Astronomical Prediction Based on Patterns

This page will demonstrate that prediction in astronomy is based solely on patterns in the sky. Celestial events come in patterns and trends. By analyzing the patterns of past behaviors from historic tables it is possible to create an equation that will predict a future event. This is how prediction in astronomy has been performed for thousands of years, and how it is still performed today.

Ancient Astronomy

Ancient Babylonians

Astronomy for Physical Science - Cal State Long Beach (Archive)

  “ The Babylonians accumulated records of astronomical observations for many centuries. The records enabled them to see repeated patterns in the motions of the celestial objects. They used the patterns to predict the positions of the Moon and planets. ”

Mathematical Thought from Ancient to Modern Times: Volume One

  “ Babylonians calculated the first and second differences of successive data, observed the consistency of the first or second differences, and extrapolated or interpolated data. Their procedure was equivalent to using the fact that the data can be fit by polynomial functions and enabled them to predict the daily positions of the planets. They knew the periods of the planets with some accuracy, and also used eclipses as a basis for calculation. There was, however, no geometrical scheme of planetary or lunar motion in Babylonian astronomy. ”

Modern Astronomy

Perturbations

Description and Function

Gravitation Vs. Relativity

by Charles Lane Poor, PhD

Full Text Link

Motion of the Planets p.132

  “ The deviations from the “ideal” in the elements of a planet’s orbit are called “perturbations” or “variations”.... In calculating the perturbations, the mathematician is forced to adopt the old device of Hipparchus, the discredited and discarded epicycle. It is true that the name, epicycle, is no longer used, and that one may hunt in vain through astronomical text-books for the slightest hint of the present day use of this device, which in the popular mind is connected with absurd and fantastic theories. The physicist and the mathematician now speak of harmonic motion, of Fourier’s series, of the development of a function into a series of sines and cosines. The name has been changed, but the essentials of the device remain. And the essential, the fundamental point of the device, under whatever name it may be concealed, is the representation of an irregular motion as the combination of a number of simple, uniform circular motions. ”

Motion of the Planets p.138

  “ The Tide Predicting Machine of the Coast and Geodetic Survey at Washington is a note-worthy example of the application of the mechanical method [of prediction via epicycles]. The rise and fall of the tide at any port is a periodic phenomenon, and it may, therefore, be analyzed, or separated into a number of simple harmonic, or circular components. Each component tide will be simple, will have a definite period and a constant amplitude; and each such component may be represented mechanically by the arm of a crank, the length of which represents the amplitude; each crank arm being, in fact, the radius of one of the circles in our diagram.

Such a machine was invented by Sir William Thomson and was put in operation many years ago. The machine at present in use at Washington was designed by William Ferrel. It provides for nineteen components and directly gives the times and heights of high and low waters. In order to predict the tides for a given place and year, it is necessary to adjust the lengths of the crank arms, so that each shall be the same proportion of the known height of the corresponding partial tide, and to adjust the periods of their revolutions proportionally to the actual periods. Each arm must also be set at the proper angle to represent the phase of the component at the beginning of the year. When all these adjustments have been made, the machine is started and it takes only a few hours to run off the tides for a year, or for several years. This machine probably represents the highest possible development of the graphical or mechanical method. It is a concrete, definite mechanical adaptation of the epicyclic theory of Hipparchus.

But, because the Coast Survey represents and predicts the movements of tidal waters by a complicated mass of revolving cranks and moving chains, does any one imagine for a moment that the actual waters are made up of such a system of cranks? No more did Hipparchus believe that the bodies of the solar system were actually attached to the radial arms of his epicycles; his was a mere mathematical, or graphical device for representing irregular, complicated motions.

While the graphical, or mechanical method is limited to a few terms, the trigonometrical, or analytical method is unlimited. It is possible to pile epicycle upon epicycle, the number being limited only by the patience of the mathematician and computer. ”

Use in Astronomical Almanacs

From the Wikipedia section on Special Perturbations (Archive):

  “ In methods of special perturbations, numerical datasets, representing values for the positions, velocities and accelerative forces on the bodies of interest, are made the basis of numerical integration of the differential equations of motion.[6] In effect, the positions and velocities are perturbed directly, and no attempt is made to calculate the curves of the orbits or the orbital elements.[2] Special perturbations can be applied to any problem in celestial mechanics, as it is not limited to cases where the perturbing forces are small.[4] Once applied only to comets and minor planets, special perturbation methods are now the basis of the most accurate machine-generated planetary ephemerides of the great astronomical almanacs.[2][7] ”

General Application

Perturbation methods are, in fact, prevalent in many areas of science. From Perturbations in Complex Molecular Systems | (Archive) we read the following:

  “ In general perturbation methods starts with a known exact solution of a problem and add “small” variation terms in order to approach to a solution for a related problem without known exact solution. Perturbation theory has been widely used in almost all areas of science. Bhor's quantum model, Heisenberg's matrix mechanincs, Feyman diagrams, and Poincare's chaos model or “butterfly effect” in complex systems are examples of perturbation theories. ”

The Wikipedia article on Perturbation Theory echoes the same description, and its general use:

  “ This general procedure is a widely used mathematical tool in advanced sciences and engineering: start with a simplified problem and gradually add corrections that make the formula that the corrected problem becomes a closer and closer match to the original formula. ”

History

The article also provides a history of Perturbation Theory:

  “ Perturbation theory was first devised to solve otherwise intractable problems in the calculation of the motions of planets in the solar system.

...Since astronomic data came to be known with much greater accuracy, it became necessary to consider how the motion of a planet around the Sun is affected by other planets. This was the origin of the three-body problem; thus, in studying the system Moon–Earth–Sun the mass ratio between the Moon and the Earth was chosen as the small parameter. Lagrange and Laplace were the first to advance the view that the constants which describe the motion of a planet around the Sun are "perturbed", as it were, by the motion of other planets and vary as a function of time; hence the name "perturbation theory". ”

VSOP

VSOP (French: Variations Séculaires des Orbites Planétaires) is a popular software package used to generate planetary ephemeris, the position of astronomical objects in the sky. It is used in astronomy software such as Stellarium and Celestia. It has been alleged that VSOP uses a geometric RET model to make its predictions, and so VSOP and the astronomy software which use it is therefore validation of the theory. We find, however, that VSOP is based on the ancient pattern methods of epicycles and perturbations:

Comparing VSOP to the Ptolemaic System

The following is left by an editor on VSOP's Wikipedia Talk Page (Archive):

  “ Modelling VSOP on a ubiquitous PC computer program, starting with only one element for each of the three parameters (L, B R) and then slowly incrementing the number of elements, gives a sense of irony that it is in fact nothing more than a more complex development of the ancient deferent / epicycle system used by Ptolemy. A system that despite being totally dismissed out of hand for being intellectually "wrong", was able to provide a prediction service accurate enough to match the observational resolution available (naked eye, with no reliable mechanical timekeeping). A system that, astoundingly to this author, was able to detect and measure, accurately, the lunar evection, one of the still-used perturbations of the Earth-Moon system. Summing powers of sines and cosines is certainly tantamount to circles upon (or perhaps within) circles; recursing, or perhaps simply nesting, almost endlessly. Whilst of course this is totally irrelevant to the mathematics, it perhaps behooves Wikipedia's wider terms of reference to include this as a philosophical point. ”

Comments from Celstia Developers

Celestia Developers comment on the large number of planet-specific terms used in computing positions:

https://celestia.space/forum/viewtopic.php?f=2&t=8285 (Archive)

  “ VSOP87 is a set of polynomials describing the orbits of the major planets. There are over 1000 terms in each series. ”

https://celestia.space/forum/viewtopic.php?f=3&t=2592 (Archive)

  “ I could add more terms to the VSOP-87 series, but there are already over 1000 per major planet ”

Quotes

R. J. Morrison, F.A.S.L., R.N., in his "New Principia," says:

  “ Eclipses, occultations, the positions of the planets, the motions of the fixed stars, the whole of practical navigation, the grand phenomena of the course of the sun, and the return of the comets, may all and every one of them be as accurately, nay, more accurately, known without the farrago of mystery the mathematicians have adopted to throw dust in the eyes of the people, and to claim honors to which they have no just title.

The public generally believe that the longitudes of the heavenly bodies are calculated on the principles of Newton's laws. Nothing could be more false. ”

Sir Richard Phillips in his Million Factssays:

  “ The precision of Astronomy arises not from theories, but from prolonged observations, and the regularity of the mean motions, and the ascertained uniformity of their irregularities.

...Nothing therefore can be more impertinent than the assertion of modern writers that the accuracy of astronomical predictions arises from any modern theory. Astronomy is strictly a science of observation, and far more indebted to the false theory of Astrology, than to the equally false and fanciful theory of any modern.

We find that four or five thousand years ago, the mean motion of the Sun, Moon and Planets were known to a second, just as at present, and the moon's nodes, the latitudes of the planets, &c., were all adopted by Astrologers in preparing horoscopes for any time past or present. Ephemerides of the planet's places, of eclipses, &c., have been published for above 600 years, and were at first nearly as precise as at present.' ”

Eclipses

Sir Robert Ball, in his work The Story of the Heavens, on page 58, informs us:

  “ If we observe all the eclipses in a period of eighteen years, or nineteen years, then we can predict, with at least an approximation to the truth, all the future eclipses for many years. It is only necessary to recollect that in 6585 ⅓ days after one eclipse a nearly similar eclipse follows. For instance, a beautiful eclipse of the moon occurred on the 5th of December, 1881. If we count back 6585 days from that date, that is, 18 years and 2 days, we come to November 24th, 1863, and a similar eclipse of the moon took place then. …It was this rule which enabled the ancient astronomers to predict the occurrence of eclipses at a time when the motions of the moon were not understood nearly so well as we now know them. ”

Somerville in Physical Sciences pg 46 tells us:

  “ No particular theory is required to calculate Eclipses, and the calculations may be made with equal accuracy, independent of every theory. ”