posted January 07, 2008 04:52 PM
Glaucus ~I don't know if I still have a copy of my Tables of Houses (they were essential in the 70's, but not now
) -- these calculations seems a little bit involved.....
"CALCULATION
To obtain the East Point is simple. Use your standard Table of Houses (Placidus, Koch, Campanus, whatever system you prefer). Once you have calculated the correct local sidereal time of birth (LST), find that LST in your Table of Houses. Rather than looking to the latitude of the birth you are interested in, go to zero latitude (the Equator). Interpolate as necessary to obtain the Ascendant at zero latitude for the exact local sidereal time. (As indicated, the East Point can also be called the Equatorial Ascendant.) If your Table of Houses does not include zero latitude, there is an alternative method. Add six hours to the correct local sidereal time (LST) of birth. This rotates the Midheaven exactly one quarter of the circle. (The East Point can also be defined as 90 degrees east, along the Equator, of the intersection of the Meridian with the ecliptic.) For that LST (six hours later), perform any necessary interpolation to calculate the Midheaven. That Midheaven (six hours later) is the correct East Point.
The Antivertex is slightly more complicated to calculate.
1. Subtract the latitude of birth from 90 degrees. Call your answer the co-latitude.
2. Add 12 hours to the LST of birth.
3. Take the LST from Step #2 into the Table of Houses as if you were going to calculate the house cusps from it.
4. Look for the Ascendant for that LST at the co-latitude. Interpolate as needed.
5. The result is the Vertex. The Antivertex is directly opposite (same degree and minute; opposite sign).
A variation is:
1. Same as above.
2. Note down the IC of the chart.
3. Find that IC in the Table of Houses AS IF it were a Midheaven.
4. Find the Ascendant for THAT Midheaven (which was originally the IC of the chart) at the co-latitude. Interpolate as needed.
5. Same as above.
For those who prefer working directly with trigonometric functions, the formulae for these angles are:
East Point = arctan (cosST/(-sinST * cos obl))
Vertex = arctan ((-cosST)/(sinST * cos obl-sin obl/tanlat))
Antivertex = Vertex +/-180 degrees
Where obl is obliquity and lat is latitude and ST is local sidereal time, and the quadrant of the answer can be determined from the algebraic signs of the answer and the numerator in the arctan.
Is there an astro program that will calculate the East Point for you??