The Parans of
Aldebaran and Antares
WB"rtFannin
FIEN TWO OR MORE CELESTIAL
bodies are on the local
angles at the same time, the
configuration is called
a
paran, which is short for
the Greek parantellonta'. to
cross together. A paran can be two bodies
on the
same angle, opposite angles or
adjacent angles.r In the last instance the
combination is called a mundane square.
The paran is widely considered a very
powerful class of aspect.
If the Right Ascension GA) of a body
is the same as the RA of the MC (local
sidereal time) then that body is in the upper
meridian.
If
the difference between the
RA
of a body and the RAMC is twelve hours,
then the body is on the lower meridian.
This is true regardless ofthe latitude ofthe
observer.
Because Right Ascension is measured
along the celestial equator eastward from
the vemal equinox, it is a tropical coordinate and subject to the effect ofprecession.
The declination (Decl.) of a body is its
measure above or below the celestial
equator. RA and Decl. are analogous to terrestrial latitude and longitude extended out
into space. The declination circle has its
nodes at the equinoctial points where it
crosses the celestial equator. Declination
is also a tropical coordinate, and like Right
Ascension, must be corrected for precession to the epoch in question. When the
longitude of a body is reckoned in terms of
the sidereal zodiac it is not measured from
the vernal point but from a fiducial point
fixed against the background of the stars.
Most bodies also have celestial latitude (B)
which is the measure of a body above or
Only the Sun, whose apparent path defines
the ecliptic, has no latitude.
The most practical way to correct for
the effect of precession is to first determine
the tropical longitude of a body with respect
to the equinox of the current epoch. The
difference between the sidereal fiducial star
alpha Virginis (i.e. Spica in 29"06'05"
Virgo for the epoch 1950.0 A.D.) and its
tropical longitude equivalent places the
mean longitude of the vernal point in
terms of the sidereal zodiac at 5"57'28.64"
Pisces for that epoch. The value that western siderealists call the synetic vernal point
(SVP) is the receding point of the equinox
when measured from Spica in the sidereal
zodiac. When the SVP for the epoch in
question is subtracted from the sidereal position of a body and 30o is added to the
result, the ex-precessed value ofthe tropical
longitude for that epoch is obtained. As an
example, for the epoch February 1,7993,
the SVP is 5'21'05" Pisces and the obliquity ofthe ecliptic (e)is23'26'23" (e is the
angle between the equator and the ecliptic),
values necessary to translate from tropical
to sidereal (and vice versa) and from ecliptic coordinates (celestial latitude and longi-
alpha Tauri ( Aldeb aran)
15'Tau 03'00" (SZ)
2l'05" (SVP)
-
5"
9'Tau 41'55"
+30o
9"Gem 41'55" (TZ) or 69.6986111"
B= 5'S28'
alpha Scorpii (Antares )
15'Sco 01'00" (SZ)
2l'05" (SVP)
-
5"
9"Sco 39'55"
+30o
9'Sag 39'55"
(fZ)
or 249.66527'178
B=4'S34'
We may now calculate the declination
of the two stars from the ex-precessed tropical longitude (I-), latitude (B) and obliquity
of the ecliptic (e). The figonometric formula for this operation is: sin decl. = [cos B
sin L sin el+lsin B cos e] where decl. or d is
the value of the ex-precessed declination.
The arc sin of the result of this expression
will be the value of the ex-precessed declination of the body. We fust convert the degree, minute, second values of B, L, and e
into decimal form, then the trigonometric
functions of those numbers are plugged into
the formula:
tude) to equatorial coordinates (right
ascension and declination).
B = 5"528'=-5.46666667", the cos of
which = 0.99545179
L = 69"41'55" = 69.6986111i,", the sin of
which = 0.93788052
e = 23o26'23" = 23.43972222", the
sin of which = 0.39778406
and for the other halfofthe above formula:
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The Parans of Aldebaran and Antares
from page 79
Substituting these numbers into the formula
given above we get the expression:
68.8869539'
sin d = [(.99545 179X.93788052)(.397'7 84060)l
+\C.09 52666 4) (.9 17 47 9 01 )l
= 4h35 m33s of R.A.
= 0.37137'71,0 + -0.08740515
= 0.28397196
In order to derive the degree value from this
number which is really the ratio of an angle,
the arc sin (sin-l ) of it must be taken, so: arc
For Antares: 249.66521778"- 180 =
69.66521118 (because Antares is in the
16'N29',50.67"
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Tell them
you saw it in
Tlrc
Astrolnger
1993. In the same manner and for the same
date the ex-precessed value of the declination of Antare s is 26o524' 57 .31" .
Now, with the ex-precessed values of
longitude, declination and celestial latitude
(which latter value, it will be recalled, is a
sidereal coordinate and therefore does not
precess), we may calculate the right ascension of the stars for epoch. For bodies with
latitude there are two formulae for determining Right Ascension; which is used will
depend upon which quadrant of the ecliptic
210""
cos RA
d
sinM=sinLcosB
cos
astrologY
biorhythms
d
It must be recalled to add back the value of
moon phases
the quadrant of the circle that the longitude
void-of-course
hourly transits
mercury retrograde
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falls into. The worked example with
Antares illustrates this requirement. For
Aldebaran:
cos 69.69861 1 1 cos -5.46666667
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B
2'70o to 360o the procedure is:
your pocket Planner
for the nerd age
t, fits
li9!
For longitudes from 90o to 180o or from
simplicity
utility
detail
I
= tos
cos
Tttxsau*Il!tfi*x
ODY9 d.4ht(Y9
1,
circle, reckoned from the vernal point in
tropical longitude (but ex-precessed), the
bodies in question are found. For longitudes (L) from 0o to 90o or from 180o to
Mourtain
an" bui
cos
=
Aldebaran's declination for February
I
PsyPl
cos 69.665217'78 cos 4.5666666'/
etc.
= (.34695839X .99 545 17 9)
.95883259
=A36020W3
arc cos = 68.8869539 which must be
divided by 15 to put into hours, minutes and
seconds ofRieht Ascension, so:
264A%819
(0.3 47 5039 6) (0.99 682s37 )
This is the ex-precessed value of
Chakra Balancing Oils
@
quadrant 180-270). Then,
sin 0.28397196 = 16.49140733 which is
A Qrf
)
15
toSS560lotl
= 0.38678023, the arc cos of which
= 67.24569606 + 180"
= 24'l .24569606"
= RA 16h28m59s
The RAMC with which a body rises or
function of its Right Ascension and
sets is a
Declination and the terrestrial latitude of
the place in question. The relationship between terrestrial latitude and declination,
known as the ascensional difference (AD),
is determined by the formula:
sin AD = tan Decl. tan Lat.
(Note: we are speaking here of terrestial,
NOT celestial latitude. )
If the ecliptic were exactly pelpendicular to the celestial equator there would be
no seasons and the arc a body describes
from meridian to horizon, known as the
semi-arc, would be exactly 90o at all latitudes on Earth. But the ecliptic is inclined
to the celestial equator by the slow but
steadily changing value of the obliquity
of the ecliptic. For that reason we do have
seasons on the Earth and the semi-arc
(S/A)
of a body will vary from 90o at different
latitudes as the ascensional difference,
S/A = 90 + AD. Worked examples for
Aldebaran and Antares for the latitude of
San Francisco (37"N47' geographic) are
shown below.
Aldebaran:
sin AD = tan Decl. tan Lat.
sin AD = tan 16"29'50.67" tan3'1"47'
sin AD = tan 16.49740'133 tan 31 ;78333333
sin AD = (0.29616427) (0j775213'71)
0.22959061, the arc sin of which
13.2'/29'7076'+90"
=
=
= 103.27297016"
Antares:
Table 1
Effects of Precession on Equatorial Coordinates
sin AD = tan -26.41426819 tan 3'7 .'78333333
sin AD = (4.4961 l4'7 4)(0.77 5213'7 1)
= -{.38506008, the arc sin of which
= -22.64746987o+90o
of Aldebaran and Antares Over Three Millennia
= 67.3525013'
l5
Year
= RA 4h29m25s
1
Now, as a body must rise before it can
culminate MC) and set before it can anticulminare (IC), it follows rhat the RAMC
for rising is RA -semi-arc and the RAMC
for setting must be RA +semi-arc. Thus, for
our two stars lor San Francisco:
Aldebaran has RA 4h35m33s
(borrowing 24 hours)
-6h53m06s (semi-arc)
=zlh4ztr2k
which is the RA of the MC when Aldebaran
rises ln mundo at San Francisco. and conversely:
RA 4h35m 33s
+6h53m 06s
11h28m39s
is the local sidereal time or RAMC when
Aldebaran sets in mundo at San Francisco.
And likewise for Antares:
RA 16h28m59s
- 4h29m25s (semi-arc)
i th59m34s
which is the RAMC with which Antares
59s
+ 4h29m 25s (semi-arc)
20h58m24s
is the local sidereal time when Antares sets
at San Francisco.
It can be seen that while the two stars
are in close opposition through the meridian circle, they are further apart across the
horizon because their semi-arcs are very
different at the latitude of San Francisco.
Table 1 shows how precession
SVP
RA Ant.
5'Pis21'05"
,19"Fis18120'
,-7
23'26'23',
2334'14',
3"Ari10'09rt
23'42'02
-'t007 16"Ari58'3i " 23049150"
has
affected the equatorial coordinates ofthese
two stars over the span of three millennia.
A calculation of the rate of change of RA
4h35m33s
3h38m55s
2h44m27s
t h52m00s
epoch
1993
A
Ald. rise as Ant. set @ 7'558'08"
Ant. rise as Ald. set @ 8'N 15'00"
By testing various latitudes the exact
l- o
+ 5e51 44"
Settinq
22h44m56s
1
Della
Ql
0h45m24s
5"05'37"
epoch 992
Ald. rise as Ant. set @ 13'503'45"
Ant. rise as Ald. set @ 13'N20'38"
:
21h52m10s
th52m35s
21
5005'38',1
h52m04s
th52m28s
4029'45',
epoch -7
424',22"
Ald. rise as Ant. set @ 17'527'30"
Ant. rise as Ald. set @ '17"N45'00"
20h57m38s
8h57m59S
20h57m31s
8h57m52s
3e27'53"
epoch
-1
107
Ald. rise as Ant. set @ 20'55'23"
Ant. rise as Ald. set @ 21'N13'07"
3"28'07"
20h01 m00s
8h01m15s
20h00m53s
8h01 m08s
The value Delta 0 refers to the change
parans
during the three millennia period listed.
Taken with Table 1 it demonstrates that
as the value of true E (obliquity of the
ecliptic) decreases, the rate ofchange in terrestrial latitude (where the parans obtain)
increases.
It is perhaps noteworthy that as the
exact parans haye moved toward the
equator, the major power centers of
the planet have moved away from the
tropical zones into the temperate zones
which is suggestive of the malefic nature
these stars, especially Antares.
of
fhc nnininnc
the rate of precession.
'15h28m39s ;23043',22!l
t,+hst m2ss -19'531251'
13h37mO2s ,l501 1155"
Risinq
snhere nnd one in the cnrrfhern\ non
coordinates in addition to, but slower than,
+13'5911111
+1,0?21'49:'|',
22h45m03s
1 0h45m30s
places where the two stars rise and set with
the same RAMC (one in the northern hemi-
of the obliquity of the ecliptic and stellar
16h-28m59s
The Rising and Setting of Aldebaran and Antares
In the 19th century the great English
astrologer A. J. Pierce employed reasoning
similar to that expounded herein to examine
the specific nature of stars which made
mundane relationships with English locales
in particularly strong and exact configurations. Short of examining many individuals
with stars conjunct their angles in mundo,
there is probably not a better way to verify
and Declination suggests a direct relationship between the direction and acceleration
Decl. Ant.
-2624'51t'
+16"29151"
Table 2
in the geographic latitudes of the
rises in mundo at San Francisco and,
RA 16h28m
993
992
nf anniant
@ 1993
Bert Fannin - all rights reserved
References
1. The term "angles" refers to the horizon
and meridian circles.
2. Hynes, James, The Synetic Vemal Point
Tables, Registry of Sidereal Asfiologers,
Los Angeles, 1976.
Bert Fannin is a sidereal astrologer who lives
and practices in South San Francisco, Califurnia. He has practiced astrology for the past 24
years, 20 of which have been devoted to sidereal astrology and research, Bert has also
written for American Astrology magazine.
Contact him at 18 Magnolia Avenue, South San
Francisco, CA 94080, (415) 875-3905.