Sky & Telescope - November 2023 - 25

ward, though packing the necessary gears into the available
space required great ingenuity.
The front plate showed the positions of the Sun, Moon,
Sun
Day 29.53
Sun
and planets in the zodiac. Displaying this information correctly
presented an entirely different problem because each of
those bodies moves at variable speeds. Let's take a look at the
mathematics that astronomers used to explain that fact in 60
BC before seeing how it was implemented in bronze.
Eccentric Circles
Astronomy flowered as never before during the Hellenistic
period that followed the death of Alexander the Great in
323 BC. Greek astronomers had always been accomplished
at abstract reasoning and geometry. For instance, they were
the first to realize that eclipses are caused when the Moon
passes into Earth's shadow and vice versa. But they tended to
have a casual attitude toward data before Alexander's conquests
brought them into direct contact with Mesopotamian
civilization, the world's oldest. Babylonian astronomers - as
they're usually called, even though most of them worked
outside the city of Babylon - started recording a series of
continuous, consistent astronomical observations around 650
BC, resulting in a wealth of empirical data. They were also
brilliant at detecting mathematical patterns within the data,
including the Metonic and saros cycles, though they apparently
never sought to examine the underlying causes.
Hipparchus (c. 190-120 BC) is widely credited with
combining Babylonian data analysis with the Greek flair for
theory to create geometric models that could accurately forecast
the motions of the Sun and Moon for many centuries
into the future. His models worked beautifully despite being
based on several false assumptions.
With the striking exception of Aristarchus of Samos (c.
310-230 BC), Hellenistic astronomers erred by assuming that
Earth was stationary instead of in orbit around the Sun. That
assumption creates major problems for predicting the motions
of the planets, but as far as the Earth-Moon-Sun system is
concerned, it makes no difference at all whether the Sun
orbits Earth, or vice versa, as shown in the diagram at right.
Nonetheless, Hipparchus had a number of embarrassing
anomalies to explain. Observations proved that both the Sun
and Moon move through the " fixed " stars at slightly variable
rates. This clashed with the deeply rooted Greek conviction
that all celestial objects travel in circles at uniform speeds.
His solution was simply to place Earth a little off-center. That
way, the Sun and Moon appear to move faster when they're
closer to Earth. And he was partly right. Half the variation
in the Sun's and the Moon's angular motions are due to this
perspective effect, while the other half is due to the fact that
celestial objects actually do move fastest at the closest points
of their orbits, as Johannes Kepler and Isaac Newton proved
almost two millennia later. But Hipparchus compensated by
assuming twice the actual eccentricity, yielding results essentially
identical to Kepler's.
Today we know that orbits are elliptical rather than circuDay
27.32
Moon
Day 29.53
Sun
Earth
Moon
Day 0, Day 27.32
Geocentric View
Day 0
Day 0
Sun
Day 27.32
Day 29.53
Heliocentric View
Not to scale
ROTATIONAL RELATIVITY The diagram on top shows why the 29.53day
synodic month is longer than the 27.32-day sidereal month based on
the ancient Greek assumption that Earth lies stationary at the center of
the universe. After 27.32 days the Moon makes one full orbit and returns
to the same position, but in that same time the Sun has advanced about
1
/12
of the way on its orbit around Earth. It takes the Moon an additional
2.21 days to catch up. It's conventional today to depict the same scenario
based on the assumption that the Sun is stationary, as shown below.
As the ancient Greeks were well aware, the two models yield identical
predictions. The geocentric model is more convenient for describing the
Earth-Moon-Sun system, but the heliocentric model is vastly superior for
describing the motions of the planets, a fact that eluded the Greeks.
lar, but the difference between ellipses and off-center circles
is barely perceptible. Mercury's orbit has an eccentricity of
0.206 - the biggest of any planet. That means the Sun is displaced
a whopping 20.6% from the geometric center of Mercury's
orbit. Yet it's out-of-round by a barely perceptible 2.1%.
The orbits of the Moon and Earth are flattened just 0.15% and
0.01%, respectively. So, using eccentric circles yields almost
exactly the same answers that using ellipses would have.
The gears driving the Sun pointer on the Mechanism's
front dial are lost, so we can't be sure that it moved at a nonuniform
rate. But enough of the Moon gearing survives to
sk yand tele scope .o r g * NOVEMBER 2023 25
BEATRIZ INGLESSIS / S&T
http://skyandtelescope.com
Sky & Telescope - November 2023

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