P. Svarogich(English editing by Ed Falis)
Principia of polyzodiacal astrology
|6. Astronomers notes|
6.1 Coordinates of planets for the location
of a born. The correction for parallax.
6.1 Coordinates of planets for the location of a born. The correction for parallax.
The positions of planets on the celestial sphere depend on the observers location. As an extreme but very convincing example it is very easy to see that the geocentric and heliocentric coordinates of the Moon or some planet differ considerably. But even displacement along the Earths surface results in displacements of the planets - or more exactly their images on the celestial sphere. The closer a planet to the Earth, the larger its angular offset when moving an observer along the Earths surface. For the planets nearest the Earth, this offset from a geocentric position, called parallax, is some tens of angular seconds. For the Moon the difference on the celestial sphere can reach almost 2° (Fig. 7).
Fig. 7 Diagram illustrating the origin of the parallax correction for the ecliptic coordinate of the Moon. The local (topocentric) ecliptic longitude of the Moon can differ from the corresponding geocentric longitude by up to 50'. This correction is at its maximum when the Moon is near the horizon, and at its minimum near the celestial meridian.
For medieval astrologers this was not a problem they simply observed the sky. With the appearance of ephemeredes compiled for an observer at the Earths centre, many people have used them without understanding the nature of the coordinates listed in the tables. At that, if the error in the position of planets and Sun is small, for the Moon it can reach one degree. When the Moon is close to the MC, its true position62) (topocentric coordinates) is determined practically correctly by the geocentric ephemeris, but when it is close to the Ascendant or Descendant, its true position is differs from the geocentric one by almost a degree63).
6.2 Direct and retrograde planets. Stationary points.
The comprehensive account of geometric and physical effects in the calculation of the visible motion of the planets not only enables us to improve the accuracy of astrological calculations; it also reveals a number of new phenomena valuable to the astrologer in an interpretive context.
Fig. 8. Diagram of the daily motion of a planet relative to the local vernal point: a) when the planet is direct (prograde) in its ecliptic coordinates; b) when the planet is retrograde in its ecliptic coordinates.
What we see is a change in the direction of a planets motion with respect to the local vernal point from direct to retrograde and vice-versa. The local vernal point oscillates with respect to the usual vernal point (true or mean) with a period of 1 day. This is caused by the daily oscillation of the local ecliptic plane with respect to the astronomical ecliptic. The amplitude of the fluctuation of the local vernal point is not large - only 10'-20'. But the velocity of this fluctuation is so high at times that all planets except the Moon become retrograde for part of the day. For instance, if Mercury is fast direct it becomes retrograde for several hours a day. If on the other hand it is retrograde it becomes direct for several hours a day.
This information can be a powerful instrument for the determination of the effectiveness of various kinds of action during a day in some location. Periods when the local vernal point moves quickly backwards, making even outer planets fast direct, are best for expansion, attack, the propagation of ideas - any activity influencing the surrounding world. Periods of general retrogradation are suited for internal work, contemplation, and heart-to-heart meetings those activities where it is important to listen to ones internal state and to become transparent to outer influences.
When the velocity of the local vernal point changes sign with respect to the usual vernal point, the planets change their direction at times that depend on their own velocities with respect to the stars. Nearly all the planets except the Moon and periodically the Sun, Mercury and Venus, change their directions relative to the local vernal point twice a day.
The most interesting aspect of this is the analysis of local stationary points in the context of symbolic temporal mappings directions and progressions. In conform progressions and directions the local stationary points of planets play a greater role in horoscopes of people for whom planets change their direction in the first 2-3 hours of life. The presence of such points in Ptolemaic-Placidean directions should strongly manifest, since these points require a reorientation of the corresponding spheres of life from expansion to internal development or vice-versa. Such moments could manifest as serious life crises. Similarly, in progressed time analogous changes occur in each sphere of life twice a year.
Observation of such periods in a persons life is of interest since it allows us to sense the difference in interpretation of progressed and directed planetary configurations and the events corresponding to them.
When a planet at a stationary point makes an aspect to a natal house cusp, this should be powerfully revealed by an event. If the stationary point, which can be determined to some minutes of real time using a computer with ephemeredes accurate to 1", does not show in some event, it will still be noticeable subjectively. Most relevant here are calculations not in transit time, but in progressed or directed time. Let us repeat again that for each point on the Earths surface the exact moment of stationarity of a planet is different. The accuracy in determination of the stationary moment of about 1-2 minutes of progressed time corresponds to about one day of transit time64).
6.3 Zodiacal conjunctions.
The full use of the terrestrial zodiac reveals another unusual phenomenon. A planet can be in exact conjunction with a star twice a day throughout a period of several days or even weeks. This pertains to two slow planets as well. Consider the conjunctions of Uranus and Neptune that from a solar zodiacal perspective occurred three times in 1993 (February 2, August 19 and October 25). Since the planets had different ecliptic latitudes, they coincided only in ecliptic longitude. However, the conjunction can take place at other moments using a different definition of longitude. Terrestrial zodiacal longitude is an example. Because of the complex geometry of the terrestrial zodiac even motionless objects on the celestial sphere (e.g. stars) move along the it with varying relative velocities. A consequence of this non-uniformity of motion was that Uranus and Neptune were conjunct in the terrestrial zodiac twice a day throughout all of 199365). Our personal experience shows that these moments of exact conjunction can reveal themselves in events66).
If we consider the fundamental reference point on the solar zodiac, all planets other than Mercury and Venus are always retrograde, and the Moon is always direct. It is interesting to study the stationary points of Mercury and Venus from the standpoint of this fundamental reference point, i.e. those moments when the zodiacal velocities of Mercury and Venus are equal to that of the Sun.
6.4 The Natal horoscope as a multi-dimensional chart.
The use of a zodiacal circle for both psychological study and event calculation illustrates the reduction of the interactions of sensitive points on the two-dimensional celestial sphere to a one-dimensional approach on a zodiacal circle. Marking house cusps (or station cusps or signs) on a zodiac does not make the approach two-dimensional. In our opinion, a two-dimensional approach comprises the simultaneous consideration of two zodiacs. Since planets have a non-zero latitudinal coordinate, i.e. planets are not moving exactly along the local equator of one or another zodiac, they can be in exact conjunction in one zodiac and in the aspect in another. For example, let us examine the horoscope of a person born when Pluto and Uranus were both on the plane of the horizon. For the terrestrial zodiac this means that planets are both in conjunction with the cusp of the 7th station. At the same time they were in a semi-square aspect in the ordinary solar zodiac. Horoscopes of this kind obviously call for special interpretation (Fig. 9).
In addition, as soon as we move to the joint analysis of two events, this consideration takes on an extra dimension. The first event is usually the moment of creation (birth). The second is some event on the world line of the same born. As the second event one can take the event itself, or another on the same world line related to it by a symbolic mapping (progression, direction, or profection).
Practically we try to analyse the second event as it is determined by the preceding event (most often event of birth). We place the elements of the transit or symbolic zodiacal configuration on the zodiacal circle of the natal configuration, thereby equating the two zodiac circles of one central body for the born, but calculated for different points on the borns world line (fate). No new analytical possibilities appear in such a one-dimensional view - we merely consider mutual aspects of the points of both configurations.
A real two-dimensional consideration does yield new analytical possibilities. Let us consider an example that is easily understood by any astrologer. The intersection of a slowly transiting planet or progressed planet to a natal house cusp, particularly the Ascendant, often causes if not an event, a noticeable change in the structure of consciousness of a born (however, such a change still needs to be anchored by an external event). But the conjunction of a planet with the Ascendant does not mean the intersection of the planet with the plane of the horizon, which is the cusp of the first house treated as a two-dimensional station of the terrestrial zodiac. This is connected with the fact that the planets are not in general exactly on the ecliptic (equator of solar zodiac). For example, the Moon or Venus can cross the horizon one hour later or earlier than the time of their conjunction with Ascendant (Fig. 10). The rising of the Moon is defined as the conjunction of the Moon with the cusp of 1st station of the terrestrial zodiac. As another example, transiting Pluto can conjunct the natal Ascendant seven years earlier than it will cross the natal horizon.
Fig.9 Example of the simultaneous consideration of two zodiacs for one birth event. Arabic numerals mark the stations of the terrestrial zodiac.
Fig.10 A view of the celestial sphere near the east point of the terrestrial zodiac. It is easy to see that even with the house cusps marked on the solar zodiacal circle, the one-dimensional view of the solar zodiac gives a deceptive picture of the positions of Pluto and Venus. If we treat this picture as the sky of the natal horoscope, and transit planets move only by changing their ecliptic coordinates, it is easy to see that the ecliptic point of Pluto (its point on the usual solar zodiac) crossed Ascendant some years ago and is now in the first house, whereas Pluto itself is above the horizon within the 12th station of the terrestrial zodiac.
For analysis of such situations it is useful to consider a special chart that we call the "transit in the natal sky". We set a one-to-one correspondence of the zodiacal coordinates of two zodiacs as it existed at the moment of creation. We place the elements (planets) of the event under consideration with latitudes on the first zodiac, and then project the elements of the considered event onto the second zodiac, as if the second zodiac were oriented with respect to the first as it was oriented at the moment of creation. If for the pair, we select the solar zodiac as the first element and the terrestrial as the second, we have the "transit in the natal sky" chart. Such a construction is possible for any pair of zodiacs. The single technical restriction is that it is impossible to take the terrestrial zodiac as the first element of the pair. This is because of the current uncertainty about the treatment of a latitude coordinate in the terrestrial zodiac.
|62. For an observer on the Earths
63. The coordinates giving the true position of a planet for an observer on the Earths surface are called topocentric in astronomy.
64. It turns out to be rather curious to observe oneself on the days of the progressive planet turnabout in ones own horoscope.
65. For Moscow the last such conjunction took place 16 January 1994.
66. Here we mean the events of everyday life.