This is a copy of Prof. Sam Cox's letter, as it was posted on www.cosmologyreview.com, in response to Karl-Heinz Homann's paper 'Beelzebub's Buried Dog'.

Hello!

Most of the "stars" which are nearest the earth are protostars and are a few times the size of Jupiter. It is completely possible that a "Brown Dwarf" is affecting gravitational interactions in the solar neighborhood. Locating these objects would be of value to science.

My mother told me 100 times if she told me once, that "if I took care of the little things, the big things would take care of themselves." Accounting for a previously(unaccounted for) precession of 23 seconds of arc in the orbit of Mercury was one of the experimental verifications which ushered in Einsteins model of the cosmos. Gravitational bending of light from stars as it went by the sun during solar eclipses was another, but at first the precision of those measurrements was very bad. Later, improving precision confirmed the Einsteinian effects. Today, Einsteinian effects have been measured to a very high degree of precision (not necessarily 17 places in all effects!) gives SR, GR and QM their veracity or credibility. Little things, and a high degree of accuracy are important!

However, I view the precession (or wobbling of, as a top slowing down) of the earths axis as a fact, and not just for astronomical reasons. The ancient pyramids were aligned very precisely with the star Thuban, the pole star when they were built. The stars Yildun and Kokab are refered to in historical records as pole stars by the Turks and Arabs. The brightest pole stars in the northern hemisphere are Vega (pole star in 13,000 BC and AD (sorry I missed a few hundred years!). In the southern hemisphere, there is no pole star now, but in the future there will be a procession of them.

The precession of the earths axis is dictated by physical principles. Manned lunar exploration found that the chemical composition of the surface of the moon is identical to the Earths mantle. This led to computer studies which show a very high probability that the moon was created by a glancing impact between the Earth and another planet (possibly Mars, which has an almost identical inclination of its axis to the ecliptic) early in the history of the solar system. This impact, (and with even extra-solar system data to go on now) and associated "near-misses",believed to be common in the early formation of any planetary system, caused the precession, which is observable and measurable in historic times....even in one lifetime! Precession has small direct effects on the Earths rotation on its axis and revolution about the sun, but fundamentally, rotation, revolution and precession are separate processes....just as time, space and energy are defined as different qualities in GR.

The Earth is not a good clock, by atomic clock standards anyway. The change in relative positions of both the Sun and moon, the elipse of the earths orbit itself, the movements of Venus which is astronomically close, Mars and even Jupiter and Saturn, affect the exact period of our day and year. The Author used the star Sirius as a fixed star, but Sirius is only 8.6 light years from the Earth. A better fixed star would have been at least 100 light years away. There is continental drift of several inches a year, and the Earths tides; not only the oceans, but the land masses themselves. The author lives in Alberta, an area within a few hundred miles of active plate tectonic movement. Every time the earth rotates, millions upon millions of tons of seawater slide up on the land like disk brakes, impeding its rotation. Much of this energy moves to the moon, which is becoming more distant. In only 150,000 years, there will be no more total solar eclipses, only annular. In several Billion years, the Earth will lose the moon, which will become a planet in its own right. It is estimated from fossil records that 350 million years ago during Devonian times, an Earth day was only 18 hours long. The rate of slowing now is much reduced, but it is still significant. Even so, over short periods, the Earth actually speeds up slightly and slows down. Its time of rotation against the fixed stars at this time is roughly 23 hours, 56 minutes, 4.09 seconds...and slowing.

For readers who are interested, the precession of the Earths axis is easily measured in one lifetime, in fact the axis of the Earth precesses one Degree every 71.6 years...very easy to measure. The figures are as follows: one day=1/7"; one week=1"; one year, 50.274"; 30 years 25.14' (1950-1980); 71.6 years, one degree; 100 years 1.397 degrees; 2150 years (one sign of the Zodiac) 30 degrees; 25,800 years, 360 degrees.

The author talks about an "Axis Star" which is "orbited by our solar system". It would require a massive body for that to occur, so massive, it would be observable as a binary companion of the Sun. However, I really appreciate this intuition, for in an Einsteinian Hyperspherical Universe every frame of reference moves about every other. Frames of reference are not prioritized by the respective increasing masses of heavenly bodies in a given system. Each point in Einsteinian Space Time has its own equally valid frame of reference. This prediction is experimentally verifiable, and as I recall, some expensive equipment was sent into space this year (1999) to test Einstein once again. I haven't heard the results, but if the Einsteinian prediction was incorrect, the whole world would know about it by now!

My final comment is on "significant" figures: The letter JPL (Jet Propulsion Laboratory-NASA) sent to Mr. Homann stressed the fact that because of many factors (many of which I have mentioned), most of the places in his mathematical figures are not significant. This means they are not really meaningful, and it is not good science to try to use them. Even seconds of arc in Mercuries orbit are significant, but millionths of seconds of arc? There are just to many factors here. The problem is much like the one we have in physics when we try to evaluate an eggs coming together and jumping on the table using forces and vectors. As the recent experiments with infinite points in space/ time, each representing a separate frame of reference, evaluating Humpties "resurrection" requires that the world-line of each atom be taken into consideration...a job for an advanced form of probability theory, and computers about 10,000 times larger than anything we have today!...if we want to learn anything significant.

I am impressed with Mr. Homanns interest in Astronomy! Little things are important, and we need to be watchful of experimental deviations from our models of any kind, however seemingly insignificant. If we begin to see a pattern of deviation, it is time to take a hard look at our models and re-evaluate them mathematically.

I wish Mr. Homann my best in his personal quest for exactness!

Sincerely,

Sam Cox: College of Micronesia

December 23, 1999

Dear Mr. Cox,

Thank you very much for commenting on my paper "The Mathematical Problem of the Precession-Time Paradox". I am very glad that you have taken the time to review and evaluate my work. Thanks to your critical and objective comments it seems to me that it is necessary to try to explain a few details a little better. I sense a certain misconception that most people might have regarding my "desire for utmost precision" and therefore I must clarify an important point.

Because of the jobs I have done in my lifetime I learned to love mathematics and mechanical precision. But the issue here is not really about small and insignificant fractions of a second, but about the immense time difference of 1223 seconds per revolution period. These 1223 s per year can only exist if a precession of the earth's axis exists. There is, however, absolutely no scientific proof that this enormous time difference does indeed occur in reality. Therefore, it can be concluded that earth's precession cannot be viewed as a physical fact. The slow regression of the fixed stars (including our pole star) with respect to earth's equinoctial points must have a different cause.

We seem to agree that the mean rotation time of the earth on its axis is about 23h56m4.09 s, or about 86164.091 s relative to the fixed stars. This figure by the way coincides with my measurement of Sirius. Of course, this is a "mean" time based on continues measurement over a period of 5 years. As a matter of fact, I have observed and measured significant variations in earth's sidereal rotation time from anywhere up to roughly plus minus one second per day. But it is important to remember that all these fluctuations in earth's rotation time average out with each complete period of revolution; i.e. earth's actual orbit time remains nearly constant. It is said to deviate by no more than 0.1 seconds in roughly 6500 years. As we can see, such a tiny difference in time is very insignificant as compared to the time discrepancy of more than 1223 seconds, which should occur due to a precession of the earth's axis.

You mentioned that rotation, revolution and precession are separate processes and that precession has only small direct effects on the earth's rotation on its axis and revolution about the sun. Basically, I must agree with what you say. But unfortunately astronomers view the effect that precession has on our earth's revolution period very different - due to precession we are suppose to have two different years which differ by more than 1223 s per revolution from each other. It looks like we have no other choice as to first examine physically what effect precession would really have on the earth's mean rotation and revolution time.

We said that earth's mean rotation time relative to the fixed stars is about 86164.091s (86164.09054 s to be more exact). With every rotation of the earth a retrograding precessional motion of the earth's axis causes a time delay of about 9.12 ms relative to the position of the fixed stars. This means, the mean sidereal rotation time of the earth increases to about 86164.1 s (86164.09966 s). For example, after 366 rotations of the earth this time difference accumulates to about 3.34 s, which is equivalent to the observed regression of the fixed stars of about 50.26" per year. We must keep in mind that no matter by how much earth's actual rotation time on its own axis may vary, the "apparent" time delay caused by precession will remain at its constant rate of about 9.12 ms per day. Obviously this "apparent" time delay has no direct effect on the earth's actual rotation time on its axis. Precession can also have no influence on the actual revolution period of the earth about the sun relative to the fixed stars, since this time interval is independent of earth's rotation period. So why is there a time difference of about 1223 s with every revolution of the earth about the sun? Why does precession cause during every rotation of the earth a time delay of 9.12 ms relative to the fixed stars and simultaneously a time delay of about 3.34 s relative to the sun?

Here begins the problem of a unique physical and mathematical paradox. Because a precession of the earth's axis causes a gradual shift of the earth's seasons (equinoctial points) relative to the sun, the earth appears to move "backwards" around the sun by 50.26" per day (!) or about 1° every 72 periods of revolution. In other words, precession is responsible for a steady "decrease" in earth's orbit time about the sun, when compared to the position of the fixed stars - the essential sidereal point of reference. We know that earth's actual 360° orbit time around sun is 31,556,925.9747 s - this is the defined time interval of a tropical year. Question: If the fixed stars regress from this essential time interval by about 3.34 s, then where do those mysterious 1223 s fit in? Answer: Nowhere. Since they are definitely not a physical fact that can be verified and substantiated by actual sidereal time measurement, these 1223 s per year are an just an illusion, seemingly created by a so-called precession of the earth's axis. In order to solve this problem we must understand two very important things:

The fundamental principle of the civil calendar.

The actual revolution period of the earth around the sun relative to the inertial position of the fixed stars.

Our civil calendar is nothing more than a precise "chronometer" that counts full mean solar days of 86400 seconds with each rotation of the earth relative to the sun during earth's complete 360° revolution period of exactly 365.24219878 rotations. A complex system of leap days, as well as the occasional insertion of so-called leap seconds, is necessary so that our civil calendar remains synchronized to the absolute criterion for time, the time interval of the tropical or actual sidereal year of 31,556,925.9747 seconds - the basis for all astronomical calculations. The leap seconds have to be inserted so that the precise atomic time second or TAI does not deviate by more than 1 second (0.9 s) from the even more precise "cosmic clock". That means even the most stable atomic clocks must always be synchronized to earth's 360° revolution period relative to the sun and, believe it or not, relative to Sirius.

Also, it must be noted here that the difference in time between a mean solar day and a mean sidereal day is always exactly 86400 s - 86164.0905382 s = 235.9094618 s. When a calendar year ends, precisely 365 × 86400 s = 31,536,000 s have passed. However, relative to the essential sidereal point of reference (inertial space - vernal equinox) or actually relative to Sirius 366 × 86164.0905382 s = 31,536,057.137 s have elapsed, i.e. about a 57.14 s time difference. After four calendar years this ignored time difference accumulates to 4 × 57.137 s = 228.548 s. Only every four years (365.25 day cycle) we will finally have a leap day which brings us the essential solar-sidereal day difference of 235.9094618 seconds to compensate for the previous time-difference of 228.548 s. Because the compensation is a little too much, it means that every four years another time difference must occur: 235.90946 s - 228.548 s = 7.36 seconds. It is these crucial 7.36 s that will accumulate again to the mentioned solar-sidereal day difference of 235.90946 s, and a leap day is again required in roughly 128 years (235.90946 × 4 ÷ 7.36 = 128.18). In order to come close to this crucial figure of 128.18, the actual leap cycle of our civil calendar is 133.33 years (97 leap days in 400 years). Since this fixed time span of 365.2425 days is still not perfectly synchronized to the actual tropical year, another leap day is required about every 3320 years.

The division of the mean solar day in 24 hours or 86400 seconds is for us a more practical measure of time than the actual sidereal rotation period of the earth. Based on the rigorous mathematical relationship between a mean solar day and a mean sidereal day, with respect to the complete 360° revolution period of 31,556,925.9747 seconds, the mean sidereal day has to be exactly 86164.0905382 seconds. That value can only apply to a very specific inertial or sidereal point of reference, which has to be truly fixed in relation to our solar system. This sidereal point of reference is Sirius, the central sun to our entire solar system. Relative to other fixed stars, earth's sidereal rotation period should be about 9.12 ms on average longer, since this delay in time occurs due to the fact that our solar system revolves around Sirius. We will see that the Sirius system (Sirius B orbiting Sirius A) determines our calendar. Besides these mentioned time intervals, which are essentially used in astrometry, no other time interval is relevant with respect to the stars or the sun. A year of about 31,558,149.8 s (1223 s more) does not exist, consequently it cannot have any relevance whatsoever, except to support a false theory called the precession of the earth.

Perhaps to better visualize the fundamental problem, we can try to imagine the following celestial mechanical process if a precession of the earth were indeed to occur as it is claimed. Assuming that a ¼ precession motion (90° shift of the axis) is completed in just one calendar year, then our earth has reached the same position of its axis relative to the sun already after three quarters of its complete revolution period. For example, if we begin the year during the winter season on the Northern Hemisphere, we will have winter again by September 21. This means, that by December 31, at the end of an entire calendar year of 365 days, as the earth completes its orbit around the sun, it will be spring instead of winter on the Northern Hemisphere. And just like our calendar would have not been adjusted to this situation, the same does not happen during a period of 6450 years (¼ precession). Evidently, almost 6 additional leap days should have been taken into consideration ever since the calendar reform of 1582 AD (417 years × 20.38 minutes = about 5.9 days). In other words, at present the spring equinox should occur on March 15. But this is not the case. And since earth's period of revolution did certainly not increase or decrease by about six mean solar days during the mentioned time interval of the last 417 years, the assertion can be made that an assumed precession of the earth's axis never ever occurred in reality.

I hope that some of this information may help to understand the essential nature of this problem. Is precession a paradigm that is so deeply entrenched in our minds that it makes us blind to see a simple scientific truth, which we rather prefer to ignore than to deal with it?

If you have any questions or comments, please do not hesitate to contact me. I would love to hear from you.

With the very best wishes from Karl-Heinz Homann and my son Uwe

uhomann@telusplanet.net

PS: Something else to ponder about why a precession of the earth's axis itself cannot occur and how the Sirius system may in deed have an influence on our solar system.

It is said that the gravitational pull of the sun and the moon causes the earth to precess against its direction of rotation. If we look at the inclination of the axis of some of the other planets in our solar system, like Mars, Saturn and Neptun, we will notice that the inclination of each of those axis' steadily increases (from 1.75° to 2.25° compared to earth) with an increase of their distance from the sun, while the gravitational pull of the sun decreases. And this phenomenon is independent of the quantity and masses of their moons!

Another example: Our outermost planet Pluto does not only have a very eccentric orbit of about 17° below the average planetary orbital plane, but its revolution period of 248.421 years is in relation to the Sirius B - Sirius A orbit period of 49.68 years* exactly 5 to 1. Furthermore, in the spring of 1989, when the sun, Sirius B and Sirius A were in direct conjunction, Pluto went through its perihelion. Is all of this coincidence?

* (average figure based on Volet's measurement of 49.94 and Auwers' of 49.42 years)