Sky & Telescope - November 2023 - 26

Astronomy History
reconstruct its workings with confidence,
and it did indeed use an eccentric
circle to mimic the lunar anomaly. This
was accomplished with two gears with
parallel faces connected by a pin on the
driver running through a slot in the
driven gear. The axles of the two gears
were offset by about 1.1 mm, and the
pin was about 9.6 mm from its axis,
yielding an eccentricity of 1.1/9.6, which
is about 0.115 - almost exactly the right
amount to explain the lunar anomaly.
The pin in this system rotates in a
Moon's
orbit
Moon
¼ month
after apogee
Line of sight
Perigee
Earth
Apogee
Line of apsides
ECCENTRIC CIRCLES Ancient Greek astronomers
often explained the varying speeds
of celestial objects through the zodiac as the
result of eccentric (off-center) circular orbits.
A quarter sidereal month after the Moon is at
apogee (farthest from Earth), it has traveled
precisely one-fourth of the way around its circular
orbit, but an observer on Earth sees it as
having traveled less than 90° against the distant
stars due to perspective effects. (The Moon's
eccentricity is greatly exaggerated for clarity.)
Any resulting error was due more to play
in the gears than to faulty design.
circle at uniform speed around the driver's axle, just as the
Moon in Hipparchus's model rotates uniformly around its
orbit's center. The off-center axle of the driven gear corresponds
to Earth, and its groove corresponds to an earthly
observer's line of sight. Both gears turn at the same rate on
average, but the driven gear rotates fastest when the pin is
closest to its axle and slowest when the pin is farthest.
In addition, the entire ellipse rotates around Earth so that
the line of apsides, which connects perigee and apogee (the
points of closest and farthest approach, respectively) makes
one full circuit every 8.85 years. During the time required for
the Moon to reach two successive perigees (the anomalistic
month), perigee itself has advanced a little with respect to the
distant stars. That's why the anomalistic month is slightly
longer than the Moon's orbital period.
It's difficult to measure the precession of the apsides accurately,
and the Mechanism's designers assumed a value of 8.88
years. To implement this so-called precession of the apsides,
they mounted the pin-and-slot gears for the lunar anomaly on
a much bigger gear that rotated at that rate, ensuring that the
Moon pointer operated according to the very latest theories.
SOLAR SYSTEM IN A BOX
This is roughly what the Antikythera
Mechanism originally
looked like, complete with the
hypothetical front dial from the
2021 reconstruction. In addition
to protecting the dials, the front
and back covers contained
operating instructions.
The Problem with Planets
Lunar and solar anomalies are subtle. You could spend your
whole life observing the Moon without noticing that its speed
against the background stars varies by plus or minus 10%.
The planets are another matter entirely. They actually briefly
stop in their tracks and then move backward for a few weeks
or months in a phenomenon called retrograde motion.
Babylonian astronomers were particularly fascinated by the
planets because they were always examining celestial phenomena
for abnormal behavior that could be interpreted as portents.
Eclipses are the most obvious example and were often
thought to portend the downfall of rulers. Planetary appearances,
disappearances, and " stations " (standing still with
respect to the stars) are less dramatic but also much more
frequent, providing ample material for astrological forecasts.
The development around 400 BC of personal horoscopes
upped the ante. Previously, astrology had applied only to
countries and kings - great clients if you can find them, but
in short supply. The idea that the stars actually ruled everybody's
life greatly expanded the potential customer base,
setting off the quest for greater accuracy.
Star events
Month
names
characteristics
Eclipse
Planet cycles
Calendar
structure
Moon-Sun
cycles
Star events
Eclipse
glyphs
Front cover
26 NOVEMBER 2023 * SKY & TELESCOPE
Back cover
Cosmos
description
ECCENTRIC MOON ORBIT: BEATRIZ
INGLESSIS / S&T; MULTI-SIDED VIEW OF
MECHANISM: © 2021 TONY FREETH
Sky & Telescope - November 2023

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