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)

From Mathematical Thought from Ancient to Modern Times: Volume One by Professor Morris Kline (bio) we see:

Ancient Greeks
The Ancient Greeks believed in an stationary round earth-centered system, around which the Sun, Moon and planets revolved. Prediction in Ancient Greek astronomy was dominated by the epicycle; a small circle whose center moves around the circumference of a larger one. Originally devised by Hipparchus of Rhodes and later extended by Ptolmy of Alexandria, the purpose of the epicycle and related mechanisms were to account for differences from the ideal state.

In Chapter 2 of The Logical Leap: Induction in Physics by David Harriman (bio) we read:

=Modern Astronomy=

Perturbations
In order to predict the path of planets modern astronomers calculate perturbations.

Description and Function
Gravitation Vs. Relativity (1922) Charles Lane Poor, Ph.D. (bio) Professor Emeritus of Celestial Mechanics, Columbia University Full Text Link

Motion of the Planets p.132

Professor Poor gives an example of epicycles being used to predict patterns of phemomena:

Motion of the Planets p.138

Replacing the Foundations of Astronomy
In a 2017 paper Replacing the Foundations of Astronomy (Archive) its author Dr. Gopi Krishna Vijaya (bio) gives us a historic overview of the foundations of Astronomy. He describes that perturbations are epicycles, and that they are used in astronomy to 'make the observations fit' the theory:

Epicycles Once More



Underlying Model
Instead of than Ptolmy's perfect circle, perturbation theory in celestial mechanics uses a two body problem as the underlying model. From The Ever-Changing Sky: A Guide to the Celestial Sphere (Archive):

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

The Wikipedia article on Perturbation Theory (Archive) echoes the same:

The book Approximate Analytical Methods for Solving Ordinary Differential Equations states on p.65 (Archive):

Special Perturbations
From the Wikipedia section on Special Perturbations in celestial mechanics (Archive):

History
The Wikipedia article on Perturbation Theory provides a history:

Moon Model - Ancient to Present
The following paper by physicist Martin C. Gutzwiller (bio) describes a history of the model of the Moon. See the illustration on page 600 and its caption, and note that the lunar model was "adopted ever since."

Moon-Earth-Sun: The oldest three-body problem (Archive) Martin C. Gutzwiller

The Foundations of Astrodynamics
In a paper titled The Foundations of Astrodynamics its aurthor Dr. Samuel Herrick (bio) says the same as all of the above, explaining that epicycles are still used.

Kepler's Epicycles

The above paper describes that there were still epicycles in Kepler's version with elliptical orbit, and that they were never eliminated. Kepler just reduced it a little more. We can see that Jupiter is on an epicycle in Kepler's version:



Dr. Herrick explains that Kepler's epicycles were adopted into Newtonian mechanics (as Newtonian pertubations), and that progress then reversed, favoring the Copernican system of circles and epicycles.

Newton's Epicycles
After Kepler came Newton. Historian of Science William Whewell (bio) informs us that Newton used epicycles for the Moon:

History of the Inductive Sciences (1846)

See Also: A Reintroduction of Epicycles - Newton's 1702 Lunar Theory and Halley's Saros Correction

University of Toronto Quarterly
At the end of the 19th century, long after Copernicus, Kepler and Newton made their contributions to astronomy, we read about the state of astronomy in a 1895 edition of University of Toronto Quarterly (Archive):

Evolution of the Solar System
A work by Dr. Hannes Alfvén (bio) titled Evolution of the Solar System (1976) shows that epicycles are still in use in celestial mechanics, more than 365 years after Kepler's discovery of elliptical orbits and 289 years after Newton's publishing of his Principia. Dr. Alfvén uses a combination of Kepler and epicycles:

https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19770006016.pdf

https://history.nasa.gov/SP-345/contents.htm

The Motion of Planets and Satellites

3.1 The guiding-center approximation of celestial mechanics 3.2 Circular orbits 3.3 Oscillations modifying the circular orbit

p.40



"FIGURE 3.3.1.—The guiding-center method of approximating the Kepler motion. The guiding center moves with constant velocity along the dashed circle of radius r0 in the center of which the gravitating mass Mc is situated. The body M moves in an “epicycle” around the guiding center. The epicycle is an ellipse with the axis ratio 2/1 and semiminor axis of er0. The epicycle motion is retrograde. The resulting motion of M is an ellipse which almost coincides with the undashed circle which has its center at O. The distance from O to Mc is er0. The position of the pericenter is given by Φp. The difference between the undashed circle and the exact Kepler ellipse is really less than the thickness of the line."

Perturbation Search
A search for 'perturbation' on nasa.gov shows that perturbations are used widely for many applications, including heavy use in celestial mechanics.

https://www.google.com/search?&q=perturbation+site:nasa.gov

No. of Results: 50,600

Jet Propulsion Laboratory Development Ephemeris
The Jet Propulsion Laboratory Development Ephemeris (JPL DE or DE) is a 'mathematical model of the Solar System' produced by the Jet Propulsion laboratory in Pasadena, California. It has been claimed that JPL DE is a simulation of the Solar System which is based on gravity. However, it is seen that it uses perturbation-based methods.

https://en.wikipedia.org/wiki/Jet_Propulsion_Laboratory_Development_Ephemeris

NASA Horizons
NASA's Horizons On-Line Ephemeris System system makes similar statements in its methodology, suggesting that it is based on perturbation theory:

https://ssd.jpl.nasa.gov/?horizons_doc

Laskar, Lapace, Le Verrier
Great figures of science, such as Jacques Laskar, Pierre-Simon Laplace, and U. Le Verrier, used perturbation methods to predict movement in the solar system.

From p.157 of The KAM Story by Professor H. Scott Dumass we read:

VSOP
VSOP (French: Variations Séculaires des Orbites Planétaires) is a popular software package used to generate planetary ephemeris, which are the positions of the planetary 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 uses it is therefore a validation of the theory. On assessment we find, however, that VSOP is based on the ancient epicyclic methods.

Comparing VSOP to the Ptolemaic System
The following is left by an editor on VSOP's Wikipedia Talk Page (Archive):

VSOP Perturbations
On p.331 of Planetary theories in rectangular and spherical variables - VSOP 87 solutions we read that VSOP is based on perturbation theory:

http://articles.adsabs.harvard.edu//full/1988A%26A...202..309B/0000311.000.html (Archive)

Comments from Celestia 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)

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

Fourier Analysis
In Encyclopedia Britannica's Celestial Mechanics article (Archive) by physics professor and astrophysicist Stanton J. Peale (bio) it says:

Fourier Transforms
An Interactive Introduction to Fourier Transforms

http://www.jezzamon.com/fourier/ (Archive)



Seen above: Fourier Transforms (Archive)

The Forgotten Revolution
In The Forgotten Revolution - How Science Was Born in 300 BC and Why it Had to Be Reborn, mathematician and science historian Lucio Russo (bio) relates the equivalence between Fourier and epicycle theories (Archive):

3.8 Ptolemaic Astronomy

Fourier, Perturbations, and Patterns
It is seen that Fourier Analysis and Perturbation Theory are used to find patterns. From Perturbation Theory in the Solar System (Archive) by theoretical physicist Carl Johnson we see:

Further Reference

 * Math for Scientists: Refreshing the Essentials - Section 3.4.1 An Alternative Explanation of Fourier Analysis: Epicycles (Archive)

Non-Dynamical Simulations
The pertubation theory simulations are not dynamical systems. See the following:

Perturbation Theory for Restricted Three-Body Orbits 1991 Thesis by David A. Ross

I. Introduction

Ross quotes Dr. William Weisel (bio) who admits that there is no dynamical gravity model. The dynamical way is not simply a nuisance—it is impossible and not even attempted. They are using a workaround. The paper goes on to talk about perturbation theory and fourier methods. Also see the Three Body Problem

Galactic Dynamics
It is seen that the science of the galaxies is also based on epicycles.

Lindblad’s epicycles – valid method or bad science? (Archive) Charles Francis

~

Conclusion

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

Sir Richard Phillips in his Million Facts (Archive) reports:

The Eclipses
In Chapter 11 of Earth Not a Globe (Archive) its author gives us an overview of the eclipse calculations:

Rowbotham also provides pattern-based equations for finding the time, magnitude, and duration of the Lunar Eclipse at the end of Chapter 11.

Royal Astronomer Robert Ball
The Royal Astronomer Sir Robert Ball (1840-1913), in his work The Story of the Heavens (Archive), on page 58, told us:

Sommerville
Somerville in Physical Sciences pg. 46 states:

Earth Review
T.G. Ferguson in the Earth Review for September 1894, says:

NASA Eclipse Website
Website URL: https://eclipse.gsfc.nasa.gov

If one visits NASA's eclipse website they will find that NASA explains eclipse prediction through the ancient Saros Cycle, rather than the Three Body Problem of astronomy.

From Resources -> Eclipses and the Saros (Archive) we read a description of the Saros Cycle:

The reader is encouraged to visit NASA's eclipse website and count how many times the Saros Cycle is mentioned, and then count how many times the Three Body Problem is mentioned.

Google Search Term: "saros" site:https://eclipse.gsfc.nasa.gov

No. of Results: 14,400

Google Search Term: "three body" site:https://eclipse.gsfc.nasa.gov

No. of Results: 2 (duplicate text)

From the result:

The Three Body Problem refers to the greatest problem in the history of astronomy. It is the inability of science to simulate or recreate a model of the Sun-Earth-Moon system. It is for this reason that pattern-based methods must be used for prediction in astronomy.

Eclipse Prediction
The ancient Saros Cycle method is taught in modern astronomy courses. A slideshow from a University of Florida astronomy course (Archive) shows:



Under the heading How are eclipses calculated? on a University College London page by Dr. Mike Dworetsky for the Ask an Astronomer service we see only the Saros process described:

A Text-Book of Astronomy
Read any astronomy textbook and the same will be seen:

A TEXT-BOOK OF ASTRONOMY by George C. Comstock Director of the Washburn Observatory and Professor of Astronomy in the University of Wisconson

Full Text Link (Archive)

p.116



(Click to Enlarge)

One should notice that there is nothing in the book about the three body problem, the geometry of the sun-earth-moon system, or Newton's equations as being the basis for the eclipse predictions.

Sun-Moon Epicycles
Physicist and computer scientist Stephen Wolfram (bio), creator of Wolfram Alpha, provides another assessment, regarding how the positions of the Sun and Moon are calculated:

https://www.wired.com/story/when-exactly-will-the-eclipse-happen/ (Archive)