherence at the ~20-year cycle, which is clearly present in the Sun's barycentric dynamic that could in turn be linked to some features of the quasi-decadal solar activity variations.
... Jose (1965) descobriu que, embora este movimen- to seja complicado (Fig. 5), o Sol retorna à mesma posição a cada 179 anos, fenômeno conhecido como ciclo de Jose. Encontrado em teste- munhos da atividade solar nos últimos 8.000 anos, o ciclo de Hallstatt (~2.400 anos) tem como causa o movimento solar (Charvátová 2000), especificamente causado por uma grande res- sonância estável envolvendo os quatro planetas jovianos -Júpiter, Saturno, Urano e Netuno (Scafetta 2016). ...
Article
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A periódica mudança climática na Terra pode ser explicada por um número reduzido de fatores terrestres e astronômicos. Nas escalas anual/diária, o clima obedece aos movimentos de translação e de rotação. Ciclos climáticos de períodos médios (décadas/séculos/milênios) relacionam-se a mudanças na radiação solar, provocadas pela influência de grandes planetas do Sistema Solar. As oscilações oceânicas (ordem decadal) são possivelmente causadas por influências planetárias e lunares. Ciclos climáticos longos (dezenas a centenas de milhares de anos) são causados por variações nos parâmetros da órbita da Terra (excentricidade, obliquidade e precessão). Eventos de impacto de grandes corpos no planeta e extinções em massa de espécies advêm de superciclos (dezenas de milhões de anos) provocados pela oscilação vertical do Sistema Solar em relação ao plano galáctico. Tectonismo, vulcanismo e a evolução de supercontinentes exibem superciclos (centenas de milhões de anos) induzidos pelo deslocamento do Sistema Solar ao redor do centro da Via Láctea e pela variação de raios cósmicos. Fatores astronômicos permeiam praticamente todas as ordens dos ciclos climáticos e atuam direta ou indiretamente nos processos bio-geo-oceânico-atmosféricos. Conclui-se que o clima na Terra é caracterizado por ciclos controlados astronomicamente pela Lua, o Sol, os planetas, o Sistema Solar e, até mesmo, a Galáxia.
... The planetary system's barycenter is far from the solar interior, with a high value of the planet juncture index and a low value of the variation in its heliocentric longitude. The variation in the planetary system's heliocentric longitude is less than 0.523 each year during the periods of 1940-1945, 1980-1985, and 1995-2000 At this point, the planet juncture index is nearly the maximum. The planetary system barycenter is near the solar interior or it overlaps the low value of the planet juncture index and the high value of the variation in its heliocentric longitude. ...
... This finding is theoretically valuable for studying solar activity and global climate change. Charvátová (2000) has noted that the same phenomenon can be observed in the orbit of the Sun around the center of mass of the solar system. Our results reinforce previous findings by Charvátová. ...
... These findings illustrate that the planet movement influences solar activity to some extent. Similar results have been obtained when Charvátová studied the orbit of the Sun around the solar system barycenter (Charvátová., 2000). ...
Article
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The relationship between the periodic movement of the planetary system and its influence on solar activity is currently a serious topic in research. The kinematic index of the planet juncture index has been developed to find the track and variation of the Sun around the centroid of the solar system and the periodicity of solar activity. In the present study, the kinematic index of the planetary system's heliocentric longitude, developed based on the orbital elements of planets in the solar system, and it is used to investigate the periodic movement of the planetary system. The kinematic index of the planetary system's heliocentric longitude and that of the planet juncture index are simulated and analyzed. The numerical simulation of the two kinematic indexes shows orderly orbits and disorderly orbits of 49.9 and 129.6 years, respectively. Two orderly orbits or two disorderly orbits show a period change rule of 179.5 years. The contrast analysis between the periodic movement of the planetary system and the periodicity of solar activity shows that the two phenomena exhibit a period change rule of 179.5 years. Moreover, orderly orbits correspond to high periods of solar activity and disorderly orbits correspond to low periods of solar activity. Therefore, the relative movement of the planetary system affects solar activity to some extent. The relationship provides a basis for discussing the movement of the planetary system and solar activity.
... years). About the secular solar oscillations Charvátová (2000) showed that the inertial motion of the Sun varies from a trefoil ordered state, where the orbital patterns nearly repeat while rotating relative to the fixed stars, to a disordered one, where the orbits show confused and chaotic patterns. The ordered cases correspond to stable patterns correlated with historical solar maxima while the disordered ones correlate with historical solar minima. ...
... The lower list of panels reveals that during these periods the Sun-PMC orbits are more regular, more circular, symmetric and more uniformly cover all areas within a 7 AU radius distance from the Sun. The dynamics observed in Fig. 5is also reminiscent at the larger Hallstatt time scale of the trefoil ordered and disordered state of the inertial motion of the Sun which is correlated to the grand maxima and minima of solar activity, respectively, as suggested by Charvátová (2000Charvátová ( , 2009) inspired by the 178.7 year cycle found by Jose (1965). However, as Fig. 5shows, here it is during the transition periods from an orbital state to the other that correlates with periods of maximun or minimum radionucleotide production. ...
Article
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.
... (Climate and the Role of the Sun; Eddy, 1981) Solar activity (SA) has non-linear characteristics that influence multiple scales in solar processes (Vlahos and Georgoulis, 2004). For instance, millennia-scale solar oscillations have been recently detected, like those of about 6000 and 2400 years, by Xapsos and Burke (2009) and Charvátová (2000) , respectively, with important and interesting influences in the near, past and future climate. These millennialscale patterns of reconstructed SA variability could justify epochs of low activity, such as the Maunder minimum, as well as epochs of enhanced activity, such as the current Modern Maximum, and the Medieval maximum in the 12th cen- tury. ...
... These millennialscale patterns of reconstructed SA variability could justify epochs of low activity, such as the Maunder minimum, as well as epochs of enhanced activity, such as the current Modern Maximum, and the Medieval maximum in the 12th cen- tury. Although the reason for these SA oscillations is unclear, it has been proposed that they are due to chaotic behavior of non-linear dynamo equations (Ruzmaikin, 1983 ), or stochastic instabilities forcing the solar dynamo, leading to on-off intermittency (Schmitt et al., 1996), or planetary gravitational forcing with recurrent multi-decadal, multi-centennial and longer patterns (Fairbridge and Sanders, 1987; Fairbridge and Shirley, 1987; Charvátová, 2000; Duhau and de Jager, 2010; Perry and Hsu, 2000 ). It should be noted that all proponents of planetary forcing have forecasted a solar grand minimum for the upcoming decades, but one of them has also forecasted a super minimum for the next centuries (Perry and Hsu, 2000 ). ...
... The tested existence of the ∼ 9.5 kyr period recurrent pattern suggests that SA is characterized by solar dynamics with long-term patterns. Considering that it has been suggested that the modulating oscillations of SA, around 84, 178 and 2400 years, are possibly related to the Sun's rotation rate and impulses of the torque in the Sun's irregular motion (Landscheidt, 1999; Fairbridge and Sanders, 1987; Charvátová, 1995 Charvátová, , 2000), our results also suggest that similar mechanisms on the solar dynamo must be proposed for solar oscillations of around 9.5 kyr. This hypothesis should be tested, taking into account the results presented in this paper. ...
Article
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Solar activity (SA) oscillations over the past millennia are analyzed and extrapolated based on reconstructed solar-related records. Here, simple recurrent models of SA signal are applied and tested. The consequent results strongly suggest the following: (a) the existence of multi-millennial ( ∼ 9500-year) scale solar patterns linked with planetary gravitational forcing (PGF), and (b) their persistence, over at least the last glacial–interglacial cycle, but possibly since the Miocene (10.5 Myr ago). This empirical modeling of solar recurrent patterns has also provided a consequent multi-millennial-scale experimental forecast, suggesting a solar decreasing trend toward grand (super) minimum conditions for the upcoming period, AD 2050–2250 (AD 3750–4450). Taking into account the importance of these estimated SA scenarios, a comparison is made with other SA forecasts. In Appendixes A and B, we provide further verification, testing and analysis of solar recurrent patterns since geological eras, and their potential gravitational forcing.
... Several authors have associated the SBM with climatic and solar activity series (Jose, 1965;Charvatova, 2000;Leal-Silva andVelasco Herrera, 2012 Scafetta, 2010;Cionco and Compagnucci, 2012;McCracken et al., 2014;Cionco and Abuin, 2016;Okhlopkov, 2016;Sun et al., 2017;McCrann et al., 2018). However, other authors criticize the statistical methods adopted and the significance of some of the results (Cameron and Schussler, 2013;Holm, 2014Holm, , 2015. ...
Article
The precipitation over Tucuman (26.8°S, 65.2°W), Argentina, and Sidney (33.8°S, 151.2°E), Australia, present similar long-term variation patterns. In this work anthropogenic and solar forcings are analyzed as possible drivers of this behavior. Due to the nature of the processes that lead to precipitation, the discernment between solar and anthropogenic effects, and the link between precipitation and solar activity are highly complex and hard to detect. The aim of this work is to convey the importance of recognizing and quantifying the different forcing acting on precipitation which sometimes are not exposed by a statistical analysis. Annual mean precipitation time series together with solar and geomagnetic activity indices and atmospheric CO2 are analyzed. In order to survey the role of different forcing on precipitation variation we used wavelet and regression analysis with CO2, Rz and aa as independent variables acting as anthropogenic, solar and geomagnetic activity forcing respectively. In the long-term, all of them, considered separately, would induce a similar mean increase in precipitation. The increasing concentration of greenhouse gases, which is thought to be the main factor causing the global warming, is expected to induce an increasing trend of ∼0.8 mm/year, according to some authors. In our case, we obtain a much smaller value: ∼0.15 mm/year which in addition, is similar to the expected forcing from Rz or aa. The wavelet analysis yield significant results for the quasi-decadal and longer-term variations only in the case of Sydney. Significant correlations at time-scales longer than 22 years are also obtained through the regression analysis for Sydney. Although Tucuman do not present significant results, there is a clear similar behavior in the long-term trend. In spite of the fact that the present analysis do not allow us to determine the “true” forcing of the overall increasing trend observed in precipitation, it points out not only anthropogenic but natural mechanisms as possible origins of the precipitation variations.