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ANY MODERN ASTRONOMY program will work for this lesson.
I recommend using the freeware Astrolog 5.41G with the
freeware JPL-DE406 Swiss Ephemeris, Carte du Ciel 2.75
which is also freeware, and includes links to download
dozens of freeware catalogues and other plugin options,
or check out the SkyMap 9 demo version on my links URL:
This is very basic, and will show you how every planet
visible to the naked eye, which includes the Sun, Moon,
Mercury, Venus, Earth, Mars, Jupiter, Saturn, & Uranus,
this will show you how these planets move as seen from
the Earth in conspicuously repetitious and predictable
patterns which are easily counted by days, months, and
years between repeating sidereal and synodic multiples.
This absolutely destroys any and all arguments against
the ancients being perfectly able to see the motion of
the planets against the night sky and counting by days,
months and years to predict sidereal & synodic periods
for each planet at least out to Saturn and possibly to
Uranus, since it rarely can be seen with the naked eye.
This is a big deal because secular academia has closed
their eyes to timeless science and its reproducibility.
This clearly transcends simple astronomy, but includes
astrology, metaphysics, and all spiritual implications.
Limit your program to what is visible to the naked eye.
No guesswork & no speculation. Your astronomy software
reliably emulates what we'd see when viewing the night
sky in that direction, at that time from that location,
conveniently, efficiently and with impressive accuracy.
Of course, the view is better through a good telescope,
or through the unaided, human eye, since it is assumed
that ancients didn't have other means to see the stars.
That's a humongous ad hoc assumption, but I'm granting
modern-day atheistic science that much and I still win.
Accurate positions of planets and stars is all we need
for this lesson. Your favorite software will work fine.
No telescope needed. We can see this all with our eyes,
so reduce your software's star magnitude limit to five,
and assume Uranus, Neptune and Pluto to be nonexistent
(not as Gods, but to pacify the unbelieving scientist).
For this lesson, we're concerned only with heliacal ri-
sings of each planet separately, which depends only on
sufficient angle between the planet and the Sun, so it
can be spotted against background stars before sunrise.
The Sun must be about 18 degrees below the horizon for
full darkness and a little less for heliacal phenomena.
This angle varies with each planet, and each star, and
time of year, temperature, pressure, how good your eye-
sight is, the geographical latitude of observation and
local horizon, obstructions and circumstances of light
pollution, smog, haze from forest fires, volcanos, etc.
While these conditions can vary to extremes, generally,
provided reasonably good seeing conditions towards the
eastern horizon about an hour or so before sunrise, as
you look to the east (from moderate latitudes) you can
barely make out a planet that you expect to see rising
heliacally on or about that date. If you miss it, then
try again in a couple of days and you're bound to spot
the planet you're looking for if it's Mars, Jupiter or
Saturn; or plan ahead and begin looking sooner if it's
Mercury whose orbit you can see is eccentric. You know
that each planet has predictable orbital patterns, and
although these patterns vary over the short-term, over
the long-term they become more and more predictable to
fractions of a degree in sidereal longitude & latitude.
That's how you know that Venus is the most predictable,
since Venus has the least eccentric orbit. We see this
behavior of Venus through heliacal risings or settings,
especially at maximum elongations inferior or superior.
If getting up at four in the morning is not your style,
simply open your astronomy program and set it for your
geographical location and voilla! You're ready to view
to heliacal risings of every planet--against the stars.
In the next part we focus on Saturn's heliacal risings.
Open your favorite astronomy program. As always, I use
Astrolog, so all examples given refer to JPL ephemeris
DE-406 with Abramov's expanded version of fixstars.ast
provided by S. Moshier using the Astronomical Almanach.
All data is accurate to within several milliarcseconds,
which is vastly better accuracy than the plus or minus
half a degree or thirty arcminutes we can achieve with
an extended pinky finger at arm's length measuring one
arcdegree...twice the apparent diameter of a full Moon.
Three closed middle fingers spans five degrees, or the
whole hand equals about ten degrees. You can calibrate
simple hand measurements by memorizing bright "marking"
stars near the ecliptic by their approximate longitude
on the caelestial zodiac. The constellations and their
associated myths help us to easily locate and identify
stars as we become familiar with their appearances and
their order in the sky. This is where Carte du Ciel or
SkyMap comes in handy, since they depict the stars and
planets graphically, and include millions more objects
and dozens of unabridged catalogues for the astronomer.
However, only Astrolog can chart the marking stars and
planets by their zodiacal, constellational coordinates
as used by ancient stargazers for tracking the planets.
The complete list of almost 1000 stars is posted on my
website, but here's an abbreviated list for convenient
reference with the values rounded off to whole degrees
and favoring brighter stars in the northern hemisphere.
Remember the goal is not to memorize every star but is
to estimate a planet's position at its heliacal rising,
setting, opposition and other repeating synodic phases
against the fixed background of this caelestial sphe
Name Longit. Lat. Bayer
Al Pherg : 2 Ari + 5 etPsc
Sheratan : 9 Ari + 8 beAri
Caph : 10 Ari +51 beCas
Hamal : 13 Ari +10 alAri
Shedir : 13 Ari +47 alCas
Cih : 19 Ari +49 gaCas
Ruchbah : 23 Ari +46 deCas
Segin : 0 Tau +48 epCas
Algol : 1 Tau +22 bePer
Alcyone : 5 Tau + 4 etTau
Mirphak : 7 Tau +30 alPer
Aldebaran : 15 Tau - 5 alTau
Rigel : 22 Tau -31 beOri
Bellatrix : 26 Tau -17 gaOri
Capella : 27 Tau +23 alAur
Mintaka : 28 Tau -23 deOri
Alnilam : 29 Tau -25 epOri
Alnitak : 0 Gem -25 zeOri
Saiph : 2 Gem -33 kaOri
Polaris : 4 Gem +66 alUMi
Betelgeuse: 4 Gem -16 alOri
Menkalinan: 5 Gem +21 beAur
Alhena : 14 Gem - 7 gaGem
Sirius : 19 Gem -40 alCMa
Castor : 25 Gem +10 alGem
Pollux : 28 Gem + 7 beGem
Procyon : 1 Can -16 alCMi
Asellus Au: 14 Can + 0 deCnc
Kochab : 19 Can +73 beUMi
Dubhe : 20 Can +50 alUMa
Subra : 29 Can - 4 omiLeo
Alphard : 2 Leo -22 alHya
Algieba : 5 Leo + 9 ga1Leo
Regulus : 5 Leo + 0 alLeo
Thuban : 13 Leo +66 alDra
Dhur : 17 Leo +14 deLeo
Denebola : 27 Leo +12 beLeo
Vindemiatr: 15 Vir +16 epVir
Spica : 29 Vir - 2 alVir
Arcturus : 29 Vir +31 alBoo
Menkent : 18 Lib -22 thCen
Zubenelgen: 20 Lib + 0 al2Lib
Dschubba : 8 Sco - 2 deSco
Antares : 15 Sco - 5 alSco
Rastaban : 17 Sco +75 beDra
: 21 Sco -12 epSco
Sabik : 23 Sco + 7 etOph
Rasalhague: 28 Sco +36 alOph
Sargas : 1 Sag -20 thSco
Gal.Center: 2 Sag - 6 SgrA*
Eltanin : 3 Sag +75 gaDra
Sacred T 5 Sag + 0 -----
Solar Apex: 7 Sag +53 HerA*
Kaus Austr: 10 Sag -11 epSgr
Nunki : 18 Sag - 3 siSgr
Vega : 21 Sag +62 alLyr
Altair : 7 Cap +29 alAql
Dabih : 9 Cap + 5 beCap
Sadr : 0 Aqu +57 gaCyg
Enif : 7 Aqu +22 epPeg
Fomalhaut : 9 Aqu -21 alPsA
Deneb : 11 Aqu +60 alCyg
Markab : 29 Aqu +19 alPeg
Scheat : 5 Pis +31 bePeg
Algenib : 14 Pis +13 gaPeg
Alpheratz : 20 Pis +26 alAnd
Since we're beginning with Saturn, set restrictions in
Astrolog to restrict all then uncheck only the Sun and
Saturn. Set the date & time to December 31, 2003 12 AM,
and you'll see Saturn at opposition in 15 Gemini. This
is just one "pinky finger" in longitude from Alhena at
14 Gemini. With the Sun in 15 Sagittarius, then Saturn
will be at southing about midnight LAT January 1, 2004.
- From this we can estimate Saturn's next opposition, by
adding 378 days, which is January 13, 2005. But Saturn
is a little slow in getting there, reaching opposition
the next day January 14, in 29 Gemini. The oppositions,
which we'll skip for Jupiter and Mars, prove to us the
planets Mars, Jupiter and Saturn, are orbiting the Sun
beyond Earth's orbit, and these orbits are predictable,
especially over long-term observations. As with Saturn,
by adding 3781 days to its synodic phase, we arrive at
Saturn's tenth opposition counting from January 1 2004,
which is May 9, 2014, again missing exactitude by only
one or two days, due to Saturn's moderate eccentricity
and about 2.5 degrees inclination to the ecliptic. For
long-term predictions, the ancient Babylonians noticed
that 9 sidereal orbits of Saturn coincided with around
256 synodic periods and 265 tropical years speaking in
round numbers. Add 265 years to January 1, 2004 and we
have January 1, 2269. Sure enough, there's Saturn near
opposition in 14 Gemini directly above Alhena and just
two days from true opposition January 3, 2269, showing
that the Babylonians knew what they were talking about
two thousand years before Christ. It's no mystery, but
is readily observable, predictable and reproducible in
the laboratory of the night sky, like heliacal risings.
The predawn risings of stars and planets have been the
carefully watched and predicted since men could mark a
cave wall with a piece of coal, blood or whatever else
has handy. Primitive stone observatories emerged which
had much greater longevity, and showed the teamwork of
prehistoric stargazers, and the importance they placed
on the ephemeris of the Sun, Moon & Stars to the Earth.
Naturally, the Sun is the single most important object
visible in the Earth's sky. Man has watched the Sun as
it rises and sets every day since humankind has walked
the Earth. All life forms follow the diurnal circadian
rhythm of Earth's daily rotation in one way or another.
Hence the Sun formed the fundamental basis of tracking
time from the beginning of every civilization that has
come and gone, from primitive tribes of early hominids
to more advanced human cultures, most of which are too
distant in the past for their records to have survived.
More recently, the Egyptians, Babylonians, Mayans, and
others around the post-deluvian world are close enough
in time for many of their records to be extant, mostly
bits and pieces, some fairly intact, like the pyramids.
In mans present time, secular-religious archaeologists
prefer to believe that civilization is basically under
7000 years old worldwide, due to their historical ties
to the Roman church, and continued use of the language
in their laws and their sciences. This is not to blame
the ancient translation of the bible, the Vulgate, but
has been the politics of religion, as men serve mammon.
After all the bible predicted this would happen, so it
isn't surprising that the schism of religious-apostasy
should continue to rule the minds of men. Yet the Moon
& Stars have continued to illuminate the night sky for
geological aeons and shall continue to do so for aeons.
So it is that Saturn has been rising and setting helia-
cally in very predictable intervals and shall continue
to do so for many long ages to come. Since the initial
date and time for observation of Saturn before sunrise
will vary, we know the Sun needs to be some 18 degrees
below the horizon to ensure visibility of any brighter
star or planet from moderate latitude any time of year,
weather permitting. But in fixed locations, i.e. where
ancient and antediluvian population centers flourished,
the heliacal risings of stars and planets were readily
estimated to within a few days time and by the seasons
of the year, tied directly to planting, harvesting and
every single aspect of their lives. Thus astrology was
the natural result of watching and predicting when the
stars and planets would rise and set, by knowing where
the planets are day and night. This knowledge was made
by simple observation, counting days, months and years
between cycles and phases. When Saturn rose heliacally,
it was always about 378 days give or take a day or two
since the last time it was observed to rise heliacally.
With each consecutive heliacal rising of Saturn, fixed
stars in the background showed that Saturn moves about
13 degrees in keeping with the Sun's progress relative
to the stars some 13 days later each year--again, give
or take a day or two, talking about long-term averages
rounded off to integer days since the whole premise is
to show that ancient stargazers could and did see that
the planets clearly orbit the Sun, and that they could
readily observe and recognize the sidereal and synodic
orbits by watching the heliacal risings of planets and
stars. The accuracy of the ancient ephemeris increased
commensurate with continued calibration by observation
of heliacal phenomena over the centuries and millennia
of that civilization from its rise until its fall. The
quality of long-lost very ancient ephemeredes is known
by mans inherent ability as a man to see the night sky
and to notice patterns and repetition in nature. These
are perfectly natural talents that all people are born
with--at least most people are. Once again, this comes
down to how much credit we give prehistoric man. There
are anthropologists who have recognized that early man
was smarter than modern day, secular-religious science
had theretofore acknowledged. Likewise the recognition
that at least semi-intelligent hominids have been here
many millions of years earlier than the orthodoxy used
to believe albeit some still cling to their hopelessly
obsolete superstitions about the antiquity of man, etc,
it is clear that man and man-like sentient beings have
roamed the Earth for aeons. One might reasonably argue
that dolphins or whales are smart enough to notice the
planets and stars rising and setting, and to count the
days and years of these events. Elephants are known to
remember things very well. At a minimum, we can safely
say that early man was intelligent enough to count the
days, months or years of observable heliacal phenomena
and we see that such observable events are predictable,
simply counting these events by days, months and years.
I think this is what makes modern astronomers angry at
those of us who have realized that planetary motion is
not nearly as mysterious as they'd like you to believe.
The Egyptians, Babylonians and Mayans showed admirable
levels of sophistication in their astronomical records
and their ability to predict very long-term periodical
events, the great year of precession being among these,
since the Earth's axis of rotation visibly gyrates one
degree against the fixed stars about every 26000 solar
days, which is about 71 tropical years, two months and
nine days, therearound. This is according to the Mayan
astronomers, whose astronomical skills were comparable
to those of the Babylonians. Both left records proving
that they could see the night sky, and that they could
accurately count and predict periodic planetary orbits
against the starry background of the caelestial sphere.
As in this case, we *see* Saturn observably progresses
about twelve degrees every year against the stars seen
from Earth. Every twenty-nine and a half years, Saturn
goes full circle against the stars, and over centuries
of observation we see that Saturn circles the Sun nine
times every two hundred sixty-five years--meaning that
Saturn advances closer to twelve and a quarter degrees
longitude per year thereby making short-term estimates
of Saturn's motion a little more accurate and reliable
than our round number of twelve degrees per year. Thus
we may safely predict that Saturn will have moved east
by closer to forty-nine degrees every four years, plus
our ephemeris for Saturn has improved significantly by
repeated observation and simple mathematical deduction.
We'll notice Saturn's thirteen degree advance at times
of entering or leaving retrograde motion and that this
retrograde lasts for about one hundred thirty-eight or
so days centered on inferior conjunction or opposition
to the Sun. Every three hundred seventy-eight days, we
see these motions repeat, when Saturn appears to stand
still in the sky then begin to move backwards for some
four and a half months before standing still again and
returning to normal motion. Every time we see it again,
about 378 days have passed and Saturn is approximately
13 sidereal degrees from where it was last time around.
Carte du Ciel is especially useful for animating these
apparent synodic motions against the background of the
stars, since you can fine-tune increments down to days,
hours and minutes, and mark the locations with "finder
circles" to readily observe a planet's motion relative
to the stars & constellation figures, and to the other
planets. Although the accuracy of the ephemeris is not
very reliable beyond plus or minus four thousand years,
especially for the Moon, you can view distant dates to
circa 20,000 years BC / AD. While tropical seasons can
be way off the mark the apparent motion of a planet to
the stars may not be far off the mark for say, 9000 BC.
You just won't know the season, or the Moon's position
at such a distant date, but other planets are probably
within a couple of degrees of where they actually were.
Not that this matters much, since you are simply using
the present-day ephemeris to view synodic and sidereal
motion of the planets that are visible and predictable.
For example, most of us'll probably be up and about at
midnight January 1, 2004. If your skies are clear, you
should remember to walk outside for a moment and check
out Saturn in 15 Gemini--just above and east of Alhena,
and right below Mebsuta which marks sidereal 15 Gemini
just 2 degrees above the ecliptic. Your extended thumb
at arm's length spans about two arcdegrees thus you'll
see that Saturn is maybe a pinky fingernail's width or
so (about 2/3's of a degree) below the ecliptic at the
time of observation. Since Asellus Australis (see list
above) marks 14 Cancer right on the ecliptic (actually
+0:04'38" but round degrees are all a stargazer needs),
and bright Regulus at 5 Leo is less than half a degree
above the ecliptic, you can quickly visualize the line,
rather the arc of the ecliptic across the sky. Jupiter
at 24 Leo and about a degree above the ecliptic should
be visible in the eastern sky. Sirius at 19 Gem and 40
degrees below the ecliptic will be hard to miss in the
southern sky (unless you live north of Barrow, Alaska).
If you live in the southern US or similar latitude you
might spot bright Canopus at 20 Gem -76 degrees barely
above the south horizon. Orion should be in clear view
below right of Saturn. See if you can spot Al-debaranu,
the prime fiducial of the caelestial zodiac at 15Tau00
and 5 degrees below the ecliptic. As you see, when you
look at a planet in the night sky the background stars
help you to locate the planet's longitude and latitude,
hence confirming previous predictions, and calibrating
future predictions. In ancient times this was done for
centuries & millennia. Let's look at Saturn heliacally.
Just to be on the safe side, we'll put 30 degrees past
Saturn for the predawn Sun. That ought to make it easy
to spot Saturn before sunrise, whether you're watching
from the old, royal Greenwich observatory at 25 meters
above sea level & 00E00:00 longitude 51N28:38 latitude,
or viewing atop the Great Pyramid at 31E09:00 29N58:51,
or from the Sun Pyramid in Teotihuacan, Mexico ~19:44N
98:50W or from the site of ancient Babylon 44E24 32N33.
Use your own default observation location, set up your
favorite astronomy program to watch the sky from there.
I'm using my own location here in central Colorado USA.
Saturn is plainly visible at heliacal rising August 14,
2004 after about 3:30 AM MST. For continuity, I've set
Astrolog to 12 PM August 14 2004 or Julian Day 2453232,
with Saturn 27 Gemini and the Sun 27 Cancer. We'll add
the 378 days for Saturn's synodic period, to August 27,
2005, with Saturn 10 Can and Sun 9 Leo. Like before we
are just a day short, so on August 28, 2005, Saturn is
rising about 3:50 AM, and it is apparent that Saturn's
some 13 degrees further along in the caelestial zodiac
than it was back on August 14 2004. Add twice 378 days,
which is 756 days, and we have September 9, 2006 which
is about two days shy of Saturn 30 sidereal degrees to
the Sun, thus September 11 2006 finds Saturn rising at
4 AM. Let's jump ten times 378, which we know from our
previous observations is closer to 3781 than 3780. The
date is December 21, 2014. Low and behold, Saturn's at
5 Scorpio and the Sun is 5 Sagittarius, right where we
expected it to be. Remember, Saturn was at 27 Gem back
on August 14, 2004 with the Sun 27 Can. Now, ten times
Saturn is heliacally risen we see that Saturn is 5 Sco
and the Sun 5 Sag. That's near 128 degrees that Saturn
has progressed in ten synodic periods or ten times our
round figure of 13 degrees. Again, as observations are
made over longer and longer periods of time, ephemeris
calibration and improvements are the inevitable result.
By the way, Saturn rises near 6 AM on December 21 2014.
These long-term observations of the heliacal phenomena
inevitably reveal the limits as to how far the planets
can appear to stray from Earth's ecliptic with the Sun,
revealing each planet's orbital inclination to Earth's,
and also revealing other obvious limits, such as Venus
and Mercury display their orbital eccentricity when at
maximum elongation, Venus very little, Mercury a whole
lot more. This plainly shows the observer that Venus &
Mercury are closer in heliocentric orbit than Earth is,
and of course the paths of Mars, Jupiter & Saturn show
that they are further away from the Sun in their helio-
centric orbits than Earth is. We'll cover more on this
in later parts. Jupiter is next on the list of planets.
Julian Day 2453309, 12 UT October 30, 2004. Jupiter is
at 13 Virgo, 30 sidereal degrees from the Sun 13 Libra.
Jupiter rises about 4:50 AM (here in central Colorado)
just below bright Venus at 7 Virgo. Zaniah (etaVir) is
between them near 10 Virgo. Remember, we are measuring
the sky with our naked eye and extended hand, so round
degrees, maybe down to a sixth of a degree, or ten arc-
minutes, is as good of accuracy as we can achieve. You
can see that the modern accuracy of JPL's ephemeris is
based on observations made by large observatories, and
formulated using advanced knowledge of mathematics and
physics. E.g. here's a chart for Sat 30-Oct-2004 12 UT.
These values are rounded off to the nearest arcseconds
of longitude and latitude, while the internal accuracy
of the software is good to milliarcseconds (JPL-DE406):
Aldebaran : 15Tau00'00" -5:28'00"
Venus : 6Vir55'17" +1:32'47"
Zaniah : 9Vir30'15" +2:35'21"
Jupiter : 12Vir35'49" +1:07'05"
Sun : 12Lib32'48" +0:00'00"
Ancient observers would commonly use a measuring stick
or metal rod notched with linear increments calibrated
by the observer which he or she could comfortably hold
at arm's length between both hands, ensuring a uniform
perspective of sidereal measurement. But we will limit
our ancient observers as having nothing but themselves
to view the heavens, since that's all that they needed
to clearly view the predictable motions of the planets
against the fixed background of stars. Easily accurate
to plus or minus one degree, simple enough so children
could be taught to do this and carry on the stargazing
tradition, counting the days, weeks, months, and years,
planting, harvesting, worshipping by the ephemeris and
its religiously-observed calendar--the religion of the
stars. As each civilization developed, and became more
sophisticated, they organized and specialized, so that
astronomical observation, astronomy, and their logical
deductions based on astronomical observations--meaning
mathematics--ergo astrology, became the disciplines of
specialists so that others in their community could go
about their business. In ancient times, the astrologer
was synonymous with the mathematician, "star-logician"
in the most literal sense. Even in our day and age, it
was only within the last few centuries that astrologer
and astronomer reached a schism, since astrologers had
long-since ignored the proper mathematics of astrology,
and astronomers became disenchanted with the illusions
yet perpetuated by today's tropicillogical astrologers
and other schisms of astrology,--all who've hopelessly
lost their grasp on the ancient practice of star-logic.
Since this schism, astronomers have changed their ways
of measuring the sky such that "constellations" became
synonymous with unequal boundaries associated with the
asterisms or some 88 familiar groups of brighter stars
instead of the ancient method which divides the entire
caelestial sphere into twelve equal meridians as signs
with meridians of latitude from the caelestial equator.
Modern astronomers began referencing positions only to
Earth's terrestrial equator by its intersection on her
ecliptic. Next time there's a "pole shift", or crustal
displacement (or both?), that'll screw up their method
of measuring the sky in a heartbeat. Meanwhile Earth's
slow gyration of precession continues to change modern
astronomer's coordinates. For example, look at Regulus
at 5 Leo near the ecliptic. In 8000 BC, Regulus was at
5 Leo. In 8000 AD, Regulus will still be at 5 Leo. The
position of Regulus is easy to see and easily recalled.
Only the slight, very long-term wobble of the ecliptic
itself affects how we chart latitude of stars near the
ecliptic, and also the longitude of stars farther away
from the ecliptic. As a result, Regulus might be close
to a degree from the ecliptic at some remote epoch but
it's still going to mark 5 Leo for a long time to come,
irrespective of precession, pole-shift or annihilation
of civilization. Any survivors can point up at Regulus
and confidently say "Look! There's Regulus 5 Leo", and
any planet passing nearby will certainly be identified
by its position--relative to a recognizable fixed star,
and certainly not by its "RA/Dec". As for this example,
on Julian Day -1200514, 1-Jan--7999 (8000 BC Gregorian)
Carte du Ciel shows Regulus at 0h46m35s +4*36'06", and
Carte du Ciel shows Regulus at 15h29m45s -17*53'29" on
Julian Day 4643000 1-Jan-8000 (8000 AD). For a caveman
marking scores on a cave wall to remember positions of
planets relative to nearby stars counting days, months
and years between repeating heliacal risings and other
predictable synodic phases relative to the Sun, anyone
can see that the positions of planets are most readily
and easily tracked by their positions to visible stars,
and that those stars remain fixed in their position on
Earth's caelestial sphere with subtle proper motion so
slow that it takes millennia even to be noticed by the
best of naked-eye astronomers. Hence Orion's Belt, for
example, is very close to the same position in the sky
as it was when they built the Great Pyramids 10,500 BC,
since the three stars of the belt have very low proper
motion. So Mintaka 28 Tau, Alnilam 29 Tau, and Alnitak
the "Great Pyramid" star at 0 Gem have illuminated the
same positions on Earth's caelestial zodiac ever since.
So when we say Jupiter is in 13 Virgo October 30, 2004,
we can easily see where it is in relation to the stars
before sunrise, since the stars tell us where 13 Virgo
is. In this case, Zaniah at 10 Vir is nearby, so it is
easy to estimate Jupiter's position to plus or minus a
degree of certainty. With this simple observation, the
next heliacal rising of Jupiter is easily predicted by
adding 400 days to October 30, 2004, since 400 days is
the average period that Jupiter has been seen for ages
to repeat its synodic cycles. That is December 4, 2005,
but Jupiter is about five days past the 30-degree mark
from the Sun. November 29, 2005 finds Jupiter 12 Libra
and the Sun in 12 Sco, and Jupiter will be rising near
5:30 AM from my location. With Spica and Arcturus over
rising Jupiter, you can be sure where 29 Virgo is. But
Kappa Virgo at 10 Lib and +3 latitude--although it's a
lot closer to Jupiter--may be difficult to see at 4.18
magnitude. The star called "109 Vir" is a bit brighter
at 3.72 magnitude and marks 13 Libra near +17 latitude.
The important thing is to know which stars that you're
looking at, and their approximate longitude & latitude
in the zodiac. In the 395 days between heliacal rising,
Jupiter has moved some 29 degrees. From this we expect
Jupiter will complete one sidereal orbit approximately
every 12 years. Jump ahead 4000 days from October 30th
2004, and we arrive at October 13 2015--eight days too
late. We must go back to October 5, 2015, with Jupiter
17 Leo and the Sun 17 Virgo. From this we find Jupiter
has moved from 13 Vir to 17 Leo, 26 degrees before the
completion of one sidereal year for Jupiter. Estimates
from our observations in 2004 & 2005 led us to believe
that Jupiter would take about 12 years to complete one
sidereal orbit. Jupiter's tenth heliacal rising showed
us that Jupiter moved about 334 degrees over 3992 days.
We might extrapolate off this, and figure that Jupiter
will make about 360 degrees in another 311 days making
a rough estimate 3992 + 311 = 4303 days for a sidereal
year of Jupiter based on a total of three observations.
Let's look at the next rising of Jupiter 400 days from
October 5, 2015, November 8 2016. Now we're about four
days late, so go back to November 4, 2016, for Jupiter
17 Virgo and the Sun 17 Libra, rising about 4:50 AM at
my location. So for eleven heliacal risings 30 degrees
from the Sun, it took 4388 days, and Jupiter transited
through the zodiac from 13 Vir October 30, 2004, to 17
Virgo on November 4 2016. That's fully 360 degrees and
4 extra degrees that Jupiter was observed to move over
the course of 4388 days and a touch more than 12 years.
Simple interpolation estimates a sidereal year at 4340
days, 37 days higher than our previous estimate but is
now based on four observations not just three. Further
observations empirically calibrate our rough estimates.
- From simple observation we were able to deduce Jupiter
takes a little less than 12 years to complete one side-
real orbit, since we are plus 4 degrees after 12 years.
Repeated observation refined our estimate to 4340 days.
After centuries, the ancients were able to winnow this
down to some 4332 days or about 11 tropical years plus
around 316 days that it takes Jupiter to orbit the Sun.
It doesn't take any "rocket scientist" but only common
sense with a little simple addition and subtraction of
round degrees, days and years. The stargazer could see
Jupiter go retrograde for some 121 days centered on in-
ferior conjunction (opposition), and see these synodic
events repeat every 400 days by the long-term averages.
Ancient Babylonian astronomers were sufficiently adept
to notice that 36 sidereal orbits of Jupiter was quite
close to 427 tropical years and 391 synodic periods of
Jupiter. Just add 427 years to October 30, 2004 to see
if they knew what they were talking about. Try October
30, 2431. Just 6 days later Jupiter is 30 degrees from
the Sun with Jupiter 12 Vir and the Sun 12 Vir. That's
just one degree from where they were back in 2004. The
ancient synodic multiple for Jupiter is right in there.
Next we'll look at Mars, which has the longest synodic
period of all the planets. We can see that Mars is the
first planet beyond Earth's orbit since Mars is moving
much faster through the caelestial zodiac than Jupiter
or Saturn. But like the Jovian planets we can see that
the elongations of Mars from the Sun reach oppositions
on an observably predictable periodic basis as is true
for heliacal risings, settings, squares, trines or any
repeating angle of aspect to the Sun. Heliacal risings
are being treated as semisextile aspect for continuity,
and the nice round number thirty degrees is convenient,
easy to remember and to measure by hand, since a whole
hand or fist plus three closed middle fingers at arm's
length together makes 15 degrees, two whole fists make
about 20 degrees, depending on your physical type. The
angle from outstretched thumbtip to pinky fingertip is
some 25 degrees, but you must calibrate your own hands
and fingers to estimate a perspective angle accurately.
An easy way to do this is to stand in a rectangular or
square room and see how many hands, fists, and fingers
it takes to measure 90 degrees, i.e. from wall to wall.
Six times a fist plus 3 closed middle fingers ought to
be about 90 degrees. Experiment to see what works best.
Three times your outstretched thumbtip to pinky finger-
tip plus three closed middle fingers equals 90 degrees.
Calibrating by the stars assures the greatest accuracy.
No matter how close or far away an object is, ten feet
or ten thousand lightyears, the angle subtended to you
viewing those objects will be the same. A really sharp
naked-eye astronomer can discern down to one arcminute.
But I'm being conservative, so that ancient stargazers
would need only resolve twenty arcminutes and estimate
positions of stars and planets to plus or minus one de-
gree, which for the Sun's apparent motion is about one
day equals one degree. This is essential to know since
adding one or more days to a predicted heliacal rising
adds ~1 degree per day to the Sun's ecliptic longitude.
Each consecutive heliacal rising for Mars occurs about
780 days apart. With a spectacular opposition for Mars
just days away at this writing which will be August 27,
2003, Mars will rise heliacally about December 12 2004
at 26 Libra to the Sun 26 Scorpio. Mars will rise near
5:50 AM from my location with two marking stars rising
above Mars, Zubenelgenubi at 20 Lib +0 & Zubeneshamali
at 25 Lib +8. Add 780 days and we have January 31 2007.
There's Mars at 16 Sagittarius to the Sun 16 Capricorn,
30 degrees apart. Mars rises locally about 6:40 AM. It
is nearly impossible to see Kaus Borealis at 12 Sag -2
this close to sunrise (past astronomical twilight) and
Mars may be difficult to spot here in the mountains of
central Colorado. 16 Sag is 20 degrees past 26 Lib but
we've witnessed Mars at opposition back on August 27th
2003 and again November 7, 2005, an 803-day difference.
This also tells us that Mars is zipping along, so must
have circuited the zodiac past 360 degrees, and is now
360 add 20 equals 380 degrees from where it was before.
Simple interpolation tells us Mars takes some 739 days
to complete one sidereal orbit. This is a rough figure
as further observation shows. 10 times 780 is 7800. Ex-
rience shows Mars has significant orbital eccentricity,
and orbits quite rapidly through the caelestial zodiac.
We find through experience that Mars is frequently off
by a month or more from where we predicted it would be
last we predicted its next heliacal rising, setting or
any other repeating like-phase. Mars is at 14 Pis, and
the Sun is 6 Ari on April 21, 2026. We must jump ahead
to May 28, 2026, fully 37 days later, to find Mars and
the Sun separated by 30 degrees sidereal longitude. As
the apparent velocity of Mars is nearly as fast as the
Sun's past superior conjunction it takes a few days to
compensate for being just a degree off from 30 degrees.
Thus to compensate for 8 degrees delta took us 37 days.
Come May 28 2026, Mars is 12 Ari and the Sun is 12 Tau.
Hamal at 13 Ari +10 and Sheratan at 9 Ari + 8 makes it
easy to estimate Mars' position at 12 Aries. Shedir at
13 Ari +47 draws a nearly perpendicular line or arc to
Hamal relative to the ecliptic making measurement easy.
26 Libra is 166 degrees from 12 Ari, meaning Mars went
under eleven & a half times or 4126 degrees around the
zodiac in 7837 days, making our observable average 684
days per sidereal orbit based on just two observations
ten heliacal risings apart. Babylonians over centuries
of observation and calibration found this to be around
687 days based on the long-term averages, which is one
year, three hundred twenty-two days per sidereal orbit
of Mars. These ancient astronomers-astrologers noticed
that 151 sidereal orbits of Mars nearly coincided with
284 tropical years and 133 repeating synodic phases of
Mars to the Sun. Add 284 years to December 12 2004 and
we arrive at December 12, 2288. There's Mars at 23 Lib
and the Sun 22 Sco, 29 degrees apart. Merely four days
later finds Mars 26 Lib & Sun 26 Sco--right on the dot.
So the ancient Babylonian sidereal-synodic multiple of
Mars is off just 4 days in 284 years...very impressive.
We also notice that Mars goes retrograde centered near
inferior conjunction for an average of 73 days. Try it.
Astrolog charts the synodic velocities of every planet.
The presently-imminent opposition August 27 2003 shows
Mars turned retrograde back on July 29, 2003, and will
leave retrograde September 27 2003, a difference of 60
days. With every empirical observation for retrogrades
and oppositions, the accuracy of this average improves.
Observation proves 73 days is Mars' retrograde average.
Next on the list is Earth, meaning the Sun relative to
Earth. Since circa ~200,000 BC, the heliacal rising of
stars has consistently demonstrated to stargazers that
the tropical year precesses against the stars by about
five-sixths of one arcminute per year or approximately
one degree per 26000 solar days, i.e. 71 years 68 days
on average. The ancient Mayans were superb astronomers.
They used a "Haab" intercalation interval so that 1508
haabs was commensurate with around 1507 tropical years
(C.P. Bowditch, published 1906) since the value of one
mean tropical year takes 365.2422 mean solar days, and
one Haab equals exactly 365 days--you do the math. The
very long-term Mayan average for the great year of pre-
cession equals 5 times 13 Baktun, or 5 ages of the Sun.
Interesting, since Leo is the fifth sign of the zodiac.
One Baktun is 144,000 days. 13 Baktun = 1,872,000 days.
Five times 1,872,000 days equals 9,360,000 days a year
of precession ergo one 360-degree sidereal gyration of
Earth's axis of rotation against the caelestial zodiac
takes some 25,626 years 303 days. From this we predict
one zodiacal age of precession is 2,135 years 208 days.
Cf. modern secular-religious estimates of ~2,150 years.
The Mayan long-count is undoubtedly more accurate. The
well-known date of December 21, 2012 was predicted not
by modern science but by ancient Mayan astronomers. It
predicted the winter solstice Sun conjunct the "sacred
tree" or apparent intercept of the galactic & ecliptic
planes at 5 Sagittarius +0...accurate to one arcminute.
If we subtract 9360000 days from December 21 2012, the
last conjunction of the winter solstice Sun was likely
not too far from Julian Day -6903717, which the modern
Gregorian calendar shows as March 1, 23615 BC, clearly
way off the mark...the Gregorian calendar is erroneous
for long-term prediction. The Mayan calendar is better
by far but how they achieved such mastery is a mystery,
unless they actually observed for many, many millennia.
I believe this is how they did it, and that the Mayans
and other pre-Columbian civilizations are vastly older
than secular-religious archaeologists have admitted to.
By watching the precession of Earth's axis, really the
whole rotating Earth, long-term prediction of sidereal-
synodic-tropical cycles gained accuracy over centuries
and millennia of observation. The length of solar days
was always the basis for counting longer periods, such
as a lunar month was some 29 1/2 days, a tropical year
was about 365 1/4 days, four tropical years about 1461
days etc. Each multiple was numbered by days, months &
years, by the Sun the Moon & Stars also as per Genesis.
Hence the multiples for the planets out to Saturn were
referenced to Earth's solar days, lunar months and the
Earth's tropical and sidereal years. As we've seen for
Mars, Jupiter & Saturn, the sidereal motion of planets
is fundamental to determining not only the position of
a planet but also its sidereal year around the Sun. It
is perfectly obvious that Mars, Jupiter & Saturn orbit
the Sun and it is equally obvious that Mercury & Venus
also orbit the Sun. Hence it follows that Earth orbits
the Sun, since we can see that Mars is further away in
its orbit than Earth is and Venus is closer than Earth
is by its heliocentric orbit. Only the Moon sidereally
appears to orbit the Earth, and the phases of the Moon
show that both Earth and Moon are orbiting the Sun--in
reference to the caelestial sphere. Incommensurability
between Earth's tropical and sidereal years is easy to
understand, yet has confounded more than a few amateur
astronomers and astrologers for centuries to millennia.
In tracking the synodic and sidereal motion of planets,
we are referencing all positions, that of the Sun, and
the planet(s) in question, to the caelestial zodiac of
the stars. We are counting in solar days independently
of years at first, only later by counting fractions of
years in days instead of decimal places. Thus the side-
real year of Earth reveals to an observer how tropical
years are slightly faster than sidereal years, as year
after year we see this disparity compounding enough so
that we can correctly estimate the value of precession.
The difference between a solar day and sidereal day on
Earth is dependent on the length of a sidereal year vs.
the length of a sidereal day. The faster Earth rotates
sidereally, then the more solar days per sidereal year
the observer will witness. The faster the Earth orbits
the Sun, the fewer solar days per sidereal year we see.
Since the tilt of Earth's axis circa 200,000 BC, solar
days have numbered 365 and change per year with barely
50 arcseconds per year difference between sidereal and
tropical year relative to the stars to wit, precession.
That is why a solar day is slightly longer than a side-
real day, since Earth's orbit makes the Sun rise later
than distant stars which, comparatively, care not that
Earth orbits the Sun with its sidereal-annual parallax
having generally undiscernible effect, sidereal diurnal
parallax/geocentric parallax having thousands of times
less effect on the apparent positions of stars--albeit
planets are affected slightly more, Moon more than any-
thing else. At about a quarter million miles, the Moon
can appear up to a degree off from geocentric position.
So far we've looked at Saturn, Jupiter, Mars & the Sun.
Next on the list is Venus, the venerated planet nearly
the same size as Earth, and whose orbit is least eccen-
tric of any planet in our solar system, with an almost
perfectly circular orbit, proportionally just ~0.00677
between the major and minor axis although Venus orbits
the Sun some three and a third degrees inclined to the
Earth's ecliptic. All in all Venus has the most predic-
table orbit of any planet in the solar system with the
exception of Earth itself, whose orbit with the Sun is
only about 0.0167 eccentric -- a ratio more than twice
that of Venus. The Venusian orbit is around 72% as far
from the Sun as Earth's orbit, hence has a faster side-
real year of about 225 solar days, or about 61.5% that
of Earth. Look at July 1, 2004. Venus rises heliacally
at 15 Taurus, 30 degrees from the Sun 15 Gemini. Venus
is about 4 degrees below the ecliptic, just one degree
above Aldebaran (alpha Tau) at 15 Tau -5, and just one
degree in longitude from Ain, epsilon Tau at 14 Tau -3.
Venus'll rise approximately 4:40 AM MDT at my location.
- From past experience we know that Venus takes 584 days
to repeat its synodic phases. Add 584 days to July 1st
2004 and you have February 6th 2006, which is two days
past 30 degrees from the Sun, so we have to back up to
February 4th 2006, with Venus at 21 Sag and Sun 21 Cap.
Venus will rise about 6 AM MST. In 582 days, Venus has
moved from 15 Tau to 21 Sag, which is 576 degrees from
Venus' last heliacal rising. Simple interpolation says
that Venus will move 360 degrees against the stars per
364 days or near the period of the Sun's sidereal year
to Earth. From our perspective on Earth, Venus appears
to orbit the Sun epicyclically, so we can think of the
planet Venus (and Mercury, which we'll cover later) as
a "moon" of the Sun especially since Venus and Mercury
are the only two planets in our solar system that have
no moons of their own. The sidereal motion of Venus is
easily rectified by watching every 5th heliacal rising,
since 5 x 584 = 2920 days. Our past experience reveals
that every 2919 to 2920 days Venus will appear to rise
heliacally at about the same time of tropical year and
against about the same background stars. Meaning every
eight years, Venus will appear at about the same phase
relative to the Sun and also in the sky (on the caeles-
tial zodiac). Try it. Add 2920 days to July 1 2004 and
you have June 29 2012. The Sun is 13 Gem, Venus 13 Tau,
30 degrees to the Sun and 2 degrees from 15 Tau. Venus
has repeated 5 consecutive synodic orbits and about 13
sidereal orbits. Which means Venus has orbited the Sun
13 times in 2920 days making an average of 224 and six-
tenths days per sidereal orbit--very close to the mark.
Subsequent observations over decades to centuries will
confirm that Venus' sidereal year is closer to 224 and
seven-tenths mean solar Earth-days, this, according to
ancient Babylonian astronomers cir. 1800 BC. They said
1871 sidereal periods of Venus is close to 720 synodic
phases of Venus and 1151 tropical years on Earth. This
is readily demonstrated by adding 1151 years to July 1,
2004, bringing us to July 1 3155. Try it. We must jump
ahead 29 days to July 30, 3155. Venus is 27 Tau to the
Sun 27 Gem. The default semisextile aspect 30 sidereal
degrees between each planet and the Sun is the natural
default for our planetary analysis of heliacal risings.
Over 1871 orbits and we're off by half the zodiac from
Venus 21 Sag to 27 Tau. That's 150 sidereal degrees we
missed by using a Babylonian sidereal-synodic multiple
for Venus. But wait! Out of almost two thousand orbits,
being off by less than one orbit is actually very good,
and being one month off in 1151 tropical years is also
very impressive, and is subordinate to the 720 synodic
repeating phases of Venus, thereby exact to one degree.
The accuracy of the Babylonian multiple for Venus is a
testament to their tremendous astronomical aptitude. I
doubt that anyone before or since has presented a grea-
ter degree of accuracy in their long-term ephemeris if
you examine the actual evidence. Twice 1871 is 3742 or
allegedly 2302 mean-tropical years on Earth, so try it.
2004 + 2302 = 4306. We already know that JPL's current
estimates for tropical precession are off by 500 years
per great year, thus it's no surprise we jump ahead to
August 29 4306 with Venus some 30 degrees from the Sun.
Venus is 10 Gem, and the Sun is 10 Can. Remember Venus
was 15 Taurus on July 1, 2004. So we jumped ahead 2302
years to 4306. Venus and the Sun have moved 25 degrees
ahead in 2302 years. The "Habb" intercalation interval
tells us that the ancients figured 365.2422 days every
tropical year, so 2302 years makes around 840,788 days.
That's the long-term tropical-to-day interval, but the
inference to Venus is also made, at 1151 years per 720
repeating phases. Hence 420,394 solar days ought to be
about 1151 tropical years, and 1871 sidereal years for
Venus is 30 degrees from the Sun, at regular intervals.
We must show that a planet is visible to the naked eye,
weather permitting, at moderate latitudes, at heliacal
rising especially...by using 30 degrees as our default.
This renders consistency to our empirical observations,
even as rendered virtually by our modern computer soft-
ware. We know it's accurate and we can thank dedicated
astronomers for making such software possible and also
commendably accurate and reliable. That's all fine and
good. But let's not forget that these same astronomers
have persistently ignored the ancient evidence for the
astronomers throughout time, to be able to immediately
see the sidereal and synodic orbits of the planets and
be able to deduce which planets are closer and further
away from the Sun, and also from Earth in their orbits.
Anyone can see that the planets are not invisible, nor
do they fail to show to their orbits to anyone looking,
whether they looked at ten million BC or anytime since.
Look at Julian Day 2453022 or January 17 2004 12 PM UT,
with the Sun acquiring a semisextile aspect to Mercury
of about 6 degrees with Sun in 2 Capricorn which is 24
degrees from Mercury 8 Sagittarius. Owing to Mercury's
considerable ratio of orbital eccentricity, or about a
fifth again larger between major and minor axis, we'll
see Mercury rising heliacally at maximum elongation to
the Sun, 6 degrees short of the 30 degree mark like we
used for the other planets. Recall from my new book on
Planetary Awareness Technique that Mercury needs to be
at least 18 degrees separated from the Sun in order to
become visible before sunrise or after sunset. Mercury
never exceeds around 28 degrees of separation from the
Sun in any case, so we'll never see 30 degrees between
them. Mercury is seen to rise heliacally about 6:50 AM
from my location, with Polis (muSgr) at 8 Sag +2 right
next to Mercury, with Sabik (etOph) at 23 Sco +7 above
right of Mercury. Bright red Antares (alSco) at 15 Sco
and 5 degrees below the ecliptic points the way to the
waning Moon at 2 Scorpio -1 and about 24% phase to the
Sun. On the long-term average, Mercury will be seen to
repeat its phases approximately every 116 days. We add
116 to January 17 2004 bringing us to November 10 2004.
There's Mercury at 13 Scorpio to the Sun 24 Libra. But
wait! Now Mercury's setting heliacally just 19 degrees
from the Sun, at about 5:20 PM my local time, with the
cascading Rocky Mountain 14-ers on the western horizon.
But how did we go from heliacal rising to heliacal set-
ting in just 116 days? It's because Mercury has a very
high orbital eccentricity, and whose orbit is inclined
to Earth's ecliptic by about 7 degrees. The centennial
rate between consecutive Mercury perihelions increases
by 573.57 arcseconds per century on this jpl/nasa site
http://ssd.jpl.nasa.gov/elem_planets.html meaning that
each consecutive perihelion advances by 5.7 seconds of
arc each mean-tropical year. Cf. Earth's sidereal year
of 365.25636 mean solar days, with Earth's anomalistic
year of 365.25964 mean solar days per consecutive peri-
helion, or five minutes longer than a sidereal year of
the Earth-Sun barycenter, so that the perihelion point
advances on average about 1.1 arcminutes per annum. At
present, Earth's perihelion repeats around January 4th.
Thus, Mercury's orbit is increasing ever so slowly out-
wards from the Sun at a rate of about 61 miles per cen-
tury (1 AU = 92,956,229.4 miles, Earth's mean distance
from the Sun) or 6/10ths of a mile every tropical year.
This also shows the orbit of Mercury increasing in its
eccentricity by a ratio about 0.00002527 between major
and minor orbital axis per century or about 0.00000025
per year on the semi-major axis of Mercury's orbit. By
watching Mercury's heliacal phenomena over decades and
centuries, a long-term average of 116 days is realized.
We can jump ahead by ten synodic periods to see if our
116-day number holds up under scrutiny, bringing us to
March 21 2007, since past experience has shown Mercury
repeats ten average synodic phases closer to 1159 days,
or 1 day less per every ten heliacal risings, settings
etc. There's Mercury at 8 Aquarius to the Sun 6 Pisces,
separated by 28 degrees in caelestial longitude, which
is Mercury's maximum elongation from the Sun. Note the
velocity fields in Astrolog, which shows the following:
Astrolog 5.41G chart for Wed Mar 21, 2007
12:00:00pm (+0:00 GMT) 0W00:00 0N00:00
Body Location Latitude Velocity
Sun : 5Pis36 +0:00'00" +0.9935813\
Mercury : 7Aqu53 -1:03'20" +0.9725359/
The following day, March 22nd shows Mercury's velocity
to be overtaking the Sun's velocity, if only barely at
+1.0177906 for Mercury, compared to the Sun +0.9929804.
The velocity numbers tell how many degrees per day the
object appears to be moving through the zodiac meaning
the Sun is moving slower than Mercury is by March 22nd.
Since Mercury appears to be moving slower than the Sun
on March 21st, it follows that the angle of separation
between Mercury & the Sun reaches its maximum on March
21, 2007, which is about 28 degrees sidereal longitude.
Ancient Babylonian astronomers found that 191 sidereal
orbits of Mercury lasted about 145 synodic periods and
46 tropical years. Try it. Add the 46 years to January
17th 2004, which will bring us to January 17, 2050. We
find Mercury rising heliacally at 8 Sagittarius to the
Sun at 2 Capricorn. As you'll recall Mercury was 8 Sag
to the Sun 2 Cap back on January 17, 2004, making this
ancient sidereal-synodic multiple for Mercury right on
the money. You'll notice Mercury begin to overtake the
Sun on the very next day, January 18 2050, which means
that Mercury reaches its maximum elongation January 17,
2050. Clearly the Babylonians knew precisely what they
were talking about--at least two thousand years before
Christ. So much for the secularist "flat-earth" theory
claiming that ancient astronomers didn't know that the
Earth and other planets are in orbit around the Sun or
their similarly-ridiculous contention that astronomers
believed the world to be "flat" before the Johnny-come-
lately Copernican astronomers figured out the contrary.
The second-brightest object in the sky next to the Sun
is the Earth's moon. Since time immemorial, humans and
other hominids have watched the Moon wax and wane over
the skies of Earth. The lunar orbit takes about 27 1/3
solar days to complete one sidereal revolution. That's
more than two days faster than the lunar synodic month
of about 29 1/2 days, and reveals to the observer that
the phases of the Moon are a function of the Earth and
Moon together orbiting the Sun. The Moon appears to be
almost exactly the same size as the Sun as viewed from
Earth, since the Moon is in fact 400 times smaller and
400 times closer than the Sun on average. This is easy
to see during a total solar eclipse, during which time
the Sun's corona becomes distinguishable from the dark
background, and the Moon is seen to be closer to Earth
than the Sun is. The relative distances of the Sun and
Moon to Earth don't appear to change all that much and
both Sun & Moon orbit Earth in a fairly linear fashion,
albeit the Moon's orbit with the Earth is more complex.
As a result, we can be sure that both Sun & Moon orbit
the Earth sidereally. We already know from observation
that the planets orbit the Sun, and we've also deduced
the length of every planet's sidereal year and average
synodic period. We've learned to count these repeating
intervals by their observable averages in days, months
and years, by their repeating synodic aspects relative
to the Sun, and by their repeating sidereal aspects to
fixed stars on the Earth's caelestial firmament. There-
by we see that the Moon's phases take consistently lon-
ger than the Moon's sidereal month by about 2 1/6 days.
We have learned that the difference between the Moon's
sidereal and synodic month is directly attributable to
the length of a sidereal year of the Earth-Moon system
orbiting the Sun verses the length of a sidereal month.
We view the Moon orbiting Earth on a long-term average
of some 13 1/3 sidereal lunar orbits per sidereal year,
i.e. as seen against the fixed background of stars. Re-
member, that the distant stars care not that Earth and
the other planets orbit the Sun or more accurately the
solar system barycenter along with the Sun, since even
nearby stars a few dozen lightyears away are yet 1000s
of times more distant than Earth is to the Sun. To wit,
one lightyear is the linear equivalent of about 63,240
astronomical units where 1 AU equals ~92,956,230 miles,
and just one lightyear equals ~5,878,482,160,000 miles.
Even Spica (alpha Virginis at 29 Virgo -2, magnitude 1)
at 262 lightyears is some 1 1/2 quadrillion miles from
Earth...16.5 million times Earth's distance to the Sun.
Hence Spica's trigonometric parallax is barely one one-
hundredth of an arcsecond or nearly 5000 times smaller
than one arcminute ergo undiscernable to the naked eye
by a factor of five-thousand to one. If Spica were but
one-twentieth of a single lightyear from Earth then we
might barely be able to discern one arcminute parallax.
At 2160 miles in diameter, and ~239,000 miles distance
from Earth, the Moon's diurnal parallax can be as high
as one arcdegree from its geocentric position. For the
Moon, annual parallax has no effect, since the Moon is
forever orbiting Earth epicyclically some 13 1/3 times
per sidereal Earth-year. Thus the Earth-Moon system is
averaging 360 divided by 13 1/3 makes about 27 degrees
per sidereal month on average that the Earth-Moon bary-
center has advanced in its heliocentric sidereal orbit.
This means that the Sun advances on average 27 degrees
per sidereal month through the caelestial zodiac along
the plane of the ecliptic, and Moon orbits Earth about
387 sidereal degrees per synodic month totalling 12.37
synodic months per sidereal Earth-year. Eclipse cycles
are tied to where the lunar orbit crosses the ecliptic,
also called the nodical month, and is about 27.21 days.
The anomalistic month averages 27.55 days which is the
approximate interval between lunar perigees or apogees,
and which determines an annular or total solar eclipse.
There are numerous eclipse cycles running concurrently
due to the complexity of the lunar orbit. Most popular
of these are Saros cycles of 18 tropical years plus 10
or 11 days. Next comes the Moon's nutation cycle every
18.61 years, and is the average time that it takes for
the head of the dragon, or north lunar node to regress
full circle through the caelestial zodiac. Next is the
so-called "Metonic" cycle, although Meton was far from
the first one to have discovered this very predictable
19-year cycle. The ancient calendars revealed intimate
knowledge of this cycle by its affect on intercalation,
i.e. when an extra lunar month was computed in advance
to make every second or third year have 13 months, not
just 12 months as usual. This intercalation cycle runs
every 19 lunisolar calendar years, following a pattern
so perfect that it is off +two hours every 19 tropical
years like clockwork. Two hours each 19-years added up
to one extra day every 220 years or about ten days per
zodiacal age ergo 10 extra days in 2135 tropical years.
This enabled precise calculation of a calendar decades
in advance by the tribal mathematician, the astrologer.
This allowed ritual observance of seasonal holidays or
holy-days in season and at the right phase of the Moon,
all imperative considerations for calendar calculation,
for planting, harvesting and all religious observances.
We've seen how Earth's tilted axis results in tropical
years, such that 1508 Mayan Haabs is commensurate with
1507 tropical years, meaning 1508 contiguous intervals
of 365 mean solar days apiece total 550,420 solar days
per every 1507 mean tropical years. This intercalation
interval of the ancient Mayan calendar makes 365.24220
average solar days per average tropical year, which is
an hairbreadth from modern averages i.e. less than one
second in time difference per year between ancient and
modern averages for a tropical year. 1 second per year.
^ ^^^^^^ ^^^ ^^^^
We've seen how the heliacal risings of stars & planets
attest to planetary motion in our solar system visible
to the unaided human eye. We've learned how to use the
human hand to estimate subtended angles between planet
and star readily to within one degree of longitude and
latitude, and we know from experience that the best of
naked-eye astronomers can discern as little as one arc-
minute between objects. We've seen how a man can count
by days, months and years to estimate repeating cycles
of the planets, chiefly sidereal years relative to the
Sun and distant stars, and by synodic aspects to Earth
relative to the Sun. We've learned from experience how
one sidereal year on Earth is barely 20 minutes longer
than a tropical year, and that this tiny disparity can
add up over time to the tune of one constellation--one
zodiacal age--every 2,135 tropical years plus 208 days.
There are longer eclipse cycles, like the Inex some 29
years minus 20 days. After this is the exeligmos cycle
of 54 Years plus 34 days, basically three Saros cycles.
There's an eclipse cycle each 58 Years less 40-42 days.
Similar types of eclipses return every 65 Years plus 0
to 3 days. Then there's the triple Inex cycle every 87
years less 61 days. Beyond this is solar totality each
approximately 410 years. Above this, 18 Inex cycles is
521 Years plus or minus 1 or 2 days and is very useful
for making very long-term eclipse predictions. There's
one longer luni-solar cycle which is called the "grand
century of the Moon", and repeats like clockwork every
800 years. Lunar eclipses occulting the "bearded star"
Regulus at 5 Leo recur in predictable, 800-year cycles.
The last series ended in 1943, thus 2510 marks a point
567 years into this 800-year period, which is when the
next eclipsed-Moon occulting Regulus series begins and
lasts 233 more years, with a 19-year plus a 65-year se-
paration between eclipse intervals which overlaps with
metonic cycles of 19 years (235 solunar synods) and by
similar eclipse-type cycles that repeat every 65 years.
So 2510 AD marks the point 567 years + 233 years since
the beginning of the last series in 1710. Backtracking
in time shows that the last complete series ended 1143
AD, preceded by 343 AD, 458 BC, etc. Note here, Ezra's
7th year for king Artaxerxes was from October 2 458 BC
through September 20 457 BC. This was year 3304 in the
proleptic civil calendar which began October 1, 458 BC.
Most notably, 458-457 BC was a grand jubilee year that
always follows a 49th ecclesiastical "spring-to-spring"
year in which all of the land lays fallow by Torah law.
In Ezra 7:6-9 in the old testiment, 1 Abib was Tuesday,
March 26, 457 BC, on which day Ezra left Babylon bound
for Jerusalem--with achaemenid Persian king Artaxerxes'
decree in hand. The first day of the fifth month found
Ezra reaching Jerusalem, which was 1 Ab[Av] 3304, July
22, 457 BC which Ezra confirms is still in the seventh
year of the gentile king as reckoned by the priesthood.
The paramount importance plus astronomical historicity
of these ancient calendar dates is thoroughly analyzed
and documented in my book Historical Calendar Of Jesus,
which, like all of my other books and articles, is pub-
lished into the public domain on these usenet archives.
Daniel Joseph Min
*Min's Planetary Awareness Technique (chapters 1 thru 6):
*Min's Official PGP Public Key on the MIT server:
*Min's Home Page On The World Wide Web:
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"Nomen Nescio" wrote in message
In article ,
24 Aug 2003 00:43 +0200 elhead (Cash) spake:
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ANY MODERN ASTRONOMY program will work for this lesson.
Good article. You really can see those planets just like this guy sez.
I tried it on my computer " sky map, " and it works. I'll be a monkey's
So you are amazed and delighted that a program designed to show the
positions of the stars and planets shows the positions of the stars and
planets--and are vastly impressed when someone says that program designed to
show the positions of the stars and planets shows the position of the stars
You're either one easily impressed hombre, or a vacuous dolt. Pick one.
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