Difference between revisions of "Astronomical Prediction Based on Patterns"
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{{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]}} | ||
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| + | <center>'''Gravitation Vs. Relativity'''<br> | ||
| + | By Charles Lane Poor, PhD<br> | ||
| + | [https://archive.org/stream/gravitationvers00chamgoog Full Text Link]</center> | ||
| + | |||
| + | ''Motion of the Planets p.132'' | ||
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| + | {{cite|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.}} | ||
Revision as of 04:02, 1 October 2018
Perturbations
https://en.wikipedia.org/wiki/Perturbation_(astronomy)
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] ”
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. ”