Summary of this model. It explains:
1) Long and short sunspot cycles
2) Very low sunspot activity.
3) Why there is a difference between the sunspot numbers
South and North of the equator (slightly different speed
Southern and Northern polar field)
4) Why there is very low sunspot activity South or North
of the equator, while there is sunspot activity in the
opposite place!
5) Outburst of magnetic field activity are seen on the
theoretical model. Even in declining and low sunspot
activity!
HEREWITH THE RIGHT EXPLANATION!
1) Open the excell file
2) Chart 3 is an example of an end result
3) Click on sheet 1
4) Change A5
5) The end formula will be changed immediately
6) Change A6
7) Put the mouse on row I number 1
8) Pull it lower
9) Push F11
10) The new chart will appear!
How to enlarge it?
1) Put the mouse on the last number from row C (now
486)
2) Pull it lower with the black dot on the right
3) Do the same with row F and I
4) Repeat 7 till 10
A Theoretical Calculation of the Sunspot Cycle
With the help of a simple integral, a theoretical sunspot
cycle of eleven years can be imitated (copied) as follows:
The polar magnetic field of the sun rotates (theoretically)
in about 37.2 days; the equatorial field in 25.75 days
(the average of the last 75 years: see Long Term Variations
of the Torsional Oscillations of the Sun, Solar Physics
170: 373/388, 1997, by Dirk K. Callebaut). At a certain
moment, the equatorial field takes over from the polar
field. Therefore we can only investigate the relationship
between the field of the sun and an independent observer
by measuring only each take-over movement. Through this
we always compare only two variants: the converging
positions of the fields in relation to the shifted point
of observation. In fact we are doing nothing more than
calculating the winding process of the magnetic field
of the sun. At this moment we can calculate the numbers
of the fields together with the converging position:
Subject: Re: Re:
360 ¸ 25.75 = 13.9805825 degrees
360 ¸ 37.19 = 9.6800215 degrees
The difference is: 13.9805825 – 9.6800215 = 4.30055848
degrees
The polar field is taken over by the equatorial field
after the following number of days:
360 ¸ 4.30055848 = 83.710058 days = 1 bit
The number of circles traveled by the equatorial field
is:
83.710058 ¸ 25.75 = 3.25087545
The number of circles traveled by the polar field is:
83.710058 ¸ 37.19 = 2.25087545
0.25087545 circle forms a bit and will be used as a
basic unit in the calculation
First point:
0.25087545 x 360 = degrees
= 91,3 degrees
= A
Put this in relation with an observer who travels the
length of the mean of the polar and equatorial field
in one day.
Total length equator field = 4.370.880 km
Mean of Polar field = between 700.000 km and 900.000
km = 800.000 km
4.370.880 + 800.000 = 5.170.880 km
mean =2.585.440 km
=> This is about equal with the speed of an object
that travels 360 days around the sun in one year (plus/
minus)
=> To be corrected when we know the circumference
of the polar field more excactly
Comparisson speed earth
Speed earth = 29,77 km sec
29,77 x sidereal day = 2.565.000 km/day
Conclusion
Point B goes in plus minus 360 days around the sun
in this case = 83, 7 days = 83,7 degrees because days
is same as degrees
= B
A - B = end formula
When you calculate and subtract both graphics, the
result will be the difference between the magnetic field
of the sun and an independent observer. Filling in the
previous numbers in the Excel file this results in a
sunspot cycle of 54.5 bits. 54.5 x 83.710058 days =
4,562.2 days = 12.49 years.
Note:
The changes of speed of both the equatorial and polar
fields were not taken into account.
Sunspot cycle of 9 years
We change the hypothetical speed of the polar field
into 37.16 days:
360 ¸ 25.75 = 13.9805825 degrees
360 ¸ 37.16 = 9.68783638 degrees
Difference = 4.292746117 degrees
360 ¸ 4.292746117 = 83.86240187 days = 1 bit
83.86240187 ¸ 25.75 = 3.2567923
0.2567923 circle = 1 bit
When you put these numbers in the Excel file the result
is a sunspot cycle of 42 bits.
42 x 83.86240187 = 3,522.2 days = 9.64 years.
Important conclusions:
1) Only a small change in the speed of the polar or
equatorial field can result in a considerable prolongation
or deceleration of the sunspot cycle.
2) From a mathematical point of view there has to exist
a very close correlation between the equatorial and
polar field.
3) The sunspot cycle together with the polar reversal
of the magnetic field of the sun lasts longer when the
polar field rotates somewhat slower. A difference of
only (!) 0.0807 percent causes the cycle to rise from
9.64 to 12.49 years!
Third example: the cycle of 11 years
Speed of the polar field: 37.176 days
360 ¸ 37.176 = 9.683666882 degrees
360 ¸ 25.75 = 13.9805825 degrees
Difference: 4.296915618 degrees
360 ¸ 4.296915618 = 83.7810262 days = 1 bit
83.7810262 ¸ 25.75 = 3.25363208 circle
0.25363208 circle = 1 bit
When you put these data in the Excel file, the result
is a sunspot cycle of 48.0 bits.
48.0 x 83.7810 = 4,021.5 days = 11.01 years.
Very low sunspot activity.
Equator field: 25.75
Polar field: 37.291
Very long cycle
=> ALMOST ZERO SUNSPOT ACTIVITY!
To be studied:
Speed equator field: 25.75
When you slow down the speed of the polar field further
to 37.4075, the length of the sunspot cycle DECREASES
again to 11 years!
Question:
Is this a possible explanation for the change of the
magnetic field every 11 years?
1) Cycle of 11 years based on a speed of 25.75 days
(equator field) and 37.176 days (polar field)
2) Cycle of 11 years based on a speed of 25.75 days
(equator field) and 37.4075 days (polar field)
=> First cycle + and other - ?
Sunspot Cycle Theory (Excel File)
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