Difference between revisions of "Astronomical Prediction Based on Patterns"
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| − | From the Wikipedia [https://en.wikipedia.org/wiki/Perturbation_(astronomy)#Special_perturbations section on | + | From the Wikipedia [https://en.wikipedia.org/wiki/Perturbation_(astronomy)#Special_perturbations section on Special Perturbations]: |
{{cite|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]}} | {{cite|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]}} | ||
Revision as of 16:50, 3 October 2018
Ancient Astronomy
Ancient Babylonians
Astronomy for Physical Science - Cal State Long Beach
“ 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. ”
Modern Astronomy
Perturbations
by Charles Lane Poor, PhD
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 is 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. ”
From the Wikipedia section on Special Perturbations:
“ 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] ”
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:
“ 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 "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. ”