Sky & Telescope - August 2021 - 26

Computational Astronomy
third of a slice left over. However, it's
worth noting that these arc sizes are
mean values. Because the planets' orbits
are ellipses, not circles, the actual values
will differ, sometimes substantially.
Yet in the long run, by defi nition, the
mean works pretty well.
The Babylonians were keenly interested
in knowing how many complete
sets of synodic arcs (those full slices
plus the leftover bit) would be required
for Mars to return to exactly the same
place in the sky. There were good reasons
for this preoccupation.
In Mesopotamian cosmology, the
will of the gods determined planetary
appearances in the sky. The positions
of the planets among the stars served as omens of good
or bad earthly events, varying according to the ominous
infl uences inherent in each planet. Venus and Jupiter were
benefi cent; Mars and Saturn were malefi c; Mercury was
ambivalent. It was vital to know when a planet would return
to the same place in the sky to correlate this occurrence with
important events, such as a fl ood, a failed harvest, an important
birth or death, or war.
For an astonishing six centuries, Babylonian astronomers
meticulously inscribed their observations in cuneiform
characters on tablets. These so-called Astronomical Diaries
accounted for planetary synodic phenomena along with the
mundane fl uctuations of daily life of Mesopotamia, such as
commodity prices, the weather, or the ever-changing level of
the Euphrates River.
The Goal-Year Periods
Babylonian astronomers had succeeded in discovering the
synodic returns of the planets with impressive accuracy. Modern
scholars call these planetary returns Goal-Year periods.
COMING AND GOING The 2018 Mars apparition is displayed with
this superb image sequence from March 2018 through January 2019.
Over that span the Martian disk grew from a diameter of 6.7″ to a maximum
of 24.3″ during its late-July close approach.
WRITTEN IN STONE Shown here is a
cuneiform procedure text for the planet
Jupiter. Procedure texts are the rulebooks that
describe how to calculate ephemerides with
astronomical information recorded on other
tablets. Analysis of Jupiter's well-represented
procedure texts gave scholars confi dence
that their interpretations of the Mars texts
were correct.
For the outer planets, the Goal-Year
periods are those exceedingly rare
oppositions when a planet returns to
(very nearly) the same place in the sky
as it was at a prior opposition. For the
exacting Babylonians, there were only
two oppositions of Mars in a century
that fi t the bill, occurring at intervals
of 47 years (after 22 synodic cycles)
and 79 years (37 synodic cycles). The 79-year period, for
example, means that Mars will reach opposition in 2099 very
close to where it was during its October 2020 opposition. Just
how close is the question.
Babylonian stargazers tracked the planets in their courses
by noting when they passed certain stellar waypoints along
the zodiac known as normal stars. They incised ephemerides
on spreadsheet-like clay tablets known as the Astronomical
Cuneiform Texts (ACT). Some of the centuries-long synodic
recurrences found in the ACT turned out to be even more
accurate than the shorter Goal-Year periods - Babylonian
astronomers, for example, discovered that Mars completes
133 synodic cycles in 284 years. How did they accomplish this
impressive computational feat?
Modeling Martian Recurrence Periods
To fi nd out, I experimented with a simple computer model I
created to see if the Babylonian Goal-Year periods for Mars
were at least plausibly correct from a purely mathematical
perspective. I took Mars as my case study because of its recent
opposition, its prognostic signifi cance to the Babylonians, and
my own enduring fascination with the planet.
Using a home computer and simple mathematical software,
I simulated Mars's synodic cycles over 100- and
500-year periods. The program searched for oppositions
26 AUGUST 2021 * SKY & TELESCOPE
CUNEIFORM TABLET: THE TRUSTEES OF THE
BRITISH MUSEUM; MARS IMAGE SEQUENCE:
DAMIAN PEACH / CHILESCOPE
Sky & Telescope - August 2021

Table of Contents for the Digital Edition of Sky & Telescope - August 2021
