A sidereal year relative to Sirius

Based on the original German text by Karl-Heinz Homann, this appendix tries to explain the fundamental mistake of the mathematical calculations for a "mysterious" sidereal year of 365.256361 mean solar days. For comparison, the following different sidereal days will be examined:

1. The mean sidereal day of 86164.091 s, as published in educational textbooks (exactly 86164.0905382 s).

2. The 9.12 ms longer sidereal day of 86164.09966 s, the basis for the roughly 1223 s longer sidereal year, supposedly due to precession.

3. The mean sidereal day relative to Sirius, as determined by direct transit measurements for the periods indicated:

I.

1999 05.04. 21h16'36.5"

2000 05.04. 21h13'41"

(366 solar days × 86400 s - 175.5 s) ÷ 367 Sirius transits = 86164.09946 s

II.

1994 06.04. 21h11'50"

1998 05.04. 21h15'37"

(1460 solar days × 86400 s + 227 s) ÷ 1464 Sirius transits = 86164.08948 s

III.

1994 06.04. 21h11'50"

2000 05.04. 21h13'41"

(2191 solar days × 86400 s + 111 s) ÷ 2197 Sirius transits = 86164.0924 s

It must be noted that such time variations could be due to either a precessing -, or an oscillating axis of rotation. The time difference in seconds between each mean sidereal day and the mean solar day of 86400 s is the basis for the calculations of the different length for a complete 360° revolution of the Earth around the sun:

86400 s ÷ (86400 s - mean sidereal day in s) = n (number of rotations per 360° orbit)

86400 s × (n-1) = n × mean sidereal day in s

It follows:

1.

86400 s ÷ 235.9094618 s = 366.4219878 365.24219878 × 86400 s = 31 556 925.9747 s

2.

86400 s ÷ 235.90034 s = 366.256361 365.256361 × 86400 s = 31 558 149.59 s

3.

I. 86400 s ÷ 235.90054 s = 366.25605 365.25605 × 86400 s = 31 558 122.73 s

II. 86400 s ÷ 235.91052 s = 366.24056 365.24056 × 86400 s = 31 556 784 s

III. 86400 s ÷ 235.9076 s = 366.24509 365.24509 × 86400 s = 31 557 175.71 s

According to equation 2, the 9.12 ms longer sidereal day causes an increase of 1223 s in the length of the 360° orbit of the Earth around the sun, as compared to equation 1. In comparison, the minor variations in the mean sidereal day relative to Sirius cause the actual 360° orbit to be 196.76 s longer (I) and even 141.91 s shorter (II). Based on the transit period of 6 years, the average difference is an additional 249.74 s (III) per year.

However, according to the actual difference between the mean sidereal day relative to Sirius and the mean sidereal day of 86164.0905382 s, Sirius passes by ONLY 0.68 s per tropical year later through the transit, NOT 249.74 s.

The fundamental mistake of equation 2 and 3 is as follows:

It was said that the difference between the mean sidereal day of 86164.0905382 s and the mean solar day of 86400 s is exactly 235.9094618 s. This value is essentially a constant. If the mean sidereal day varies due to oscillations of the axis of rotation, logically the same variations MUST occur relative to the sun. This mathematical-physical fact would also apply in case of a precession of the axis. Hence, the true 360° orbit period of the Earth around the sun can ONLY be 31 556 925.9747 s, as described by equation 1.

Oscillations of the Earth's rotation axis have no affect on this orbit period. The observations of Sirius have shown that such variations will average out to approximately the value of the mean sidereal day of 86164.0905382 s. A precession of the axis does not cause the observed phenomenon of the steady regression of the stars, because the time interval of about 31,558,149 s is NOT the true 360° orbit period of the Earth around the sun. According to the model of lunisolar precession, essentially no star can exist that has a mean transit time that closely matches the mean sidereal day of 86164.0905382 s. However, the mean transit time of Sirius, as determined by method of direct transit measurement, does not conform to this model.

"Why Sirius? Isn't it too far away?"

These are the questions of a few readers who have dealt with the problem of a so-called companion star of our sun, and who believe it could perhaps be a neighboring dark dwarf or black hole. I received calculations relating to a 24000-year orbital period and distances of stars having a 0.33 to 6-fold solar mass. Such calculations, which I found very interesting, correctly conform to Kepler and Newton. A star with the 0.33-fold solar mass could be an extinguished white dwarf, whereas stars with the 2 and 6-fold solar mass are more likely classified as a Neutron star, due to the Chandrasekhar limit. It would be desirable for astronomers to proceed with the search in order to discover such a "companion star". Since it has not yet been discovered, given that it should only be about 23 to 38 times more distant than Pluto, Sirius remains the only candidate.

There is no argument that galaxies exist, which rotate so fast that the centrifugal force of the outer region is larger than the centripetal attraction of the inner visible mass. But according to Newton, the outer stars would literary have to fly away. Furthermore, the search for the over 90% of the missing mass, which supposedly holds together the universe, has not been abandoned. In order to get out of this dilemma, one has decided that ultimately a modification of Newton's law of gravitation is necessary. For instance, the Dutch astronomer R. H. Sanders of the Kapteyn Institute of the University of Groningen proposed to use, instead of the Newton gravitation-potential, the potential of a punctiform mass, similar to the nuclear forces. This would imply that over short distances a repulsive force compensates for more than 90% of a far-reaching "normal" gravitation. At short distances, as for example within our solar system, we would be looking at a reduced force of gravitation ("Gesucht: Die neue Welt-Formel", Prof. Hans Jörg Fahr, Bild der Wissenschaft 5/1991). This fits precisely to Einstein's theory of non-linear gravitation.

My long-time observations of Sirius suggest the same. The required orbital speed of more than 500 km/s for our solar system to move around Sirius is thus quite possible. Typical individual velocities in the universe of about 500 km/s have been observed in practice. The solar system moves at such a velocity relative to the cosmic background radiation, which, as the "echo of the Big Bang", is considered to be a non-moving cosmic reference system ("Neue Zweifel am Urknall", Prof. Hans Jörg Fahr, Bild der Wissenschaft, 7/1990).

The long-term transit measurements of Sirius prove that the orientation of the Earth's axis is fixed between Sirius and Procyon. Since the precession of the Earth is not a physical occurrence as proven by mathematical equations, alternatively Sirius could be the star that our solar system orbits. Furthermore, it is conceivable that both our sun and Sirius, together with Procyon, Alpha Centauri and other neighboring stars, jointly revolve around a larger central sun (in the Pleiades?).

Karl-Heinz Homann

"Precession is the observed phenomenon of our solar system orbiting another star, not a physical occurrence!"