How to Predict Eclipses: The Three-Body Problem

Nearly 3,000 years ago, ancient Babylonians began one of the longest-running science experiments in history. The goal: to predict eclipses. This singular aim has driven innovation across the history of science and mathematics, from the Saros cycle to Greek geometry to Newton’s calculus to the three-body problem. Today, eclipse prediction is a precise science; NASA scientists predict eclipses hundreds of years into the future. (Featuring Stephen Wolfram.)

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Chapters:
00:00 Solving the three-body problem is key to predicting eclipses
00:52 Importance of eclipses to ancient civilizations
01:20 The lunar phase cycles, plane of ecliptic, draconic month, anomalistic month
02:18 Discovery of the Saros cycle by the Babylonians
03:34 The Antikythera mechanism encodes the Saros cycle
04:22 Newton's discoveries lead to new calculations of the eclipse
00:48 How to solve the three-body problem
05:24 NASA's solution to the three-body problem, location of the Earth, moon and sun
06:51 JPL Development Ephemeris
07:25 Predicting future eclipses
08:14 The end of the current Saros series

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[williamvyner]

I love how closely the title is riding the algorithm, not just timing it with the eclipse, but also with the popularity of “The Three-Body Problem” on Netlfix 😂

[lozoft]

The coolest part about the Babylonian method of predicting eclipses is that, for them to have discovered it, the pattern would've had to have repeated multiple times in their part of the world in pretty close succession for them to have known about it. If you could work backwards and determine where on earth ancient eclipses had occurred, you might be able to find the plausible time period during which the Babylonians discovered this.

[CarlNeal]

Thank you for always making this incredibly interesting and complicated research so accessible!

[lucasfc]

I applaud the work each of you put in videos like this. This channel is by far the best for science nerds

[Academath]

Brilliant! And a good moment for such a video, with the notorius series TBP release and the eclipse that just happened.

[sadullarizayev]

I was there when they made the first computer. You had to be there it was just a moment in history.

[dylanparker]

I don't know whether it is historically accurate, but I read that an explorer (Columbus perhaps?) had impressed the natives of some island by predicting an Eclipse. So much so that the natives honored them, by sharing their food, or by not eating them, etc.

[ckq]

0:50 that Josh Sokol name seems familiar.

Scrabble player?

[kyle]

When was the first time we were able to predict an eclipse path? Was it after 1960? If it is, that's crazy that I'm living during a time which is so close to that discovery.

[SeekingTruth]

Is there any videos on research of new saros series?

[estmeta]

where can I find historical saros series and eclipse location?

[David-yylb]

Through the history of the first eclipse path explain why the totality paths of an eclipse will never ever take the same exact path again and why not...however could it happen

[markshiman]

i was really interested in the older charts and maps from 0:26, how did they predict them with that accuracy before 1960?

[abhishekcp]

Its so amazing how ancient astronomers/astrologer used to predict such things, especially in india during solar eclipse the temples will close and they know exactly when and at what time it will happen.

[qingyangzhang]

The first useful approximations to the three-body problem was found by Euler et al. in the 18th century, which made predicting the location of eclipses possible. But cruder predictions of eclipse locations certainly happened before. The Jesuit missionary Matteo Ricci gained fame in China for predicting an eclipse of Saros 118 that would fall on Sep 22 1596. Ricci was only familiar with the first six books of Euclid's Elements, which don't cover 3D geometry, and we don't know how he could have arrived at the prediction himself. But he was a student of the Jesuit astronomer and mathematician Christopher Clavius, who published a lot on Saros 118 eclipses.

[ValidatingUsername]

Didn’t the avatar: the last air bender find that device in the library of knowledge?

[bijoychandraroy]

I remember the time when I was the only one in school hyped about this kinds of stuffs... now everyone is all of a sudden....

*Even though it's never(seldom) visible from where I live

[Stacee-jxyz]

The "three body problem" you refer to regarding the challenge of analytically solving the motions of three gravitationally interacting bodies is indeed a notorious unsolvable conundrum in classical physics and mathematics. However, adopting the non-contradictory infinitesimal and monadological frameworks outlined in the text could provide novel avenues for addressing this issue in a coherent cosmological context. Here are some possibilities:

1. Infinitesimal Monadological Gravity
Instead of treating gravitational sources as ideal point masses, we can model them as pluralistic configurations of infinitesimal monadic elements with extended relational charge distributions:

Gab = Σi, j Γij(ma, mb, rab)

Where Gab is the gravitational interaction between monadic elements a and b, determined by combinatorial charge relation functions Γij over their infinitesimal masses ma, mb and relational separations rab.

Such an infinitesimal relational algebraic treatment could potentially regularize the three-body singularities by avoiding point-idealization paradoxes.

2. Pluriversal Superpositions
We can represent the overall three-body system as a superposition over monadic realizations:

|Ψ3-body> = Σn cn Un(a, b, c)

Where Un(a, b, c) are basis states capturing different monadic perspectives on the three-body configuration, with complex amplitudes cn.

The dynamics would then involve tracking non-commutative flows of these basis states, governed by a generalized gravitational constraint algebra rather than a single deterministic evolution.

3. Higher-Dimensional Hyperpluralities
The obstruction to analytic solvability may be an artifact of truncating to 3+1 dimensions. By embedding in higher dimensional kaleidoscopic geometric algebras, the three-body dynamics could be represented as relational resonances between polytope realizations:

(a, b, c) ←→ Δ3-body ⊂ Pn

Where Δ3-body is a dynamic polytope in the higher n-dimensional representation Pn capturing intersectional gravitational incidences between the three monadic parties a, b, c through infinitesimal homotopic deformations.

4. Coherent Pluriverse Rewriting
The very notion of "three separable bodies" may be an approximation that becomes inconsistent for strongly interdependent systems. The monadological framework allows rewriting as integrally pluralistic structures avoiding Cartesian idealization paradoxes:

Fnm = R[Un(a, b, c), Um(a, b, c)]

Representing the "three-body" dynamics as coherent resonance functors Fnm between relatively realized states Un, Um over the total interdependent probability amplitudes for all monadic perspectives on the interlaced (a, b, c) configuration.

In each of these non-contradictory possibilities, the key is avoiding the classical idealized truncations to finite point masses evolving deterministically in absolute geometric representations. The monadological and infinitesimal frameworks re-ground the "three bodies" in holistic pluralistic models centering:

1) Quantized infinitesimal separations and relational distributions
2) Superposed monadic perspectival realizations
3) Higher-dimensional geometric algebraic embeddings
4) Integral pluriversal resonance structure rewritings

By embracing the metaphysical first-person facts of inherent plurality and subjective experiential inseparability, the new frameworks may finally render such traditionally "insoluble" dynamical conundrums as the three-body problem analytically accessible after all - reframed in transcendently non-contradictory theoretical architectures.

[finalGambitShedinja]

so did all the early astronomers laser beam their own retinas?

[danleger]

I'm no math genius by any stretch and I'm curious if it's possible that one source of the problem to get formulas to work and line up with empirical observations is due to the fact that one of the highly influential key variables - the sun's mass - diminishes by approximately 100, 000 metric tonnes per year? (and, yes, my American friends, that's how you spell "tonnes" when expressed in metric! ;) ) What is loses when weighted against the sun's total mass may appear comparatively "insignificant", however, is it possible that it's effect becomes exponentially compounded within a 3 body model? (And good luck, because between our 8 planets, 1 dwarf planet, and an asteroid belt, someone's going to need a really big calculator to work that one out!)