[AATW]

This is a good illustration of another tactic FE engage in. This thread started by saying they don’t engage in certain debates - I’ve seen a bunch of threads where they’ve just walked away from a debate when they run out of argument.

But this is another thing they do - divert the discussion down a rabbit hole: how accurate is GPS in one thread, can the 3 body problem be solved in this one. Debates which aren’t really relevant to the actual shape of the earth.

[xenotolerance]

from the Wired article, referring to a numerical solution:

But the most important note—BOOM, we just solved the three-body problem and wasn't even that difficult.

from abstract of this paper:

We describe the general and restricted (circular and elliptic) three-body problems, different analytical and numerical methods of finding solutions, methods for performing stability analysis, search for periodic orbits and resonances, and application of the results to some interesting astronomical and space dynamical settings.

If you think that because there isn't a closed-form solution to the general three body problem, it can't be solved and it's a stain on classical physics or whatever, you are wrong. If you think that every source says it can't be solved, you are not reading them. If you think that the supposed unsolvability of the three body problem means the Saros system is the only way to predict eclipses, you are willfully misconstruing the information shared in this thread. If you think Ptolemy's and Columbus's predictions are equally accurate to NASA's computer simulations, you are wrong.

This isn't a 'well believe what you want' impasse, this is flat Earth belief at its purest. A believer made an assertion that turned out to be wrong, but conceding the point means admitting that flat Earth belief is wrong. Distract, divert, avoid; do not concede at any cost, or flat Earth is debunked.

well it's debunked in the first place, but that's how this place works

[AATW]

Physicists are unable to predict the motion of three bodies in a system, and it is a rather embarrassing stain on classical physics.

Why is it embarrassing?
Some problems ar simply harder to solve than others.
Trisecting an angle is another, an apparently simple task.

And it’s a bit rich coming from someone who believes a theory which is so poorly understood that you can’t even collectively decide whether there is one pole or two and has no agreed map.

[garygreen]

eclipse tables do not derive from saros cycles.  here's espenak's 50 year canon of solar eclipses: https://ntrs.nasa.gov/search.jsp?R=19870014944.  on page a-5 of the appendix begins a section titled "modern eclipse prediction."  he explains at the end of this section that details of the actual calculations can be found in the explanatory supplement to the astronomical almanac.  those calculations can be found starting on page 450.

this paper details both the history of eclipse prediction, and the equations of motion, in great detail: https://www.scribd.com/doc/316255061/Gutzwiller-Moon-Earth-Sin-Rmp-70-589

once you've determined when an eclipse will occur, local conditions (size of the umbra/penumbra, duration, location on the globe, etc.) are calculated using besselian elements.

nasa also publishes a work called the "five millennium canon of solar eclipses."  this work relied on a table of lunar positions (ephemeris) called epl-2000: https://eclipse.gsfc.nasa.gov/SEpath/ve82-predictions.html

this is the 1982 paper published with that ephemeris: http://adsabs.harvard.edu/abs/1983A%26A...124...50C

here's a program in c that constructs a lunar ephemeris using the epl-2000 method: https://github.com/variar/elp2000-82b

here's a python program that uses ephemerides to do all kinds of stuff, including eclipse prediction.  the documentation describes functions that output the angular separation between two astronomical objects and can be minimized to find eclipse times/locations/whatever: http://rhodesmill.org/pyephem/index.html

[Frocious]

eclipse tables do not derive from saros cycles.  here's espenak's 50 year canon of solar eclipses: https://ntrs.nasa.gov/search.jsp?R=19870014944.  on page a-5 of the appendix begins a section titled "modern eclipse prediction."  he explains at the end of this section that details of the actual calculations can be found in the explanatory supplement to the astronomical almanac.  those calculations can be found starting on page 450.

this paper details both the history of eclipse prediction, and the equations of motion, in great detail: https://www.scribd.com/doc/316255061/Gutzwiller-Moon-Earth-Sin-Rmp-70-589

once you've determined when an eclipse will occur, local conditions (size of the umbra/penumbra, duration, location on the globe, etc.) are calculated using besselian elements.

nasa also publishes a work called the "five millennium canon of solar eclipses."  this work relied on a table of lunar positions (ephemeris) called epl-2000: https://eclipse.gsfc.nasa.gov/SEpath/ve82-predictions.html

this is the 1982 paper published with that ephemeris: http://adsabs.harvard.edu/abs/1983A%26A...124...50C

here's a program in c that constructs a lunar ephemeris using the epl-2000 method: https://github.com/variar/elp2000-82b

here's a python program that uses ephemerides to do all kinds of stuff, including eclipse prediction.  the documentation describes functions that output the angular separation between two astronomical objects and can be minimized to find eclipse times/locations/whatever: http://rhodesmill.org/pyephem/index.html

I have a feeling we won't be hearing from Thork anytime soon.

Anyway, thanks for those links -- that's actually fascinating stuff.

[Tom Bishop]

NASA does use the Saros Cycle for its Lunar Eclipse and Solar Eclipse predictions, which is an ancient pattern-based method for finding the time of the eclipse. They are not using a geometric model.

Go to NASA's Eclipse Website -> Resources -> Eclipses and the Saros

That is the only method given on that entire website. They do not describe "motion laws" and "gravitational theory". They describe a method used by an ancient society of people who believed that the earth was flat.

It is mentioned on the NASA site that the Solar Eclipse may also be predicted with Besselian Elements, but we can see from this description of the method on stackexchange (at the bottom) that it is just another pattern-based method.

[Tom Bishop]

nasa also publishes a work called the "five millennium canon of solar eclipses."  this work relied on a table of lunar positions (ephemeris) called epl-2000: https://eclipse.gsfc.nasa.gov/SEpath/ve82-predictions.html

elp-2000, which tells us lunar positions, is also based on patterns. The moon has done the same thing for thousands of years. Don't you think it is possible to create an equation or pattern to tell us what it will do this year?

The timing of the eclipse is achieved with the Soros, a pattern model, as described on NASA's Eclipse website. The location of the moon during the eclipse is determined by pattern models such as elp-2000. The Saros Cycle is just a pattern which tells us when the Lunar Eclipse will occur, not necessarily where the moon will be at that time to see it.

[garygreen]

NASA does use the Saros Cycle for its Lunar Eclipse and Solar Eclipse predictions, which is an ancient pattern-based method for finding the time of the eclipse. They are not using a geometric model.

all of the material i posted describes the geometric model and the equations of motion.  whether you believe it to be right or wrong, i don't understand why you don't dive into the literature to see what the actual arguments are before going through the efforts of making these posts.  the material is free and online.  if you are going to make an attack you should address the actual source material.

Go to NASA's Eclipse Website -> Resources -> Eclipses and the Saros

That is the only method given on that entire website.

you must not have read the words on that website: "All eclipse calculations are by Fred Espenak, and he assumes full responsibility for their accuracy. Some of the information presented on this web site is based on data originally published in Fifty Year Canon of Solar Eclipses: 1986 - 2035, Fifty Year Canon of Lunar Eclipses: 1986 - 2035, [etc]..."

my last post contains the relevant works by espenak.  he didn't use saros cycles.  he made a table of solar and lunar positions using a computer and some equations of motion derived by hill/brown/some other nerds.

[Opeo]

For anyone interested in the original topic of this thread, which was about one certain FE model and the FE community's apparent lack of desire to improve it, I made a follow up thread over here (https://forum.tfes.org/index.php?topic=9273.0) since we basically came to the conclusion "the north-azimuthal projection doesn't work" in this one.

For solar eclipse talk, by all means continue in this thread.