Ancient Astronomy

Reading Graham Hancock's latest book The Magicians of the Gods, I came across a reference to the humble 3:4:5 right-angled triangle and its connection (according to him) with the precession of the equinoxes and the Great Year. The connection he draws is this:

The cube of 3 is 27, the cube of 4 is 64 and the cube of 5 is 125. The sum of 27, 64 and 125 is 216. One astrological age comprises 2160 years. He argues that ancient astronomer/astrologists were aware of this connection and incorporated 3:4:5 into the siting of the structures that they built. Use was made of the two acute angles that comprise a 3:4:5 triangle, namely 51.13˚ (arctan 4/3) and 36.87˚ (arctan 3/4).

He cites Harran, a major ancient city of Upper Mesopotamia, as an example. It is situated at 36.8631° N in modern day Turkey.

He goes on to mention the Ziggurat of Ur (a Neo-Sumerian ziggurat in what was the city of Ur near Nasiriyah, in present-day Dhi Qar Province, Iraq) situated at 30.9628° N. According to Hancock, the two cities of Ur and Harran were closely linked in ancient times but how is an angle of 30.9628° linked to the 3:4:5 triangle? Well, at this point Hancock introduces the notion of colatitude. This is defined by Wikipedia to be: in spherical coordinates, colatitude is the complementary angle of the latitude, i.e. the difference between 90° and the latitude, where southern latitudes are denoted with a minus sign. So the colatitude of Ur is 59.0372° which is arctan(5/3) in degrees. Thus the 3:4:5 triangle is involved, albeit indirectly.

Note these connections hold regardless of the system of angular measurement used (degrees, grads, radians or whatever). There are other sites he mentions, such as Baalbek in Lebanon, situated at 34.0047° N that don't have any apparent connection to 3:4:5 but I'm sure I could find one if I set out to do so. At the moment, I'm still a little skeptical and will need to test it out with the location of other ancient sites. If the majority prove to have some direct or semi-direct connection, then there may be something in it.

Getting back to the Great Year, the number 43200 = 2160 x 20 is mentioned as significant because of its connection to the dimensions of the Great Pyramid. Hancock states in his book that the polar radius is 43200 times the height of the Great Pyramid and that the circumference of the Earth at its equator is 43200 times the perimeter of its base. Let's try to verify those figures.

The height is a bit of problem because now its only 138.8 metres high due to erosion and the absence of its pyramidion whereas it was originally 146.5 metres high. Let's go with the latter figure. The polar radius of the Earth is 6356.8 kilometres and so 146.5:6356800 --> 1:43391 which is reasonably close but far from exact. Let's try the circumference. The perimeter of the base of the Great Pyramid is given as 4 x 230.4 metres, while the equatorial circumference of the Earth is 40,075 kilometres. The ratio 4 x 230.4:4007500 --> 1:43465. Again this is close but by no means exact.

To get some idea of the discrepancy involved, consider that a height of 147.15 metres gives a very close approximation to the exact ratio. This is a difference of about 65 centimetres, so looked at in this way the difference is very slight. With the circumference ratio, a base side of 231.92 metres gives a very close approximation and this represents a difference of only 1.52 metres, which again isn't much. The thing is of course that when multiplying a much smaller numbers by 43200, small increases or decreases in those numbers become greatly magnified. Thus we need to lenient about exactitude, especially given that we are working only with what we think were the original measurements.

There's been a great deal written about the mathematics of the Great Pyramid and I don't want to go any further into it at this point. There's a danger in playing around with numbers that you can find connections to anything you want. It could be that what's being encoded into the pyramid is just the squaring of the circle and if that's the case then it's just a coincidence that the scale factor of 1:43200 happens to have a connection with the precession of the equinoxes (43200 = 2160 x 20). The perimeter of the base of the pyramid (4 x 230.4 metres) when considered as the circumference of a circle gives 3.145392491467577 when divided by twice the height of 146.5 metres, the length of its diameter. This can be compared to the actual value of π = 3.141592653589793 ... and it is seen that the accuracy is only good to two decimal places. Link to more about 432.

The "heartbeat" of the Great Year as Hancock emphasises is the number 72. This is the number of years that it takes the vernal equinox to precess by one degree. From this other numbers of apparent significance derived. For example, 72÷2=36, 72+36=108 and 108÷2=54. I'm learning a lot from Hancock's book, not least of all about the Younger Dryas Boundary or YDB as it's known. I'm sure that I'll learn a lot more as I make my way through the rest of the book.

The Fixed Stars in Astrology

Over the years I've not paid much attention to the fixed stars in my astrological analysis. Astrolog of course makes it easier to include a large number of them, so many in fact as to be overwhelming. There are four so-called royal stars that "were regarded as the guardians of the sky in approximately 3000 BCE during the time of the Ancient Persians in the area of modern-day Iran. The Persians believed that the sky was divided into four districts with each district being guarded by one of the four Royal Stars" (Wikipedia).

The four stars with their modern and ancient Persian names are:

• Aldebaran (Tascheter) – vernal equinox (Watcher of the East)
• Regulus (Venant) – summer solstice (Watcher of the South)
• Antares (Satevis) – autumnal equinox (Watcher of the West)
• Fomalhaut (Haftorang/Hastorang) – winter solstice (Watcher of the North)

At the time of my birth, these stars were situated as shown:

As can be seen, Saturn (0d01m Virgo) is conjunct Regulus (29d07m Leo) while Chiron (8d57mR Sagittarius) is conjunct Antares (9d03m Sagittarius) and opposite Aldebaran (9d05m Gemini). Regulus entered Virgo in late 2011 and is now in 0d05m of that sign. Antares and Aldebaran have moved forward about a degree, to 10d01m Sagittarius and 10d03m Gemini respectively. A peculiarity of the Astrolog program when viewing transits is that it only shows the progressed positions of the stars in the inner circle where the natal planets are located. 

It would seem then that three out of the four royal stars are influential in my natal chart. It might be time to explore the significance of their positions. The following notes are from ASTROTHEME but largely based on Vivian Robson's book "Fixed Stars":

Aldebaran, Alpha Tauri, 9°55' Gemini, in the left eye of Taurus (Oculus Tauri australi), from Al-Debaran, the follower, or the Eye of God, or Pallilitium, or the Small Torch, Facula, or Stella Dominatrix: according to Ptolemy, Aldebaran is of the nature of Mars and brings about firmness, courage, integrity, and strength. Honours and wealth may be favoured, but Aldebaran usually tends to withdraw what it offers since durability is not its feature. Robson mentions danger, violence, and illnesses. Like Algol, when Aldebaran is in conjunction with the Sun, the Moon, the ruler of the Ascendant, sometimes when it is on the Ascendant or ruler of the 8th House, it may cause a violent death, according to Garcoeus. 

Regulus, Alpha Leonis, 29°57' Leo, the Lion's heart (cor Leonis) from El-Maliki, the Royal one, Regulus or Basiliscos, the little king, or Regia Stella, or Monoualos: according to Ptolemy, Regulus is of the nature of Mars and Jupiter, according to Fludd, of the nature of Jupiter and Mars, and according to Julevno, of the nature of Mars. Regulus brings violence, destruction, and short-lived martial honours, prison and violent death, if it is not well-aspected. It endows with courage and the will to reign, ambition, and the thirst for power, and it may bring about might and independence. This star is very active and strengthens the planet it touches, for better or for worse... 

Antares, Alpha Scorpii, 9°53' Sagittarius, in between two other stars in the body (media in corpore trium), or Kalb Akrab, the Scorpio's heart (cor Scorpii), Mars' rival: according to Ptolemy, Antares is of the nature of Mars and Jupiter, according to Fludd, of the nature of Saturn and Mars, and according to Julevno, of the nature of Mercury and Mars. According to Fludd, Antares gives violence, ambition for power, and greed. According to Robson, it brings about self-destruction through one's own obstinacy. According to Julevno, it causes success through efforts, followed by ruin and death. This star is almost as evil as Algol, and it is dangerous when it is in conjunction with the Sun, the Moon, the ruler of the Ascendant, the ruler of the 8th House, or when it is dominant on the Ascendant. It is all the more so if it is not well-aspected. If Antares is in very good celestial state, without dissonance, it may nonetheless bring about honour through courage and efforts. 

Fomalhaut, Alpha Piscis Australis, 3°59' Pisces, the star of the mouth at the beginning of the water (in ore, atque eadem, quae in extrema aqua), from Fom-Al-Hut, the mouth of the fish: according to Ptolemy, Fomalhaut is of the nature of Saturn and Mercury, according to Fludd, it is of the nature of Saturn, whereas according to Leowick, it is of the nature of Saturn and Jupiter, and according to Argol, it is of the nature of Venus and Mercury. Fomalhaut may bring wealth, power, fame, and honour. It may also endow with a not too materialistic temperament and gives a spiritual orientation if it is well-aspected. When it is adversely-aspected, Fomalhaut may give a malicious character in order to achieve a sublime objective: the end justifies the means becomes one of the individual's rules.

These descriptions are clearly dated and not all that helpful but it's a start. I suspect the influence of these stars on the planets with which they are conjunct is subtle and far less dramatic than the above descriptions assert. What can be said is that Saturn is closely linked to Regulus in my chart and Chiron to Antares and Aldebaran.

Regulus, the Great Pyramid and the Great Year

I was watching a two part video on YouTube concerning the mathematics and astrology inherent in the Great Pyramid. The second video focuses on the astrological aspects of the pyramid and the commentator says that the two diagonals of the square base correspond to the four fixed signs of the zodiac: Taurus-Scorpio and Leo-Aquarius. Taurus is represented by a bull and Scorpio by an eagle; Leo is a lion and Aquarius as a human or an angel in human form. The sphinx is a human-lion hybrid and thus represents Aquarius and Leo. The commentator goes on to say grandiloquently that "when the Sphinx's eyes line up with the star Regulus, the Lion's Heart, then a new cycle of the equinoxes begins".

In 8786 BC or 10804 years ago (as of 2018), Regulus was aligned with the vernal equinox but this is not to say that 0˚of the sidereal zodiac begins here. What if this marked the point between the constellation of Leo and Cancer? After all, it is from just such a point that the planetary rulerships are assigned in the tropical zodiac.

On this basis, the ages would proceed as follows:

-8786 --> Cancer: Earth Mother worship
-6626 --> Gemini
-4466 --> Taurus: Bull worship
-2306 --> Aries: Ram worship
  -146 --> Pisces: Christianity
 2014 --> Aquarius: The Age of Man
 4174 --> Capricorn

It's not unreasonable to view the confluence of the vernal equinox and Regulus, the Lion's Heart, as marking the real beginning of Leo rather than the equinox's arrival at some ill-defined boundary between Leo and Cancer. Interestingly, this means that just about now the Age of Aquarius is dawning. It's a possibility.

Online Astrological Charts

Reading about Google's Pixelbook that runs the Chrome OS, I was thinking what would I do if I were using this as a laptop. I wouldn't be able to run Astrolog under WINE as I do on my Macbook. So what are the online options for constructing astrological charts and following the transits to such charts. I thought I would do a little investigation.

I first looked at ASTRODIENST that freely creates a reasonable-looking chart as well as a detailed summary of aspects, chart positions and so on. Here is the chart:

The summary is provided as a PDF file (I've taken a screenshot here):

The houses are created using the PLACIDUS system and can't see how to change them to KOCH houses. Transits to a chart can be calculated for any given time as shown but a new chart has be generated for every change of time:

There's even an interesting astro-twin feature that will locate persons in the ASTRODIENT database that were born on the same date as you. There were three such persons but none with an Aries Ascendant. Overall, what's provided is quite reasonable for a free service.

Astro-Charts also calculates natal charts and the house settings can be adjusted from the default Placidus to Koch. Here is the result for my chart:

A summary of planetary positions and salient aspect patterns follows this chart. Transits are analysed but not displayed in a visual format.

AstroApp runs in the browser and offers a pop-up window with an enormous range of options. However, most require a subscription but a basic chart can be drawn up for free. Here is a link to a list of astrology software that will run under Linux.

Summer Solstice 2017

Here is the Greenwich-based chart for the Southern Hemisphere's Summer Solstice and Northern Hemisphere's Winter Solstice:

What's particularly noticeable and applicable world-wide is the very close conjunction between the Sun and Saturn in Capricorn. Here is the timetable of Saturn's passage over the next few years:

Saturn will occupy the sign of Capricorn from December 19, 2017 --> March 21, 2020; and then finishes up its transit from July 1 to December 17, 2020. Here are some key dates:

• December 19th, 2017 - Saturn enters Capricorn 
• March 21st, 2020 - Saturn enters Aquarius 
• July 1st, 2020 - Saturn Rx enters Capricorn Dec 17, 2020  Saturn enters Aquarius

Of course Pluto has been in Capricorn for quite some time now, entering most recently on January 26, 2008, at 2:50 AM in Greenwich Mean Time and "because of retrograde motion, Pluto backed into Sagittarius on June 14, but re-enters Capricorn on November 27, to stay in this Zodiac sign until March 2023, making its first entry in Aquarius on March 23.
So we have some fifteen years of Pluto in Capricorn" (taken from this site).

Saturn will be conjunct Pluto on January 12, 2020 at 22d37m (for one time only during the current cycle). The period around this time should be pivotal in ushering in a new world economic order.

Synodic Periods

A friend of mine had noticed that significant events or changes in a person's life occurred at 47 years of age. I decided to see what Wikipedia had to say about the number 47 and was surprised to discover the following:

The 47-year cycle of Mars: after 47 years (22 synodic periods of 780 days each), Mars returns to the same position among the stars and is in the same relationship to the Earth and Sun. The ancient Mesopotamians discovered this cycle.

The synodic period is defined as "the amount of time that it takes for an object to reappear at the same point in relation to two or more other objects ... the time between two successive oppositions or conjunctions is also an example of the synodic period." Source. In the case of Mars, the 47-year cycle relates to the positions of Mars and the Sun. After 47 years years, the Sun and Mars should return to their original positions. My calculations showed that the exact figure is 46.97856377 years which seems close but is actually almost eight days less than 47 years. Further calculations revealed that there is a much closer alignment after 79 years or 79.00940271 to be more exact. This turns out to be about 3.43 days past the 79 years.

It's a fairly easy matter to set up the calculations in a worksheet. The formula is:

where SP1 and SP2 are the sidereal periods of the two bodies of interest. The sidereal period by the way is "the amount of time that it takes an object to make a full orbit, relative to the stars." The table below, copied from my worksheet, shows the sidereal and synodic periods for the various planets.

The multiples of these synodic periods when divided by 365.24217 give the number of years that have elapsed. When the number is very close to an integer, it means that the configuration between the two planets at time zero recurs near the same point in the zodiac. For example, such a conjunction between Venus and Mars recurs after 31.99799406 years which is very close to 32 years (about 0.73 days less to be precise). The synodic period of Venus and Mars is less than a year (333.9 days) and for someone like myself, with the two planets conjunct, it is important but because of its frequency there is a tendency to undervalue its significance. The synodic cycle becomes more meaningful when viewed as part of a larger, "super-synodic" cycle in which the two planets return to the same relationship but in close proximity to their original zodiacal positions.

For Venus and Mars, this larger super-synodic cycle involves 35 synodic cycles and, because the prime factors of 35 are 5 and 7, the 5th, 7th, 10th, 14th and so on cycles become particularly important. They resonate with the larger cycle while the others (2nd, 3rd, 4th, 6th, 8th and so on) do not. Other patterns emerge: the 14th/15th and 20th/21st cycles form twin resonating pairs and occur after 12.79919762/13.71342603 years and 18.28456803/19.19879644 years. The next pairing is the 49th/50th and 55th/56th occurring after 44.79719168/45.71142009 years and 50.28256209/51.1967905 years. In the life of an individual with Venus and Mars conjunct in the natal chart, the periods around the 44th/45th and 50th/51st birthdays should be significant, especially in terms of relationships. I can assure you that they were.

These resonating cycles can be applied of course to all super-synodic cycles. For example, the 47 year synodic cycle of the Sun and Mars occurs after 22 cycles. The factors of 22 are 2 and 11 so every even numbered cycle is resonant but so is the 11th. This means that the 10th, 11th and 12th cycles are all resonant and thus the energy of the Sun-Mars relationship will find emphatic release during the period from 21.35389262 through 23.48928189 to 25.62467115 years. This is illustrated in the diagram below:

For someone like myself with Sun conjunct Mars, this period from my 21st to 25th birthdays was a very energetic time. It is of course for most young people but during this time I was indeed very focused, completing a university degree that I had started years earlier but never finished. After this period, I rapidly lost focus again and never quite summoned up that same level of motivation and concentration ever again. The second time around the 32nd, 33rd and 34th cycles are all resonant corresponding to 68.3324564 through 70.46784566 to 72.60323492 years. Now that I'm approaching my 68th birthday, I'm hoping for a similar infusion of energy. I can only hope my old bones are up to it.

Of course with the outer planets of Jupiter, Saturn, Uranus, Neptune and Pluto, the synodic periods are less frequent. Jupiter and Saturn have a famous synodic period of a little under 20 years that has been linked to the deaths in office of United States president taking up office in 1960, 1940, 1920 etc. This pattern of deaths is known as the Curse of Tippecanoe or Tecumseh's Curse (source). While it is not likely that two outer planets will return to their natal positions during the life of an individual, their return would be important in mundane astrology.

Autumn Equinox in Brisbane

The above chart shows the configuration of planets at the time of the 2017 Autumn Equinox in Brisbane, corresponding to the Vernal Equinox in the Northern Hemisphere. Since the Northern Hemisphere is the dominant one, the chart marks the official start of the astrological year. Below is the same chart with annotations.

The almost exact ☽/♄ conjunction suggests considerable control and constraints ♄ will be imposed on the public ☽ by governments and their leaders ☉ especially since the two luminaries are in a square aspect ☉ □ ☽. The trine from ♅ to ☽/♄ suggests some help in resisting this control will come from sources independent of governments like Wikileaks. The T-square in cardinal signs between ♃ and ♅ and ♇ is potentially dangerous throughout the year if other transits cross or aspect the three sensitive points. Where ☽/♄ on an angle, the oppression felt by the public should be more acute. In Caracas, Venezuala, the conjunction is at the MC with ☉ on the Ascendant. 

In Beijing and Jakarta, the conjunction is near to but not exactly on the IC with ☉ on the Descendant.