Re: Placidian and Gauquelin sectors

[Ray Murphy]

> DUHH!!!!
>
> I used the same symbol for two different things and I reversed two
> terms in a formula. Okay, I am editing the text that follows, so
> (hopefully) all stupidities shall have been corrected.
>
> Ray, can you erase the previous post?

RM: I think posts can only be removed by the authors unless Google
needs to intervene.

It seems that if we go to any of our own posts and click on the line
"more options" at the right side of the text, it will allow us to
remove our own posts.

If we have posts on Google that were not entered via a Google group
(such as usenet posts) then there's a special web page for deletions.

Ray

[xl...@sympatico.ca]

Okay, third time lucky. Now that Ray has told me how to delete posts
via Google, I have tried to clean up the line breaks in the last post
and removed *two* previous posts.

On Apr 21, 1:45 pm, "x...@sympatico.ca" <x...@sympatico.ca> wrote
[AMENDED #2]:
The following is written in ASCII maths. The general idea is that
given any point (which rises and sets), one wants to know how far it
is has gone its travel between the meridian and horizon, expressed as
a proportion of the entire time of travelling between them.

A = RAMC or sidereal time expressed as degrees
B = geographic latitude of birthplace
a = a planet's right ascension (in degrees for this formula)
d = the planet's declination
s = the sign of the planet's altitude, +1 if above the horizon, -1 if
below

The latter must be calculated not approximated, especially with bodies
like the Moon or Pluto when they are near the horizon.

Q = arccos (-tan d * (tan B))

Then the "Placidian domitude" p of the planet, expressed from 0 to 360
degrees, is

p = 90*(s + 1) + (180*[ a - A + s*Q ] ) / [ 2*s*Q ]

Note: the square brackets indicate reduction modulo 360 and this
operation has priority: it must be done immediately following the
operations inside the brackets and before the multiplication and
division outside the brackets.

The Ascendant, with ecliptic latitude 0 of course, will give p = 0;
the second Placidian cusp will give p = 30, and so on.

Naturally this convention follows conventional house systems which are
numbered Zodiac-wise rather than according to diurnal motion. This
means that planets move backwards. A planet with p = 160 is 1/3 of the
way from beng on the curve of cusp VI to lying on the western horizon
in terms of frozen zodiacal space; but actually it has travelled 2/3
of the way from the horizon to cusp VI. In their diurnal movement
planets go clockwise.

The Gauquelins made it easier to relate numbers to physical reality by
counting their positions clockwise. Let the Gauquelin sector position
be g; then g = -p modulo 360.

Whether you choose to use p or g, the advantage of reducing diurnal
positions to a 360-degree scale is that you can have any number of
sectors you want. If only eight, let them go from 0 to 45, 45 to 90,
90 to 135, and so on. If you want 18 sectors, they will go from 0 to
20, 20 to 40, etc.

PS - The forumula is indeterminate in the rare case that a planet's
altitude is exactly 0. You can easily program a fudge to determine
whether its p should be 0 or 180.

[Ray Murphy]

RM: I delayed my response to this valuable post and formula to give
myself time to try and think of something half-intelligible to add to
it, but the only thing I can say is that I am semi-clueless about the
whole concept of Gauquelin sectors.

I understand the difference between RA and zodiacal degrees, and
partly understand what Oblique Ascension is but I still have no idea
which one is used for the sectors. Up until now I've just relied on
others' calculations.
I suppose it would become easy for everyone to understand if we could
make some sort of moving graphic or a set of overlay graphics which
showed how the whole thing worked at a few different latitudes.

Ray

[xl...@sympatico.ca]

Ray and all,

On Apr 23, 5:41 am, Ray Murphy <ray...@chariot.net.au> wrote:

> RM: I delayed my response to this valuable post and formula to give
> myself time to try and think of something half-intelligible to add to
> it, but the only thing I can say is that I am semi-clueless about the
> whole concept of Gauquelin sectors.
>
> I understand the difference between RA and zodiacal degrees, and
> partly understand what Oblique Ascension is but I still have no idea
> which one is used for the sectors. Up until now I've just relied on
> others' calculations.

I too loathe the old explanations that use oblique ascension; you will
notice that I avoid the concept in my formula.

> I suppose it would become easy for everyone to understand if we could
> make some sort of moving graphic or a set of overlay graphics which
> showed how the whole thing worked at a few different latitudes.

Yes - it would be good if there could be a set of interactive Java
applets that would help people learn about celestial geometry, with
options to see things from above (the celestial sphere) or from below
(the sky over the landscape). But for precision, of course, diagrams
are not good enough.

The principle of the Placidian cusp is quite simple: it is the line in
the sky where any body, whatever its declination (as long as it sets
and rises) has travelled either 1/3 or 2/3 of its way from horizon to
meridian or vice-versa. Keep that definition in mind and you won't
need oblique ascension. If you take the exact zodiacal longitude of
cusp XII, say, and give it a latitude of 0, then convert its position
to equatorial coordinates and apply the formula I have given, you wil
get 330 degrees of Placidian domitude (p). The same principle of
proportionality applies inside a house, so a point halfway up from the
eastern horizon to cusp XII will have a domitude of 345 degrees.
Halfway up, that is, in terms of the sidereal time it takes to go
through the house.

The field of Gauquelin sectors is essentially that of Placidian houses
numbered the other way and divided sometimes into more than 12 sectors.