MilutinMarjanov, 27 marta 39, Beograd, Srbija, email: firstname.lastname@example.org
There are solid evidences that the gravitational forces of the planets circling the Sun are the external triggers of the solar activities. It seems that these phenomena mostly initiate two outer and two inner planets: Jupiter, Saturn, Venus and Earth.
Matching of the results obtained in this work and the results, obtained by observations of the solar activities in the past, suggests possibility of the more reliable predicting of these activities in the future.
Key words: solar activity, sunspots, solar cycle, orbit, velocity and acceleration of the Sun
Solar activity. Like most stars, Sun generates its thermal and light energy by nuclear fusion of hydrogen nuclei into helium. This primary part of the energy is predominantly constant. Another, secondary part, produced by transformation of the kinetic energy of the motion of plasma through the magnetic field of Sun into electromagnetic energy, is variable.
The term solar activity comprises this second part of energy emitted by the Sun.
Solar activities are mainly manifested by series of the magnetic storms on the surface (photosphere) of the Sun. These storms can seriously affect Earth’s weather.
Sunspots. Zones in which magnetic storms occur are visible from the Earth and are called sunspots. Sunspots appear dark because they are cooler than the surrounding photosphere. The powerful magnetic fields around sunspots produce active regions on the Sun, which often lead to the solar flares and to the coronal mass ejections.
Fig 1. Sunspots
Individual sunspots can last from hours to months. They expand and contract as they move across the surface of the Sun with sizes ranging from 1 500 kilometers to 50 000 kilometers in diameter. Sunspots usually appear in pairs of opposite magnetic polarity.
They tend to be concentrated in two mid-latitude bands on either side of the solar equator. Sunspots begin appearing around 25 to 30 degrees north and south of the center. As the solar activity progresses, new sunspots appear closer to the equator, with the last of them appearing at an average latitude of 5 to 10 degrees.
Sunspot number and solar cycles. Sunspot number indicates a measure of solar activity. That is the number of sunspots and groups of sunspots present on the surface of the Sun during given period of time.
The average number of visible sunspots varies over time, increasing and decreasing in the almost regular cycles containing sunspot maxima and sunspot minima. Cycles of the increased sunspot number correspond to the high solar activity, while, conversely, near sunspot minima the Sun is much quieter.
The notion of the solar cycle was introduced in 1843 by German astronomer S.H. Schwabe, who, after 17 years of observations, revealed a periodic variation in the average number of sunspots. He estimated that the period of cycle activity is about 10 years.
It was adopted, in accordance with tradition, that the length of the cycle is 10, 7 ~11 years. The first numbered cycle was 1755 – 1766, and it seems that now, in 2018, we are near the end of the cycle 24.
A typical sunspot number diagram as a function of time is given on the Fig 2. /10/.
Fig 2. Sunspot number diagram: cycles 19, 20, …,24
In fact, cycle duration ranges between 9, 5 to 11 years, although cycles as short as 9 years and as long as 14 years have been observed. We will try to show later that the cycle duration of ~10 years is closest to the truth.
In 1919 G. E. Hale and collaborators showed that the magnetic polarity of sunspot pairs:
- is constant throughout a cycle,
- is opposite across the equator throughout a cycle,
- reverses itself from one cycle to the next.
There is one more fact that needs to be emphasized. Almost all cycles are characterized by – north – south asymmetry in the sunspot numbers, in two hemispheres /13/.
The Sun’s magnetic field. The Sun has a very large and very complex magnetic field. Generally, with some uncertainty, during a cycle, one hemisphere has positive and another, negative magnetic polarity. The entire Sun’s magnetic polarity flips in approximately equal intervals of time.
This is a regular part of the solar cycle. When the Sun is the stormiest, that’s when its magnetic field flips. Scientists are not sure what the storminess has to do with the magnetic field reversal, if anything. About every 11 years, the Sun’s magnetic poles flip – North becomes South and vice versa.
But, there are a lot of irregularities in the magnetic field reversals and it seems that this fact is the main cause of the unequal cycle durations.
For example, from cycle 20 to cycle 23 there were increasing length of periods between polar field flips in each hemisphere. For the northern pole, the periods between polar field reversals were ~ 10 years (cycles 21 -22 and 22 – 23) and ~14 (cycles 23 – 24). For the southern pole, there were ~ 11 years (cycles 21-22), ~ 9 years (cycles 22-23), and ~ 14 years (cycles 23-24), accordingly /13/.
Causes of the solar activity. What are the main causes of solar activity? For a long time it was believed that the proximate cause is a self-sustained solar dynamo which converts mechanical energy into electric-magnetic energy related to the Babcock-Leighton mechanism /11/.
In accordance with Babcock’s model, the Sun is a dynamo that converts convective motion, differential rotation and torsional oscillations of plasma within the Sun to electric-magnetic energy. Such systems are called self-sustained or self-consistent dynamos.
However, one supporter of this model admits that “detailed way of functioning of the solar dynamo is not known and is the subject of current research”.
In fact, in the meantime researchers had found out that the plasma convective motions were much (a hundred times) weaker than predicted /12/.Another serious deficiency of Babcock’s model is complete disregard of the external influence: gravitational attraction of the planets inducing inertial transverse movements of plasma. Neglecting the inertial motions inevitably leads to the adoption of “self-sustainable” model.
There are also assumptions that planets tidal forces may be the cause of the solar activity /5/, /14/, /15/.
As a matter of fact, although tidal forces undoubtedly distort outer layers (chromosphere and corona) of the Sun, they are too week compared to the gravitational forces that they could represent the origin of the solar activity phenomenon. It is easy to show that sizes of the total tidal forces acting on the Sun are only a few thousandths of the total gravitational forces.
The remaining possible cause is the resulting gravitational force exerted by the planets on the Sun. This force produces changes in the speed and direction of Sun, and consequentially, inertial displacements of plasma in the opposite direction of the resultant.
At the end of 1995 NASA launched Solar and Heliospheric Observatory (SOHO) Satellite. It was maneuvered to orbit the first Lagrangian point (L1), a point some 1,5 million kilometers from Earth toward the Sun, where gravitational attraction of Earth and Sun combine in such a way that small body remains approximately at rest relative to both. While all previous solar observatories have orbited the Earth, from where their observations were periodically interrupted as our planet ‘eclipsed’ the Sun, SOHO enjoys a continuous view of our star.
SOHO carries an electronic instrument called the Michelson Doppler Imager (MDI). The MDI maps the solar interior by measuring the velocity of sound waves passing through the Sun. This technique is named helioseismology and it works on the same principle as medical ultrasound. The obtained results revealed the fact that sunspots are not static but they consist of very strong downward flows of plasma traveling toward the interior of the Sun at speed of almost 5 000 km per hour /7/.
It seems that P. D. Jose was the first one who seriously started to consider influence of the inertial forces on the activities of the Sun /1/. He claims in his work that “certain dynamic forces exerted on the Sun by the motions of the planets are the cause of the sunspot activity”.
Jose plotted diagrams of change of the angular momentum dL/dt of the Sun around barycenter of the solar system in time and of change of the angular momentum dP/dt about the instantaneous center of curvature of the orbit in time and compared these functions with the diagram of relative sunspot number in time. He states that similarity of these functions is obvious.
Function dL/dt covers influence of the inertial forces in whole; while function dP/dt covers centrifugal inertial forces acting on the Sun. Taking into account only outer planets Jose neglected very important influences of the inner planets (see further: Acceleration of the Sun).
We stand on the position of those authors who consider that the external factors are the main triggers of the solar activity /1/, /2/, /3/, /5/, /6/….. According to our estimation, this phenomenon is mostly influenced by movements of two outer and two inner planets: Jupiter, Saturn, Venus and Earth.
For better understanding our attitude, let us first examine characteristics of the Sun’s motion in the invariable plane.
Adopted model, coordinate systems
Besides translation, spin around its axis and rotation around center of the Milky Way, the Sun performs relative motion in the solar system Laplace plane under influence of the planets movements, also. If the solar system is treated as a stable, isolated system of the point mass particles moving under mutual gravitational interactions, two dynamic conservation principles may be used for study of the motion of this system: momentum conservation and angular momentum conservation principle.
The consequence of the first rule is uniform motion of the system’s mass center C, while the consequence of the second is motion of the system in one, Laplacian, or invariable plane /17/. This plane is within 0, 5 of the Jupiter’s orbital plane and may be regarded as the weighted average of all planetary orbital planes. The point mass particles solar system model, involves the need to disregard differences between the orbital planes mainly originated in the transfer of the (small, but changeable) Sun’s and planet’s spin angular momenta to its total angular momentum. Neglecting turning of the entire solar system around the center of the galaxy, this plane moves uniformly in the same direction, together with the mass center C through the space.
Existence of the invariable plane permits introduction of an “inertial” reference frame xCy lying in it. Another Cartesian coordinate system x’Oy’ (Ox’ and Oy’ parallel with Cx and Cy) was adopted as the relative, that is, the heliocentric frame of reference (Fig 3). Here coordinate Ox’ (and consequently Cx) have primary direction, that is, it points from the Sun toward the vernal equinox of the Northern Hemisphere of Earth.
Fig 3. Inertial and relative frames of reference
Motion of the Sun in the inertial frame of reference. Using astronomical data on the positions of outer planets from 1653 to 2060, P. D. Jose was the first one to determine the Sun’s orbit, in his work /1/. Thus, he used Kepler’s model of relative planetary motion.
In his article /6/ R. Bitsch has determined the Sun’s orbit integrating differential equations of motions of this celestial body exposed to the resultant of the planets’ attracting gravitational forces. It was supposed that these heavenly bodies are in circular, uniform motions around the Sun. In short, he applied Copernican model. The initial positions of the planets were adopted arbitrary in this work, because the author assumed that, in the long term, it does not affect the shape of the orbit.
In fact, the choice of either model in determining the trajectory, velocity or acceleration of the Sun is completely irrelevant, since the sizes of the position vectors, as well as the velocity and acceleration vectors of the Sun’s center of mass are very small compared with the correspondent kinematic parameters characterizing motions of the planets. For example, the largest distance of the Sun’s center of mass from the solar system barycenter is only a few thousandths of average radius of the Jupiter’s orbit. But, on the other hand, correct determination of the initial conditions does matter, of course.
Bearing this in mind, the simpler, Copernican model is the adopted here: the planets move in the invariable plane, at constant average distance, with constant average angular velocity around the Sun.
Taking the planets’ configuration on 21 March 1978 as initial conditions and the mentioned simplified model of planetary motion, M.Marjanov/17/ obtained, practically, the same form of the Sun’s path as Jose had. This trajectory covers the time interval of fifty years: 21. 03. 1978. + 50. In the same paper, velocity and acceleration diagrams of the Sun were given for the adopted period of time.
As known, in the inertial coordinate system the following relations are valid:
Index k = 0 is reserved for the Sun, while indexes k = 1,2..,8 correspond to the planets.
According to the Figure 2, we can write
Obviously, positions, velocities and accelerations of the Sun’s center of mass are completely defined by the relative positions, velocities and accelerations of the planets with respect to the Sun.
Sun’s orbit. If the initial heliocentric longitudes of the planets are , k = 1,2,…,8 , numerator of the right hand expression (2) may be represented in the Cartesian coordinates in the following way
Multipliers define influence of each planet on the orbit of the Sun. Thus, we come to the conclusion that outer planets are the main causes of the Sun motion:
Jupiter ~ 49, 2 %, Saturn ~ 27, 0 %, Uranus ~ 8, 3 %, Neptune ~ 15, 4 %,
while, on the first glance, influences of the inner planets: Earth ~ 0, 03 %, Venus ~ 0,02 % … seem to be insignificant.
Fig.4 shows the path of the Sun from 21. 03. 2 000. to 21. 03. 20 40. The contour of the Sun’s disk is given as referential and the dot marks on the orbit denote halves of years.
As can be seen trajectory of the Sun consists of large and small loops.
When Jupiter and Saturn are on the same side of the Sun (conjunction phase), Sun goes with higher average velocity along the large loop while, when these two planets are on the opposite sides from the Sun (opposition phase), with the lower average speed along the small loop (see Fig 4.). Travel time duration around the loops are equal: about 10 years.
Every large loop envelopes the small one and Sun passes the same points – knots (in the invariable plane) twice: at the entrance and at the exit of the small loop, when Jupiter’s and Saturn’s heliocentric position vectors are orthogonal (difference between their longitudes Δl=l – l=π/2, 3π/2). The small loops are “closed” while the large loops are “opened”: they go from the end of one small loop to the beginning of the next. As said, Sun needs about ten years to pass every loop. Fig 4. contains dispositions of the giant planets in characteristic points (Δl = 0, π/2, π, 3π/2).
We shall see that all the other elements of the Sun motion are marked by the time cycle of, about, ten years. This cycle is mostly determined by the time period between two successive alignments between Jupiter and Saturn – 9, 93 years. It may be a little longer, or a bit shorter, depending on the configurations of the other planets.
On the whole, the time period between two giant planets alignments determines the pace of all the elements of the Sun movements, as well as, we shall see this later, of the activity of the star.
Fig 4. Orbit of the Sun from 2 000 to 2 040 and dispositions of the giant planets in characteristic points
We emphasize the fact that orbit, “loops” and “knots” in the figure above are obtained as projection of the Sun’s path that has a spiral shape in space,on the invariable plane.
Velocity of the Sun. Since
Comparing the sizes of multipliers for each planet, we come to their percentage share in the Sun’s velocity:
Jupiter ~ 78,0 %, Saturn ~ 17,2 %, Uranus ~ 1,9 %, Neptune ~ 1,8 % .
Influences of the inner planets (Earth ~ 0, 6 %, Venus ~ 0, 5 %,…) seem to be almost irrelevant, again.
Velocity diagram of the Sun’s barycenter from the year 2 000 to the year 2 040 is represented in the Fig 5.
Fig 5. Velocity of the Sun from 2 000 to 2 040.
Full line represents the influence of all outer planets on the velocity of Sun, while the dash line and the interrupted line present the influences of Jupiter&Saturn and of Jupiter
(~12, 32 m/s), solely.
Maximal velocities ~ 15 m/s arise every 19, 86 years and they correspond to the Great Conjunctions of Jupiter and Saturn, while minimal velocities, around ~ 9 m/s, correspond to their oppositions with respect to the Sun.
Acceleration of the Sun. In accordance with the simplified model of planetary motion in this paper, relative accelerations of the planets with respect to the Sun’s mass center are
Comparison of the multipliers (k=1,2,…,8) indicates that the greatest influences on the acceleration of the Sun have
Jupiter ~ 74, 3 %, Saturn ~ 6, 6 %, Venus ~ 9, 8 %and Earth ~ 6, 3 %,
while total influences of the other planets is less than 3 %:
Mercury ~ 2, 3 %, Mars ~ 0, 3 %, Uranus ~ 0, 2 % and Neptune ~ 0, 1 %.
The similar results obtained Roy Martin /5/ by use of the Newton’s law of gravitation.
Gravitational attraction forces planets to circle the Sun. Because of their great radiuses (and also due to the adopted model) gravitational fields in which they lie, their orbits are uniform and stationary. Compared to the gravitational attractions with the Sun, gravitational interactions between planets are insignificant /17/.
On the other hand, as said, the Sun moves, also, under gravitational attractions of the planets. But its path passes through the exceptionally non stationary gravitational field. The consequence of this fact is very uneven movement of this heavenly body.
Fig 6. Acceleration of the Sun from 2 000 to 2 040.
Figure 6. represents acceleration diagram of the Sun’s barycenter in the same interval (2 000 – 2 040) of time. Full line presents acceleration of the barycenter of the Sun, produced by the four enumerated planets, while the dash line and the dot line displays influence of Jupiter&Saturn and solely Jupiter, respectively.
Accelerations of Sun goes from ~ 0, 15 μ/s, when Jupiter and Saturn are on the opposite sides of the Sun, to ~ 0, 27 μ/s, when two giant planets are in conjunction.
Jumps and falls in the graph drawn by the solid line correspond to the all possible combinations of alignments and close alignments of three or four bodies. Near conjunctions of four planets occurs only around Great Conjunction, every 19, 86 years.
Here again, ~ 10 years accelerations and decelerations are in the higher, and a further ~ 10 years, in the lower range.
Jupiter, Saturn, Venus, Earth and Solar Activity
Mechanical energy caused by unified differential rotations, torsional oscillations, transversal movements and convective motions of plasma within the Sun is converted into electric-magnetic energy. In such a way an enormous quantity of the energy is produced, resulting in the emergence of the magnetic storms and occurrences of the sunspots on the photosphere.
Acceleration diagram (Fig 6.) reflects diagram of the inertial forces acting on the Sun. It points to the fact that gravitational actions of the planets mentioned above are the main causes of the plasma movements (except of convection, of course) in the Sun and therefore, drivers of the solar activities.
Sun is a huge ball of gas and plasma with a solid core. The core has a radius that accounts for about a quarter of the Sun’s radius and a mass that accounts for about a third of the Sun’s mass Let us divide this body into layers parallel to the Laplace plane: the layer around the equator has by far the largest mass while other masses, going towards the poles, are reduced.
That shows how inertial force acts on such a body: it is maximal around the equator and it decreases with latitude.
According to our model, Jupiter causes constant centrifugal acceleration of the Sun’s center of mass (Fig.6): a(J) ~ 0, 207 μ/s. The corresponding inertial force causes stratification of its body: maximal part of this force acts on the middle layer of the ball and then its action decreases toward the poles. As directions of the Sun’s rotation and Jupiter’s orbital motion coincide, the corresponding inertial forces increase rotational speed of the individual layers. Actions of the inertial forces of different intensities can be, at least, a partial cause of differential rotations.
As for the torsional oscillations representing time variations in the solar differential rotation, it is possible that they are a partial consequence of the joint action of two giant planets (Fig. 6): a(J,S) or, more precisely, of all the outer planets. Close relation of the periods of these oscillations with the time between Jupiter – Saturn alignments is an indicator that this assumption has a solid basis.
Transversal inertial forces which are probably the starter of the solar activity may provide explanation for most of the sunspots properties.
It is obvious that gravitational attractions of four planets – Jupiter, Saturn, Venus and Earth create a non-stationary gravitational field in which lies the path of the Sun. Moving along this course provokes inertial strikes which cause rapid transverse motions of plasma /7/ and magnetic storms on the surface of the Sun.
Markedly erratic diagram of accelerations caused by movements of Earth and Venus implies the fact that, for better understanding of the Sun’s motion, influences of the inner planets on the path and speed have to be taken into account, also.
Indeed, the path (Fig 4.) and the velocity graph (Fig 5.) of the Sun are not smooth lines. For example, if we take into account influences of Earth and Venus on the velocity, then we shall have, in the increased scale, the following diagram (Fig 7.).
Fig 7. Velocity of the Sun from 2 000 to 2 002
Accordingly, orbit of the Sun is also not a smooth, but a wavy line. The winding path of its barycenter (Fig. 4) would be evident only in the, at least, a few thousand larger scale.
As known, change in magnitude of the velocity is consequence of the tangential component of acceleration, while the aftereffect of the normal component is change in direction of the velocity.
The very small accelerations and decelerations of the Sun’s center of mass, of order of few hundredths of μ/s multiplied by the great mass of the Sun causes enormous inertial forces corresponding to the resultant of planets gravitational attractions. These forces cause transverse movement of plasma from the surface toward the center, and vice versa.
One author /6/ proposed a plausible comparison of inertial motions of plasma within the Sun with motions of the liquid in an oil tanker if this ship accelerates and slows down movement along a winding path.
It is evident that the immediate drivers of the rapid transverse motions of plasma are alignments of two and close alignments of three or four planets: Jupiter, Saturn, Venus and Earth.
As said, Sun is a huge ball of gas and plasma. The resulting gravitational force of planets provokes uneven motion of the Sun causing inertial forces which produce transversal movements of different layers of the Sun, at different rates.
– Because the inertial forces are parallel to the invariable plane, they cause differential transverse displacements of plasma parallel the same plane. Since middle stratum of solar sphere has the largest mass, the inertial force acting on this layer has to be greatest and the movements of plasma in this zone have to be most intense. That’s why the sunspots are concentrated in the mid-latitude bands of the solar equator.
– The fact that sunspots appear in pairs across the equator and that they are of the opposite polarity across the equator through a cycle can be explained as the result of the transverse movement of plasma through the magnetic fields of opposite polarities of two solar hemispheres. Of course, during the next cycle, after reversal of the Sun’s polarity, the sunspots will have polarities of the opposite signs.
– As for the north south asymmetry in magnetic activity (i.e. number of sunspots), this is consequence of tilt of the Sun’s axis. Circling the loop inclination of the axis toward the ecliptic goes from zero to ±7, 25. Since the axis is tilted, impact of inertial force on one hemisphere is different than on the other, during the cycle.
There is no doubt that the giant planets cause massive displacements of plasma. However, since the changes in velocity caused solely by these planets are very slow, the appropriate inertial forces cannot cause rapid movements of plasma /7/ and the resulting solar activity. We have seen that Jupiter and Saturn are, at least, partial causes of the differential rotations and torsional oscillations of the Sun, but important role in the emergence of transverse motions phenomenon have the inner, fast rotating, planets Venus and Earth. (In this paper the influence of the planet Mercury, of the order of 2, 3%, was neglected, but its impact must also be noticeable).
It should be kept in mind that acceleration, as well as decelerations produces inertial strikes.
In order that the similarity of sunspot number diagram and diagram of inertial forces which directly cause rapid transversal movements of plasma was more clearly emphasized, it is opportune to plot the | – | diagram (Fig 8.).
One can see that part of this diagram, from 2 004 to 2 017 (thicker line), quite well coincides with the sunspot number results obtained by Royal Observatory of Belgium
(2 017 August 1) for last 13 years (Fig. 9).
This indicates that obtained results provide a good basis for a more precise and more extensive predictions of the solar activities in the future.
Analysis of the diagram in the Figure 8. leads to an interesting conclusion. It seems that augmented frequency and probably diversity of directions of the gravitational impacts is the main cause of the increased solar activity. Namely, when heliocentric position vectors of Jupiter and Saturn are orthogonal (Δl = π/2 and 3π/2), number of planet’s alignments (gravitational strikes) is doubled in relation to the case when these vectors lie in the same direction (Δl = 0 or π).
Hence, these strikes change in cycles and we can see that these cycles approximately correspond to the solar activity cycles.
Fig 8. Diagram | – | from 2 000 to 2 040.
Fig 9. International sunspot diagram S from 2 004 to 2 017
One of important characteristics of the solar activities is its periodicity, which is evident in the, more or less regular repetitions of forms in the sunspot number diagram (Fig. 2).
In the diagram in the Figure 8 of the gravitational impacts periodical repetition can be clearly seen. Among all the factors that cause the solar activity, only their direct initiator – gravitational strikes are marked with a clear periodicity, while reversals of magnetic field have a certain tendency to repeat in the regular intervals. If we look the orbit of the Sun (Fig. 4), maximal activity corresponds approximately to the “knots” of the loops and minimal activity is roughly opposite of these points (conjunctions or oppositions of the giant planets).
As mentioned, flips of the magnetic field occur around the time when the Sun is most active, that is, when it passes the knots of the loops, when heliocentric radiuses of Jupiter and Saturn are orthogonal.
It seems that Jupiter and Saturn do not determine only the form of the orbit, rhythm of velocity and acceleration of the Sun, but, in a way, behavior of the magnetic field of the star, also.
We mentioned earlier that solar cycles durations as short as 9 years and as long as 14 years have been observed and that now, it is generally accepted that the cycle duration is 10,
7 ~ 11 years. One would obtain this number by simple dividing the number of years elapsed since 1755 with the number of past cycles. But one should bear in mind that this number is an average for the interval of ~260 years. Solar cycles durations over the past 11 000 years have been reconstructed using Carbon-14-based dendroclimatology. Almost all earlier high-activity periods were shorter than the present episode/9/.
All this, together with the results obtained in this paper leads to the conclusion that the average solar cycle duration is closer to the period of time between two successive alignments of the giant planets is actually 9, 93 ~ 10 years and not 10, 7 ~ 11 years. It seems that Schwabe was right.
Of course, there is a possibility that the current configurations of the other planets, as well as some, for now yet unclear way of functioning of the “solar dynamo” and primarily, irregularities in the reversals of the Sun’s magnetic field /13/ shorten, or extend the cycle time.
It is quite certain that motions of Jupiter, Saturn, Venus and Earth are initiators of the solar activity.
We have seen that motions of Jupiter and Saturn determine path, velocity and acceleration of the Sun. Two giant planets are, at least partly, the causes of differential rotations and torsional oscillations of the Sun. It seems that movements of these two planets, together with the changes in the Sun’s magnetic field, also set the pace of the solar activities.
On the other hand, changes in the Sun’s velocity produced solely by Jupiter and Saturn are too slow to be able to produce rapid inertial motions of plasma in the Sun. Therefore these giant planets alone cannot be the direct cause of the solar activity. Actually, the main triggers of the rapid transverse displacements of plasma are inner, faster orbiting planets and their alignments with each other, as well as their alignments or close alignments with the giant planets.
Matching of the results obtained in this work and the results, obtained by observations of the solar activities in the past, suggests the possibility of more accurate and more extensive forecasting of these activities in the future.
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