Sky & Telescope - August 2021 - 29

2099
2020
1941
1862
Earth
2003
0.1 a.u.
80 YEARS OF MARS Left: This diagram illustrates the orbital path of Mars from a geocentric frame of reference and was plotted using 80 years of
data (1940-2020) drawn from the NASA/JPL Horizons online database. Earth is the blue dot at center. The upper orange dot is Mars at its 2020 opposition,
and the lower orange dot shows Mars at its historically close 2003 opposition. Right: This zoomed-in view plots Mars's positions at the 79-year
(37-synodic cycle) oppositions in 1862, 1941, 2020, and 2099. Included for reference is Mars at its remarkably close 2003 opposition. The direction of
the vernal equinox is indicated by the dashed line. (The planet disks are not plotted to scale.)
their perpetuation: " These motions, continued farther,
would become unintelligibly intricate, for the continuation is
boundless, never returning to its previous path. "
To see what application of a Goal-Year period specifi cally
means today, I again took as an example the 37-cycle/79-year
period, anchored on the October 13, 2020, opposition of Mars.
Here are the 79-year oppositions before and after that date:
79-Year Mars Oppositions
Year
Date
1862
1941
2020
2099
October 5
October 10
October 13
October 18
ment with each other because, as we saw, the Babylonian cycle
itself is not perfect and because predicted positions are based
on mean motions. My accompanying computer-generated
simulation of Mars at each of the ecliptic longitudes highlights
their closeness. Now your grandkids will know where to look
when the October 2099 opposition comes around!
It's incredible to think that with nothing other than keen
Constellation
Cetus
Pisces
Pisces
Pisces
Ecliptic long.
14.31°
17.49°
20.69°
23.76°
As you can see, all are October oppositions in Pisces
(except for the 1862 opposition, which occurred in Cetus
near the border with Pisces) and are separated by about 3°
of ecliptic longitude at each successive opposition. That's a
remarkably close grouping and attests to the accuracy of the
79-year period. The 79-year positions differ from perfect aligneyesight,
diligence, and exceptional ingenuity, Babylonian
astronomers were able to achieve such accurate predictions.
With modern mathematical tools we can, in effect, get into
their minds and test their thinking. Whether for the purpose
of gaining a better understanding of ancient astronomy,
simulating plausible scenarios, testing scholarly hypotheses,
or creating marvelous teaching tools, nothing beats the power
of simple mathematics to explore and enrich the stories of
astronomy's long history.
 DOUGLAS MACDOUGAL writes about the history of astronomy
and mathematics from his home in Portland, Oregon, and
is the author of Newton's Gravity: An Introductory Guide to the
Mechanics of the Universe (Springer, 2012). He fondly remembers
decades ago coaxing his fi rst comet-orbit calculation into
a reluctant and overwhelmed Apple IIe computer. You can visit
his website and blog at www.douglasmacdougal.com.
sk yandtelescope.org * AUGUST 2021 29
ORBITAL DIAGRAMS: DOUGLAS MACDOUGAL

http://www.douglasmacdougal.com http://www.skyandtelescope.org

Sky & Telescope - August 2021

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