Posições actuais dos planetas
22-Mai-2015, 11:31 UT/GMT | |||||
Sol | 1 | 4'24" | 20n22 | ||
Lua | 24 | 39'55" | 16n21 | ||
Mercúrio | 12 | 42'26"r | 22n35 | ||
Vênus | 15 | 40'31" | 25n15 | ||
Marte | 7 | 17'25" | 21n56 | ||
Júpiter | 15 | 23' 3" | 17n04 | ||
Saturno | 1 | 40'51"r | 18s21 | ||
Urano | 18 | 54' 1" | 6n49 | ||
Netuno | 9 | 41'55" | 8s39 | ||
Plutão | 15 | 15' 0"r | 20s32 | ||
Nodo Lun.true | 8 | 31'48"r | 3s23 | ||
Quíron | 21 | 4'15" | 0n37 | ||
Explanations of the symbols | |||||
Mapa do momento |
The ordinary two-person composite chart is calculated from the birth charts of two people and gives information on the nature of the relationship between them. In principle, the composite chart can be erected for any kind of relationship, i.e. not only for love relationships but also for friendships, work relationships, for people we have trouble with, or even for enemies, such as Sharon and Arafat etc.
Similar uses are possible for the 'multi-personal composite' or, in short, 'multi-composite' chart. The multi-composite method provides charts for triangular relationships such as love triangles, family charts or group charts for work colleagues or friends. Particularly interesting: It is possible to examine how the dynamics within a group change when a new member joins or an old member leaves the group.
The usual two-person composite chart is calculated as follows: The Sun of the composite chart is located exactly in the middle of both natal Suns of the people involved. We can call this point 'midpoint', 'mean value' or 'balance point'. The other planets in the composite chart are calculated in the same way: They are midpoints or mean values of the birth position of the respective planets.
Venus and Mercury, however, constitute a special situation. In the 'real' sky, these two planets can never be more than 45 degrees away from the Sun. However, the composite position can occasionally more or less oppose the Sun. In such cases, some astrologers prefer moving the respective planet to the opposite side of the chart (a shift of 180 degrees).
There are two methods for calculating the MC, Ascendant and houses in the composite chart. The so-called 'reference place method' takes the mean value of the Midheaven, and from that the Ascendant and houses are calculated for a certain reference place of which only the geographic latitude is taken into account. A suitable reference place would be the place where the relationships of both partners "takes place" or "happens".
The other method, the so-called 'midpoint method', calculates the mean values for MC, Ascendant and house cusps individually. This method does not need a reference place.
Astrodienst offers both methods.
How can we extend the method of the composite chart to more than two people? Unfortunately, the situation in this case is more complicated. Two techniques are at our disposal which result in different charts. With two people only, they result in the same chart: the ordinary two-person composite chart.
So, in the two-person composite chart, the position of the Sun is calculated as the mean value of both natal Suns, the position of composite Mercury is the mean value of both natal Mercuries, etc. In concrete terms, the positions of both natal planets are determined by degrees between 0° and 360°, they are added up, and the result divided by two. The resulting point / position is, however, only one of two possible solutions. The other point is exactly opposite. For the composite chart, we choose the point which is closer to both natal planets.
We could be tempted to use exactly the same method for calculating a composite chart for three or more people: Take the degrees of the three natal Suns, add them up and divide them by three. However, the result makes sense only in some cases while in others it doesn't make sense at all.
An example: |
Three people with their Suns at |
10° (10° Aries) |
60° (0° Gemini) |
350° (20° Pisces) |
420° : 3 = 140° (20° Leo) |
This solution obviously doesn't make sense. The correct point would have to be inside the area of the three natal Suns, i.e. at around 20° (20° Aries).
What's wrong here? Why does it not work? The problem is that the result depends on the reference point from which we calculate. In the example, this is the vernal equinox, i.e. 0° Aries. However, if we calculate it starting from 20° Pisces (=350°), we get the correct result:
10° - 350° | = 20° |
60° - 350° | = 70° |
350° - 350° | = 0° |
90° / 3 = 30° | |
30° + 350° = 20° Aries - correct! |
It turns out that our example has three possible solutions, depending on the reference point we choose:
Reference point | Solution |
60° < r <= 350° | 20° Aries |
350° < r <= 10° (370°) | 140° (20° Leo) |
10° < r <= 60° | 260° (20° Sagittarius) |
So, no matter from which point we start the calculation, we always end up with one of three points which are 120° apart.
Now, we remember that there are two symmetrical points in the two-person composite chart of which we have to select the more suitable one. The more suitable one is the one closer to the natal planets involved. The multi-composite works in a very similar way. However, with three people, there are three possible symmetrical points at a distance of 120° from each other. Each of these balances, in a way, the three Suns that participate in the composite chart. The point at 140°, for example, is 210° away from the Sun at 350°. If we add both distances, from this point to the other two Suns, we also get 210° (80° + 130°). Similar calculations are possible for each of the three symmetrical points. This leads to the assumption that all three symmetrical points are astrologically relevant in some way or another, and still, it is obvious that the point at 20° is the most important one.
The same phenomenon occurs with a larger number of people. There are always as many symmetry points as there are persons making up the composite chart. So, with n people there are n symmetrical points which are at a mutual distance of 360°/n.
How do we find the correct symmetry point so that we can draw it into the chart as the composite Sun? In order to find out, we can do the following for every symmetrical point: Calculate its distance from each of the natal Suns, take the square of each distance and add up all squares. Do this for all symmetry points. The composite point you're looking for (i.e. the "mean value of the Sun") is the symmetry point of which the sum of all squared distances is smallest.
This is our concrete procedure when we calculate a multi-composite chart. However, the method can also be defined more simply like that:
The composite point is that point in the zodiac for which the sum of the squared distances to the natal planets involved is minimal.
Or, more technically:
The composite point is that point in the zodiac for which the standard deviation of the natal planets involved is minimal.
Applying this technique to two people results in the ordinary two-person composite chart.
To illustrate this method, here's a thought experiment: We have a rod, 360 cm in length, with the 360 cm corresponding to the 360 degrees of the zodiac. This rod is made of ultra light metal and has virtually no weight at all, but at the same time is very strong and inflexible (comparable to the material UFO's are made of). We now attach three identical weights to this rod at the appropriate zodiac degrees, the weights representing the three natal Suns. Now, we try to balance this rod on one finger. The question is: at which zodiac degree would we have to put the finger in order to keep the rod in complete balance? This is the sought-after balance point (or mean value). An Example: Three people have their natal Suns at 0° Aries, 0° Gemini (60°) and 0° Libra (180°). The balance point is at 20° Gemini (80°).
However, this thought experiment doesn't illustrate the multi-composite chart well enough. In actual practice, the rod would only give the correct symmetry point in a third of all cases, in all different cases it would give the wrong one. Let's take the example we used before: For the three Suns at 10°, 60° and 350°, we would get the symmetry point at 140° (the same as further above), which is not correct. In order to get the other symmetry points, the beginning of the rod has to fall on a different zodiac degree. If we choose the scale on the rod so that it reaches from 350° to 350°, we will get the correct result: the composite Sun at 20°.
Of course, a comparable composite machine can also be constructed with terrestrial materials, not only with extra-terrestrial ones. The construction will, however, be more complicated, because we have to make sure that the weight of the rod doesn't carry any weight.
For the other possible procedure, we put ourselves in the centre of the zodiac, we place the three natal Suns in their respective positions and find out into which direction they are pulling us. There is also an easy way of building a mechanical multi-composite calculator: Take a circular metal disc and drill a hole exactly in the centre. Draw up the zodiac around the outer edge. Then hang it up at a nail on the wall. Three (or n) magnets of the same weight represent the Suns of the three (or n) people involved. Place them on the disc at their respective zodiac positions. The disc will now start to turn and level off in a certain position with the centre of gravity taking the lowest position. The point in the zodiac which levels off in the lowest position is the sought-after position of the composite Sun. The same procedure can be applied to all other planets.
In order to calculate the thus found composite planets, it is necessary to convert the zodiac positions of the natal planets into vectors (arrows from the centre of the circle to the respective planetary position) and add them up. The direction of the resulting vector points to the composite planet.
If this procedure is applied to two people, the result is again the usual two-person composite. This method leads to the same two-person composite as the previously described 'mean value' or 'balance point' method. However, if applied to three or more people, the two techniques result in different charts!
This can be illustrated by an example. Let's assume we have two natal Suns at 0° and 180°. According to the gravity method (vector addition), the two opposing Suns cancel each other out. If they were on the circular disc, it could be stopped at any arbitrary point, because the disc's centre of gravity would be exactly in the centre. If we now add a third Sun at 60°, our disc will turn in such a way that the third Sun will level off at the lowest point. In other words: In this case, the composite Sun would be at the same position as the natal Sun of the third person, that is 60°.
What result would we get if we used the mean value method?
We add 0° + 60° + 180° = 240° and then divide
the sum by three: 240° / 3 = 80°.
This happens to be the most convenient of the three symmetry points. (The other
two are at 200° (= 80° + 120°) and at 320° (= 80° + 120° +
120°).)
So, the composite Sun is at 80° with this method, whereas it is at 60° with
the gravity method.
We can therefore conclude that there is only one type of composite chart for two people, but two different types for three or more people.
Of course, the question is, which procedure will stand the
test of experience; and it is well possible that - as so often
in astrology - both variants will
find their followers. Astrodienst prefers the 'mean value' or 'balance
point' method. However, web users are also given the possibility
to experiment with the 'centre of gravity' method.
(Extended Chart Selection -> Type of chart: Multi-Composite)
There is also a theoretical criterion which would favour the 'mean value' or 'balance point' method. An example: We want to calculate a composite chart for three friends, two of them with a near exact opposition of their natal Suns, e.g. in Aries and Libra. The third friend has a Gemini Sun. According to the gravity method Aries and Libra would cancel each other out, and the composite Sun would therefore be in Gemini. In other words, the composite Sun is determined exclusively by the third person, the Gemini. But would Aries and Libra in real life cancel each other out in a relationship of three? And only the Gemini would dominate?
It is also possible to adjust the calculation even more to the 'physical' realities by taking into account the ecliptic latitude of the planets and the real gravitational forces of the celestial bodies which depend on the distance of the planet from Earth. This method results in yet another composite chart, even for the two-person composite! However, we consider this method rather unastrological, since distance and gravity are usually not factors which are taken into consideration in astrology. Heavy Jupiter, light-weight Mars and ultra-light-weight Pluto all carry the same weight in astrology. The respective distances from Earth are not used in astrology either.
The positions of composite planets can also be "stable" or "unstable" in the sense that they react strongly or only mildly to the joining or leaving of one person. An example: If we have a composite chart of four people whose Suns roughly make a Grand Cross, the resulting distribution won't give a strong tendency towards any particular direction. The position of the composite Sun is then 'shaky'. If now a person joins or leaves the group, the new composite Sun can shift considerably. A counter-example: If we have four people with Gemini Suns, there is a definite common tendency towards a composite Sun in Gemini. A person joining or leaving will now only have a relatively small effect on the composite Sun, i.e. it will not shift considerably.
Accordingly, group horoscopes can be very stable or unstable in themselves. If all planets have a stable position, the addition or removal of one person will change the composite chart very little. However, if several planets are unstable, the chart will change dramatically.
Consequently, the composite chart is a very interesting tool for researching group dynamics and changes caused by a person joining or leaving a group.
© Astrodienst 2007, Dieter Koch, Alois Treindl
Posições actuais dos planetas
22-Mai-2015, 11:31 UT/GMT | |||||
Sol | 1 | 4'24" | 20n22 | ||
Lua | 24 | 39'55" | 16n21 | ||
Mercúrio | 12 | 42'26"r | 22n35 | ||
Vênus | 15 | 40'31" | 25n15 | ||
Marte | 7 | 17'25" | 21n56 | ||
Júpiter | 15 | 23' 3" | 17n04 | ||
Saturno | 1 | 40'51"r | 18s21 | ||
Urano | 18 | 54' 1" | 6n49 | ||
Netuno | 9 | 41'55" | 8s39 | ||
Plutão | 15 | 15' 0"r | 20s32 | ||
Nodo Lun.true | 8 | 31'48"r | 3s23 | ||
Quíron | 21 | 4'15" | 0n37 | ||
Explanations of the symbols | |||||
Mapa do momento |