BA PART I : PAPER 3.14
MATHEMATICAL ASTROLOGY 2
Celestial latitude :
The celestial latitude of a heavenly body is the angle subtended
by the perpendicular arc from the heavenly body to the ecliptic. The
celestial latitudes vary from 0° to 90° on either side of the ecliptic and
letters ‘N’ and’S’ are suffixed according to their position towards north/
south of the ecliptic.
Right Ascension :
The right ascension of a heavenly body is the angular distance of
the arc measured along the celestial equator from the vernal equinox
(movable first point of Aries) to the foot of the perpendicular drawn on
the equator from the heavenly body.
Declination of a heavenly body is the angle subtended by the
perpendicular arc from the heavenly body to the celestial equator. The
declination vary from 0° to 90° on either side of the celestial equator
and the letters W’ and’S’ are suffixed according to their position towards
north or south of the celestial equator.
The definitions in paras are explained with the
help of a diagram as ABOVE
In the figure - , ABC is the celestial equator, DEF is ecliptic, 0 is
the centre of the earth/celestial sphere. N and S are celestial poles.
P and Q are poles of ecliptic.
X is a heavenly body/star.
XG is the perpendicular arc on ecliptic.
XH is the perpendicular arc on celestial equator.
M and L are movable first point of Aries (vernal equinox) and first
point of Libra (Autumnal equinox)
Celestial longitude of the star = angle subtended by the arc MG
Celestial latitude of the star = angle subtended by the arc XG
Right Ascension (R.A.) = angle subtended by the arc MH
Declination = angle subtended by the arc XH
The circle where the earth and the sky appear to meet is called
the Horizon. It depends on the power of the telescope/eye of the observer,
how much big is this circle. The plane of this circle where it intersects
the celestial sphere is the Horizon circle.
The plumb line of the place when produced upwards, the point
where it meets the celestial sphere is known as zenith of the place. In
other words the meeting point of a straight line from the centre of the
earth and passing through the observer, with the celestial sphere is zenith.
It is one of the two poles of the Horizon circle.
The point of intersection of the straight line passing through the
foot of the observer and the centre of the earth, with the celestial sphere
is called Nadir. It is a diameterically opposite point of zenith on the
celestial sphere. It is the second pole of the Horizon circle.
Secondaries to the Horizon circle are called verticals. The great
circles passing through the Zenith and Nadir are verticals. These are
perpendicular to the Horizon.
A great circle on the celestial sphere passing through the observer’s
zenith and the celestial poles is called the observer’s celestial Meridian.
This Meridian intersects the horizon at two points. These points indicate
Elements of Astronomy and Astrological Calculations
the North and South direction of the observer.
Altitude of a heavenly body is the angle subtended by the
perpendicular arc from the heavenly body to the horizon. In other words
the angle of the arc of the vertical from the heavenly body to the horizon
is the altitude of that heavenly body.
Azimuth of a heavenly body is the arc intercepted on the horizon
between the foot of the vertical drawn through the body and the meridian
i.e. NortiV South point. The North or South point from where it is
measured should be mentioned. If the foot of perpendicular is in the
East of the North/South point ‘E’ should be suffixed to the Azimuth. If it
is towards west W may be suffixed.
Prime Vertical :
The vertical circle which is making 90° angle with the celestial
meridian is called Prime Vertical. It cuts the horizon at East and West
points. The direction towards these points is East/West of the observer.
3.19 The definitions ARE explained through
0 is the observer at the centre.
Z is Zenith.
R is Nadir.
P & Q are North and South poles
X is a star (heavenly body)
NWHSE is the Horizon.
PZQ is the celestial meridian meeting the horizon at S and N
S and N are thie South & North points of observer.
ZERW is the Prime Vertical.
ZXHR is a vertical throuth X.
Altitude = angle of the arc HX
Aizmuth = angle of the arc SH (W) or NH (W)
measured from South point or North point.
Declination circles and Hour circles:
Secondaries to the equator (The circles passing through the North
& South poles) are called Declination circles because the declination of
heavenly bodies are measured along these circles.
The angle which the declination circle through a star makes with
the celestial meridian is called the hour angle of the star.
The time interval between two successive crossing of the meridian
by a star is one sidereal day of 23” 56”” 4” (in solar hours).
In the figure -7, X is a star.
P & Q are the North and South poles.
AB is celestial equator.
NKSJ is the Horizon of the observer.
PXH is the declination circle of the star.
DJEXK is the circle parallel to the equator, in which the star appeals
to revolve daily due to earth’s rotation. It rises when it comes at J and at
maximum altitude at E and sets at K.
PZEBSQ is the observer’s meridian.
PXH is the meridian of the star. It is also called the declination
circle through it.
Hour angle of the stffr is the angle between the meridian
Elements of Astronomy and Astrological Calculations 21
of the star and the observer’s meridian. Here angle HPB or angle
XPE is the hour angle of the star. This angle is converted into time unit
360° = 24 sidereal hours
15° = I sidereal hour
1° = 4 sidereal minutes.
For the sun it will be solar daus and hour’s otr ac tho c.m alcn
moves about 1° in a day.
3-22 Paras 3.22 to 3.25 will be explained in chapter X. Here the
definitions are given.
An inner planet (Mercury and Venus) is at inferior conjunction
urhen it Is i” between the sun and the earth and its longitudes are equal
to that ofthe sun. The planet is nearer to the earth at this time.
~93 Superior Conjunction:
· L time when the inner planet is at greatest distance (the sun is
‘n between i+>o ~i-.--.
· “~ Hiaiiet ana the earth) and the longitudes of the planet
and the sun are equal, the planet is at superior conjunction.
When an outer planet (Mars, Jupiter, Saturn etc.) are at greatest
distance i.e. the sun is in between the planet and the earth and the
longitudes of the planet and the sun are the same, the planet is at
An outer planet is nearest to the earth i.e. the earth is in between
the planet and the sun and the difference in longitudes of the sun and
the planet is 180°, the planet is said to be in opposition.
4.1 Different kinds of unite tot measuring distances, weight,
time etc were prevailing in ditfierent countries. Now uniformity among
these units is observed In most of tHie tountries and the units of distances
and weight are mostly of multiples of 10. The basic unit of time are
taken as Gregorien Calender year, Hour, Minutes and seconds etc. We
shall see the various uriitS Of tirhS
(a) 6 Pran = I Ral (Vinadi) = 24 seconds
60 Pal = I Ghati (Nadi) = 24 minutes
60 Ghati = I day (civil day)
21,600 Pran = 86400 seconds = I day
100 Truti = I Tatpar
30 Tatpar == I Nimesh
ISNimesh = I Kashtha
30 Kashtha = I Kala
30 Kald = I Ghati (Ghatika)
2 Ghatika = I Muhurta
30 Muhurta = I day = 60 Ghattka
60Anupal = I Vipal
60Vipal= iPa60 Pal = I ghati
2- Ghati = I hour
7- Ghati = I Prahar = 3 hours.
8 Prahar = 60 Ghati = 24 hours = I Ahoratri (I day)
15 days = I Raksha
2 Rakshas = I Month
12 Months = I year