PLANETARY SYNODIC CYCLES
======================
John Pazmino
NYSkies Astronomy Inc
www.nyskies.org
nyskies@nyskies.org
2001 August 1
Introduction
----------
At the Observing Group meeting of 15 July 2000 Ken Brown and Susan
Andreoli asked about the interval between conjunctions of Jupiter and
Saturn. Chair Bruce Kamiat explained that the interval is based on the
orbital periods of the two planets such that conjunctions occur about
every twenty years.
Altho the question was in connexion with the invisible event on 31
May 2000, when the conjunction occurred right next to the Sun, the
behavior of the two planets takes on special meaning right now. For
they are in fall 2000 dancing together in the sky at nightfall in
downtown Taurus. They are featured targets at our starviewing
sessions, including the new series at the Hayden Planetarium
Synodic periods
-------------
We have Jupiter's period of 11.86y and Saturn's of 29.42y. Bruce
used rounded numbers, 12 and 30, to figure out the interval in his
head but the method is the same.
It's the textbook exercise of doing
(Jup-Sat per) = ((Jup per) * (Sat per)) / ((Jup per) - (Sat per))
= ((11.86y) * (29.42y)) / ((11.86y) - (29.42y))
= -19.87y
-> 19.87 years
If we take the subtraction in reverse order we merely get the
opposite signum. Only the absolute value matters in this situation, so
the signum is tossed. This is called the synodic period of the Jupiter
relative to Saturn, or of Saturn relative to Jupiter.
The interval in arc, the synodic arc, along the zodiac between
conjunctions comes directly from noting that Jupiter rounds the zodiac
once between conjunctions and thereafter it's the excess motion that
displaces the event among the stars. So
excess = (19.87y) - (11.86y)
= 8.01 year
arc = (8.01y) / (11.87y)
= 0.675 circle
-> 16h 12m
We could have banked off of Saturn, noting that Saturn doesn't
complete a whole round before the next conjunction occurs.
excess = (19.87y) - (29.72y)
= -9.55 year
arc = (-9.55y) / (29.42y)
= -0.325 circle
-> -7h 48m
The displacement is upstream from Saturn, which is exactly the
same as the downstream displacement from Jupiter. That is, you get to
the same point in the zodiac but approaching from opposite directions.
Babylonian planetary motion
-------------------------
However, after ragchewing a bit it turns out that this interval
was known long before we understood the solar system. In fact, the
Babylonian culture had no concept of a system of planets at all. The
planets were mere meandering points on the celestial sphere.
How could they have known this 19.87 year synodic period for
Jupiter-Saturn conjunctions?
History
-----
A touch of history. Astronomy in Babylonia started in about 2,500
BC as an effort to document the planets (which included the Moon and
Sun). The people were concerned with the occurrence of certain
alignments of the planets, like elongations and conjunctions. They
noted when by date and where by star background these happened.
This chronicling of the heavens was motivated by the divination of
the country's fate and fortune. Accompanying the observations were
interpretations, often pretty ludicrous, for the events.
After many many centuries they built up a database of
observations. Note well that this set was far from ideal and perfect.
The observers, altho trained under the ruler, made mistakes. They
mistook stars or misread calendars. The weather in Mesopotamia was
fickle. The horizon was shmutzed with haze and mists.
Modern reconstructions
--------------------
In the bad old days the calculations of planet positions to
correspond with the description in an ancient tablet was a hideous
chore. Today it is a trivial matter by any of the better planetarium
computer programs.
For example, from a book on Babylonian astronomy I see a [modern
typeset version of] a tablet noting that Venus was just west of Mars
in Aries, the Moon was in Scorpius, and Antares was within a halo
around the Moon. This supposedly happened on the 19th day of the 12th
month of -651. The year is 'astronomical', counting a year 0; it is
numericly one LESS than the 'BC' year.
On what day, on the modern calendar, did this occur -- if at all! -
- so we can date the inscription and other events of the people
associated with it. From a planetarium (any is valid so long as it
employs a correct longterm algorithm for the planets) I find that such
an event actually did occur on -650 February 28 in Babylon.
What looks like a wrong year, -650, is really a rollover from -651
within the one year. In Babylonia the year began in what we now call
March. The last, 12th, month was February. Think of 'September',
'October' and so on, yet an other legacy handed down to us from those
people.
Confidence in celestial events
----------------------------
This innocent diary entry brings out a very profound feature of
Earthly civilization. A peach-fuzzed boy from Norway can in a couple
minutes determine with perfect certainty the truth of the planet
positions. But no boy, no man, no army of men, no world of armies can
ever reconstruct the weather over Babylon 26 centuries ago and see if
a lunar halo did shine.
Storms, drought, insect invasion, animal migration, crop blight --
all events vital and crucial for the wellbeing of early humankind --
dismally failed of certain and dependible foretelling.
Only the stars and the planets obeyed definite rules. And so
astronomy rose above the other attempts of doping out the ways and
wiles of nature to become humankind's first true science. It and it
alone worked.
Jupiter-Saturn conjunctions
-------------------------
I do not have at hand ample historical accounts for conjunctions
between Jupiter and Saturn. I fudged a set of records by hopping among
Dance of the Planets, Earth Centered Universe, and SkyGlobe. I come up
with the list here for the span of 700 BC to 300 BC.
Universal Time Sepn 2000 RA Universal Time Sepn 2000 RA
----------------- ---- ------- | ----------------- ---- -------
01 Aug -741 *:* ~220 02h 23m | 16 Dec -522 20:04 65 14h 04m
22 Feb -740 00:13 73 02h 29m | 14 Mar -521 11:40 65 13h 58m
| 10 Jul -521 14:24 71 13h 46m
24 Jan -720 18:49 41 19h 28m |
10 Aug -720 *:* ~160 19h 27m | 25 May -502 22:40 64 05h 18m
|
21 Dec -701 *:* ~230 12h 12m | 06 Mar -482 01:11 7 21h 26m
30 Jul -700 15:18 49 12h 20m | 07 Sep -482 *:* ~90 21h 18m
|
31 May -681 00:44 70 03h 22m | 09 Oct -462 16:04 70 14h 23m
12 Dec -681 *:* ~160 03h 20m |
| 23 Sep -443 *:* ~110 05h 55m
25 Nov -661 08:57 36 19h 47m | 04 Apr -442 12:56 61 05h 49m
|
01 Nov -641 01:23 55 13h 04m | 28 Dec -423 10:59 2 21h 42m
03 May -640 *:* ~60 12h 52m |
| 09 Feb -402 *:* ~70 14h 58m
11 Apr -621 09:06 72 03h 53m | 09 Aug -402 16:37 77 14h 41m
|
16 Feb -601 10:38 24 20h 30m | 06 Jul -383 03:13 49 06h 42m
24 Aug -601 *:* ~110 20h 23m | 04 Feb -382 *:* ~210 06h 52m
|
10 Sep -581 05:00 63 13h 25m | 19 Mar -363 15:17 12 22h 19m
| 21 Sep -363 *:* ~100 22h 12m
27 Jul -562 00:07 68 04h 47m |
01 Nov -562 05:39 75 04h 37m | 30 Oct -343 21:49 73 15h 18m
10 Feb -561 04:14 76 04h 25m |
| 16 May -323 19:01 42 07h 10m
13 Dec -542 22:04 17 20h 46m |
| 10 Jan -303 14:02 20 22h 34m
The date and hour are in UT, separation is in arcminutes, location
is the right ascension of Jupiter. The actual hour is not critical in
as much as the timescale of planet motion is a full day.
I chose this span because it begins near the ascension of king
Nabonassar, starting a regime of political and social stability in
Babylonia. Under him the skywatching mission was systematized and
records were more carefully made and kept.
Some works on Babylonian history relate that in Nabonassar's first
year of rule there was a Moon-multiplanet convention that officiated
the power. Modern planetarium programs do not show anything out of the
ordinary during this timeframe, so the story may be an allegorical
appeal to celestial validation
Babylonia went thru many disasters and conquests since Nabonassar,
yet the skywatching mission was kept up by his successors, even by
those from the foreign powers.
Babylonian planetary theory
-------------------------
In the latter part of this span pure skywatching shifted to
analysis of the records and the invention of mathematical methods to
foretell in advance the various phaenomena. Among the artifacts from
the 400s BC forward we find tablets of calculations, instructions, and
ephemerides. Tony Hoffman's 'What's Up' column in NYSkies is a direct
descendant from these.
In yet an other sobering feature of human existence on Earth, the
Babyloniam calculations for the planet positions is humankind's first
use of mathematics to successfully describe events in nature. It would
be fully 19 centuries later, in the early 1600s, before maths were
applied to formulate the first true laws of physics; this was
performed by Galileo.
After about 300 BC, Babylonian culture was subsumed under Greek
culture. It is thru the tradition of Greece from this time that we owe
so very much a debt to Mesopotamian astronomy.
Conjunctions and close appulses
-----------------------------
In my gathering of conjunctions, I found an account of a grand
spectacle in the predawn sky of November -701, or 702 BC. Jupiter,
Mars, and Saturn assembled on the Leo-Virgo frontier! Such a sight
would have been an omen of some great importance.
When I searched for this conjunction I found the meeting of Mars
with Jupiter and with Saturn. Nothing turned up for Jupiter meeting
with Saturn! A closer inspection of this event showed that Jupiter and
Saturn did approach closely but never passed each other.
Today we define 'conjunction' as the achievement of equal ecliptic
longitude (sometimes equal right ascension). This is what programs
search for when asked to list conjunctions. What happened in 702 BC
was that Jupiter creeped up from the west near to Saturn, rounded its
station point, and backed away on its retrograde loop!
The closest approach came on 21 December 702 BC with no true
conjunction. Right off of the bat I had a mess on my hands. I had to
find all the other close appulses of Jupiter and Saturn because these
were noted in the tablets even tho they were not what we would call a
conjunction. Thus, the entries with no time, '*.*', are these
appulses, with the separation being approximate.
Cyclical pattern of conjunctions
------------------------------
OK, from this database of 'observations' of Jupiter against Saturn
how could the Babylonian astronomer suss out a pattern in the absence
of any notion of a planetary system? It actually ends up being very
simple. First, a few statistics.
The interval between the first conjunction in -740 (taking only
true conjunctions) and the last is quite 436.88 years. The number of
conjunctions, counting a group of passes as one event, since -740 is
22. The number of circuits of the zodiac made by these conjunctions is
7.16 and these laps were made in reverse order of the zodiac.
This third stat is a bit important, so listen up. The first
conjunction occurs near 2-1/2h RA. The next, near 19-1/2h; the third,
near 12h; the fourth, near 3-1/2h. That's one lap backwards in the
zodiac. Stepping thru the list we come up with 7+.
Then we have
(synodic period) = (total years)/(count of conj)
= (436.88y) / (22)
= 19.86 year
(synodic arc) = (count of circ)/(count of conj)
= (-7.16) / (22)
= -0.325 circle
-> -7h 49m
The minus sign means the arc is stepped westward, backward, upstream
along the zodiac.
No orbital concepts
-----------------
Note very well that there is nothing of a theory of orbit around
the Sun, Earth, Alcyone nor any use of cycles or revolutions. In fact,
to the Babyklonian astronomer the overall behavior of Jupiter and
Saturn, not pertaining to their mutual meetings, is not defined. It
was the Greeks who first conceived of a continuous motion for the
planets and devised models for simulating it.
Hence, Jupiter-Saturn conjunctions occur every 19.86 years with
each being 7h 49m westward in the zodiac. And this is essentially what
we get by the modern method involving orbital motion.