Author: Ray Tomes
A mechanism for the sunspot cycle is proposed which explains the
correlations between planetary periods and alignments and periods
found in the sunspots. The concept of "pull" described in a previous
paper titled "the effect of gravity on photons" is used to achieve
this. For the first time a quantitative prediction of forces of
the right magnitude to affect the sun (and hence weather) is achieved.
In my 1990 paper presented at the Foundation for the Study of Cycles
conference, I explained that the planets had relativistic gravity
effects on the sun, and showed some relationships to the sunspot
cycle. This paper deals with a serious omission of that paper, in
that the third spacial dimension was ignored. Only the solar system
plane was included, while the north-south direction turns out to be
the most interesting for explaining the sunspot cycle. Also dealt with
in this paper is the quantification of the planetary effects and this
shows that they are significant in solar processes. All past planetary
solar mechanisms proposed have suffered from the serious problem that
they just do not have enough effect.
RELATIVISTIC EFFECT OF THE PLANETS ON THE SUN
Einstein showed that gravity has an effect on horizontal light which
is to bend it by twice as much as would be expected by Newtonian physics.
That is, horizontal light is accelerated by gravity twice as much as
other matter! Because vertical light is affected only the same as
other matter, the average effect on randomly moving light is 5/3 times.
(Note 1-Dec-94. Jonathan Scott says factor is 2 not 5/3)
Because the centre of the sun has a greater proportion of its mass
made up of photons, it is affected differently from the surface layers.
The result is that the gravity of the planets tend to induce a
convection current in the sun. The effect is extremely small, but
because the normal rate of heat flow in the sun is even smaller, it
is actually very significant.
In my 1990 paper, the forces in the plane of the solar system were
considered, but because of the solar rotation any effect by a planet
tends to get undone about 13 days later when the sun has made half a
rotation and the planet is trying to induce a convection current in
the opposite direction. Only periodic forces matched to the rotation
period could build up over time. However, in the North-South direction,
although the forces are less by about a factor of ten (since the planets
orbits are inclined about 6 degrees to the solar equator) there is a
much larger effect, because even as the sun rotates planets remain above
or below the sun's equator for long periods, specifically for half of
their revolution periods.
The calculations performed were to calculate the position of the
planets at regular intervals in three dimensions, with respect to the
solar equator. The gravitational forces of each planet were then
calculated, allowing for their masses, distances and directions.
Then in the resulting force all but the N-S component were discarded as
the other components tend to cancel out within one solar rotation.
This N-S component is an acceleration of the solar interior relative
to the exterior, and the direction is north or south in the sun.
It is necessary to integrate the acceleration over time to obtain
a velocity, and then integrate this over time to get a displacement
of matter. The planets that dominate the different components are
different. Venus and the Earth have significant accelerations, but
because of their short periods they do not build up, but instead
reverse. Uranus and Neptune have very small accelerations, but
because of their very long periods they result in significant
displacements of matter. In the resulting displacement of solar
matter, the important planets in order are J, S, N, U. (See Table 3)
It is worth noting here that as far as accelerations go (which may
or may not be important) the formula is I*M/D^2 while for the resulting
displacements the formula is I*M*P^2/D^2 where M=Mass, P=Period and
D=Distance and I=inclination to the sun. But (as Kepler showed) P^2 is
proportional to D^3 and so the result may be expressed as I*M*D.
For the four major planets, all the I's are within 10% of 6 degrees, and
so the result is approximately proportional to M*D which is the same
formula used by COM adherents! However, only the component of COM
which is at right angles to the line of the nodes is important, the
component in the direction of the nodes is not (all the nodes of the
major planets orbits are within 10 degrees of longitude 245 of the
Note: The COM (Centre of Mass) hypothesis states that the motion of
the sun about the COM of the solar system somehow has an effect on
the sun. There has been no meaningful mechanism proposed for it to
work. The other alternative previously proposed has been tidal forces,
but although there is a mechanism, the effects are too small.
The displacements caused by the planets in the sun were calculated for
the years 1600-2000 and the absolute values (that is with the sign
disregarded) were analysed for cycles. The resulting spectrum shows
many peaks related to various planetary combinations. These are most
easily understood as combinations of the planets frequencies ( which
are just the inverse of the periods), and the frequencies are then
found to be simple combinations such as J+S, J-S, J+N, J-N, J+U, J-U.
These have periods of 8.46, 19.86, 11.07, 12.78, 10.40 and 13.81
respectively. Jupiter's period of 11.86 years also appears, but is
less important than the combinations.
When 264 years of sunspot numbers were analysed, the following periods
were found in order of importance :- 11.07, 10.01, 10.53, 12.09, 9.51,
8.53, 12.93, 13.95. Other researchers have generally reported periods
of 11.1, 9.9 and 11.8 years and sometimes 8.5.
It seems that on the whole the sunspot periods are a close match to the
solar displacement periods due to planetary action. The 10.01/9.9 year
sunspot period is probably related to half the J-S period which is 9.93.
There is no matching period to the 9.51 year sunspot period, but a
possible explanation will be given later.
The amplitudes of the periods in the sunspots are different to those
in the solar displacement periods. The 11.07, 10.40 and 9.93 year
periods are strong in the sunspots while the 12.78, 13.81 and 8.46
year periods are less strong. By comparing the amplitudes in each,
it can be seen that the sun has resonance with periods near about 10.5
years, but much less so with periods above 12 or below 9 years. This
is a classic example of a system with a natural resonant period.
Table 1 below shows the main periods compared, and the relative
amplitudes for sunspots/displacement. These are then graphed in
figure 2 below, and the resonance period is shown quite clearly.
Comparison of periods found in the calculated solar displacement
caused by the planets with the average planetary periods and with
periods found in the sunspot cycle. Also shown are the amplitudes
of the cycles in the solar displacement and in the sunspots, and the
ratio between these. The ratios indicate that the sun has a resonance
with a period of about 10.5 years.
Solar Displacement Planetary Combination Sunspots Amplitude
Period Amplitude Planets Period Period Amplitude
(years) (years) (years)
13.89 0.7 J-U 13.812 13.95 0.12 0.17
12.80 1.1 J-N 12.782 12.93 0.17 0.15
11.87 0.3 J 11.862 12.09 0.27 -
11.06 1.2 J+N 11.066 11.07 0.51 0.43
10.39 0.8 J+U 10.395 10.51 0.37 0.46
9.96 0.3 (J-S)/2 ? 9.93 10.01 0.50
8.46 1.5 J+S 8.457 8.53 0.19 0.13
It is worth mentioning that the main sunspot cycle period which is
11.076+-.009 years, based on an analysis of Schove's maxima dates for
over 2000 years, is very close to the 11.066 year J+N period. It was
an unfortunate coincidence (the solar system is full of them) that
there is a J-V-E period of 11.068 years (or really 22.135 years)
that confused the issue for many researchers, myself included.
It is worthwhile explaining the meaning of the 11.066 Jupiter+Neptune
period, and why it is the dominant cycle. In terms of their effect
on the sun, Saturn should rank ahead of Neptune, but Saturn's periods
in relation to the other planets are not generally near the "natural"
solar period. Neptune remains above the Sun's equator for 82.4 years
and then below for 82.4 years. When Neptune is above, then Jupiter
above the equator causes a sunspot maximum, and when Neptune is below
then Jupiter below causes a maximum. This means that every 164.8 years
there is one extra sunspot cycle than the number of times Jupiter goes
around the sun. Actually the timing of the solar interior displacement
is 180 degrees out of phase with the above description for each planet,
but the description is otherwise correct.
The timing of the actual peaks in the sunspot cycle do not match
those in the planets displacement of the solar interior. This is to
be expected with the discovery of resonance, which means that in
effect the sun has a memory, and that different cycles will have
different lag periods according to their distance from the resonant
period. Building a model of this is required, and this is really a
job for a solar physicist. Some attempts at a crude model have
achieved a correlation coefficient of 0.66 with the sunspot cycle,
but it is difficult to get a match in the phase variations and the
amplitude variations simultaneously.
A successful model incorporating resonance will no doubt be able to
explain the Maunder minimum when the sunspot cycle almost stopped.
Clearly what must happen is that the planetary forces get badly out
of phase with the sunspot cycle and reduce its amplitude -- a bit
like pushing a swing at the wrong time will slow it down.
Comparison of the relevant planetary attributes.
The Acceleration is calculated as M*sin(I)/D^2 and the Displacement as
M*sin(I)*P^2/D^2 (which is equivalent to M*sin(I)*D or very like COM).
Note that the inclinations are to the solar equator, and that the
periods quoted are relative to the nodes of the orbit with the
solar equator, and so are a little different to normal.
Planet Mass Distance Period Inclination Acceler. Displacement
M D P I
Mercury 0.056 0.387 0.2408522 3.18 0.021 0.0012
Venus 0.826 0.723 0.6152078 3.75 0.10 0.039
Earth 1.012 1.000 1.0000417 7.14 0.13 0.13
Mars 0.108 1.524 1.880885 5.51 0.0045 0.016
Jupiter 318.4 5.203 11.86233 6.00 1.228 172.9
Saturn 95.2 9.538 29.4568 5.45 0.099 86.2
Uranus 14.6 19.182 84.016 6.36 0.0044 31.1
Neptune 17.3 30.06 164.802 6.36 0.0021 57.6
Pluto has been omitted as its mass is small.
The Earth's mass includes the moon.
Because of the time element of building up a displacement from a
velocity, it turns out that distant objects such as nearby stars and
the galactic plane generally and the galactic centre have significant
effects on the solar displacement also. As it happens, there is a
lopsidedness of matter in the southern sky, which means that a long
term average heat flow will be biased in the direction of the sun's
south pole (not in the direction of the stars or galaxy).
Over very long periods, the sun moves up and down through the galactic
plane. This would cause major heat flow variations in the sun with
reversals about every 30 million years. It is possible that this is
another link in the chain of events leading to the major extinction
PROOF THAT THE PLANETARY RELATIVISTIC GRAVITY EFFECT IS SIGNIFICANT
The above data shows quite clearly that there is a good correlation
between the planetary relativistic gravity solar interior displacement
and the sunspots, in terms of frequencies and amplitudes (when the
"natural" oscillation of the sun of 10.25 years is allowed for.
We still need to show that the mechanism of relativity is significant.
The acceleration of gravity of Jupiter acting on the sun at mean
distance is 3x10^-8 m/sec^2.
The component of Jupiter's acceleration on the sun in the N-S direction
varies from -0.1 to +0.1 and back over Jupiter's 11.86 year period.
(0.1 is the sine of Jupiter's inclination to the sun's equator of 6 deg)
Near the centre of the sun about 1 part in 10^5 of the mass is photons
and because they frequently interact with matter, their momentum is
rapidly mixed with the matter and diluted by 10^5 as a result.
Therefore, over a period of 5.93 years Jupiter can accelerate in the
N (or S) direction the core of the sun (relative to the outside) by
0.1x0.7x3x10^-8m/sec^2/10^5 = 2x10^-14 m/sec^2. The 0.7 factor is the
average value of a sin wave over half a cycle (if you like Jupiter is
on average 0.1x0.7 above the sun's equatorial plane).
2x10^-14 m/sec^2 is a very slight acceleration, but over the course of
5.93 years (2x10^8 seconds) will achieve a velocity change of about
0.7x2x10^-14m/sec^2x2x10^8sec = 3x10^-6 m/sec. This may seem like
a tiny velocity (which it is), but it is large compared to the sun's
normal rate of heat flow.
Photons take about 10,000,000 years to get from the centre of the sun
to the surface, but the rate is quite unsteady being very slow to
begin with and gradually getting faster. In the outer 20% or so the
sun has convection currents, but in the inner part it is only by
radiation that heat flows. So the average rate of heat flow is
7x10^11m / 10^7years / 3x10^7 secs/year = 2x10^-6 m/sec.
Near the centre however the flow is slower, probably less than
10^-7 m/sec. So the effect of Jupiter is to increase the natural
internal heat flow by a factor of 30 times. Jupiter does then
reverse its effect, but no doubt there is some mixing which cannot
be reversed. This mixing may be the role played by the inner planets
and Jupiter. The displacement caused by Jupiter over a 5.93 year
period is the average velocity by the time for which it acts, or
3x10^-6 m/sec x 2x10^8 sec = 600 m. At last we have come to a
measure that is not tiny. Jupiter displaces the centre of the sun
by 600m over half a revolution. This is small compared to the sun's
size being about 10^-6 of the sun's radius. When we consider that
the sun has a temperature gradient that is a fairly steady one
amounting to 15,000,000 degrees over its radius, we see that this
small displacement should heat the surface by about 15 degrees in
one hemisphere. This is .25% of the sun's temperature at the surface
which would result in an increased energy output of 1% (as energy is
proportional to the fourth power of temperature).
Actually this figure is higher than the observed change, but the
other hemisphere has an opposite effect. The observed change is of the
order of 0.1% only. This demonstrates that the planets do have a big
enough effect on the sun to fully explain the observed changes in
Formula and calculations
The concept of acceleration is adequate for dealing with matter under
normal circumstances, but photons are also affected by gravity, and
the normal definition of acceleration takes account of only velocity
changes, while momentum may also be affected by mass changes. Gravity
does cause Energy/Mass changes in photons. Therefore, I define a new
variable "Pull" as being the time rate of change of momentum per unit
mass, and give it the symbol b. It has the same dimensions as normal
acceleration, and is normally the same for normal matter.
See my previous paper for a detailed explanation of this.
For normal matter in the sun (ignoring relativistic effects) we have
dp/dt = bm = gm while for photons dp/dt = bm = kgm. If the sun
has a proportion by mass of photons that is q, then
dp/dt = gm(1+q(k-1)), giving b=g(1+q(k-1)).
For all intents and purposes this last figure is the acceleration
of solar matter by any body where g=Gm/r^2. The term q(k-1) is the
important bit, because it is different in different parts of the sun
depending on the proportion by mass of photons. Near the middle,
q = 10^-5 while at the surface q = 0 approximately.
Next consider the components of the planets forces in the plane of
the solar equator and at right angles to it. For a planet with
(mean) distance r, mass m, period p and inclination of its orbit i
the two components of g are cos(i)Gm/r^2 in the plane and sin(i)Gm/r^2
at right angles to it. These two components of acceleration can be
integrated over time to give the velocity changes of solar matter,
and then integrated again to get displacements of solar matter.
At this point it is found that the component at right angles to the
solar equator is much larger, and the other may be ignored. This is
because the N-S component builds up over half a planets revolution
period, while the solar system plane components only build up for
half a solar rotation period.
We are not interested in the motion of the sun, but the difference
in motion of its parts. This is therefore the vertical displacement
f f f
= q (k-1) I I sin(i).Gm/r^2 dt dt I means integral
J J J
which ignoring the eccentricity of the planets orbits is
= q (k-1) sin(i) G m p^2 / 2 / r^2
The convection currents at one point in time are shown in figure 3,
and the absolute value of the N-S displacement is shown for the period
1600 to 2100 in figure 4.
(Graph not included as too difficult under character only system).
More work needs to be done to complete this work, and some of it may
have considerable consequences in a number of areas.
1. The full relativity calculations need to be done for all angles of
photons to a gravitational field, and the constant k = 5/3 (?)
determined as the average effect on photons compared to other matter.
Note added 1-Dec-94 according to Jonathan Scott this factor is k=2
for all directions of photons. It seems that I ignored the
general relativity time factor difference for vertical photons.
2. Models of the sun need to incorporate the effects of convection and
mixing caused by the planets to determine the impact on:
a. Depth of convection zone.
b. Temperature and pressure at the middle of the sun.
c. The neutrino flux.
d. Differential rotation with latitude, depth and time.
e. Variations in solar output over the whole energy spectrum
on time scales of days to millennia. Will also explain many
cycles in weather and climate, including 4600 and 2300 year
cycles and many others.
f. The details of the sunspot cycle.
3. The long term effect of the matter in the galactic plane and at
the middle of the galaxy on the operation of the sun must be
considered. It is quite significant, and may explain (with allowance
for the sun's motion through the plane) the major extinction events.
The middle of the sun will inevitably not be the hottest place.
4. The operation of binary stars needs to be considered. Unless they
have common equators and orbital planes, then close binaries will
have dramatic effects (approximately 1000x our sun's) due to the
motion of the stars above and below their equator. If stars with
very slow rotations exist then major effects can be expected also,
for example a close binary with rotation stopped due to tidal action
will have its hottest part permanently displaced from the middle,
possibly by a considerable portion of its radius, and this should be
observable as variations in brightness as they rotate.
5. In considering the relativistic effect of gravity on the planets,
there will be slight effects due to internal photons from
radioactive decay. Could these effects play some part in magnetic
field formation which is at present a mystery?
Email: Ray Tomes