The tithi, which is active at sunrise, is the angular distance between the sun and moon. The month has two paksha, which means fortnights. The first fifteenth tithis constitutes the bright fortnight and the next tithis constitutes the dark forenights.
These thirty forenights are indicated by their paksha and ordinal number within the paksha. The fifteenth tithi of the bright fortnight occurs during the full moon, which is called purnima, and the fifteenth tithi of the dark fortnight occurs during the new moon, which is called amavasya. The tithi in which the moon is at the time of sunrise of a day is taken to be the tithi for the day.
The nakshatra is when the moon resides at sunrise. The ecliptic is divided into the nakshatras eastwards starting from a reference point, which is traditionally a point on the ecliptic directly opposite the star Spica, which is called Chitra in Sanskrit. However, there are other slightly different definitions that exist. It is called Meshadi or the start of Aries, this is when the equinox, which is where the ecliptic meets the equator, was in Aries.
The difference between Meshadi and the present equinox is known as ayanangsha or fraction of ecliptic. Given the 25,800 year cycle for the precession of the equinoxes, the equinox was directly opposite Spica in 285 CE, around the date of the Surya Siddhanta. As always, there are many versions with minor differences. Nakshatras are not just single stars, but are segments on the ecliptic characterized by one or more stars. Hence there are more than one star mentioned for each nakshatra. The nakshatra in which the moon lies at the time of sunrise of a day is the nakshatra for the day.
The yoga that is active during sunrise of a day is the yoga for the day. The last property is known as karana, which is half of a tithi. To be precise, a karana is the time required for the angular distance between the sun and the moon to increase in steps of 6 degrees starting from 0 degrees. Since the tithis are thirty in number, you would expect there to be sixty karanas, but actually there are only eleven. There are four fixed karanas and seven repeating karanas.
The four fixed karanas are the Kimstughna, Shakuni, Chatushpad, and Nagava. The seven repeating karana-s are Bava, Balava, Kaulava, Taitula, Garaja, Vanija, and Vishti or Bhadra. Now the first half of the first tithi, which is of the bright fortnight, is always Kimstughna karana. Hence this karana is fixed. Next, the seven repeating karana-s repeat eight times to cover the next fifty six half-tithis, which gives us the repeating karanas.
The three remaining half tithis take the remaining fixed karanas in order, which are also fixed, which is how you get the sixty karanas from eleven. The karana active during sunrise of a day is the karana for the day. There are twelve lunar month are known as the Chaitra, Vaishakh, Jyaishtha, Ashadha, Shravana, Bhadrapad, Ashwin, Kartik, Margashirsha, Paush, Magh, and Phalgun.
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