Sky & Telescope - November 2023 - 27

CIRCLES VERSUS ELLIPSES We now know
that solar system orbits are ellipses rather than
circles, with the attractor (the Sun in this case) occupying
one of the foci. The critical factor is that
the attractor is off-center, which is also true of the
ancient Greeks' eccentric circular orbits (shown in
orange). The ellipse's flattening is barely perceptible
for Mercury. The two models yield essentially
identical results within the error of ancient
measurement.
Mercury
Center
Sun
Empty
focus
With their penchant for patterns,
Babylonian astronomers soon realized
that planetary phenomena repeat in cycles
(S&T: Aug. 2021, p. 24). For instance, they
concluded early on that Venus makes roughly five morning
appearances and five evening appearances every 8 years, yielding
a period of 1.6 years (8/5). But with the benefit of several
centuries of consistent observations, Babylonian astronomers
discovered that the 1.6-year Venus cycle falls short by 19 days
over the span of a century. They eventually settled on 720
cycles every 1,151 years, for an average of 1.59861 years apiece
- a very close match to the modern value of 1.59865 years.
In 2016, ancient-science expert Alexander Jones was able
to decipher the number 462 in the section of the Front Cover
devoted to Venus. He realized that it represented an approximation
previously unknown in ancient literature: 289 Venus
cycles every 462 years, for 1.59862 years per cycle. It seems
likely that the ancient Greeks worked this out independently.
Likewise, Jones found the number 442 in the Saturn section,
yielding the previously unknown approximation 427
Saturn apparitions every 442 years, or 1.03512 years per cycle,
which compares well to the modern value of 1.03514 years.
Unfortunately, the predictions can't have been all that
good, because they must have been based on the assumption
that a planet's retrograde loop is always of the same duration.
In fact, Mars's retrograde loops vary in length from about 60
to 80 days. Implementing uniform retrograde loops would
be relatively easy with a pin-and-slot mechanism, but there
was neither a theoretical basis nor a practical way to implement
the variations that we now know to be caused by the
fact that both Earth and the planet in question have elliptical,
variable-speed orbits. It would take another two centuries
before Claudius Ptolemy developed models that could predict
planetary motions more accurately.
The authors of the 2021 Scientific Reports paper offer a
very clever explanation of how the mathematicians behind
the Mechanism might have derived the periods for Venus and
Saturn. The authors then extend those same methods to the
other planets and present gear designs that could have implemented
them, together with uniform-length retrograde cycles.
How and Why
The Antikythera Mechanism is so sophisticated that even to
modern eyes it seems almost miraculous. Yet other, comparable
devices must have existed - nobody then (or now) could
build such a complex machine on their first try. Moreover, the
Eccentricity = 20.6%
Flattening = 2.1%
great Roman orator and essayist Cicero
(106-43 BC) described similar devices,
one of which was built by his friend and
teacher Posidonius and the other (or possibly
two more) by the legendary genius
Archimedes (c. 287-212 BC).
It may seem incredible to us today that
ancient craftsmen could hand-file gears
that had so many tiny teeth, but they had
plenty of practice with jewelry, which
requires similar levels of precision. Jones
cites as other examples various medical
and musical instruments, including the
ancestor of the modern church organ, the water-powered
hydraulis. The Mechanism's design required deep knowledge
in many fields, but there were plenty of brilliant generalists
in ancient Greece.
Many people have speculated about why the Mechanism
was built. Two plausible explanations are that it was a rich
man's plaything and that it was a device to help teach astronomy
to non-experts. Those are not mutually exclusive. This
was, after all, an era in which the rich and powerful were also
expected to be knowledgeable about a wide range of subjects.
The reconstruction by Freeth and others is compatible with
the educational theme. For instance, they suggest that the
front dial might have had a double-headed draconic pointer
showing the position of the lines of nodes - the intersection of
Earth and Moon's orbital planes. If the saros dial on the back
plate showed that an eclipse was imminent, you could then
flip the device around and see the reason at a glance: Eclipses
happen only when both the Sun and Moon pointers are very
close to the draconic pointer.
The line of nodes rotates through the ecliptic once every
18.60 years at a nice, steady rate, so a draconic pointer would
have been easy to implement. There's no evidence for it, but
that's hardly surprising given that most of the instructions
are illegible and the entire front half of the gearwork is missing.
It would be amazing if a major new fragment was found
and it confirmed the 2021 reconstruction.
Regardless, the Antikythera Mechanism is tangible proof
of the prowess of Hellenistic science, technology, engineering,
and mathematics. After the 1687 publication of Isaac Newton's
Philosophiæ Naturalis Principia Mathematica, which used
mathematical techniques far more powerful than anything
seen before, the phrase " clockwork universe " became a popular
way to describe a cosmos that could be predicted indefinitely
into the future. But it was Hellenistic astronomers who
started science down that path by producing the first rigorous
mathematical models of the universe at large. The fact that
the ancient Greeks had the vision to embark on that journey
and the genius to go as far as they did is far more important
than the fact that they made a few mistakes along the way.
¢ Contributing Editor TONY FLANDERS has been fascinated by
gadgets and ancient Greece for as long as he can remember.
sk yand tele scope .o r g * NOVEMBER 2023 27
BEATRIZ INGLESSIS / S&T
http://skyandtelescope.com
Sky & Telescope - November 2023

Table of Contents for the Digital Edition of Sky & Telescope - November 2023
