Mathematics of Tithi

 

Any Lunar Month has two halves:

• Bright Half (Shukla Paksha)= 14 or 15 days time between New Moon to Full Moon = When Moon moves to go away from Sun by 180^o and gains brightness to become fully bright finally.
   
• Dark Half (Krishna Paksha) = 14 or 15 days time between Full Moon to New Moon = when Moon moves to cover the 180^o gap between himself and Sun to finally become completely dark on meting the Sun

So in both the Bright Half and in the Dark Half, Moon moves 180^o in relation to the moving Sun (as seen by us from the Earth).

Every Half of a Lunar Month is therefore the time (of around 14 or 15 days) in which Moon moves 180^o in relation to Sun. 

We divide this 180^o movement of Moon in each half  of a Lunar Month into 15 equal parts in terms of the angle moved by Moon in relation to the Sun. Each part defines a Tithi.

Therefore,

1 tithi = 180^o/15 = 12^o of Moon's movement either away from Sun or towards the Sun.

Thus,

• The 1^st Tithi of the Bright Half = time during which Moon moves from the exact New Moon state to become 12^o away from Sun. When Moon reaches the 12^o distance from Sun , the 1^st Tithi of the bright half is completed and from that very moment the 2^nd Tithi of the Bright Half begins.

• The 2^nd Tithi of Bright half = time during whhich Moon is moving from being 12^o away from Sun to reaching the distance of 24^o from Sun. When Moon reaches 24^o away from Sun , the 2^nd Tithi of the bright half is completed and from that very moment the 3^rd Tithi of the Bright Half begins

• The 3^rd Tithi of Bright half = time during whhich Moon is moving from being 24^o away from Sun to reaching the distance of 36^o from Sun. When Moon reaches 36^o away from Sun , the 3^rd Tithi of the bright half is completed and from that very moment the 4^th Tithi of the Bright Half begins

... and in this way we have 15 Tithis in the Bright half, at the end of which Moon becomes 180^o away from Sun and Full Moon occurs.

Similary, we have 15 Tithis in the dark-half,

• 1^st Tithi of the dark half is when Moon is moving 12^o closer to Sun from the Full Moon position when he was the farthest. So during the 1^st Tithi of the dark half, the distance between the Sun and Moon decreses from 180^o to when Moon reaches 168^o hehind Sun. 1^st Tithi is finished when Moon is exactly 168^o behind Sun, and at that very moment the 2^nd Tithi begins.

• 2^nd Tithi of the dark half is when Moon is moving further 12^o closer to Sun and therefore moving from being 168^o behind to becoming 156^o behind the Sun. 2^nd Tithi is finished when Moon reaches exactly 156^o behind Sun, and at that very moment the 3^rd Tithi begins.

.... and in this way we have 15 Tithis in the Dark half, at the end of which Moon and Sun become conjunct, there is no gap between them, and New Moon occurs..

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