To reiterate the major planetary factors, most GQs are composed of:
1. the Moon;
2. Mars and/or one or two of the Sun, Mercury and Venus;
3. one or both of Jupiter and Saturn; and/
4. one or both of Uranus and Pluto, with Neptune as a rather distant third possibility.
A GQ is a synchronization between five planets in which each member is essential. For such a precise multi-planet configuration to occur, a number of optimal conditions must be met. Some planets in some signs are more likely to meet the necessary criteria than others. Without pretending to a sophisticated understanding of celestial mechanics, examination of the above tables and graphs has allowed me to form a few hypotheses around what these criteria might be.
Firstly, the role of the Moon: Luna appears on an "as-need" basis to fill in the gap wherever required. As the planet of nurture, this is not surprising in astrological terms. In this 2,500 year sample she appears most frequently in Pisces by default simply because the other planets, working in concert, are more able from their various perspectives to fill in the pentangle from other points of the zodiac.
Next, the outer planets, as stabilizing factors, are essential to these patterns. Very few GQs manifest without at least one of them. This is just as likely to be Uranus as Pluto - in fact more likely. (Neptune is another matter, as will be discussed below.) It is interesting to note that neither of the 6-day-long GQs of 190 and 952 include either Neptune or Pluto, but both include Uranus, which moves slowly enough for the rest of the participants to fall into place around it.
When Uranus and Pluto are both in play the odds of a GQ forming are strengthened by the advantage of not just one, but two, slow-moving anchors. Pluto's highly elliptical orbit is an obvious factor in determining the overall sign pattern of any GQ of which it is a member. Although it actually spends the most time in Taurus, in GQs it turns up much more often in Aries, followed by Pisces. This must be at least partly due to its interaction with Uranus.
We know that Uranus is most often found in Gemini or Capricorn in these pentagrams. This is a perfect set-up for Pluto in Aries to form a quintile with Uranus in Gemini or a bi-quintile with Uranus in Capricorn. While this is only one possible scenario it does seem that the interlacing orbits of Uranus and Pluto - with Mars - have the highest probability of any planetary combination of meeting each other in fifth harmonic formation.
Now: Mars! I believe the reason why Mars is the most dominant planet in GQs is that it moves fast enough to intercept the quintile patterns forming between more distant planets but not so fast that it disappears before the Moon has a chance to fill in the gap. Especially while doing its retrograde dance, it stays in place long enough to wait for the inner planets to catch up. Furthermore, after Pluto, Mars has the most elliptical orbit, and happens to spend the most time in Leo, where it is poised to make a quintile to Uranus in Gemini or a bi-quintile to Uranus in Capricorn.
The riddle of the Mars/Uranus connection may be susceptible to simple arithmetic. A division of the 84 year orbit of Uranus by the 1.88 Earth years of the Martian year gives 44.7. Therefore 45 Mars cycles divide almost equally by 5 (the quintile number) into one Uranus cycle. This must mean something in terms of planetary motion!1
Jupiter and Saturn are steady players in this game. They may not move quickly enough to make the impact of Mars but they are much faster than the transpersonal planets and so are in a reasonably good position to catch up with Uranus and Pluto as required. They are, after all, the social planets, mediators between the inner and outer realms. In a pinch, Jupiter and Saturn can assume the anchoring role usually held by the outer planets. They are both present, not surprisingly, in all four of the GQs without transpersonals.
Early fall seems to be the most likely fill-in-the-blank time for whichever fourth point of the pentangle is missing while the other three participants wait for the Moon. It is notable that Mercury and Venus are most often to be found in Libra in GQs, precisely when Pluto is at its least visible. Saturn (and Neptune) is also quite common in Libra, and all three of Mercury, Venus and Jupiter are conspicuous in Virgo.
The inner planets move too quickly to be determining factors in the overall picture. Because GQs rest on the basis of the slower-moving planets from Mars out to Pluto, Mercury and Venus are more or less incidental to their formation. They crop up wherever they happen to be needed and they happen to be needed most in Libra and Virgo. However they are more likely to be able to fulfil a need than the Sun.
I no longer find it mysterious that the Sun is the least frequent member of these pentagrams. Since it is always direct in motion it has even less chance than Mercury of being in place long enough to connect with the pattern. It is not fast enough to play the role of the Moon and not slow enough to do anything else. The Sun, it seems, has better things to do than dance with his lieutenants!
Now as for the question of why GQs peak in the time of Leo, here's the only answer that makes sense to me. I think it has nothing to do with the Sun itself. The critical factor is that Mercury, Venus (and Mars, for that matter) travel close enough to the Sun that if any of them land on the point of a GQ the Sun will probably be nearby. We know that Mars is weighted in favour of Leo by its length of stay in that sign. Both Mercury and Venus do well in Leo while they are scrambling towards their peak occurrence in Libra.
This is facilitated by the action of Uranus and Pluto, neither of which is prominent in July. Pluto is strongest in winter and Uranus in spring and fall. So with the outer planets busy in, say, Aries and Scorpio, this often leaves Leo to Mercury/Venus/Mars. The combined presence of these three planets in Cancer/Leo/Virgo must be enough to tip the balance if favour of a midsummer Sun. This leaves us Neptune to decipher.
1. I would be most grateful to the astronomer/astrologer who could verify or discredit any such non-scientific speculations in this paper!
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