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 ecl
ipse, 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 cyc
le 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 phas
e 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, Gre
ek 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 wer
e 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. Th
at 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 Netwo
rk, 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 sha
dow 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.
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