2
In Morinus the ZD is the arc measured on the Prime Vertical starting from the Zenith or the Nadir, whichever is the smallest, up to the point where the Circle of Houses passing through the position of the planet intersects. Therefore, ZD is related to the Campanian Mundane Position - CMP - (Prime Vertical Azimuth)

ZD is not to be confused with the Real Zenith Distance - | ZDv | -, equal to the 90 ° complement of the Astronomical Elevation: | ZDv | = 90 - | EL |.

Roberto

To Roberto

3
Thanks for the help.I notice that Prime Vertical Distance in Janus program matches Morinus ZD.I have a book by Benjamin Martin who does a Regiomontanus chart by hand.I also recently bought Morin AG book 22 which uses Regio system.I haven't seen ZD used so far in any text.Do you know of a formula to find Regio ZD? Harold

5
A simple method to calculate ZD is to first calculate the Campanian Mundane Position - CMP -. This can be done by a change of coordinates starting from one of the three ones: Equatorial -EqCS-, Ecliptic-EcCS- or Altazimuth (Horizontal) -HCS. After that:

if 360>CMP≥270 ---> ZD = CMP - 270 with prefix Z
if 270>CMP≥180 ---> ZD = 270 - CMP with prefix Z
if 180>CMP≥090 ---> ZD = CMP - 090 with prefix N
if 090>CMP≥000 ---> ZD = 090 - CMP with prefix N

Roberto

To Roberto

6
Roberto-I am not sure what points the 3 coordinates represent.I am working with a chart that has the Sun at 28 38 Scorpio .It looks like EcCS is subtracted from an ecliptic point.Could you explain what is meant by Ecliptic-EcCS? Thanks-Harold

7
Hi Harold,

EcCS means Ecliptic Coordinate System and yes, it's the astrological position in the signs (starting from 0° in Aries).

Given an astrological chart, let me try to reckon ZD starting from the EqCS, i.e from the Equatorial Coordinate System. We’ll do unnecessary intermediate passages but perhaps useful :-). Please forgive me any typing error. I am a bit rusty but I think the procedure is correct.

After several attempts I see that it is not possible to upload my answer with just one post. So I have to do it with two.

Each object has its Right Ascension and Declination - RA, δ -
Obviously we also have the Local Geographic Latitude - ϕ - and the exact time of birth, so we have the Right Ascension of the Medium Coeli -RAMC-

Let’s define first the Hourly Angle (Up Meridian Distance - UMD -) :
H = RA – RAMC
---
if H ≥ 0 ---> H = H
if H <0> H = 360°+ H (2π + H)

*****
Let's now switch from Equatorial Coordinate to Astronomical Altazimuth Coordinate.
Named:
-h the Elevation
-An the astronomical Azimuth (0 ° to the North Point, clockwise)
We have:
h=arcsen (senϕ senδ+cosϕ cosδ cosH)
---
I=arcos [(cosϕ senδ-senϕ cosδ cosH)/cosH]
---
If I>180° (I> π) ---> An = 360° – I (2π – I)
If- I≤180° (I≤ π) ---> An = I

*****
And now from Astronomical Altazimuth Coordinate to Astrological Altazimuth Coordinate:
-h remains unchanged
-Al the astrological azimuth (0 ° to the East Point, counterclockwise)
---
II = 450° – An (5/2 π – An)
---
If II ≤ 360° (II ≤ 2π) ---> Al = II
If II > 360° (II > 2π) ---> Al = II – 360° (II – 2π)

*****
Finally the Prime Vertical Coordinate from the Astrological Altazimuth ones.
-hpv Prime Vertical Elevation (horizontal coordinate)
-Apv Prime Vertical Azimuth ( vertical coordinate)

In the following post...

8
Finally the Prime Vertical Coordinate from the Astrological Altazimuth ones.
-hpv Prime Vertical Elevation (horizontal coordinate)
-Apv Prime Vertical Azimuth ( vertical coordinate)
---
III = arcsen (cosh*sen Al)
---
if Al < 180° (Al< π) then hpv = abs(III)
if Al ≥ 180° (Al≥ π) then hpv = - abs(III)

Now we define:
y = – senh
x = cosh*cosAl
IV = arctag y / x
---
if IV <0 ° (IV <0> V = IV + 360° (IV + 2π)
if IV ≥ 0 ° (IV ≥ 0) --->V = IV
---
if x <0 ° (x <0>VI = V -180° (V – π)
if x ≥ 0 ° (x ≥ 0) --->VI = V
---
if VI <0 ° (VI <0>Apv = VI + 360° (VI + 2π)
if VI ≥ 0 ° (VI ≥ 0) --->Apv = VI

Obviously CMP = Apv

After that we have ZD as already said:
if 360>CMP≥270 ---> ZD = CMP - 270 with prefix Z
if 270>CMP≥180 ---> ZD = 270 - CMP with prefix Z
if 180>CMP≥090 ---> ZD = CMP - 090 with prefix N
if 090>CMP≥000 ---> ZD = 090 - CMP with prefix N

Roberto

9
I'm sorry but the Skyscript editor doesn't like math notation very much. Some lines are obviously altered ...
I have made several attempts to fix the problem but I cannot.


In any case, I think it's all quite understandable ...

Roberto

To Roberto

10
Hello Roberto- I want to express my gratitude for your post.I realize you must have spent a lot of time in this formula.I am in the process now of working through the several steps to obtain the CMP-Regards-Harold New York USA

11
Hi Harold,

At least under the editor viewpoint I have found the solution.
All numerical values are in degrees.

Each object has its Right Ascension and Declination - RA, δ -
Obviously we also have the Local Geographic Latitude - ϕ - and the exact time of birth, so we have the Right Ascension of the Medium Coeli -RAMC-

Let’s define first the Hourly Angle (Up Meridian Distance - UMD -) :
H = RA – RAMC
---
if H≥0 -> H = H
if H is negative -> H = 360+H

*****
Let's now switch from Equatorial Coordinate to Astronomical Altazimuth Coordinate.
Named:
-h the Elevation
-An the astronomical Azimuth (0 to the North Point, clockwise)
We have:
h=arcsen (senϕ senδ+cosϕ cosδ cosH)
---
I=arcos [(cosϕ senδ-senϕ cosδ cosH)/cosH]
---
If I>180 -> An = 360–I
If I≤180 -> An = I

*****
And now from Astronomical Altazimuth Coordinate to Astrological Altazimuth Coordinate:
-h remains unchanged
-Al the astrological azimuth (0 to the East Point, counterclockwise)
---
II = 450 – An
---
If II≤360 -> Al = II
If II>360 -> Al = II–360

*****
Finally the Prime Vertical Coordinate from the Astrological Altazimuth ones.
-hpv Prime Vertical Elevation (horizontal coordinate)
-Apv Prime Vertical Azimuth ( vertical coordinate)

---
III = arcsen (cosh*sen Al)
---
if Al is less than 180 -> hpv = abs(III)
if Al≥180 -> hpv = - abs(III)

Now we define:
y = – senh
x = cosh*cosAl
IV = arctag y / x
---
if IV is negative -> V = IV+360
if IV≥0 -> V = IV
---
if x is negative -> VI = V-180
if x≥0 -> VI = V
---
if VI is negative -> Apv = VI+360
if VI≥0 ->Apv = VI

Obviously CMP = Apv

After that we have ZD as already said:
if 360>CMP≥270 -> ZD = CMP - 270 with prefix Z
if 270>CMP≥180 -> ZD = 270 - CMP with prefix Z
if 180>CMP≥090 -> ZD = CMP - 090 with prefix N
if 090>CMP≥000 -> ZD = 090 - CMP with prefix N

Roberto

To Roberto

12
Roberto-I was able to use your formula to find ZD and CMP.I have used books by George Noonan and Benjamin Martin to see how astronomy applies to astrology.Names I have found on Skyscript.I have an astronomy program (Voyager).I know as you said in the first post that ZD is a point on the circle of position which is not so clear on an astronomical program.I also have a program called Horizons (Matrix/Winstar) which shows the chart as it applies to the earth.Are there any books or websites which use or explain the CMP/ZD formula? Harold