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Can origin of the 2400-year cycle of solar activity be caused by solar inertial motion?


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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 alignments (9.8855 × 243). Within each cycle an exceptional segment of 370 years has been found characterized by a looping pattern by a trefoil or quasitrefoil geometry. Solar activity, evidenced by 14C tree-ring proxies, shows the same pattern. Solar motion is computable in advance, so this provides a basis for future predictive assessments. The next 370-year segment will occur between AD 2240 and 2610.Key words: Solar physics (celestial mechanics)
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Can origin of the 2400-year cycle of solar activity be caused
by solar inertial motion?
I. Charva
Geophysical Institute AS CR, Boc
ÂII, 141 31 Praha 4, Czech Republic
Received: 30 September 1999 / Revised: 14 January 2000 / Accepted: 17 January 2000
Abstract. 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 alignments (9.8855 ´243). With-
in each cycle an exceptional segment of 370 years has
been found characterized by a looping pattern by a
trefoil or quasitrefoil geometry. Solar activity, evidenced
C tree-ring proxies, shows the same pattern. Solar
motion is computable in advance, so this provides a
basis for future predictive assessments. The next 370-
year segment will occur between
2240 and 2610.
Key words: Solar physics (celestial mechanics)
1 Introduction
To ®nd a cause of solar variability is a key task for solar
physics. It is an important subject also for geophysics
due to the in¯uence of this variability on the Earth's
climate. Over recent centuries, enormous eorts have
been given to this problem. In recent decades satellites
have provided much data and in particular the obser-
vations of the satellite SOHO provides a more reliable
view of the solar interior.
It is now generally accepted that the two most
prominent long-term cycles are permanently present in
solar activity: a cycle of about 200 (160±210) years and
a cycle of about 2400 (2200±2600) years, see e.g. Suess
(1980), Sonett and Finney (1991), Damon and Linick
(1986), Damon et al. (1989), Damon and Sonett (1990),
Hood and Jirikowic (1991), etc. These studies have been
made on the basis of indirect, proxy
C record in tree
rings. A scatter of the cycle lengths observed is probably
due to the mixed quality of the records, the dierent
parts of the record being processed, and the various
methods of spectral analysis used, etc. It is dicult to
observe this periodicity of 200 years because the record
of sunspot numbers covers only 300 years. It is easier to
observe a periodicity of about 100 years (Gleissberg
cycle) connected with the amplitude modulation of the
sunspot number series. An origin of the prominent, and
permanently present, period of about 2400 years in solar
activity has still not been settled (i.e., is it solar,
geomagnetic, or extraheliospheric) or even enigmatic;
the underlying `forcing' being so far unknown. ``The
2400-year period appears to be stationary'' according to
Damon and Linick (1986).
The 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 á10
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 ás
, i.e. 30 and 60 km áh
. This solar
motion is computable in advance, a great advantage that
opens up the possibility of establishing predictive
assessments of solar activity.
To understand the 2402-year cycle, it is necessary to
describe ®rst and explain the basic cycle of solar motion,
the cycle of 178.7 years and its relations to solar activity
behaviour over recent centuries. Both cycle values have
been found to correspond to the intervals between the
exceptional patterns in solar motion. The values repre-
sent, in both cases, the mean of the dispersion intervals of
the prominent cycles found in solar activity mentioned.
Ann. Geophysicae 18, 399±405 (2000) ÓEGS ± Springer-Verlag 2000
2 The ®rst basic cycle of 178.7 years in solar motion
and its response in terms of solar activity
The ®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
, and by Fairbridge and Sanders (1987) since 777
Âand 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 ´178.7=5004.5 (252 ´JS; 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 (JS/2)].
The Sun moves in the plane of the solar system,
so this action is essentially planar (Z-coordinates have
been neglected for initial studies). Therefore, besides the
motion characteristics, the geometry of the solar orbit
should be most carefully considered. Eventually, this
geometrical approach did provide a key for the solution
of the solar motion ± solar activity relationship.
A key to solution consists in the separation of solar
motion into two basic orbital types (Charva
Â, 1988,
1990a, b), see Fig. 2: the ordered (according to JS
motion order, 117.3°, 19.86 years in a trefoil) and the
disordered. The Sun enters into the orbital trefoils with
a spacing, on average, of 178.7 years and moves along
a trefoil (in one loop) in about 50 years (10 years),
respectively. While the trefoil orbits are, after a rotation,
nearly the same, the disordered orbits dier from one to
another. After separation, the solar motion itself was
discernible and ®xed in time as a precise and homoge-
neous basis suitable for solar-terrestrial studies. Then,
it has been possible to observe separated solar motion
from a particular view point. The trefoil intervals which
recur in regular steps of 178.7 years can be taken and
employed as the exceptional and stable pattern of solar
A response to solar motion has been observed in solar
activity. In fact, it was noticed that the intervals of
disordered solar motion coincide with particular
prolonged minima in solar activity, such as the Wolf,
Èrer, Maunder and Dalton minima of this millennium.
The results obtained for mutual relationships be-
tween solar motion and solar activity during the latest,
basic 178.7 year cycle are summarized in Fig. 3a±d. If
solar motion is really a cause of solar variability, then
the motion along the same (trefoil) orbit should create
the same series of sunspot cycles. In fact, the Sun
moving along the same orbits during the trefoil intervals
of the eighteenth century (1734±1785) and the twentieth
century (1913±1964) (taken from minimum to minimum
of the sunspot cycles), created nearly the same sets of
®ve sunspot cycles (Charva
Â, 1990b, 1995a, 1997a, b):
cycles )1 to 3 and cycles 15 to 19. Small deviations can
be mainly ascribed to lower quality of sunspot numbers
in the eighteenth century. Unfortunately, the Wolf
number series is not homogeneous. It can be taken as
reliable only since about 1850. Earlier, it is of lower
quality and before 1749 not even the monthly data are
available. This is not sucient to con®rm an exact
response of the solar trefoil motion in the Wolf series.
The highest and the only signi®cant coecient of
correlation between the successive groups of ®ve sunspot
cycles since 1700 and the series from the trefoil intervals
is that (r= 0.81) between the two series of ®ve cycles
from both trefoil intervals. The basic cycle of 179 years
in those two phenomena, the mutual relation between
solar motion and solar activity thus became evident
(Fig. 3d).
It was shown (Charva
Â, 1995b, c, 1997a) that the
lengths of ®ve sunspot cycles (15±19) created by the Sun
moving along the trefoil orbit where motion along one
motion loop lasts 10 years (see Fig. 2, top), is stable and
equal to 10.1 (~JS/2) years. The more precise length of
the cycles )1 to 3 cannot be calculated, mainly due to
the lack of monthly data before 1749. However, the
mean length of the respective ®ve cycles is also about
10 years. In the surrounding and intermediate intervals,
the lengths of sunspot cycles are variable and generally
greater (Fig. 3a). The dominant period of 10.1 (JS/2)
years was detected in sunspot numbers from the both
trefoil intervals (Charva
Â, 1990b, Fig. 4), in contrast
to the longer dominant periods found for the other
intervals, up to 11.9 (J) years detected for the Dalton
minimum in solar activity (1790±1843) (Charva
Âk, 1994). Rabin et al. (1986) and Wilson (1988)
found that solar behaviour is bimodal, with modes being
10.1 and 11.9 years.
Fig. 1. The orbit of the centre of the Sun around the centre of
mass of the solar system (in units of 10
AU, astronomical
unit = 149 á10
km), for further details see Fig. 2. The dashed
horizontal abscissa in the upper part of the ®gure represents the
diameter of the Sun
400 I. Charva
Â: Can origin of the 2400-year cycle of solar activity be caused by solar inertial motion?
3 The second basic cycle in solar motion: 2402 years,
and its response in the proxy solar activity record
C in tree rings)
On the very long (millennial) time scale only indirect,
C records of solar activity (radiocarbon in tree-
rings) are available. Radiocarbon production in the
atmosphere and consequently in tree-rings, is owing to a
cosmic ray ¯ux which has signi®cantly varied, being in
inverse relationship with solar activity. The radiocarbon
record in tree-rings thus provides a reliable archive of
past solar activity.
The regularity of the 178.7-year cycle is sometimes
disturbed: e.g. between 158
and 208
, the ®rst
178.7-year basic cycle (the interval between the two
consecutive orbital trefoils) was twice shortened to 159
years and during the intermediate intervals the Sun
moved along an orbit that is not too far from a trefoil.
These 370-year segments of exceptional and nearly
stable motion of the Sun (along a trefoil to quasitrefoil
orbit) have been found to recur in steps of 2402 years,
the mean value being 2402.2 years.
Figure 4 displays the last three such segments: the
®rst from 158
to 208
, the second from 2561
to 2193
and the third from 4964
to 4596
. The
solar orbits are the same in all three cases, if we
imagine them after a rotation. Further back in the
past, the Sun moved along the same orbital pattern
between the years 7366
and 6998
. The next such
segment will occur between the years 2242
The strongest variations in solar activity occurred
during each of the second millenia, approximately,
where the longest on prolonged solar minima of Spo
(S) and Maunder (M) type occurred. The patterns of the
S- and M- minima have always been observed to be
dierent. Hood and Jirikowic (1991) note that the 2400-
year cycle modulates the amplitude of the cycle at about
200 (160±210) years. Charva
Â(1995b, c) pointed out
the coincidence of S (M) solar orbital patterns with the
respective S (M) types of solar minima occurrence,
(see Damon and Linick, 1986).
Note should be made here of the symmetry between
the moments of the Sun's entrances into the 50-year
trefoil orbits during the ®rst millennium (158, 338, 516,
695, ...,
) and the ®rst millennium (159, 338, 516, 695,
). The centre of symmetry is the year 25
details see Charva
Â, 1995b, c). In the centre of the
2402-year cycle, smaller irregularities occur in 178.7-
year cycle.
The exceptional segments of 370 years that regularly
recur in steps of 2402 years have served as a further tool in
searching for a response to solar inertial motion in solar
activity (Charva
Â, 1998). The properties of the 370-
year segment (exceptionality and approximate stability)
are found in the corresponding intervals of the proxy
(radiocarbon) record and provide evidence for a solar
motion response and indicate that the solar motion could
be a cause of solar variability also on a millennial scale.
An analogy with a response of the 50-year trefoil
orbital pattern in solar activity (high solar activity cycles
with constant 10-year length) suggests that the behav-
Fig. 2. The orbit of the centre of the Sun around the centre of mass of
the solar system (in units of 10
AU) separated into two basic types,
the ordered (in a JS-trefoil) (top) and the disordered (bottom). The
area in which the Sun moves has a diameter of 0.02 AU or 4.4 r
being the solar radius, or 3 á10
km. The most disordered sections of
the intervals lying between the trefoils are plotted. The Sun enters into
the trefoils with a periodicity of 178.7 years, on the average (see the
times, years at the top of the respective ®gures). The value represents
the ®rst basic cycle of solar motion. While the trefoils are nearly
identical (after a rotation), the disordered orbits dier one from the
other. The Wolf, Spo
Èrer, Maunder and Dalton prolonged minima of
solar activity coincide with the intervals of disordered solar motion.
The Sun moves along a trefoil (along one of the loops), over 50 (10)
years, respectively. The two latest and the following trefoils are
denoted by triangles
I. Charva
Â: Can origin of the 2400-year cycle of solar activity be caused by solar inertial motion? 401
iour of solar activity during the exceptional 370-year
orbital pattern can be characterized as trefoil to quasi-
trefoil, or could be close to that described for a trefoil.
Figure 5 shows radiocarbon
C records for the three
latest exceptional segments (the respective solar orbits
are plotted in Fig. 4) together with the adjacent millen-
nia, i.e. from 5800
to 3800
, from 3400
to 1400
and from 1000
to 1000
. In all three cases,
exceptionality and approximate stability (without pro-
longed minima) is seen. In this ®gure, local or regional
data (Irish or German oaks and pine) are taken from
Pearson and Quay (1993), Stuiver and Becker (1993)
and Stuiver and Pearson (1993). The most stationary
part of the record is seen precisely during the 370-year
exceptional segments of solar motion.
Figure 6 represents the whole series of data (marine
C ages calculated from atmospheric tree-ring
data with a smoothing spline through coral data) taken
from Stuiver and Braziunas (1993) since 6000
. One
can see that the most stationary parts of the record
occurred precisely during the 370-year exceptional
segments of solar motion denoted there by the dashed
vertical lines and by three triangles.
4 Predictive assessments for solar activity
up to the year 2610 AD based on analogies
with the previous solar motion patterns
Predictions of solar cycle heights and lengths have
mostly been made on the basis of broad set of recent
solar and geomagnetic data and on the basis of relations
found only in the latest high activity solar cycles. Not
knowing the underlying source of solar variability, such
predictions can be false, as manifested at present in the
case of the current cycle number 23 when a high to
extremely high cycle has been predicted (R
140±225) (e.g. Wilson, 1992; Schatten et al., 1996; Kane,
1997). Ahluwalia (1999) predicted that cycle 23 will be a
moderate cycle (more like cycle 17). However, it is now
clear that the cycle 23 will be one of the lowest activity
cycles of this century.
Solar motion, computable in advance, oers instead
predictive possibilities, so far, of course, only as anal-
ogies with the results found for the previous six
millennia. The solar orbits plotted in the intervals of
50 to 65 years from 1680 to 2001 (or 2135) are seen in
Fig. 3b, 2. The Sun's orbit in the years 1985±2035 is of
disordered (nontrefoil) type and similar to that of the
second half of the nineteenth century. By analogy,
mostly weaker and longer solar cycles should occur.
Their lengths could vary between 9.6 and 12.3 years,
their R
could lie between 65 and 140. The predictions
of R
for the cycle 23 made during the last decade vary
between 140 and 225 (an unacceptable range). Our own
prediction made on the basis of solar motion was the
only opinion to express the opposite: i.e. a low solar
cycle was predicted (Charva
Â, 1988, 1990a, b; Char-
Âand Str
Âk, 1991). Charva
Â(1990b) wrote:
``The current cycle 22 is probably the last of the high ones.
It should be followed by an epoch of about 40 years, in
which the solar motion will be chaotic (disordered) and
solar activity, therefore, should be low. The cycles will
probably be longer and irregular.'' Charva
Â(1995a, b)
pointed out that the lengths of future cycles should be
variable. As indicated by the initial, 3-year part of the
cycle 23 in comparison with the respective part of the
cycle 22 (in smoothed form, about R
80±90 in
comparison with R
155 in the same time since the
Fig. 3a±d. This ®gure summarizes the results obtained for solar
motion ± solar activity relation around the latest basic 178.7-year
cycle. aThe lengths of sunspot cycles since
1700: notice a constant
cycle length equal to 10 (JS/2) years during the trefoil interval 1913±
1964 (taken from minimum to minimum). During the previous trefoil
interval (1734±1785) the cycle lengths cannot be calculated more
precisely (see text). However, the mean value of cycle lengths is also 10
years there. In the surrounding and intermediate intervals, the cycle
lengths are variable and mostly greater. bThe solar orbit from
1680 to 2001 in sections of 50±65 years. Two trefoil intervals are
denoted by the triangles.Theblack circles denote the positions of the
sunspot cycle maxima. cThe Wolf sunspot numbers since
The letter A(A¢) denotes the trefoil interval of the eighteenth
(twentieth) century. dCoecients of correlation between the series of
®ve sunspot cycles that occurred during the trefoil intervals [1734±
1785 (A) and 1913±1964 (A¢)] and the successive groups of ®ve
sunspot cycles in steps of one cycle since 1700. The only signi®cant
coecient (r
= 0.81) is that between the groups of ®ve cycles
belonging to the trefoil intervals. The letter Ddenotes the Dalton
minimum of solar activity
402 I. Charva
Â: Can origin of the 2400-year cycle of solar activity be caused by solar inertial motion?
minimum), our prediction was true. After 2085
, the
Sun will move into the orbital trefoil. The activity series
of the cycles 15±19 should be repeated.
The next 370-year exceptional segment will occur
2240. Until 2610
, approximately stationary
activity should occur as a repetition of solar behaviour
during the previous exceptional segments (Figs. 5 and
6). High solar activity cycles with lengths of 10 years
could prevail, corresponding to the 10-year lengths
occurring for the trefoil type of solar motion.
5 Conclusion
These results show that the solar motion around the
centre of mass of the solar system could be considered as
the cause of solar variability. Not a static, but a dynamic
Sun should be taken into account. It appears that solar
motion is also the cause of the 2400-year cycle found in
proxy of solar activity. The results indicate that the so
far uncon®rmed source of the approximately 2400-year
cycle in solar activity, somewhat surprisingly, could be
in solar motion.
The discovery of the exceptional 370-year segments
of solar motion that recur in steps of 2402 years and
their imprint in the radiocarbon record is the main result
presented here. The basic cycle of 178.7 years, being the
interval between consecutive 50-year orbital trefoils, is
twice shortened by about 20 (JS) years, and during the
intermediate intervals the Sun moves along the trefoil to
a quasitrefoil orbit (Fig. 4). The 50-year orbital trefoils
in steps of 178.7 years and the 370-year exceptional
segments in steps of 2402 years represent the exceptional
patterns of solar motion (Figs. 2, 4). A response of the
50-year trefoil motion in solar activity is a series of ®ve
high, 10-year solar cycles (Fig. 3a). A response of the
370-year segments of trefoil to quasitrefoil motion is
approximately stationary (linear) with higher solar
activity (Figs. 5 and 6). The 10-year cycle length prevails
Since solar motion is computable in advance, this
permits predictive assessments for future solar behav-
iour. Moving along the disordered orbit to 2035
(Fig. 2, bottom), which is similar to that of the second
half of the nineteenth century (Fig. 3b), the Sun should
develop lower solar cycles (R
from 65 to 140) of very
variable length (from 9.6 to 12.3 years). The initial
development of the cycle 23, now in its third year,
con®rms this for the present cycle. Between 2086 and
, a set of cycles comparable to 15 to 19 should be
Fig. 4. The 370-year segments of the exceptional, stable pattern of
solar motion recurring in steps of 2402 years: notice the twice
shortened distance of 159 years between the three trefoils in each
segment (from 158
to 208
, from 2561
to 2193
from 4964
to 4596
). The next such segment will occur between
2240 and 2610
I. Charva
Â: Can origin of the 2400-year cycle of solar activity be caused by solar inertial motion? 403
repeated because the Sun will again move along a trefoil
Predictive assessments for the following centuries can
be based on the 370-year exceptional segments and the
related results. The next such segment will occur from
2240 to 2610. In correspondence with solar behav-
iour during the three previous exceptional 370-year
segments, approximately stationary, high solar activity
will be observed. The 10-year cycle lengths should
prevail. A very long term maximum of solar activity
comparable to that which was last observed during
classical antiquity should occur in the mentioned inter-
val (also see Stothers, 1979).
Statistical processing of the solar activity records
in context with two types of solar motion formations
is needed to estimate whether solar motion responds
in solar activity and to understand mutual relations
between the two phenomena. According to the results
obtained, the appropriate mechanism could eventually
be established. A key to this is likely hidden in the 50-
year trefoil interval. The mutual relations found between
solar motion and solar activity and the latest knowledge
about the internal structure of the Sun (obtained by
SOHO, e.g. Turck-Chieze et al., 1997; Kosowichev
et al., 1997) should be considered for this purpose.
The individual solar spheres must surely respond to
solar motion in distinct ways, provoking on the bound-
ary layers a solar dynamo. The thin layer at the
boundary between radiative and convection zones,
where a shear ¯ow was found by SOHO ± MDI,
`is likely to be the place where the solar dynamo operates'
(Kosowichev et al., 1997). The results indicate that
`solar dynamo' that was long sought in the solar
interior, operates more likely from the outside, by
means of the varying planetary con®gurations. As has
been shown in Charva
Â(1995a, b, c, 1997a), the solar
motion could aid predictions also for terrestrial phe-
nomena including climate.
Acknowledgements. This research was performed under the sup-
port of the Grant Agency of the Czech Republic, grant 97/205/
Topical Editor E. Antonucci thanks R.W. Fairbridge and
G. Bonino for their help in evaluating this paper.
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Â: Can origin of the 2400-year cycle of solar activity be caused by solar inertial motion? 405
... 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.
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As the globe has witnessed the pandemic, epidemic diseases exert a strong impact on human beings and ecosystems. Since the Sun is the primary energy source of the Earth, some scientific pioneers attempted to search for the discernible relation between solar activity and the incidence of epidemics. In this study, the periodic changes and trends of ancient Chinese epidemic data were analyzed in comparison with those of sunspot numbers, a solar activity proxy. The results show that the epidemic and solar activity changes are in good agreement to a certain extent, especially during the Gleissberg and the de Vries cycles. The wavelet coherence shows that the frequency of the epidemic data and sunspot numbers are highly associated. In addition, results from the ensemble empirical mode decomposition illustrate consistent variations in low-frequency decompositions. This study has important implications for further understanding of the potential impact of solar activity on Earth’s biosphere, the underlying mechanism of which needs further exploration.
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Commenting the 11-year sunspot cycle, Wolf (1859, MNRAS 19, 85–86) conjectured that “the variations of spot-frequency depend on the influences of Venus, Earth, Jupiter, and Saturn.” The high synchronization of our planetary system is already nicely revealed by the fact that the ratios of the planetary orbital radii are closely related to each other through a scaling-mirror symmetry equation (Bank and Scafetta, Front. Astron. Space Sci. 8, 758184, 2022). Reviewing the many planetary harmonics and the orbital invariant inequalities that characterize the planetary motions of the solar system from the monthly to the millennial time scales, we show that they are not randomly distributed but clearly tend to cluster around some specific values that also match those of the main solar activity cycles. In some cases, planetary models have even been able to predict the time-phase of the solar oscillations including the Schwabe 11-year sunspot cycle. We also stress that solar models based on the hypothesis that solar activity is regulated by its internal dynamics alone have never been able to reproduce the variety of the observed cycles. Although planetary tidal forces are weak, we review a number of mechanisms that could explain how the solar structure and the solar dynamo could get tuned to the planetary motions. In particular, we discuss how the effects of the weak tidal forces could be significantly amplified in the solar core by an induced increase in the H-burning. Mechanisms modulating the electromagnetic and gravitational large-scale structure of the planetary system are also discussed.
We introduce here in the current research the revisiting of approach to the dynamics of Sun center relative to barycenter of Solar system by using self-resulting photo-gravitational force of the Sun as the main reason of such motion. In case of slowly moving in the direction outwards with respect to the initial position of barycenter of Solar system (together with the current position of Solar system barycenter, of course) with average established velocity not less than 1050 Km/day, we should especially note that hierarchical configuration of Solar system will be preferably the same during this motion. As the main findings, we have suggested algorithm how to move towards stars using Solar self-resulting photo-gravitational force. The obvious physically reasonable assumption is that the Solar system will have been increasing its size during the evolution in a future (due to losses of the total angular momentum taking into account the tidal phenomena).
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Efforts to place recent climate observations in a long-term context have been driven by concerns about whether the global warming trend of the 20th century is part of natural climate variability or whether it is linked to increased anthropogenic emissions of greenhouse gases in the atmosphere. A new perspective on the climate and its changes is offered, highlighting those that occur due to natural cycles, which are generally not widespread. With the historical background on how the climate varied in the past, statistical research was conducted using time series techniques and spectral/harmonic analysis (Fourier series and spectrograms), which allowed the determination of periodic natural phenomena and their magnitudes in national variations of temperature. It was identified that the air surface temperature in Brazil expresses cycles of 4 years (oceanic-atmospheric origin related to ENSO), 33 years (Brückner cycles, lunar-solar origin) and 82 years (lower Gleissberg cycle, solar origin). Based on an alternative oscillatory model that incorporates such natural cycles, future projections of the air temperature in the country were prepared. For the year 2100, it is predicted that the air temperature in Brazil may reach the value of +1.8 ± 0.6 °C, according to the natural oscillatory model. In comparison, conventional models typically used by the IPCC indicate, by the end of the century, an increase of: +2.9 ± 1.2 °C (RCP4.5 model, with mitigation); +3.9 °C (SRES A1 model); and +5.7 ± 1.7 °C (RCP8.5 model, without mitigation). The most extreme values of conventional models reach proportions up to 4 times greater than the results obtained in the alternative model provided here. Analyzing the adherence of the models, it is concluded that the conventional models are overestimating and exaggerating a warming rate in Brazil that, in reality, has not been observed. The proposed natural oscillatory model, which has a high correlation with the data observed so far, indicates an increase in temperature in Brazil that may reach a modest value of +0.8 °C in 2040. For the same year, the SRES A1 and RCP8.5 models indicate values around +2.0 °C – which represents more than double of the projection based on natural climate cycles. Based on the projections that indicate a moderate warming, not so exaggerated, a new perspective of a less terrifying future climate is offered. In a context in which pernicious alarmist discourses predominate, spreading scenarios of apocalyptic global warming, it is hoped that new pondered views could help to appease the level of concern that today, has culminated in undesirable side effects - especially the high levels of eco-anxiety that has afflicted significant portions of society.
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To detect the cyclic component in time series of annual water runoff of rivers of the Siverskyi Donets River Basin structure, it is necessary to have a hydrological gauge, which closes a large river basin and has long continuous observations of water runoff. The only hydrological gauge that meets these conditions is the Siverskyi Donets – Lysychansk – the catchment area is 52,400 km2 and the beginning of observations of water runoff since 1892. The Siverskyi Donets – Lysychansk is quite intermittent. Analysis of annual water runoff data of “neighboring basins” for the Siverskyi Donets Basin showed that the longest series of continuous observations has a hydrological gauge the Desna River near Chernihiv – since 1895, the catchment area is 81400 km2. So, we can consider this basin as basic for calculations and determination of patterns of long-term variability of annual water runoff of rivers of the Siverskyi Donets Basin. The study used data from eight hydrological gauges: the Desna – Chernihiv, intermediate river basins – the Sula – Lubny, the Psel – Zapsillya, the Vorskla – Kobeliaky, within the study basin – the Siverskyi Donets – Lysychansk, the Bakhmut – Siversk, the Aidar – Novoselivka, as well as the Southern Bug – Oleksandrivka. To confirm the spatial consistency of the annual water runoff of the studied rivers, a correlation matrix between the time sequences of the water runoff of neighboring basins was determined. To obtain a generalized characteristic of long-term water runoff variability of the studied rivers, chronological graphs of changes in modular coefficients were constructed, initial time series smoothing was performed, graphical analysis of difference integral curves was applied. In the course of the research regularities in long-term variability of average annual water runoff of rivers of the Siverskyi Donets Basin were identified, cyclic component was identified, duration and nature of water runoff cycles and within them low and wet phases were identified. The prediction of annual water runoff in the near future was done. Joint autocorrelation and spectral analysis allowed to identify a mutually confirmed cycle lasting 19-24 years for the rivers of the Siverskyi Donets Basin. According to the criterion of series, it is established that the periods of low phase can be 9±2 years. Knowing the length of the cycles, water-specific phases were identified. As a result, for the rivers of the Siverskyi Donets Basin it was found that the runoff in the wet phase exceeds the norm by an average of 18%, and the runoff in the low phase is lower by an average of 17% than normal. Therefore, the difference in river water phases is ≈ 35%. Forecast estimates show that by 2020±2, the rivers of the basin will have a low phase, which began in 2008. A wet phase is expected from 2020±2 to 2029±2, then in the period 2030±2 – 2038±2 years – low phase. In the period from 2039±2 to 2048±2, we should expect an increase of annual water runoff of the rivers of the Siverskyi Donets Basin.
In general, although the climate during the Holocene has been warm, nine well-recognized cold events with an average time interval of more than one thousand years have been highlighted. The forcing mechanism of these cold events with millennial-scale cycles is still widely discussed. In the present study, two different Solar System dynamical processes collectively driven by all eight planets were considered together: the solar inertial motion and the combined planetary tidal force acting on the Sun. In this context, an attempt was made to analyze their effects on solar activity and Holocene North Atlantic cold events at the millennial-scale. These two Solar System dynamical processes were proxied by the distance between the Sun and the Solar System barycenter (DS–S) and the intensity of the combined planetary tidal force (IP–S), respectively. Using the ensemble empirical mode decomposition (EEMD) method, time series data of Solar System dynamics proxies (i.e., DS–S, and IP–S), solar activity proxies (i.e., ¹⁴C and ¹⁰Be), and a proxy of Holocene North Atlantic cold events (i.e., hematite-stained grains) were decomposed into several intrinsic mode functions (IMFs). After extracting IMF components containing millennial-scale cycles, a correlation analysis was performed. As a result, it was found that the solar inertial motion had ∼2,300- and ∼1,000-year cycles and the combined planetary tidal force had a ∼1,500-year cycle, while the solar activity and Holocene North Atlantic cold events proxies had ∼2,300-, ∼1,500-, and ∼1,000-year cycles, respectively. The correlation analysis revealed that the millennial-scale periodic components of the two Solar System dynamics proxies were largely correlated with that of solar activity and Holocene North Atlantic cold events, suggesting that the solar inertial motion and combined planetary tidal force may work together to impact solar activity, and thus the climate in the North Atlantic. Consequently, solar activity was weaker and the North Atlantic temperature was cooler when the Sun was far from the Solar System barycenter and/or the combined planetary tidal force was weakened. This might indicate the involvement of Solar System dynamics on Holocene North Atlantic cold events at the millennial-scale.
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The radiocarbon ages of dendrochronologically-dated wood samples, each covering 10 years, are now available for the cal AD 1950–6000 BC age range. The decadal calibration curve constructed from these data comprises 1) the previously published AD 1950–2500 BC portion (Stuiver & Becker 1986), to which minor 14 C age corrections were applied, and 2) the new 2500–6000 BC extension.
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The radiocarbon ages of dendrochronologically dated wood spanning the AD 1950–6000 BC interval are now available for Seattle (10-yr samples, Stuiver & Becker 1993) and Belfast (20-yr samples, Pearson, Becker & Qua 1993; Pearson & Qua 1993). The results of both laboratories were previously combined to generate a bidecadal calibration curve spanning nearly 4500 years (Stuiver & Pearson 1986; Pearson & Stuiver 1986). We now find that minor corrections must be applied to the published data sets, and therefore, give new bidecadal radiocarbon age information for 2500–6000 BC, as well as corrected radiocarbon age averages for AD 1950–500 BC. Corrected average 14 C ages for the 500–2500 BC interval are given separately (Pearson & Stuiver 1993). The Seattle corrections (in the 10–30 14 C-yr range) are discussed in Stuiver and Becker (1993), whereas Pearson and Qua (1993) provide information on Belfast corrections (averaging 16 yr). All dates reported here are conventional radiocarbon dates, as defined in Stuiver and Polach (1977). Belfast 14 C ages back to 5210 BC were obtained on wood from the Irish oak chronology (Pearson et al. 1986). Wood from the German oak chronology (Becker 1993) was used by Belfast for the 5000–6000 BC interval. For the overlapping interval (5000–5210 BC), Belfast reports weighted Irish wood/German wood 14 C age averages. The Seattle 14 C ages for the AD interval were either on Douglas fir wood from the US Pacific Northwest, or Sequoia wood from California (Stuiver 1982). The BC materials measured in Seattle were mostly part of the German oak chronology. Thirteen samples (5680–5810 BC) from the US bristlecone pine chronology (Ferguson & Graybill 1983) were measured in Seattle as well. Here, the final Seattle decadal 14 C ages resulted from averaging German oak and bristlecone pine ages.
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The detailed radiocarbon age vs calibrated (cal) age studies of tree rings reported in this Calibration Issue provide a unique data set for precise 14C age calibration of materials formed in isotopic equilibrium with atmospheric CO2. The situation is more complex for organisms formed in other reservoirs such as lakes and oceans. Here the initial specific 14C activity may differ from that of the contemporaneous atmosphere. The measured remaining 14C activity of samples formed in such reservoirs not only reflects 14C decay but also the reservoir 14C activity. Model calibrations are made for the global marine response for surface (0-75m) thermocline (75-1000m) and deep (1000-3800m) waters. Model calculations yield information of atmospheric Δ14C values, production rates, Q, and alternative changes in oceanic mixing rates Kz, and demonstrate the validity of the production modulation approach to calibration. -from Authors
The coarse structure of the 14 C spectrum consists of a secular trend curve that may be closely fit by a sinusoidal curve with period ca 11,000 yr and half amplitude ±51. This long-term trend is the result of changes in the earth's geomagnetic dipole moment. Consequently, it modulates solar components of the 14 C spectrum but does not appear to modulate a component of the spectrum of ca 2300-yr period. The ca 2300-yr period is of uncertain origin but may be due to changes in climate because it also appears in the δ 18 O spectrum of ice cores. This component strongly modulates the well-known ca 200-yr period of the spectrum's fine structure. The hyperfine structure consists of two components that fluctuate with the 11-yr solar cycle. One component results from solar-wind modulation of the galactic cosmic rays and has a half-amplitude of ca ±1.5. The other component is the result of 14 C production by solar cosmic rays that arrive more randomly but rise and fall with the 11-yr cycle and appear to dominate the fluctuation of the galactic cosmic-ray-produced component by a factor of two.
Reports minor corrections to 14C data originally published in 1986 and based on standards measured between 1981 and 1986. Two standards had anomalous losses and are responsible for most of the errors corrected here. -K.Clayton
The mean period of 11.8622 years of the Sun's motion round the barycentre and its time variability were observed. Some of the characteristics of this motion were computed and the seismic energy release by global earthquake activity with time was correlated with F = (V), where (V) is the absolute value of the change of the Sun's acceleration with time. A relation between the basic period of 178.4 years and other periods pi in the Sun's motion (pi = 178.4/i; i = 1, 2,...) was found. The periods in the Sun's motion were assigned to the periods in different solar-terrestrial phenomena. The surprising coincidence of all these periods indicates that the dynamics of the planetary system governs solar- terrestrial phenomena.-from Authors
New Arizona high precision L\14C data back to 6500 BC plot close to an 11,300-yr period sinusoid extrapolated from the post 5300 BC data (offset = +32%o, half ampli-tude = 51%o and phase lag = 2.29 radians). The trend curve is modulated by high latitude components of the non-dipole field with a fundamental period of 2400 yr. Based upon a model of Lund and Banerjee (1985), the non-dipole field rotates and every 1200 yr the high latitude maxima pass over the north magnetic pole and near the south magnetic pole in reversed polarity. This modulates cosmic ray production producing extended maxima ca AD 1700, 700 BC, 3100 BC, and 5500 BC. The 2400 period appears to be stationary. The magnetic field also modulates the amplitude of the solar activity induced cycles of periods 200, 80, and 11 yr as can be seen in the Zurich-Bern Camp Century ice core data as well as in the &4C fluctuation data. Reinterpretation of the Camp Century 10Be data indicates that it is in agree-ment with magnetic field as well as solar activity modulation of terrestrial radioisotope produc-tion. INTRODUCTION At the time of the Twelfth Nobel Symposium, 16 years ago, three major causes of atmospheric 14C fluctuations were identified and discussed (Olsson, 1970). These were astrophysical effects, in particular, solar modu-lation of the 14C production rate, geophysical effects, specifically changes in the earth's magnetic field, and climate effects involving changes in carbon reservoir parameters and exchange rates. Recent reviews of archaeomagnetic and rock magnetic data suggest an increase of the virtual axial dipole moment (VADM) by ca 60% from ca 5500 to 2300 BP followed by a decrease to the present value of close to 8.0 x 1022 Amt (Barton, Merrill & Barbetti, 1979; Champion, 1980).
It has become generally accepted during the last year that 14C fluctua-tions, the so-called "wiggles", observed in wood, dated by its tree rings, do indeed exist. Furthermore the La Jolla measurements show that apart from experimental noise, they do not represent random red noise, but characteristic, recurring features. In 1971, Houtermans found indications for the existence of cyclic components and recent Fourier analyses of all the available data by Neftel and Hartwig show a 200-year com-ponent. Cyclic oscillations with other periods appear to be present during limited time intervals. The character of the oscillations is not harmonic. The time derivative of many fluctuations is remarkably constant and such that the 14C rises by 1 percent in about 20 years and decreases by 1 percent in slightly more than twice that length of time. The properties of the overall radiocarbon record have to be considered in at-tempts to explain the variations in terms of variations of the cosmic ray-production rate and changes of the geochemical distribution of radiocarbon.