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.
