In Sanskrit 'ahoratra' means one full day and 'gana' means count. Hence, the Ahargana on any given day stands for the number of lunar days that have elapsed starting from an epoch. As we have seen before, an 'epoch' is the starting point of an era.

How to go about to calculate the Ahargana on a particular day? In Indian astronomy the problem of finding the ahargana is posed as follows: Starting from the epoch given, one has to find out the number of days that have elapsed till some date specified by its year, chaandra maasa and tithi. How'll you find it? The following diagram will help you.


Procedure for calculating Ahargana:


Here, the time interval AB = X, BC = Y and CD = Z


A - Beginning of epoch

B - Beginning of the current year

C - Beginning of the current Month

D - Beginning of the day for which Ahargana is to be calculated

X - No. of luni-solar years elapsed

Y - No. of lunar months elapsed

Z - No. of tithis elapsed.

From the figure, we can easily calculate the number of days elapsed, but watch out for a tricky one out there. As we have already seen, the Adhika maasa may be defined roughly as a lunar month in which two Amavasyas occur. So, the significant (though subtle) point we have to take care of here is the number of Adhika maasas (say X1), in X years. Why should we do this? This is because we cannot be sure that all the X years would have had only 12 lunar months. It may lead to a miscalculation for we are dealing with the number of lunar days elapsed. To calculate the number of Adhika maasas, we take the number of Adhika maasas in a Mahayuga as the reference. The calculations are shown below:

Number of Adhika maasas in a Mahayuga = Number of lunar months - Number of solar months.

Therefore, the number of Adhika maasas in X years is,

X1 = (Number of Adhika maasas in a Mahayuga * X) / Number of solar years in a Mahayuga.

{ Note that there are 4320000 solar years in a Mahayuga.}

Having done this, we can easily calculate the number of days elapsed = [ ( 12 x + x1 + y + z/30)*29.530589]

In the above formula, we have converted X and Z into lunar months units by multiplying by 12 and dividing by 30 respectively. We have also used the empirical value of the number of days in lunar month as 29.530589.

Because of the non-uniform motion of the moon, the number of days elapsed (calculated as above) may not be consistent with the actual value of Ahargana. So, we add or subtract 1 (or leave it as it is), depending on the coincidence of the actual day and the day calculated, to get the Ahargana. Dividing the answer obtained by 7 and checking the remainder obtained does this crosscheck. The first day of the epoch corresponds to the remainder 0 and so on. For instance, Kaliyuga started on a Friday. Then for correct calculation, R=0,1,2,3,4,5,6 shall correspond to Friday, Saturday,..., Thursday.

The importance of Ahargana

What can one do by knowing the Ahargana on a particular day? This may be the question ringing in your mind. We'll answer this question now. Suppose we know the position of the Sun, the Moon and the planets at some epoch. We also know the rate at which these celestial objects move in the stellar background in the celestial sphere. If these celestial objects moved uniformly, then their positions can be found at any instant of time if we know the exact time-interval between the epoch and the given instant. (Actually, the rate of motion is not a constant. But at this stage, it suffices if we know that 'Ahargana' helps us to find the position of the celestial objects).