How the Ancients Predicted Eclipses 3,000 Years Ago

Summary

This script explores the history and science of eclipse prediction, from the ancient Babylonians' discovery of the 18-year saros cycle to the Antikythera mechanism, an early analog computer. It discusses the challenges of the three-body problem involving Earth, moon, and sun, and how modern methods like NASA's JPL Ephemeris and Besselian elements allow for precise eclipse predictions. The script highlights the evolution from early astronomical records to advanced mathematical models, showcasing the pinnacle of predictive astronomy.

Takeaways

• 🌞 The first known analog computer was designed 2000 years ago to predict solar eclipses, a significant event in astronomy and science.
• 📚 Eclipse prediction has evolved over 3000 years, with modern science achieving accuracy to within a second or two for hundreds of years into the future.
• 🌐 Eclipse prediction involves solving the Three-Body Problem, which considers the complex motions of the Earth, Moon, and Sun.
• 📈 Ancient civilizations like the Babylonians kept detailed astronomical records, identifying patterns and cycles in the Moon's movements.
• 🌕 The synodic month, draconic month, and anomalistic month are three lunar cycles identified by ancient astronomers, crucial for understanding eclipses.
• 🔄 The saros, a period of approximately 18 years, was discovered by the Babylonians and is when the relative positions of the Sun, Earth, and Moon repeat, potentially leading to an eclipse.
• 🎓 Greek astronomers combined the saros with mathematical models to create the Antikythera mechanism, an early device for predicting astronomical positions and eclipses.
• 🚀 Modern methods of eclipse prediction involve numerical approximations and solving differential equations based on Newton's laws of motion and gravitation.
• 🌌 NASA uses the JPL Development Ephemeris, a mathematical model, and laser-ranging data from the Moon to predict the positions of celestial bodies with high precision.
• 📊 Besselian elements, a set of numbers, are used in conjunction with the JPL Ephemeris to predict the timing and visibility of eclipses on Earth's surface.
• 🔮 The saros series, though no longer the primary method for predicting eclipses, remains a significant tool for approximating them and is part of the ongoing story of human innovation in astronomy.

Q & A

What is the significance of the Antikythera mechanism mentioned in the script?

The Antikythera mechanism is significant as it is considered the first known analog computer, designed around 2000 years ago to predict astronomical events, particularly solar eclipses. It was an early attempt to understand and predict the complex motions of celestial bodies using mechanical means.

How accurate are modern eclipse predictions compared to ancient methods?

Modern eclipse predictions are extremely accurate, with the ability to predict when an eclipse will occur to within a second or two for many hundreds of years into the future. This level of precision is a result of thousands of years of scientific and mathematical advancements beyond the capabilities of ancient methods.

What is the 'Three-Body Problem' mentioned in the script?

The 'Three-Body Problem' refers to the challenge of accurately predicting the motion of three celestial bodies that interact gravitationally, such as the Earth, Moon, and Sun. It is a complex problem in physics that has no general closed-form solution, but can be approximated numerically.

What are the three periodic cycles of the Moon that ancient astronomers observed?

Ancient astronomers observed three periodic cycles of the Moon: the synodic month (29.5 days, from one new moon to the next), the draconic month (27.2 days, the time for the Moon to pass through the plane of the ecliptic at two different nodes), and the anomalistic month (27.5 days, the time for the Moon to return to the same size in the sky due to its elliptical orbit).

What is a 'saros' and how does it relate to eclipse prediction?

A 'saros' is a period of approximately 18 years (6,585 days and 8 hours) after which the cycles of the Moon's phases, its size, and its position relative to the ecliptic plane align in a way that can produce an eclipse. The saros cycle was used by ancient astronomers to predict eclipses, although it could only approximate when an eclipse would occur, not where it would be visible.

How did the Babylonians contribute to the understanding of eclipses?

The Babylonians contributed to the understanding of eclipses by keeping detailed astronomical records, known as astronomical diaries, which recorded the positions of celestial bodies. They identified patterns and periodic cycles, leading to the discovery of the saros cycle, which was a significant step in predicting eclipses.

What role did the saros cycle play in the development of the Antikythera mechanism?

The saros cycle played a pivotal role in the development of the Antikythera mechanism as it was encoded into the device to help predict eclipses. The mechanism used the saros cycle to approximate the timing of eclipses, although it could not predict their visibility on Earth.

How do modern methods for predicting eclipses differ from using the saros cycle?

Modern methods for predicting eclipses use advanced mathematical models and numerical approximations, such as the JPL Development Ephemeris, which takes into account the positions and velocities of celestial bodies with high precision. This differs from the saros cycle, which is a simpler, more approximate method that does not account for the exact positions of the Earth, Moon, and Sun.

What is the role of the Deep Space Network in determining the Earth's position relative to the Sun?

The Deep Space Network, an array of spacecraft missions across the solar system, provides data that helps NASA determine the Earth's position relative to the Sun. This data is crucial for accurate eclipse predictions and is processed through complex mathematical models.

How is the position of the Moon determined with such precision today?

The position of the Moon is determined with precision using laser ranging to reflective mirrors placed on the Moon by Apollo astronauts. Laser pulses are sent to these mirrors, and the time taken for the pulses to bounce back allows for the calculation of the distance between the Earth and the Moon with centimeter-scale accuracy.

Outlines

00:00

🌒 Ancient Eclipse Prediction and the Antikythera Mechanism

This paragraph delves into the historical significance of eclipse prediction, highlighting the development of the first analog computer, the Antikythera mechanism, designed 2000 years ago. It underscores the importance of eclipses in the evolution of astronomy and science, and how they've been used to regulate time and predict astronomical events. The Babylonians' astronomical diaries, which recorded planetary positions and lunar phases, are mentioned as the longest-running scientific experiment. The paragraph explains the three periodic cycles observed by ancient astronomers: the synodic month, the draconic month, and the anomalistic month, which led to the discovery of the saros cycle. The saros, a roughly 18-year period where the sun, earth, and moon's geometry repeats, was used to predict eclipses. The Greeks later combined this knowledge with mathematical models to create the Antikythera mechanism, an early computational device with 37 gears simulating celestial motions and encoding the saros cycle for eclipse prediction, despite its limitations in predicting visibility locations.

05:03

🚀 Modern Methods for Predicting Eclipses

The second paragraph focuses on the modern techniques used to predict eclipses, moving from the historical context to contemporary scientific advancements. It discusses the three-body problem, which involves the complex interactions between the Earth, moon, and sun, and how it has been tackled through numerical approximations since the 1960s. The paragraph explains the importance of knowing the initial conditions of these celestial bodies to solve the differential equations that govern their motion. It mentions the use of reflective mirrors on the moon, placed by Apollo astronauts, to measure the Earth-moon distance with laser pulses. The Deep Space Network is highlighted as a source of data for the Earth's position relative to the sun. The JPL Development Ephemeris, a mathematical model that uses Chebyshev polynomial coefficients to store and predict the positions and velocities of celestial bodies, is introduced. The paragraph concludes with the use of Besselian elements to predict the exact time and location of moon shadows on Earth during an eclipse, showcasing the precision of modern eclipse prediction methods and the transition from the saros cycle to more accurate computational models.

Keywords

💡Analog Computer

An analog computer is a type of computer that uses continuous physical quantities, such as electrical, mechanical, or hydraulic quantities, to model the problem being solved. In the video, the first known analog computer was designed to predict solar eclipses, demonstrating the historical use of such devices for astronomical calculations.

💡Total Solar Eclipse

A total solar eclipse is an astronomical event where the moon completely covers the sun, as seen from a specific location on Earth. The video emphasizes the significance of predicting this event, which has been a pursuit of astronomers for thousands of years, to understand celestial mechanics.

💡Three-Body Problem

The three-body problem in physics refers to the difficulty of accurately predicting the motion of three celestial bodies interacting through gravity alone. The video discusses how this problem was central to the development of more accurate eclipse predictions, as it involves the complex interactions between the Earth, moon, and sun.

💡Synodic Month

The synodic month, also known as the lunar month, is the time interval between two consecutive new moons or full moons, which is approximately 29.5 days. The video uses this concept to explain one of the periodic cycles observed by ancient astronomers, which was crucial in understanding the moon's phases and predicting eclipses.

💡Draconic Month

The draconic month is the period of approximately 27.2 days during which the moon passes through the same node of its orbit around the Earth. This term is mentioned in the video to illustrate another of the periodic cycles identified by ancient astronomers, which is relevant to eclipse prediction.

💡Anomalistic Month

The anomalistic month is the time it takes for the moon to complete one orbit and return to the same position in its elliptical orbit relative to the Earth, which is about 27.5 days. The video explains this as a factor in the moon's varying distance from Earth, affecting its apparent size and thus the occurrence of eclipses.

💡Saros

The saros is a period of approximately 18 years that represents a repeating cycle of solar and lunar eclipses. The video highlights the saros as a significant discovery by ancient Babylonian astronomers, which allowed for the approximation of eclipse timings.

💡Antikythera Mechanism

The Antikythera mechanism was an ancient analog computer used to predict astronomical positions and eclipses. The video describes it as a 'clockwork computer' with gears simulating celestial motions, which was a significant step in the development of predictive astronomy.

💡JPL Development Ephemeris

The JPL Development Ephemeris is a highly accurate mathematical model used by NASA to calculate the positions and velocities of celestial bodies. The video explains that this model, which uses Chebyshev polynomial coefficients, has replaced older methods like the saros for precise eclipse predictions.

💡Besselian Elements

Besselian elements are a set of astronomical parameters used to predict the circumstances of solar and lunar eclipses. The video mentions these elements as part of the modern method for determining when and where the moon's shadow will intersect with the Earth's surface during an eclipse.

💡Differential Equations

Differential equations are mathematical equations that describe the rate of change of a quantity relative to another quantity. The video discusses how these equations, based on Newton's laws of motion and gravitation, are used to model the motion of the Earth, moon, and sun, which is essential for precise eclipse predictions.

Highlights

The first known analog computer was designed 2000 years ago to predict total solar eclipses.

Eclipse prediction has been a significant part of astronomy and science history.

Modern science can predict eclipses with a high degree of accuracy, to within a second or two.

Eclipse prediction involves solving the Three-Body Problem of the Earth, moon, and sun's motion.

Ancient governments had responsibilities in regulating time and predicting astronomical events like eclipses.

The Babylonians recorded astronomical diaries, marking one of the longest-running scientific experiments.

Ancient astronomers identified three periodic cycles in the moon's movements.

The synodic month, draconic month, and anomalistic month are key lunar cycles identified by ancient astronomers.

The saros, a period of 6,585 days, was discovered by the Babylonians, syncing lunar and solar cycles.

The Antikythera mechanism, an ancient Greek analog computer, used the saros cycle to predict eclipses.

The quest for precise eclipse prediction has driven scientific innovation for millennia.

Newton's laws of motion and gravitation were pivotal in advancing the understanding of celestial bodies' motion.

The three-body problem remains challenging, despite advancements in mathematics and physics.

NASA uses numerical approximations and initial conditions to compute the positions of celestial bodies.

Lunar ranging using reflectors on the moon allows for precise measurement of the Earth-moon distance.

The Deep Space Network and JPL Development Ephemeris are used to determine the positions of celestial bodies.

Besselian elements are used in conjunction with the JPL Ephemeris to predict the moon's shadow on Earth during an eclipse.

Eclipses represent a pinnacle of achievement in traditional mathematical science and precise prediction.

The saros series, while not used for precise predictions, remains a powerful tool for approximating eclipses.

The North American Total Solar Eclipse of 2024 is part of Saros Series 139, which will end in 2750.

Transcripts

This is the first known analog computer.

It was designed 2000 years ago to predict an extraordinary cosmic event...

when the moon passes in front of the sun causing a total solar eclipse.

Eclipses are intimately tied into the history of astronomy and science.

It's sort of a triumph of exact science and mathematical science that it's

become possible over the course of 3000 years of work to predict when the

eclipse will arrive to within a second or two.

We can very accurately predict the solar eclipse, when it's going to happen,

how it's going to happen for many, many hundreds of years.

Eclipse prediction is the giant kind of geometry exercise,

but the real thing that had to be solved for eclipses was a Three-Body Problem

of the motion of the Earth, moon and sun.

What do you actually have to work out to know when the eclipse is going to happen?

Eclipses are part of a really larger set of astronomical responsibilities that

lots of ancient governments had

in regulating time and predicting astronomical events.

For centuries, people were keeping good records about when eclipses happened.

The Babylonians, they recorded these astronomical diaries,

what planets were where in the sky, where the moon was.

It's probably the longest running scientific experiment in history.

They started being able to see patterns.

Ancient astronomers saw three periodic cycles

hidden in the movements of the moon.

They noticed it takes 29.5 days to go from one new moon to the next.

This full lunar phase cycle is known as the synodic month.

They also saw that the sun and the moon are confined to

two different paths in the sky.

That's because of a cosmic quirk.

The moon's orbit is tilted at five degrees above the Earth's orbit around the sun,

known as the plane of the ecliptic.

Every 27.2 days, the draconic month,

the moon passes through the plane of the ecliptic at two different nodes.

Finally, ancient astronomers observe that the moon appears closer and further away,

returning to the same size in the sky every 27.5 days.

This is the anomalistic month caused by the moon's elliptical orbit.

Armed with centuries of data,

the Babylonians noticed something striking

every 6,585 days and eight hours, which is about 18 years.

These cycles sync up and this happens.

This number came to be known as the saros,

a harmonic separating two eclipses.

After a saros length of time, the geometry of the sun,

Earth, moon system repeats again.

The Babylonians realized that in 223 repetitions of the

lunar phase cycle,

you would have 239 repetitions in the apparent size of the moon oscillating

and 242 plunges through the plane of the ecliptic.

All of these roughly equal the same amount of time.

That coincidence is what leads to these saros cycles.

Every saros cycle,

the postiion of the moon relative to line between the earth and the sun,

and relative to the plane of the ecliptic is sort of in the same configuration.

That's what produces an eclipse.

A few centuries after the discovery of the saros,

Greek astronomers combined it with new mathematical models

of celestial objects

to create the Antikythera mechanism.

It's this clockwork computer. It has, I think, 37 gears in it,

and as you turn these gears around,

it's kind of simulating the motions of planets and the moon and so on,

and it encodes the saros cycle and it has a very coarse

approximation to predicting eclipses.

But there are limitations.

The saros can predict roughly when an eclipse will occur,

not where it will be visible on Earth.

For the next 2000 years,

the quest for a precise method of eclipse prediction would drive scientific

innovation across the world.

You go from the earliest days of science to geometricization of astronomy and

then the calculusization of astronomy in the hands of Newton.

But then the race was on to figure out,

given Newton's law's of motion, law of gravitation, it's like,

well, then we should be able to figure out exactly where the moon is

and exactly when eclipses are going to occur.

People were impressed Newton had solved the two-body problem. It's like,

how hard can it now be to solve the three-body problem?

Well, it turned out to be really hard.

We've got these differential equations that represent the motion of Earth, moon, and sun.

according to Newton's laws.

A differential equation says that the rate of change of one thing is

determined by some other thing.

When people say solve the three-body problem,

they typically mean find a formula for where each of those bodies will be.

That formula we can't find,

but we can perfectly well work out the numerical value for the

positions of these bodies.

In the 1960s,

NASA started directly computing numerical approximations to the three-body problem.

But to solve these differential equations,

you first need to know the Earth, sun, and moon's

initial conditions or the positions and velocities at some particular time.

Roger tower.

Now we know where the moon is because there are reflective mirrors on it that

the Apollo astronauts put.

There are five reflectors on the moon.

We send the laser pulse to it,

it bounces back and returns to the Earth.

And from that information, we can figure out the distance information

between the Earth and the moon.

And we can usually process this data to about centimeter scale.

So the moon's position and its future position are better

understood than almost anywhere else we would want to go or think about.

To find the Earth's position relative to the sun,

NASA uses data from the Deep Space Network,

an array of spacecraft missions across the solar system.

The part that most occupied the ancients,

where will the celestial bodies be is effectively solved and it's solved

because NASA has missions all over the solar system and they're taking data from

all of these missions,

and then they're crunching it through a very complicated model.

This mathematical model is called the JPL Development Ephemeris.

It's stores, the positions and velocities of the sun, Earth, moon,

and other gravitational variables as a sequence of Chebyshev polynomial coefficients.

A special kind of function that is convenient for

finding new data points based on existing data points.

So you have bunch of points and try to figure out, okay,

which curve gives us the minimum difference between the

observation and the fitted line.

So of course, what we are doing is slightly more complicated,

but the essence of how we do things is just the curve fitting.

Think of the Antikythera device with that 37 cogs,

well now we've got 20,000 cogs that we happen to be implementing electronically

to compute when eclipses will occur.

To predict the next eclipse, and ones thousands of years into the future,

NASA uses the JPL Ephemeris to find out when the sun, Earth,

and moon will line up.

Then using a handful of numbers called Besselian elements,

scientists can predict when and where the moon shadow will intersect with the

Earth's surface.

One of the things that's kind of nice about eclipses is that they are the

pinnacle of kind of, achievement for something you can really predict

with great precision on the basis of traditional mathematical science.

We no longer rely on the saros to predict eclipses,

but it remains a powerful tool for approximating them.

The saros series will be hundreds of eclipses.

At any given time, there are multiple saros series active.

The North American Total Solar Eclipse of 2024

is part of the Saros Series 139, which started in 1501.

And eventually what happens is that the cone of shadow of the moon will miss the Earth.

And then that's the end of that saros series.

Saros 139 will end in 2750,

beginning another chapter in the story of human innovation.