We are starting a series on mathematical aspect of astrology and today's post is about calculating the duration of signs at any place. In
this post we are going to study the meaning of Rasinamas, Charakhandas,
calculation of charakhandas, rashimanas and ayanamsha.
Astrology is the science which is
based on mathematics and for the purpose of making accurate predictions it is
absolutely essential that the student is conversant with the mathematical
aspects. In fact, it is said that 'Suryasiddhanta' and 'Brihat Jataka'
are two wheels of chariot on which it runs. From this it can concluded that the
equal importance should be given to the mathematical aspect of the science.
Rasimanas
Rasimanas means the rising period of
the sign or rasi. The duration of each sign is a function of latitude of a
place. The average duration of any ascendant is 120 minutes. It is important to know exact duration, because without it the
ascendant cannot be ascertained.
The earth rotates round its axis. During its
rotation, the twelve signs rise and set in their respective order. However, the
rising time of each sign varies. This is because the ecliptic is angular to the
equator. For this , the duration of rasis at the equator are first identified.
This is called as "Lankodaya". (the reason for naming this as
Lankodaya is due to the fact that Sri Lanka is near to the equator). The
duration of rasis at the equator is as follows
Aries,
Virgo, Libra, Pisces 111 min. 36sec
Taurus, Leo, Scorpio, Aquarius 119 min 40sec
Gemini, Cancer, Sagittarius, Capricorn 128 min 44 sec
Charakhandas
It means that the ascensional
differences. It is the function of latitude and declination. The ascensional
difference is deducted or added from the rashimanas at equator to arrive at the
rasimanas of the defined place. The rasimanas are further used to calculate the
ascendant  one of the important mathematical point for studying horoscope.
Determination
of rashimanas at the given place
The
formula for determining charakhandas for the signs Aries Virgo Libra Pisces is
[19335312*sin(30)*sin(
latitudes of the place ) ]
________________________________________
cos(
latitudes of the place )*60*3365.3581
The
formula for the signs Taurus Leo, Scorpio, Aquarius is
[19335312*sin(60)*sin(
latitudes of the place ) ]
______________________________________
cos(
latitudes of the place )*60*7270.1068
For
the rest of the signs
[19335312*sin(90)*sin(
latitudes of the place ) ]
________________________________________
cos(
latitudes of the place )*60*20151.243
The
answer for the above formula is in minutes.
Let
us calculate the charakhandas for the place at 45N00 latitude(Longitude is not
required since it is the function of latitudes only).
The value of 45N00 latitude
charakhandas for the signs Aries Virgo Libra Pisces is
Sin
(45) = 0.707106
Cos (45) = 0.707106
[19335312*0.5*sin(
45 ) ]
____________________________
= 47.88 minutes or 47 minutes 53 seconds
The value of 45N00 latitude charakhandas for the signs Taurus Leo
scorpio aquarius is
Sin(60)=0.866025
Cos(45) = 0.707106
Sin(45) = 0.707106
[19335312
* 0.866025 * 0.707106 ]
______________________________
= 38.39 minutes or 38 minutes 23 seconds
The value of 45N00 latitude charakhandas for the signs Gemini
Cancer Sagittarius capricorn is
Sin(90)= 1
Cos(45) = 0.707106
Sin(45) = 0.707106
________________________________________
= 16.00 minutes (approximately).
Thus the
charakhandas for 45N00 latitudes are 47.88 minutes for Aries, Virgo, Libra and
Pisces signs, 38.39 minutes for Taurus, Leo, scorpio, aquarius signs and 15.99
minutes for Gemini Cancer Sagittarius capricorn signs.
If the birth is
in northern latitude then the charakhandas thus obtained by the above formulae
be added or subtracted to or from rasimanas at the equator. If the birth is in
northern hemisphere then deduct the charakhandas thus obtained for the
following signs viz. Capricorn, Aquarius, Pisces,
Aries, Taurus and Gemini. The charakhandas calculated for the rest of the signs
be added. If the birth is in the southern hemisphere then the reverse
holds true. Let us calculate rasimanas at 45N00 latitudes.
Sr.no

Sign

Rising
period at 0 Lat.

+/

Charakhandas
at 45N00

Rasimanas
or duration of signs

1

Aries

111 min.
36 sec



47
minutes 53 seconds

63
minutes 43 seconds

2

Taurus

119 min
40 sec



38
minutes 23 seconds

81
minutes 17 seconds

3

Gemini

128 min
44 sec



16.00
minutes

112
minutes 44 seconds

4

Cancer

128 min
44 sec

+

16.00
minutes

144
minutes 44 seconds

5

Leo

119 min
40 sec

+

38
minutes 23 seconds

158
minutes 03 seconds

6

Virgo

111 min.
36 sec

+

47
minutes 53 seconds

159
minutes 29 seconds

7

Libra

111 min.
36 sec

+

47
minutes 53 seconds

159
minutes 29 seconds

8

Scorpio

119 min 40
sec

+

38
minutes 23 seconds

158
minutes 03 seconds

9

Sagittarius

128 min
44 sec

+

16.00
minutes

144
minutes 44 seconds

10

Capricorn

128 min
44 sec



16.00
minutes

112
minutes 44 seconds

11

Aquarius

119 min
40 sec



38
minutes 23 seconds

81
minutes 17 seconds

12

Pisces

111 min.
36 sec



47
minutes 53 seconds

63
minutes 43 seconds

Aries Virgo Libra
Pisces 111 min. 36 sec
Taurus Leo Scorpio Aquarius 119 min 40 sec
Gemini Cancer Sagittarius Capricorn 128 min 44 sec
Ayanamsa
During every
year, the sun has two movements, one towards north called uttarayana and the
other towards south called dakshinayana. During this solar movement the sun
crosses the equator twice in the year; firstly during his northern course and
secondly during his southern course.
When the sun reaches his equinoctial point the duration of day and
night is equal. The year commence at the time at which the sun reaches this
point i.e. 0 degree Aries.
If we consider
the commencement of the year when the sun is in conjunction to the fixed star
and also at the equinoctial point and calculate the year accordingly, it will
be observed that in the subsequent year the sun intersects the equator before
the sun is in conjunction with the fixed star. The difference gets accumulated
every year.
This difference which gets accumulated every year is 50.33 seconds of an arc.
The movement is retrograde i.e. towards west and is called precession of
equinox.
The precession of
equinox is the most important factor not only for mathematical purpose but also
for predictive purpose. It has divided astrology into 2 schools of thought 
a) Sayana System also called as Moving Zodiac (Tropical System)
b) Nirayana System also called as Fixed Zodiac (Sidereal System)
Sayana system includes precession of equinox and horoscope is cast
after including the precession.
Nirayana System however
considers the precession for casting of horoscope but the accumulated
difference of precession calculated with respect to the fixed point of the
zodiac, usually a star, is deducted.
We follow nirayana system since
the Hindus adopted sayana system for mathematical purpose only and it was
reduced to niryana system for predictive purpose.