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Vedic Astrology: Charakhandas and Rasinamas (Duration of sign)


            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
cos( 45 )*60*3365.3581

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
0.707106*60*7270.1068

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


[19335312*1*0.707106 ]
________________________________________ = 16.00 minutes (approximately).
0.707106*60*20151.243

            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.

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