Sky & Telescope - January 2024 - 61

THE TRUSTEES OF THE BRITISH MUSEUM
eclipses. Accurate forecasts gave order to their cosmos and
allowed time for priests to prepare the appropriate rituals
to counter eclipse omens, or even to install a substitute
king until the perceived danger passed. Babylonian
eclipse predictions were surprisingly accurate, though
the required mathematical competence was an evolving
effort. By the last three centuries BC, however, Babylonian
astronomers had created sophisticated mathematical
algorithms for predicting portentous appearances of the
Moon and planets.
From Saros to Exeligmos
Most eclipse chasers have heard of the saros. Discovered
early in the flowering of Babylonian computational
astronomy, it's an eclipse recurrence cycle of about 18
years, or 6,5851
/3 days. That extra fraction of a day means
that Earth's surface shifts about 120° westward from its
position during the previous solar eclipse in the series. For
example, the moment of greatest eclipse along the track
of the March 29, 2006, eclipse was in Africa at a longitude
of 16.7° east. That eclipse path parallels the track
for the April 8, 2024, event, which has greatest eclipse at
a longitude of 104.1° west, over Mexico. The extra third
of a day shifts the consecutive eclipses in saros cycle 139
by a longitude of 120.8° (16.7° + 104.1°), all the way
west from Africa to Mexico. That 120° longitudinal shift
means the fourth eclipse in the sequence will return to
the longitude of the first.
We can illustrate the remarkable regularity of the saros
cycle by looking at a subset of six lunar eclipses in lunar
saros series 45 dating from 595 BC to 504 BC, around
when scholars believe the Babylonians discovered the
saros. The Moon's proximity to the center of the Earth's
shadow in each 18-year event is shown by the value of
gamma (γ) in the table presented below: The closer gamma
is to zero, the closer the Moon is to the center of Earth's
shadow. The final column shows the separation (in days)
from the previous eclipse.
Saros 45 Eclipse Sample
Eclipse Date
November 27, 595 BC
December 8, 577 BC
December 19, 559 BC
December 29, 541 BC
January 10, 522 BC
January 20, 504 BC
Gamma (γ)
.0011
.0020
.0037
.0093
.0175
.0327
WRITTEN IN STONE This tablet stored in the British Museum in
London dates from about 500 BC. Babylonian scholar-priests recorded
celestial events meticulously for many centuries. The vertical divisions
in the tablet correspond to an eclipse recurrence cycle of 18 years.
The deviation from an integer number of 6,585 days only
slightly exceeds one-third of a day. You can imagine the
comforting sense of order the discovery of the saros must
have conveyed to the ancient Babylonians in an otherwise
chaotic world controlled by arbitrary gods and demons.
Yet, despite the regularity of this cycle, the nagging
third-of-a-day excess hinted at a deeper truth. The extra
fraction practically begged to be tripled. Astute reckoners,
the Babylonians realized that three saroi would form
an integer number of days: 19,756, which is 54 years and
about 32 days. This must have appeared as a divine coincidence
to them and reinforced the idea of a great cosmic
wheel that brings events back to where they started. This
three-saroi period came to be called exeligmos, which
means " turning of the wheel. " It was known throughout
the Greco-Roman world; evidence of the exeligmos
was even found on the Antikythera mechanism discovered
in the sunken wreck of a Hellenistic cargo ship
(S&T: Nov. 2023, p. 22).
A modern example of exeligmos in action from saros
Days between
successive saroi
-
6585.370
6585.369
6585.367
6585.364
6585.359
cycle 145 will be familiar to older readers. On July 20,
1963, the Moon's shadow raced from Japan to Alaska,
across northern Canada, then through Maine and out
to sea. Its path was strikingly parallel to the track of the
so-called Great American Eclipse of August 21, 2017. It
streaked across the Pacific, through Oregon and America's
heartland, shifted slightly south from its 1963 predecessor.
The next exeligmos eclipse in the series occurs on
September 23, 2071. The path for that one is again shifted
south and crosses northern Mexico and passes through
several countries as it clips the top of South America.
sk yand tele scope .o r g * JANUARY 2024 61
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