My notes from 1990 on planetary calculationsThe calculations performed were to determine 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
sun's equator).
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 (not shown here - will try to produce this later), and
the resonance period is shown quite clearly.
Table 1
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.
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Solar Displacement Planetary Combination Sunspots Amplitude
Ratio
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
9.51 0.25
8.92 0.15
8.46 1.5 J+S 8.457 8.53 0.19 0.13
8.18 0.11
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 might confuse the issue.
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.
Table 3
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.
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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
events.