Several posters on the Bad Astronomy and Universe Today Forum (BAUT) have expressed doubts about the non-conventional “binary model” of precession. The main critic is a poster that goes by the name of “Celestial Mechanic” (CM) who has called the binary model “rubbish, pure and simple”. While this is not the most constructive way to frame a scientific discussion it does express the current attitude of most astronomers when it comes to non-conventional theories of precession. It also hints at why several seemingly unrelated solar system problems (such as the sun’s lack of angular momentum relative to the planets) have gone unresolved.

On the plus side CM appears to be an excellent mathematician. While I might disagree with many of his over simplifications concerning the distribution of the earth’s mass (which immediately creates an unrealistic model) and direction of force (he uses mainly the sun even though the moon is the main culprit in the lunisolar model), and I might also question his comment to “ignore the eccentricity of the earth and moon” and “ignore the inclination of the moon’s orbit”, etc. none of these are really the main issue. CM’s dynamist approach adheres to past practices. And I can confirm his lengthy defense of the widely accepted lunisolar model of precession (the current prevailing theory to explain why the fixed stars seem to shift about 50 arc seconds per year relative to the equinox) is within the standards of conventional thinking.

My issue with CM and other certain physicists is 1. The lack of recognition that the standard assumptions (built over a long period of time) have been selected, adopted or eliminated to fit a value that is close to the precession observable, and 2. The missing component in understanding the problem is the failure to comprehend that earth orientation measurements are made to points outside the moving frame of the solar system (to which the earth appears to wobble 50” p/y), while at the same time, failing to understand that the earth shows no evidence whatsoever of wobbling in relation to objects within the solar system. In short the problems of lunisolar theory are far more fundamental than matching assumptions about the earth’s mass and local dynamics to the observed rate of change in earth orientation. We are measuring from a moving solar system, to points outside that system, yet relying on a static solar system model.

The purpose of this writing is to address CM’s comments in enough detail so those interested may understand where CM, and other astronomers less familiar with precession mechanics have failed to solve the problems with lunisolar theory or make any logical rebuttal of the binary model. In fact, by omission CM has confirmed the current consensus view that overlooks the motion of the solar system as a factor in earth orientation calculations (relative to points outside the solar system), and makes no provision for multiple reference frames at work in earth orientation measurement practices. This recognition is key to understanding changes in the precession observable.

Precession mechanics (which underlie precession equations) are poorly understood within the astronomical community. For example, some websites and professors when discussing earth orientation parameters (EOP) lump in nutation with precession. Nutation is clearly a local phenomenon caused the moon’s orbital motion around the earth with an easily identifiable 18 year signature, but it has absolutely nothing to do with the observable of the stars moving backward across the sky at the rate of about 50 arc seconds per year (a.k.a. precession). Precession is now increasing at an exponential rate, decreasing in periodicity, its cycle duration is more than a thousand times longer than nutation, and there is much uncertainty about tidal, atmospheric and geo-dynamic assumptions needed to derive the precession rate under lunisolar protocol. Nutation has a purely local cause and a short and exacting periodicity. This is not a big point in itself but helps illustrate the tendency to involve all local dynamics in the precession observable, whether or not they have any bearing. What we call the precession observable, as we will show, is the result of non-local dynamics; the solar system’s motion through space.

The confusion is understandable considering the lunisolar theory is the only explanation presently taught in schools and textbooks to describe the earth’s changing orientation to the fixed stars, and considering the binary model requires a companion star, with no obvious candidate in view (at least within the realm of commonly accepted assumptions). Consequently the arguments of CM, even though they may be incorrect, are not unfounded or unexpected.

If the sole cause of the earth’s changing orientation were local wobble (as dictated by current lunisolar theory) then the earth would change orientation relative to near objects (i.e. the planets, moon and sun), and far objects (i.e. quasars and other common points of reference) by the same amount. However, if the precession observable (earth’s changing orientation to the fixed stars) is mostly the result of a moving solar system (as found in the binary model), then there would be practically no local wobble, and the measurement of changes in the earth’s orientation would be different to objects “inside” the moving solar system than to objects “outside” the moving frame of the solar system.

This is exactly what our lunar studies have shown: the earth appears to change orientation to very distant objects at the rate of about 50” p/y while at the same time showing less than 1” p/y of change relative to objects within the moving solar system. Unfortunately, this phenomenon has gone wholly unnoticed as objects within the solar system move to such a large degree when compared to objects outside the solar system that NASA VLBI and others do not even bother to use local objects as fixed reference points. EOP measurement systems are focused on reference points far outside the moving frame of the solar system (typically quasars beyond the galaxy) but those measurements do not consider or adjust for any motion of the solar system, meaning the measurements fail to account for the motion of the frame or platform on which the earth resides. Nonetheless, those measurements and values are given to geoscientists to model and explain, as if the solar system were static.

Consequently, geoscientists have to come up with assumptions about the earth’s viscosity, core, mantel movement, oceans and tides etc. that fit the EOP observable given to them by radio astronomers. In other words, assumptions about the content and elasticity of the earth and moon are driven by precession measurements - not the other way around. Here is a quote from the NASA VLBI website:

"Changes in the Earth's orientation in inertial space have two causes: the gravitational forces of the Sun and Moon and the redistribution of total angular momentum among the solid Earth, ocean, and atmosphere. VLBI makes a direct measurement of the Earth's orientation in space from which geoscientists then model such phenomena as atmospheric angular momentum, ocean tides and currents, and the elastic response of the solid Earth."

As you will note CM’s equations rely on these same assumptions about the earth and moon in order to derive his precession results. In short, he made the same mistake as most other scientists where protocol has forced them to rely only on local mechanics without consideration of all reference frames. This has resulted in circular reasoning where the assumptions are slowly changed to fit the slowly changing observable.

Predictability is the hallmark of scientific theory. One telltale sign that lunisolar theory does not work is its inability to predict changes in the annual precession rate. The binary model accurately predicts changes in the annual precession rate, with a high degree of precision, whereas the lunisolar model has been “constantly” (no pun intended) tweaked. Background:

1543 Copernicus said the earth has three motions; 1.it rotates on its axis, 2.it revolves around the sun, and 3. it “librates” or wobbles. He needed this third motion to explain the widely observed precession of the equinox against the fixed stars. So he assumed the earth wobbled. He could not posit a moving solar system (an unknown reference frame) as people of the time could barely believe the earth itself was moving. 

1686 Sir Isaac Newton, was also unaware that the solar system moved. However he discovered the laws of gravity, and determined that if the earth wobbled (as Copernicus said) then it must be due to the gravity of the sun and moon (the two largest local objects) acting upon the earth. He offers equations for precession but these equations do not work.

1749 Jean le Rond d'Alembert, with a new understanding of fluid dynamics,

“corrects” Newton’s equations and adds provisions for torque and inertia. These allow for much more elastic and dynamic ideas about the earth and help to create a set of assumptions, which seem plausible to “explain” the then precession observable. But they turn out to be totally lacking in predictability. d’Alembert was also unaware that the solar system moved.

Late 19^th Century Astronomers, notice the actual precession rate is changing faster than the equations predict. Although no one knows why this is so, a “constant” is introduced to help the calcualtion better match precession observations on an ongoing basis. Even though the force of the moon acting upon the oblate earth should be “decreasing” ever so slightly, as the moon slowly recedes in distance each year, a constant of  .000222” p/y is “added” to bring the equation up to speed with the observable. Solar system motion is still an unconsidered topic.

20th Century The constant seems to work for a while until a close examination of the precession observable shows it is increasing at an exponential rate, outstripping the fixed constant. Thus the equation, even with an annual addition falls a little farther behind each year. Sometime during this period scientists broadly accept the idea the solar system is moving but it is never related to the apparent backward motion of the fixed stars.

Present. Astronomers and geoscientists are still trying to tweak the precession equation through purely local dynamics so every few years they adopt new inputs and or change a few assumptions about the elasticity of the earth, tidal action, etc. These include a suspicion the outer planets might exert a larger influence than heretofore acknowledged, the inclusion of the 300 largest asteroids as a factor in precession equations, and a recent suggestion that the earth’s core might be elliptical in shape, playing some role in the ever increasing precession rate. But while these accounting “plugs” are useful in bringing the equation closer to observations they have failed so far to allow more reliable predictions. Meanwhile every scientist knows the solar system moves, and even a few realize that precession measurements are made to points outside the moving solar system, but none seem to connect the two issues. We will show the precession rate curve can finally be predicted by applying Kepler’s laws to the sun’s motion.

If our solar system were in orbit around another star, producing the observable (from earth) of stars appearing to move backward across the heavens at the rate of about 50 arc seconds per year, then that rate of change (of that observable) would be commensurate with our solar system’s change in angular direction.

In other words, the rate of change in earth orientation (what we call “precession”) would increase as we moved toward the common center of mass, peaking at periapsis, and decrease as we moved away, and therefore be most easily plotted using Kepler’s laws.

To test which model was more accurate over the last 100 years (Binary or Lunisolar) we have input our orbit parameters (24,000years and apoapsis in 500AD) as provided by Sri Yukteswar in his book, The Holy Science, published in 1894, and compared these against the leading astronomer of the time, the great Simon Newcomb, who refined his formula for precession around 1900:

Simon Newcomb’s precession calculations were quite lengthy but resulted in:
50.2564 + a constant of 0.000222” p/y  (U.S. Navel Observatory 1900)

To find the binary model equivalent we apply Kepler’s laws to a body in a 24,000-year orbit (with mild eccentricity), 1500 years past apoapsis, which yields a current rate of change of .000349 in the year 2000. It would average slightly less than this for the preceding 100 years (and a bit more each year until periapsis).

The actual observed change between 1900, when the precession rate was 50.2564” p/y and the year 2000 when the rate was 50.290966” p/y (Astronomical Almanac) was 0.0337, equating to an annual rate of change of 0.000337” p/y over the last 100 years. Thus the Keplerian approach (based on the binary model) has proved to be 10 times more accurate than Simon Newcomb over the last 100 years.

Recognizing that the phenomenon of the stars moving backward across the sky (precession) is a result of the sun’s orbit not only provides accurate rate of change information it also gives the model clear parameters. In contrast, none of the precession computer models (based on lunisolar precession theory) I have seen  include a logical terminus point. For example, the computer model Epoch v2009 (sent to me recently by a friend), if run for thousands of years, shows the precession rate declining the farther you go into the past (until it is almost non-existent), and increasing the farther you go into the future, until the speed of the wobble surpasses that of the earth’s rotation – which is just ludicrous! (We have called this to the attention of the programmer so hopefully he has now come up some logical reason under lunisolar theory to set parameters on that model).

Some say the binary model must be wrong because we posit a 24,000-year precession cycle whereas the observed rate of annual change now extrapolates to a cycle period of 25,700.035 (Astronomical Almanac 2000). But understanding Kepler’s laws we can see the reason for the high current estimate is because we are now in the slow part of the orbit, much closer to the last apoapsis (500AD), and far from the next periapsis (12,500AD). The cycle periodicity should never deviate more than about 7.0% from the average (Current: 25,700 – 24,000 = 1700, 1700/25,700 = 6.6%), unless the orbit changed, which is highly unlikely.

A requirement of lunisolar theory, computed within the constraints of a static solar system, is that if local forces wobble the earth, the earth must show the same rate of wobble relative to local objects within the solar system, as it does to distant objects outside the solar system. But the binary model has no such requirement. There can be one rate of change relative to local objects, which we find to be less than 1” p/y, and another rate relative to distant objects, which we find to be about 50” p/y.

So which is true, does the earth wobble the same locally and non-locally? Or are the measurements different?

Studies of the moon’s phases in relation to the tropical and sidereal years show beyond a shadow of doubt (no pun intended) that the earth goes around the sun 360 degrees (relative to the sun) in the period known as a tropical year (365.2422 rotations of the earth), and therefore has no meaningful wobble in relation to the sun, while at the same time anyone can see that the earth comes up 50” short of 360 degrees in a tropical year when measured relative to the fixed stars. Details of the lunar study can be found on the BRI website.

But if there is no precession within the solar system wouldn’t this present a problem for astronomers trying to determine the position of the planets and moons?

Ironically, it is rectified in everyday astronomy by the use of different frames of measurement. For example, a tropical frame, which makes no adjustment for precession is generally used to plot the position of moons and planets and objects “inside” the solar system, whereas a sidereal frame that must be adjusted for precession (i.e. J2000 + precession, times number of years) is generally used to plot the position of stars, galaxies and objects “outside” the solar system. Thus astronomers unwittingly adjust for the fact that the earth does not precess relative to local objects and does precess relative to distant objects – and everything works fine.

The inflexible model proposed by lunisolar theorists is incompatible with astronomer’s practical use of a precessing sidereal frame and non-precessing tropical frame. Whereas the binary model accounts for the two separate frames and conforms perfectly, not only with the systems used by astronomers, but with the reality of the cosmos around us.

What this means is all the efforts by dynamists to determine the local twists and torques upon the earth and convert these to lunisolar precession equation inputs is for naught. The earth does not wobble relative to local objects, more than a smidgen (excluding Chandler wobble, nutation, etc. none of which affects its rotation). But the earth does change orientation (and therefore appear to wobble) in relation to the stars but only because the solar system moves.

It is assumed that most who are reading these pages realize the delta between a tropical year (365.2422 spins) and a sidereal year (365.2563 spins) is the value of precession. The math is straightforward:
   365.2563 (rotations in a sidereal year)
 - 365.2422 (rotations in a tropical year)
=   0.0141  (delta between tropical and sidereal year = value of precession in rotations)

0.0141 x 86,400 (#seconds in a day) = 1,218.24s = value of precession in time

1218.24 divided by 31,558,144.32 (seconds in a sidereal year) = 0.0000386030 (amount of earth rotation attributed to wobble in a sidereal year)

0.00003860 x 1,296,000 (number of arc seconds in a circle) = 50.029527

This value is within 1/3 of 1 percent of the current precession value. The reason for the slight inaccuracy is the delta of the tropical year and sidereal year is slowly expanding and there may be a small bit of real local precession, plus or minus cluster or galactic rotation that is seen in the observable when measuring to quasars outside the galaxy.

Riddle: If there are 50 arc seconds of earth wobble in 365.2563 spins of the earth then how much wobble (precession) is there in 365.2422 spins of the earth? Just for fun, please take a moment to calculate your answer before reading on.

Logic would dictate the amount of wobble is proportional to the earth’s rotation time – meaning it must wobble half as much in one day as it does in two days. But lunisolar theory does not allow this answer because precession is the “delta” between the two years (Tropical and Sidereal).

Logically, if the earth wobbles 50 arc seconds in 365 days, 6 hours, 9 minutes and 9 seconds (a time period equivalent to a sidereal year) then it should wobble 99.99% of this amount in 365 days, 5 hours, 48 minutes and 46 seconds (a tropical year time period). But because the cause of precession has been misdiagnosed – the lunisolar theory has no way to logically answer the question – so the question becomes a riddle.

But the binary model provides an easy answer: The earth does not wobble. It gradually changes orientation to the fixed stars because the solar system curves through space.

In part one CM states that Sol would have to travel 630 km/s to get around Sirius in 26,000 years. This is incorrect because Sol does not have to go all the way around Sirius. In a binary or multiple star system stars orbit the common center of mass. Therefore, the speed required for Sol (1 solar mass) to travel around a common center of mass with Sirius (3 solar masses, including Sirius B) would be less than 500 km/s. This is still an incredible speed but coincidentally it is near the speed the solar system is moving (at least relative to the CMB) according to a paper by Dr. Reg Cahill, an astrophysicist at Flinders University in Australia.

CM also comments that we do not observe Sirius moving at a high rate relative to the background stars. Actually, this has been an issue in question ever since Arabic records mentioned that Sirius (and Canis minor) crossed the Milky Way. The great mathematician Fourier also noticed that Sirius seems to move with the Sun, against the background stars, although Biot disagreed. A recent article by Jed Buchwald, astronomer at Caltech, mentioned this issue and published a diagram that shows Sirius seems to track the sun “in spite of precession”. Also, the Homann’s of Canada have made specific transit measurements of Sirius for over 20 years and found no “precession” adjustments are required to track the star Sirius. I visited their fixed observatory, viewed a Sirius transit through the crosshairs of their telescope, examined their instruments (including radio beeping time from atomic clock at Fort Collins) and found the data reliable and records impeccable. Here is a quote from their website concerning their findings:

Even more surprising is the observation that the mean time interval of the sidereal year, as measured with respect to Sirius is nearly identical (by less than one second) to the time interval of the tropical year. According to the theory of 'precession', a yearly time difference of about 1223 s is supposed to occur between a sidereal year and the tropical year.

This of course is exactly what you would expect if Sirius were the sun’s companion – it would move with the sun just as the Egyptians and other ancient cultures attested. But it is all so hard to believe given the vast resources and current capabilities of modern astronomy. Who can blame CM for his position if the astronomical almanacs say nothing about Sirius racing across the sky? To be fair several more independent studies of the earth’s motion relative to Sirius should be undertaken – and they should be based on first principles. This should settle the matter.

In part one BH asks CM what is moving at 50 arc seconds per year and CM answers “the axis of the earth’s rotation…” and proceeds with the standard lunisolar answer. This is a problem among astronomers today. The observable is described in a way that is only partially correct and only supports lunisolar reasoning. The proper answer should be that it “depends on your frame of reference”.

There are many other things to be said about companion star scenarios, both in the visible and invisible spectrum, issues concerning MOND and MG, Voyager 1 and 2 and GP-B, the angular momentum of the sun versus planets, etc. all of which provide clues to the motion of the solar system, and many of which are mentioned in my book “Lost Star of Myth and Time”. Unfortunately, I am running out of time for this post.

Finally, my sincere thanks to CM, an excellent mathematician; he has properly represented the dynamists point of view. Hopefully, he will soon come to understand