February 27, 2020 0

Ancient Greek Astronomy


Let’s talk a little about how we came to know
what we know today. Now to begin the story of astronomy, we could easily take it as far
back as the earliest cavemen, who looked up to the sky and wondered what was up there.
But for the sake of brevity, we’re going to just limit our discussion for the time being
to the ancient Greeks. Turns out there’s a lot of ideas the ancient Greeks popularized
that still hold to this day, and many of course that have since been discarded. We begin our
story with Artistotle who was a major proponent of the idea of the so-called “geocentric universe”.
That is, the Moon, Mercury, Sun, and all the planets all were revolving around the Earth,
with the Earth at the center of the universe. This was a very easy idea to come to. After
all, everything in the sky appears to be moving around us, it just seemed to make sense that
so did the planets, and perhaps just fixed upon the sky were the stars themselves. Now one thing that Aristotle and indeed most
of the ancient Greeks believed was that the Earth was in fact round. And the reason why is because they observed
lunar eclipses. If you notice the way the Earth’s shadow passes
along the face of the Moon you’ll notice that the shadow was curved. And it turns out that the only object capable
of casting a circular shadow is a spherical object. So for this reason and also for some other
lines of evidence, the Greeks well-understood that the Earth was round. And today, thanks to the internet, more people
believe the Earth is flat than at any time since the 1400’s. Yay, progress. Anyway, it turns out though that the idea
that the Earth was at the center of the universe wasn’t 100% shared among all Greek thinkers. Aristarchus of Samos, for example, gave us
the first known heliocentric model. In other words, he proposed that the Sun was
the center of the cosmos and everything revolved around the Sun. He published his ideas in something called
On the Sizes and Distances and he used lunar eclipses to work out the
relative distances and sizes of the Earth, Sun, and Moon. He also proposed that the stars were distant
Suns and that the Universe was vast. However, his idea that the Sun might be at
the center of the Universe was largely rejected. The reasoning went something like this: If the stars were at varying distances from
the Sun, and if the Sun were at the center, of, well, what we now know today to be our
Solar System, and Earth were to be traveling around in an orbit, from one location we should
be able to look at a relatively nearby star, and see its apparent image projected onto
the background stars. And that means 6 months later, we should be
able to make a similar observation and see that same star, this time with its position
shifted with respect to the background stars. So this phenomenon is the phenomenon of parallax,
and it’s a phenomenon that you and are familiar with all the time. We have two eyes and our
brains work constantly to take the information from each eye and infer a distance to some
object. And it’s a useful thing for, well, not running
into everything all the time. Well what happened was that the Greeks decided
to test this idea at the time by enlisting their very best visually acute individuals.
They even pulled soldiers from their ranks who specialized in scouting. And they looked at the brightest stars hoping
to detect a parallax. Unfortunately, no parallax could be detected and therefore the Greeks
just largely gave up on the idea of heliocentricism in favor of geocentricism. Another Greek thiner was Eratosthenes of Cyrene.
He actually made the first calculation of the Earth’s circumference. And his calculation
went something like this: There was a column in the city of Alexandria
in what is now modern-day Egypt. There was also a well at Seyene. And it turned out that
the distance between the two was something about 5000 stadia. Eratosthenes learned that
the incoming sunlight on the day of the Summer Solstice, the Sun would be directly overhead
Seyene. And tat means that from the bottom of the well, the Sun would be directly visible. At the same time, Eratosthenes learned there
was a shadow being cast at the column in Alexandria. So, with a little geometry, Eratosthenes reasoned
that ‘well, the shadow cast makes a 7 degree angle, and that means the sunlight is 7 degrees
tilted from the vertical at Alexandria’. And therefore the opposite angle must also be
7 degrees. So if we were to draw an imaginary line from
both these locations, to the center of the Earth, that means that the angle there should
be 7 degrees as well. Now 7 degrees is equal to 1/50th of a circle,
and since the distance between the two cities is 5000 stadia, then 50 × 5000 stadia gives
you 250,000 stadia. Now depending up on what the actual value
of a stadia was relative to today’s units, it turns out Eratosthenes may have come very
close to measuring the actual circumference. At worst, within about 20%. But he may have
done as well as 1%. So it’s a remarkably accurate result using just some simple geometry and
reasoning. This brings us to Hipparchus of Nicaea. His
work involved making a detailed catalog of stars and also measuring the first brightness
system, something we call the Apparent Magnitude. And it’s a system that we still use today,
albeit with some modifications. Hipparchus’ magnitude system worked something
like this:as we see the Sun set toward the late afternoon and early evening, the first
stars come out and he assigned these stars magnitude 1. They were, after all, the brightest
stars and therefore they would be first magnitude since they were the first stars seen after
sunset. A little while later, more stars would come out and so he assigned these magnitude
2 for the second brightest stars. As more stars emerged they would be designated 3rd
magnitude, 4th, 5th and so on until reaching about magnitude 6. Hipparchus not only catalogued
the stars by their brightness, but he was very careful to measure their positions in
the sky. And he did something else: he compared his measurements of the positions of stars
to the ancient Babylonians and Mesopotamians. And he discovered something rather remarkable.
Now to explain this I’d like to take a different perspective. Instead of viewing things from
the Earth, let’s go ahead and view things from an imaginary viewpoint south of the Earth’s
south pole. We’re looking a a very wide angle view of the sky; we have the north celestial
pole up to our top and we have the modern-day Ursa Minor and the bright star at the very
end of the handle would be Polaris, our present-day north star. Now in the lower left we see the
intersection of the celestial equator in red and the Sun’s path through the sky, the ecliptic
in green. And to make things a little more visible for us, I chose a date when the Sun
happened to be located at the Vernal Equinox. So it looks like it’s close to Pisces but
believe it or not, in Hipparchus’ era, the Vernal Equinox was actually considered to
be in Aires. Now Hipparchus made very careful measurements of the positions of these stars.
And when he compared his measurements to the measurements of the ancient Babylonians and
Mesopotamians, he determined that their positions were a little bit different. In fact, every
star in the sky was systematically shifted by a few degrees. And what Hipparchus was
able to do was intuit that it wasn’t that the sky was moving around but rather that
the Earth itself must be wobbling like a top. And this wobbling is called “precession”.
It turns out we now know today that the Earth has a 26,000 year precession cycle. The Earth’s
axis is pointing to different locations in the sky over time. This has some interesting
implications because if we could wind the clock backwards to say 3,000 BCE, you’ll notice
that the north celestial pole is nowhere near Polaris. It is instead, rather close to the
star Thuban in the constellation Draco the dragon. Likewise, the Vernal Equinox is also
located in the constellation Taurus. Fast forward 1,000 years, the north celestial pole
now precesses away from Thuban and the Vernal Equinox makes its way toward Aries. By 1,000
BCE, we’re getting farther from Draco in the north and farther from Taurus at the Vernal
Equinox; we are certainly in the constellation of Aries. And it is for this reason that to
this day the Vernal Equinox is still sometimes known as the “first point of Aries”. In other
words, it represents the location of the Vernal Equinox when Hipparchus was doing his work.
At around the turn of the millennium, the Vernal Equinox had moved firmly toward Pisces
and if we continue to just move forward in time, you’ll see that by 2000 or so the north
celestial pole was right almost exactly where Polaris is today. So if we continue to let
things move along, and let the Earth continue to wobble along its precession, you’ll see
that over 26,000 years we will no longer have a north pole star of Polaris. We’ll instead
have Vega in a few thousand years before eventually coming around back again toward Thuban. So
we’ll be returning to an orientation of the north celestial pole that was very similar
to the orientation the Earth when the ancient Egyptians built their pyramids. So at the
center of the pyramid are the King’s burial chambers. And there are two air vents that
are directed, one on the left facing to the south, and one on the right facing to the
north. And the position and the angle of the air vent was carefully chosen such that looking
through the air vent from inside the burial chamber would reveal the star Thuban. This
was the north star of the time the pyramids were built. This way the king could gaze upon
the circumpolar stars and watch them revolve around the north star Thuban for all eternity.
This wa a very sacred idea to the ancient Egyptians. So what would that look like? Well,
there’s Thuban, circled for us. This was the north star of its day and here we are at about
3,000 years before the common era. And we can see that the stars are circumpolar surrounding
Thuban, which was almost, at the time at the location of the north celestial pole. It turns
out that most of the works of the ancient Greeks, Babylonians, and Mesopotamians were
lost in the great fire of the Library of Alexandria. However, Claudius Ptolemy was careful to compile
much of that work and published his ideas in something called the Almagest (the Greatest).
In other words, he was paying tribute to the greats that had come before him. So, he was
able to popularize the idea of the geocentric model. Again, this was the prevailing idea
of the ancient Greeks, it seemed to make the most sense, despite a few dissenters, and
it was also Ptolemy who gave the first explanation for something called “retrograde motion.”
And this idea would dominate for over 1500 years, well into the next millennium. Let’s
talk about retrograde motion for a moment. Retrograde motion is simply the apparent shift
in the position of the planets. So given the planet’s normal tendency, it would seem to
eastward or prograde, but then once in a while it will appear to backtrack. This is the retrograde
motion before resuming its prograde motion once again. Now, for everything to rise in
the east and set in the west, it would be perfectly reasonable to conclude that the
Earth was at the center of the cosmos. But this retrograde motion was an anomaly, it
didn’t make sense. So in order to make the retrograde motion work, rather than having
Mars in this example and all the planets directly revolving around the Earth, Ptolemy introduced
a new concept called the Epicycle. the Epicycle was an invisible circle that carried Mars
and the Epicycle itself revolved around something called a Deferent. And it would be this Epicycle
moving about the Deferent that would create the apparent retrograde motion. So you can
imagine yourself looking at Mars and it appears to be going in prograde motion before executing
a slight zig-zag back and forth in the sky, giving us retrograde motion. Now this was
a good first order approximation, but the problem though is that the Epicycle that we
see here just would not be accurate enough to predict when the next retrograde motions
would be. To solve this problem, Ptolemy introduced a modification to his ideas. He introduced
a Equant, that is, the Earth is still very much at the center of the cosmos, but the
Epicycle, the Deferent, and so forth now were centered on an offset point called an Equant.
And this is what helped to make the retrograde motion of Mars and all the planets be a little
bit more on time, and do a slightly better job of predicting exactly when these retrogrades
would occur. Even then, sometimes additional modifications would be required, not the least
of which was adding an additional Epicycle to the Epicycle. And things got a little bit
complex over time, and this was a major problem because while the Epicycle model did an extremely
good job of predicting retrograde motions, for about 1500 years, it was, at the same
time, a little bit messy, and it allowed some people to begin to think maybe there were
alternatives, and maybe some of these ideas of the geocentric model should be revisited.

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