Some Periodicities in the Solar system
compared with Sunspot cycle
(by P.A.Semi, 2009-2010)
Abstract:
We show various planetary phenomena, related to Sun (Tidal forces, orbital angular
momentum of the Sun, Angular momentum of Jupiter relative to Sun, Acceleration of the
Sun and its derivative, Earth and Venus angular momentum), compared with Sunspot
cycle, evaluating their resonance with the cycle. We show, that most of the planet-related
phenomena are out of sync with the Sunspot cycle, and while possibly modulating it, they
seem NOT to cause it, whereas other may be in sync, namely the Angular momentum of
Earth and Venus planets and the Derivative of Solar Acceleration..
Tidal forces on the Solar surface:
Calculation:
We use JPL ephemerides, version DE406, to calculate planet's and Sun's position and
velocity. We establish a Solar surface point mesh, usually with 5 degree spacing over the
sphere (possibly ranging 2°-10°, it would be noted if different spacing from 5° will be
used...). We calculate the Tidal force at the surface mesh points as a vector sum of all
planet's tidal forces, finally dividing the vector into 1 vertical and 2 horizontal (meridional
and longitudinal) components.
For charting, forcing over one longitude belt (equator or 20° latitude parallel) is scalarly
summed and plotted.
It is implied from the used equations [Ref: T1, Ref. T2 - oceanographic tidal equations],
that as the Tidal force is perfectly symmetric along the line toward the influencing body and
from that body, the sum over any same-latitude circle (namelly over longitude parallel
circle) is equal on both hemispheres (here North and South hemispheres with symmetry
plane at Equator), so the Tidal force may not explain the North-South assymetry in the
Sunspot cycle.
Figure T1a - meridional part of the tidal force (vector sum of all planet forces at specified
surface mesh point) at 20° heliolatitude, compared with Sunspot cycle
The main cycle in tidal forcing is due to cycle in Jupiter distance at its perihelium and
apohelium. Second most important is Mercury, whose orbit is highly excentrical and
causes most variability in tidal forcing, but with a highest frequency.
Figure T1b - tidal meridional force at Solar equator (sum of absolute values at different
points on surface), compared with Sunspot cycle.
The main cycle of tidal forcing (sum of absolute values) on the Solar equator (only!) is
about 5.92 earth-years (calculated as a length of 10 chosen cycles divided by 10), which is
a half of the Jupiter period. (at all other latitudes, it shows the 11.86-year Jupiter cycle see Fig. T1a). If summing meridional forces consistently toward one pole (for ex. north,
then southward vectors have negative value), the sum of meridional forces on equator is 0,
because the functions for calculating the tidal force are symmetric and what pulls up at one
hemisphere, the same pulls down on the other side.
Figure T2 - tidal force (meridional component) at 20° heliolatitude. Left part of the chart is
calculated without Mercury, the right one with it. (The chart does not show absolute 0, only
the variance over the cycle.)
Figure T2b - tidal force (meridional component) - comparing tidal influences of various
planets. (The rather short part for "Jupiter" may not be representative of the whole sinusoid
- rather see fig. T1a for Jupiter's variability).
Figure T2c - tidal force (meridional component at 20° latitude) - showing Jupiter-only
influence (bottom line) compared with the sum of Jupiter+Venus+Earth (middle red line)
and with the sum of all 9 planets (top olive line). Chart includes 0, the difference from
Jupiter to the first Sum is due to Venus+Earth, the difference to the top fuzzy line is mostly
due to Mercury.
Mercury's orbit is highly excentrical, so it's influence varies most of the planetary tidal
influences onto the Solar surface. On the average Mercury's tidal forcing is only little
bigger than Earth's, but at the maximum it is almost as influent as Venus or as Jupiter at its
aphelium (see Table T1).
Jupiter
Tidal
Meridional
at 20° N
Venus
-11
Emb
-11
Mercury
-11
7.656E - 8.342E - 3.772E -10
-11
-11
1.031E
8.737E
4.241E
-11
Saturn
Sum
-12
2.154E - 3.677E -11
-12
7.531E
5.173E
-10
2.245E -10
3.134E
Tidal force at 2.413E-10 - 2.603E-10 - 1.188E-10 - 6.714E-11 - 1.146E-11 - 2.777E-10 -10
-10
-10
-10
-11
-10
20° N
3.237E
2.714E
1.315E
2.346E
1.608E
9.361E
Table T1. Comparison of tidal forces at Solar surface, caused by different planets, and the
Sum. First row shows only the Meridional component of the tidal force, averaged over
latitude circle at 20° north heliolatitude, minimum and maximum values are shown. Second
row shows the sum of absolute values of tidal potential vectors over the same latitude
circle (verify AbsTidalPot function).
Meridional component of the tidal force at Solar surface has got dominantly the 12-year
(11.86) cycle of Jupiter perihelium to aphelium difference (figure T1a), then the 88-day
Mercury signature (figure T2), the other two important being Venus and Earth (the "ripple"
on the line at left part of figure T2), all other planets are negligible for the tidal force...
Most instant variability of the tidal forcing is due to Mercury's orbit.(cca 88 days, see fig.
T3d), but it may be too high frequency for the Solar surface layers to react on it(?)
Figure T3b - derivative of meridional part of tidal force at 20° heliolatitude, when only
Jupiter, Venus, Earth planets are used, and its gaussian smoothed value, compared with
Sunspot cycle.
Figure T3c - same as figure T3b (derivative of meridional part of tidal force at 20° heliolat.),
when Mercury is included (as in fig. T1a), with gaussian smoothed value near zero.
Figure T3d - detail from figure T3c.
-------------------------------------------------------------------------------------------------------------------It has been demonstrated by K. Georgieva et al. [Ref. T3], that: The speed of the surface
poleward meridional circulation is modulated by the meridional tidal force which is always
directed equatorward and its effect is to slow down Vsurf. The meridional tidal force varies
periodically and its average value does not change much (Fig,6). However, what is
important for the modulation of the solar cycle is its average magnitude during the period
when the surface meridional circulation carries the flux from sunspot latitudes to the poles
– that is, from sunspot maximum to the geomagnetic activity maximum on the sunspot
decline phase. Fig.6 which covers the period 1750-2005, have different duration and come
on different parts of the tidal force sinusoid. In Fig.7 the average meridional tidal force
acting on Vsurf during the poleward transport of the flux is compared to the maximum
number of sunspots in the following solar cycle.
Fig.7 demonstrated a very good correspondence between the planetary tidal force (solid
line) and the amplitude of the sunspot cycle (dash-ed line), with the Dalton minimum (the
beginning of 19th century) and Gleissberg minimum (end of 19th and beginning of 20th
century) coinciding with low tidal forces during the surface flux transport, and the secular
solar maxima in the 18th, 19th and 20th centuries – with maxima in the tidal forces during
these periods.
We can make a rough estimation of the magnitude of the effect of the planetary induced
tidal forces. The calculated magnitude of the tidal force is of order F ~ 10-10 N/kg. The
acceleration caused by this force is a = F/r where the density r in the surface layer of the
Sun is ~ 10-5 gr/cm3 = 10-2 kg/m3. During the time when the flux is carried poleward (of
order 108 sec), this acceleration can change the speed of the surface meridional
circulation with a few m/s, which corresponds to the observed variations in Vsurf.
Fig.6
Fig.7
[excerpt from K.Georgieva et al., Planetary tidal effects on solar activity, 2009. Is it
possible to have such a long citation including 2 images from her work?]
My comment on this idea - it seems possible, that tides (or anything else, related to Jupiter
cycle) influence the amplitude of the following cycle (by braking transport of magnetic flux
toward poles arround and after Solar maximums), but the tides are not overall in sync with
the Sunspot cycle, and therefore may not be the main cause of the cycle.
-------------------------------------------------------------------------------------------------------------------It has been claimed by more people, originally by J.P.Desmoulins [Ref. T5] in 199*, then
Ching Cheh Hung [Ref. T2], that tidal forces cause the Sunspot cycle by Jupiter-VenusEarth cycle. Anyhow it is not correct to exclude Mercury from the calculations, unless it has
been much lighter than currently estimated. The justification, given by Hung, that Mercury
moves too fast and therefore should not be counted, does not seem correct, because the
Mercury is rather a planet, that moves slowest (retrogradely) from the perspective of the
faster-rotating Solar surface beneath. Is it possible, that as its forcing changes in highest
frequency, it is nullified by some frequency filter in the response? Currently it does not
seem probable (from my perspective). Anyway, even the other three main planets without
the Mercury evince rather the 11.86 year Jupiter cycle than the 11.? cycle of Earth-VenusJupiter cycle...
Tidal bulge vector (a speculation)
The tidal forces due to planets are highly irregular on the Solar surface (fig. T4). The "Tidal
bulge vector" is hereby defined as the Principal direction of the sum of tidal forces,
computed as a vector sum of tidal vectors at the whole surface mesh (discrete 5° spacing).
One planet is selected for the vector direction, and rather-opposing tidal vectors are
inverted before summing. The tidal bulge vector is highly variable, and shows principal
sum of tidal forces on the Solar surface. It is amplified when major planets are nearby the
conjunction or opposition, and is quite small, when the major planets are rather in
quadrature. The "high tide" tends to rotate sometimes fast (when the high tides are due to
Mercury perihelions, at which times it moves fastest on its orbit), but still slower than the
Solar rotation (spin), or walks quite slowly (in non-rotating reference frame), sometimes
even rotates slowly in opposite direction (when it returns in low-tide condition to the
direction toward the major planet). [!!! verify, specify speed ranges?! ]
Figure T4 - vertical view (from above the North pole - top line) and horizontal view (from
Earth, bottom line) onto the Sun, shows tidal force vectors due to planets, amplified by
2E14 (top row) or 1E14 (bottom row), showing the examples of the variability in tidal
forcing due to planets onto the Sun. Blue are inward vectors, brown are outward vectors.
(The interactive version of the Tidal Viewer is available in the free EphView program [Ref.
T4a], with a description upon email request. The animations are available [Ref. T4b].)
Figure T5 - length of the Tidal Bulge Vector, compared with unsigned Sunspot cycle.
Figure T5b - length of the Tidal Bulge Vector, compared with unsigned Sunspot cycle, in
more detail... (Larger versions of the images are available, how to link them in PDF or
OOO?)
Figure T6 - angle between "tidal bulge vector" and Solar acceleration vector, compared
with Sunspot cycle
Figure T7 - angle between "tidal bulge vector" and "moment vector" of the Sun, compared
with Sunspot cycle
Solar motion arround the Solar System Barycenter
Figure A1 - Orbital angular momentum of Sun compared with Signed Sunspot cycle (22
year).
Figure A2 - distance of Sun from SSB, compared with Sunspot cycle (either signed or
unsigned). The horizontal lines show the Solar center (0) and radius (690Mm).
The 179-year cycle of Solar motion arround the Solar system barycenter (figures A1 and
A2) shows a different frequency than the Solar cycle but it is resonant with the cycle, at
least for present centuries, but rather for present few millenia [note: need a proof of this]...
If counting only the "major waves" on the Solar-motion curve (fig. A1), there is a harmonic
resonance of 9 waves of the motion curve to 8 waves of the 22-year signed cycle of Solar
activity, for ex. during 1780-1960. Anyhow it does not seem (but no probability computation
conducted for this claim) that the quality of this synchronization influences the strength of
the Solar activity - some well-synchronized cycles were amplified (1780,1960) and some
were subdued (1800), while some totally opposite (1850-1920) were either strong or slow.
Figure A3 - Angular momentum of Jupiter relative to Sun, compared with Sunspot cycle.
Figure A4 - Angular momentum of Jupiter relative to Sun, compared with Sunspot cycle, in
details (1950-2000 on the left, well in sync, 1880-1940 on the right, out of sync)
Figure A5 - Angular momentum of Jupiter relative to Sun, longer trend. (Note the local
minimum arround 1650 (LIA) and local maximums arround 2100 (GW) and 1150 (MO) )
Figure A6 - Angular momentum of Jupiter relative to Sun, compared with Sunspot cycle.
Angular momentum of Jupiter planet relative to the Sun shows sometimes well
synchronization with the unsigned Sunspot cycle (11-year), (for ex. years 1965-2005),
sometimes a bad synchronization (ranging to almost opposite, for ex. arround 1900). (The
outer envelope little similates to recent warm and cold climatic periods, it would be
interesting to verify, if it worked in earlier times similarly, or there is no relation...?)
Figure A7 - Acceleration of Sun, compared with Sunspot cycle (11-year unsigned)
Figure A7b - Acceleration of Sun, compared with Sunspot cycle (22-year signed)
Figure A8 - derivative of Acceleration of the Sun, compared with the Sunspot cycle (11year unsigned)
Figure A8b - derivative of Acceleration of the Sun, compared with the Sunspot cycle (11year unsigned) with marked deceleration(?) modes, matching most (not all) cycle starts.
Figure A8c - derivative of Acceleration of the Sun, compared with the Sunspot cycle (11year unsigned) with marked deceleration(?) modes
Figure A8c - derivative of Acceleration of Sun, unsmoothed and with gaussian smoothing,
compared with the Sunspot cycle, in detail.
Whereas the acceleration of Sun shows dominantly the 11.86-year Jupiter cycle (figs. A7
and A7b), chart of it's derivative (figs. A8, A8b, A8c, "difference of daily values") shows
rather the "ripple" on the wave surface, probably dominated by combined effects of other
planets. Main frequencies, determined by FFT analysis, are: 224 days, 88 days, 11.86
years, 365 days, 5.8 years and some harmonics, sorted by importance. Therefore, the
Venus and Mercury planets seem to be most important for instant changes of Solar
acceleration.
Acceleration is calculated as a vector difference between current velocity vector and
yesterday velocity vector, divided by 86400 (seconds per day), length of the accleration
vector in m/s^2 is ploted. The Solar acceleration varies in range 1.175E-7 - 3.026E-7
m/s^2 at extremes with average at 2.1E-7 m/s^2 (during 1750-2050). Derivative of
acceleration is calculated by subtracting daily values - a rate of change of the acceleration.
The daily change of the acceleration (figures A8*) is in range -2.566E-9 - 2.32E-9 m/s^2
(note, that units are inconsistent with another value in this paragraph, the "daily change" is
just a difference per day, not per second...)
Angular speed of Sun
We calculate Angular speed of Sun Ω(Moment(Sun)) as an angle between two vectors
(current and previous, with daily stepping) divided by time distance in seconds (rad/s). The
"Time Derivative" is calculated by subtracting two neighbouring values and dividing by time
distance in seconds (rad/s2).
Angular speed of Sun on its orbit (during 1750-2050) is in range 1.07457E-8 .. 2.59067E-8
rad/s with average smoothed value 1.7E-8 rad/s, it's rate of change (time derivative) is in
range -2.000036E-10 .. 2.18757E-10 rad/s2. The time derivative reveals the jerks on top of
the wave.
Figure A9 - Angular speed of Sun on its orbit (gray) and it's time derivative (red, 50x
scaled), compared with unsigned Sunspot cycle.
Extremes on angular speed of Sun seem to match some of the Sunspot cycles, and
contradict few others. There seems to be a relation, that cycles, falling out of the peak of
the influence (for ex. 1880-1930), are rather small?
Figure A9b - details from figure A9.
Figure A9c - Time derivative of Angular speed of Sun, compared with daily Sunspot
numbers, in detail.
The peaks of short-time changes (here extracted by a time derivative) of Angular speed of
Sun (caused mostly by small planets) seem to match almost exactly or with a small delay
the peaks on a Daily SunSpot Number charts.
Earth-Venus-Jupiter cycle
Figure E1 - angular momentum of Earth-Moon Barycenter relative to Sun, compared with
Signed Sunspot cycle
Figure E1b - angular momentum of Earth-Moon Barycenter relative to Sun, compared with
Signed Sunspot cycle (just inverted SS-cycle from Fig. E1)
Figure E1c - daily derivative of angular momentum of EMB relative to Sun, with a gaussian
smoothed of its absolute value
Figure E2 - angular momentum of Venus relative to Sun, compared with Signed Sunspot
cycle.
Figure E2b - angular momentum of Venus relative to Sun, compared with Unsigned
Sunspot cycle.
The angular momentum of Earth and Venus planets, relative to the Sun (not relative to the
SSB) show a similar frequency with the signed (22-year) Hale Sunspot cycle. It shows the
similar characteristics as Earth-Venus-syzygy to Jupiter cycle (or Earth-Venus-quadratures
to Jupiter?) There seems to be no relation to unsigned (11-year) Sunspot cycle.
Discussion
(Sorry, but the following discussion replacement is a first sketch, taken from the email
correspondence:)
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R.M.:
Just on the matter of barycentric orbits. All the planets and the Sun are in
freefall motion around their common center of mass. This is simply
Isaac Newton's law of gravity.
Wherever objects in the universe appear to be orbiting each other, they are
in free fall motion around their common center of mass i.e. barycenter.
(From a private corespondence with R.M.)
This is a common misconception, or rather an incorrectly applied theory...
As you may see on the very basic chart (Fig. O1), that shows the distance of EMB or Earth
from the Sun (orange) or SSB (black) (calculated from the JPL DE406 ephemerides, that
are also used for spacecraft navigation and are assumed to be precise within few
kilometers at present era, verified by Radar ranging of near planets and historical data only
(sometimes only a single century, like in the case of Neptune) in the case of large planets,
so you may worry about thier definite precision a little, but not much...),
the distance of EMB (Earth-Moon Barycenter) from the Sun (and of Earth-from-Sun also, it
differs by some +/- 3Mm (3000km) within 1.5Gm (1 AU) distance (and Earth-to-Sun
distance is thereby neglibibly less "constant" or "smooth" than the EMB-to-Sun distance)
is much more "constant" than the distance of EMB-to-SSB (Solar System Barycenter),
which clearly shows the "signature" of Solar movement arround the barycenter.
(In short - the Earth (or rather EMB) orbits the Sun, not SSB... It is being "dragged" by the
Sun arround the SSB...)
Figure O1 - distance of EMB (Earth-Moon Barycenter) from Sun (orange) and from SSB
(black)
An "intuitional" explanation for this: Does the Moon orbit SSB? No, it orbits the EMB...
Rather - does for ex. the Io moon orbit SSB? No, it orbits Jupiter. In this case, the "small"
planets behave rather like the "Sun's moons", differently from the "large" planets, which act
as a "Sun's counterweight" in its (Sun's) orbital motion... (and the Sun may not move freely
against all possible and conflicting influences...)
I feel this is rather important...
[Note: The main conserved property of the whole System is the angular momentum
relative to the barycenter. (The "work" performed to move Earth further/nearer
to the barycenter is counterweighted by the changes in angular momentum
of large planets and of the Sun (my current opinion), so it does
not contradict The Law (Newton's or others)...) The Total Angular Momentum of the Solar
System is almost constant in these ephemerides, and the rest is caused by omitting (in the
constancy verification) of the trajectories of Asteroids, which were used in ephemerides
calculation, but not in my angular momentum summing [Ref: Semi2009a Orbital
resonance, figure 83]. The new Outer Dwarf Planets were not used in ephemerides
calculation, but their overall influence is expected (by me) to be very small, nevertheless
you will not find it in the total angular momentum of the System, as you will not find the
Solar spin-orbit exchange there, just because these were not used in the Ephemerides
calculation...]
-> The Sun is thereby in "free-fall" only against the large planets. (It cannot move in "freefall" relative to all bodies. Its Moment of Innertia may not allow the high-frequency changes
of the motion(?)... Or these changes may be "feeled" (followed) by only certain layers of
the Sun, while other layers (core or surface) may move more innertially to follow only the
low-frequency influences. )
-> It is thereby different the dynamic influence of "small planets" and of the "large planets"
onto the Sun...
There seems to be some link between changes in orbital angular momentum of Earth (or
Venus) and the Sunspot cycle (fig. E1b).
(They show the same frequency for last few centuries of measured Sunspot records, and
they are one of very few, that match it. The frequency matches (of Planetary phenomena
with Sunspot cycle, there are more such - Earth/Venus opposition to Jupiter angle etc...)
always encompass Jupiter, Venus and Earth, never Jupiter alone, althoutgh some Jupiter
phenomena seems to match some amplifications/reducing of the Cycle, on various timescales (Ref. T3, K.Georgieva 2009, also the 854-935 Jup/Sat cycle)...
For the idea of "Angular momentum of the Earth planet being transfered onto Solar
surface levels", the main differences in Earth's (or Venus's) orbital energy (angular
momentum or Vorticity) are caused by meeting/separating from Venus/Earth in the
resonance cycle and with the Jupiter...)
It is a question then, whether, how and how much is the orbital energy of Earth (or Venus,
which are the two most important of the "small planets", those against which the Sun is not
in free-fall) exchanged with the surface layers of the Sun (and possibly causing eddies in
the convection, which could induce Sunspots by the Dynamo effect???). For the instant
changes of Solar acceleration, most important is the Venus planet, then Mercury, Jupiter
and Earth.
If the exchange occurs via the gravitational forces, it would rather prefer Venus, if it was
via magnetical/electrical forces, it would prefer the Earth, as only she is magnetical of
those two... But the Jupiter is much more magnetical than the Earth (it's magnetic moment
at the distance to the Sun being approx. 100x larger than Earth's magnetic moment there),
so it partially rules out the possibility of Earth's magnetical influence onto the Sun being
any important...
There may be considered also these cases:
- Jupiter's magnetic field is rather canceled by it's magnetosphere (mostly by the Io torus),
it could be somehow diminished?...
- The Sun's magnetic field is said to be approx. 100 times larger arround the Earth, than it
"should" be, due to the conductivity of IMF. [see for ex.
http://en.wikipedia.org/wiki/Interplanetary_Magnetic_Field ]
- This may also be the case with Earth's influence onto the Sun, prefering it somehow
before the Jupiter, which is further away and the IMF should be less dense and less
conductive at it's distance...?
- There have also been discovered the "flux ropes", connecting Earth's magnetosphere
electrically directly to the Sun (Ref. D1 - "Themis" mission 2007), so the conductivity of
IMF and possibility of Earth's magnetic influence onto the Sun being also larger, at least at
some times when the ropes exist...)
Another possible issue, related to this, is:
- The former tidal calculations on the Solar surface, have been using the "Earthly"
oceanographic tidal equations.
Moon-induced and Sun-induced Tides onto the Earth both share the property of the
influenced body (Earth) orbiting the (bary)center with the other body, while the centrifugal
force on the influenced body produces the symmetric tide on the other side of the body.
This is also the case, when the influenced body is the Sun and influencing body being the
large planets (namely Jupiter). But this is NOT the case with Earth/Venus/Mercury-induced
Tides on the Sun, where the centrifugal part on the Sun is probably missing, and their Tide
is rather a dipole, only on the near side, missing the symmetry?? (Is this right???)
(Without this, the Sum of "quadrupole tides" is perfectly symmetrical arround any axis
plane, namely arround the Solar equator, so there is absolutelly no hemispherical
difference in Tides on the Sun... This may not be the case with "dipole" Tides, induced by
the small planets onto the Sun, on one side only...??? - Need some more calculations,
whether it could even be interesting, and some verification, if it is "Real"...?)
- I've not get to perform the Tidal calculations corrected with this in mind yet... (I'm planning
to ask some professor on a local university (MFF UK) to correct the Tidal equations for this
case soon...)
Another possibility:
- The eddies in IMF, that form behind the planet's magnetosphere (most notably behind the
Earth's magnetosphere in this case) may involve in stretching of the (comet-like)
magnetotail behind every planet that makes a remarkable obstacle to it (to the IMF) (by the
magnetosphere, which is notably larger obstacle for IMF than the mere planet body, like is
the case with Mercury, Venus and Mars planets and with the Moon - which have got
(almost) no magnetosphere)...
Kinetic energy of E-M-bary may be transfered to Sun (Solar surface (magnetic) layers)
from the IMF eddies...
[[Then causing (inducing) eddies in Solar surface layers, that promote as Sunspots, and
then continually dragging them to ecliptic plane through The Cycle. As a response, two
Cells form on each Solar hemisphere, and the other Cell (the polar one, the first is the
Equatorial Cell) brings the dipole magnetic field to the Solar poles... At the shear layer
between the cells the eddy formation is largest and cause the observed magnetic spots
(Solar Storms, SunSpots)]].
The equatorial "Cell" diminishes within the cycle, as the Separation Layer between the
Cells moves toward the equator (The Butterfly diagram).
[091116]
(Note, that this is an unverified theory, which would need some more calculations,
whether the IMF eddies may be any reasonably important... Probably it is a nonsense and
would be deleted later...)
(... work under construction ...)
References:
Ref. T1: Coastal Processes and Tides, Department of Oceanography, Texas A&M
University, Robert H. Stewart,
http://oceanworld.tamu.edu/resources/ocng_textbook/chapter17/chapter17_04.htm
Ref. T2: Apparent Relations between Solar Activity and Solar Tides, Ching Cheh
Hung, 2007, Glenn Research Center, Cleveland, Ohio
Ref. T3: Planetary tidal effects on solar activity, K. Georgieva, 2009, Bulgarian
Academy of Sciences
Ref. T4a: EphView, DE40* ephemerides viewer program,
(http://semi.gurroa.cz/EphView/)
Ref. T4b: Tidal forces on the Sun, animations, P.A.Semi 2009
(http://semi.gurroa.cz/Astro/TidalAnim/)
Ref. T5: ***, J.P.Desmoulins 199*
(***)
Ref: Semi2009a: Orbital resonance and Solar cycles, P.A.Semi, 2009.
Ref. D1 - "Themis" mission, 2007, NASA,
(main page http://www.nasa.gov/mission_pages/themis/main/index.html)
(Flux ropes, connecting Earth to Sun, are mentioned in
http://www.nasa.gov/mission_pages/themis/auroras/northern_lights.html, cited in
http://en.wikipedia.org/wiki/THEMIS )