Motion of the Sun's nucleusMotion of the Sun's nucleus Viktor Strohm ... 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 U Days Distance difference. 3 Plot 2 In Plot 2,

1

Motion of the Sun's nucleus

Viktor Strohm

[email protected]е

Annotation

"Oscillations" of orbital radii length were detected. Radius lengths are taken from astronomical

tables. The article contains several types of "oscillations". Hypothesis of this phenomenon is

proposed.

Keywords

oscillation; orbital radius; planet; astronomical table.

Introduction

Kepler's second law - the orbit of the planets is an ellipse. The ellipse is symmetrical about the

major axis.

1. At symmetrical points of the ellipse, the radii are equal. The movement along the ellipse is

multidirectional. When moving from aphelion to perihelion, the radius decreases, and when

moving from perihelion to aphelion, it increases. The article compares the length of the radii at

symmetric points by calculating the difference in the length of the radii at symmetric points of

the radius (hereinafter simply the difference).

2. Perihelion and aphelion do not have symmetrical points. Take the sequence of the difference

in radii by years of perihelion and aphelion.

P - is the difference in perihelion radii, P2 - P1,..., Pn - Pn-1

A - is the difference between the aphelion radii, A2 - A1,..., An - An-1. Plots 4, 5, 9, 15.

The data are taken from NASA astronomical tables [1].

Tables and graphs of orbital radius length difference

Конвертированные дата

и расстояние от

перигелия к афелию

Дата и расстояние от

перигелия к афелию

Разно

сть

дата R

1

дата R

2

R2 -

R1

1

2

Table 1

The original data is in the file "horizons_results.txt". In the files файлах "full

period_hdr1_[planet name].txt", the source data is presented in table format. The maximum

difference for each period is determined and recorded in files "full period_max1_[ planet

name].txt". The program "Search_for_negative_sequences" calculates the difference in

Abstract

2

perihelion by years and writes it to the second column of the file, respectively, in the third

column writes the difference of aphelion.

Programs and files are located at the link [2].

Based on the data obtained, graphs and histograms of the difference in the length of the radii of

the orbits of Mercury, Venus, Earth, Mars were constructed.

Mercury

Table 2 and graph 1 show the difference in the length of the radius of the orbit of Mercury for

one period.

1 2000-Aug-10 00:00 0,30753 2000-Aug-10 00:00 0,30753 0

2 2000-Aug-09 00:00 0,307655 2000-Aug-11 00:00 0,308048 0,000392

43 2000-Jun-28 00:00 0,466466 2000-Sep-22 00:00 0,466636 0,00017

Table 2

Plot 1

Plot 2 shows the differences over 205 Mercury years.

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035

0.004

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43

AU

Days

Distance difference

3

Plot 2

In Plot 2, in addition to annual fluctuations, we see cycles of 32-33 years.

Plot 3 shows one of the cycles in an enlarged format.

Plot 3

Histogram 1 displays the absolute maximums of the annual differences.

-0.008

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

0.008

1 8

15

22

29

36

43

50

57

64

71

78

85

92

99

10

6

11

3

12

0

12

7

13

4

14

1

14

8

15

5

16

2

16

9

17

6

18

3

19

0

19

7

20

4

AU

Mercury 1970-2019 yy

4

Histogram 1

P - perihelion A - aphelion

Plot 4

Plot 4 shows the same multi-year cycles of 32-33 years.

Plot 5 is obtained from the astronomical tables of the Paris Observatory [3]. Plot 5 has one multi-

year cycle of 33 years, 3 - 36 points.

-0.008

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

0.008

1 8

15

22

29

36

43

50

57

64

71

78

85

92

99

10

6

11

3

12

0

12

7

13

4

14

1

14

8

15

5

16

2

16

9

17

6

18

3

19

0

19

7

20

4


-1.50E-05

-1.00E-05

-5.00E-06

0.00E+00

5.00E-06

1.00E-05

1.50E-05

2.00E-05

1 9

17

25

33

41

49

57

65

73

81

89

97

10

5

11

3

12

1

12

9

13

7

14

5

15

3

16

1

16

9

17

7

18

5

19

3

20

1

AU


P

A

5


Plot 5

Plot 6 - multi-year current time cycle, 8 - 40 points.

Plot 6

Plot 7 shows the start and end times of the current multi-year cycle.

-1.50E-05

-1.00E-05

-5.00E-06

0.00E+00

5.00E-06

1.00E-05

1.50E-05

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55

AU


P

A

-0.008

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

0.008

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45

AU

Mercury 2016 -2026 yy

6

Plot 7

The article [4] shows the annual fluctuations of the radii of other planets.

Venus

Plot 8

-0.008

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

0.008

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43

2017.10.31 - 2018.01.24

2025.07.16 - 2025.09.03

-0.0002

-0.00015

-0.0001

-0.00005

0

0.00005

0.0001

0.00015

0.0002

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91

AU

Venus 1970 - 2027 yy

7

Histogram 2


Plot 9

P - perihelion

Plot 10

Земля-Луна

-0.0002

-0.0001

0

0.0001

0.0002

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91

AU

Venus 1970 - 2027 yy

-6.00E-05

-4.00E-05

-2.00E-05

0.00E+00

2.00E-05

4.00E-05

6.00E-05

1 4 7 10131619222528313437404346495255586164677073767982858891

AU

Venus 1970 - 2027 yy

P

A

-4.00E-05

-3.00E-05

-2.00E-05

-1.00E-05

0.00E+00

1.00E-05

2.00E-05

3.00E-05

4.00E-05

5.00E-05

1 4 7 10131619222528313437404346495255586164677073767982858891

AU

Venus 1970 - 2027 yy

P

8

Plot 11

Histogram 3


Plot 12

-0.0004

-0.0002

0

0.0002

0.0004

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55

AU

Earth-Moon 1970-2027 yy

-0.0004

-0.0003

-0.0002

-0.0001

0

0.0001

0.0002

0.0003

0.0004

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55


-6.00E-05

-4.00E-05

-2.00E-05

0.00E+00

2.00E-05

4.00E-05

6.00E-05

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55

AU


P

A

9

Plot 13

Mars

Plot 14

Histogram 4

-6.00E-05

-4.00E-05

-2.00E-05

0.00E+00

2.00E-05

4.00E-05

6.00E-05

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55

AU


P

-0.0015

-0.001

-0.0005

0

0.0005

0.001

0.0015

0.002

1

22

43

64

85

10

6

12

7

14

8

16

9

19

0

21

1

23

2

25

3

27

4

29

5

31

6

33

7

AU

Mars 1970 - 2027 yy

Series1

Series2

Series3

Series4

Series5

Series6

Series7

Series8

Series9

-0.0015

-0.001

-0.0005

0

0.0005

0.001

0.0015

0.002

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

Mars 1970 - 2027 yy

10


Plot 15

Long-term cycles of Venus, Earth, Mars on plots 8, 11, 14 and, accordingly, on histograms 2,3,4

are not as clearly expressed as in Mercury. Longer data sampling is needed for Mars. Long-term

cycles of perihelion and aphelion are more pronounced, plots 4, 5, 9, 10, 12, 13, 15.

Conclusions

The authors of the HORIZONS program write: " To have an exact value, a quantity must be

either strictly constant, or else, exactly periodic.

The orbits of the planets are only approximately elliptical; their motions are only approximately

periodic; not exactly. Therefore, it doesn't make much sense to ask questions about "exact"

Keplerian (elliptical) elements.

A simple analogy would be to take a pencil and draw a free-hand circle on a piece of paper,

going round-and-round a number of times. Then ask, "what is the EXACT radius of that circle?"

It is impossible to give an answer; the curve that you have drawn is not exactly a circle.

One may define an "osculating" radius, for example: the radius of curvature at any given point

on the curve. However, this value is exact at that given point only. The value will change for a

different place on the curve; or, if averaged over some portion of the curve; or, if averaged over

some other portion of the curve.

Which result gives the "exact" answer? None; there is no "exact" radius for the curve.

It's a whole different situation with the JPL ephemerides. We do not use things such as periods,

eccentricities, etc. Instead, we integrate the equations of motion in Cartesian coordinates (x,y,z),

and we adjust the initial conditions in order to fit modern, highly accurate measurements of

planetary positions. As a result, we are able to produce ephemerides which are far more

accurate than those based upon elliptical elements.

-0.0004

-0.0003

-0.0002

-0.0001

0

0.0001

0.0002

0.0003

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28AU

Mars 1970 - 2027 yy

P

A

11

In the analogy above, it could be possible to measure each point of the hand-drawn curve very

accurately; however, one still could not give a unique value for the curve's radius."

As you can see, the authors of the HORIZONS program talk about the presence of "oscillations"

of the radii. However, nothing is said about the form and nature of the oscillations. The question

arises. Cycles have a computational or natural cause?

Let us estimate the value of the oscillation of the orbital radius

Планета Радиус

радиус

планеты а.е.

Максимальная

разность радиуса

орбиты а.е.

Максимальная

разность радиуса в

перигелии а.е.

Меркурий 1.63e-5 5.663e-3 1.48е-5

Венера 4.05е-5 1.4e-4 4.51е-5

Земля 4.26е-5 2.9879e-4

4.37е-5

Марс 2.37е-5 1.467918e-3 2.96e-4

Table 3

The difference in the radius of the orbit is one two orders of magnitude greater than the radius of

the planet. Radius oscillations at perihelion show that hypothesis number one cannot be the root

cause of radius oscillations.

It is known that the core and surface of the Sun rotate at different speeds. The solar core rotates

almost 4 times faster than the surface of a star. There is a possibility of cyclic movement of the

center of mass of the Sun, which causes a shift in the coordinates of the planets. The radii remain

unchanged. Average diameter of the Sun 1.392!109 м = 0.009305 AU. The diameter of the

motion curve of the core of the Sun is about 100 times smaller than the diameter of the Sun,

0.009305/0.0000999 = 93.14.

The rapid change in the sign of the multi-year cycle on graphs 2, 8, 11 can be mathematically

described by the existence of an intermediate axis during the rotation of the Sun's core, the

Dzhanibekov effect.

References

1. NASA HORIZONS https://ssd.jpl.nasa.gov/horizons.cgi

2. V. Strohm, programs and data,

https://drive.google.com/file/d/1qIz9BaLeQQPaOx8d2dJyV4jHgWPJ-

hF9/view?usp=sharing 3. THE IMCCE VIRTUAL OBSERVATORY SOLAR SYSTEM PORTAL,

http://vo.imcce.fr/webservices/miriade/?forms

V. Strohm, preprint, Some samples of building a system of objects of a given kind,

https://www.academia.edu/43336620/Some_samples_of_building_a_system_of_objects_of_a_gi

ven_kind , https://vixra.org/abs/2006.0118

12

Addition

On graph 16, the same 206 years of Mercury as on graph 2, the same radius, the initial radius of

the sample, is subtracted from each radius of the year.

Plot 16

Documents

Motion of the Sun's nucleusMotion of the Sun's nucleus Viktor Strohm ... 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 U Days Distance difference. 3 Plot 2 In Plot 2,