Ahargana is defined as the no of days elapsed after the start of the Iron Age, the Kali Yuga, which began on 3102 BC.
Kali Era = English Era +3102
The no of days elapsed from Kali Start was 1822903 on 01/01/1890.
Hence
Ahargana, d = ( xdate – 01/01/1980 ) + 1822903
where xdate is the date of birth.
This Ahargana is printed on every V A Horoscope. All calculations in Indian Astronomy are based on Ahargana. Ahas means day in Sanskrit and gana means calculation.
The present Kali Era is therefore
3102 + 2010 = 5112
The difference between the Malayalam & English eras are 825. Malayalam Era is 1185 now and if you add 825 to Malayalam Era, you get English Era.
Malayalam Era + 825 = English Era
The Julian Calender used the value 365.25 d ( days ) for year and was proved erroneous. There were 10 days difference and the Gregorian Calender, the present day Calender, came into being. Gregorian uses 365.2425 d for year. The Gregorian is also not perfect, as the Tropical Zodiac is moving, and may be subject to correction after some years. The actual value of the year is
year = 365.256362424815 d
with twelve decimals. In my early days of progam development, I used two decimals and there were many days of difference. This value is given by Sir Simon Newcombe, according to Western Learning and Aryabhata, according to Indian learning.
In Indian Astronomy, the great Jupiter – Saturn perturbation, is calculated using the formula given below.
The Kali year, ky, is calculated and 4660 is deducted from it to get the kyb, the kali year balance. Its Bhujamsa,x is calculated using the Equation of Bhuja and then its Bhujajya ( Sin x ) is calculated to get the value of Manda Phala, a.
Mathematically, it can be written as
Y, (Year of Birth) + 3102 = ky, the Kali Year of Birth
kyb ( kali year balance ) = ( ky – 4660 )
x = kyb*360/918
b, bhujajya = sin(x)
Since the duration is 918 years and perturbation amplitude is 1187 seconds,
Manda Phala, a = sin(x) * 1187
( Example – My year of birth is 1955. Add 3102 and we get 5057. Less 4660 is 397. 397*360/918 is 155.6 and its Bhujamsa is 25 degrees roughly ( 180-155). So Sin (25 ) is 0.41. Manda Phala, therefore is 0.41*1187 seconds or Vikalas. )
This value, Manda Phala, a is added to Jupiter’s mean longitude, if Jove’s long is less than 180 and subtracted if Jove’s long is greater than 180.
In the West, this discovery is attributed to Laplace. The duration of the perturbation of 918 years is known as Laplace period. Its amplitude of .332 degrees is similar to the Indian value of 1187 seconds.
Laplace gives the equation 2 nj – 5 ns + constant, bringing to light the 5:2 Resonance in the orbits of the two celestial giants. 2 revolutions of Saturn = 5 revolutions of Jupiter = 60 years !