Adhika masa and Kshaya masa
This article is regarding the concept of Adhikamasa and Kshayamasa (intercalary months) used in some luni-solar calendars in India. Luni-solar calendars are in vogue since lunar months determine the high and low tides while the solar year determines the seasons. But the use of luni-solar calendars create a unique problem.
Since the lunar year (12 lunar months) lags behind the solar year (~365.25 days), this creates a need to keep the lunar year and the solar year in synchrony. Hence the need to use Adhika masa (extra month) and Kshaya masa (removed month)! The reason for their asynchrony is explained next.
The synodic period of moon is ~29.54 days which makes 1 lunar month while the solar year is ~365.25 days long. So this implies that we complete 1 lunar year comprising 12 lunar months ( 29.54 * 12 = 354.48 days) for every solar year but more importantly with few days still remaining. i.e. 365.25 - 29.54 * 12 = 365.25 - 354.48 = 10.77 days to be more exact!
So we wait till this extra 10.77 days accumulates to make one additional lunar month that will be added to the lunar year (to keep it in sync with the solar year) known as Adhikamasa. We wait for 29.54 / 10.77 = 2.74 years for this to happen. The number of lunar months incurred during this time is 2.74 * 12 = 32.913 lunar months. This means the phenomenon of Adhikamasa happens every 32 or 33 lunar months.
Since 32.913 is a fraction, this necessitates the need to remove one lunar month from the lunar calendar at certain times to further ensure that the solar year and lunar year are in sync. As you guessed it right, such a month is Kshayamasa.
The rule to determine an adhikamasa is that in a particular lunar month there will be NO solar "sankraantis", while for a kshayamasa in that particular lunar month there will be 2 solar "sankraantis". It is that simple. So there is no need for say Pope to (arbitrarily) announce any such changes in the calendar. Everything is determined by nature!
For further reference: "Indian Astronomy - An Introduction", by S.Balachandra Rao, Universities Press, Hyderabad, 2000, pages 47-48.
Kshayamasa may occur once in 19 or 122 or 141 years as shown by Bhaskara II in his "Siddhaanta-shiromani" using successive convergents of a continued fraction. It is further known that a kshyamasa can occur only in one of the three lunar months: Kaartika, Maargashira and Pushya. Therefore, compared to the adhikamasa, the kshayamasa is less frequent and not completely periodic.
Since the lunar year (12 lunar months) lags behind the solar year (~365.25 days), this creates a need to keep the lunar year and the solar year in synchrony. Hence the need to use Adhika masa (extra month) and Kshaya masa (removed month)! The reason for their asynchrony is explained next.
The synodic period of moon is ~29.54 days which makes 1 lunar month while the solar year is ~365.25 days long. So this implies that we complete 1 lunar year comprising 12 lunar months ( 29.54 * 12 = 354.48 days) for every solar year but more importantly with few days still remaining. i.e. 365.25 - 29.54 * 12 = 365.25 - 354.48 = 10.77 days to be more exact!
So we wait till this extra 10.77 days accumulates to make one additional lunar month that will be added to the lunar year (to keep it in sync with the solar year) known as Adhikamasa. We wait for 29.54 / 10.77 = 2.74 years for this to happen. The number of lunar months incurred during this time is 2.74 * 12 = 32.913 lunar months. This means the phenomenon of Adhikamasa happens every 32 or 33 lunar months.
Since 32.913 is a fraction, this necessitates the need to remove one lunar month from the lunar calendar at certain times to further ensure that the solar year and lunar year are in sync. As you guessed it right, such a month is Kshayamasa.
The rule to determine an adhikamasa is that in a particular lunar month there will be NO solar "sankraantis", while for a kshayamasa in that particular lunar month there will be 2 solar "sankraantis". It is that simple. So there is no need for say Pope to (arbitrarily) announce any such changes in the calendar. Everything is determined by nature!
For further reference: "Indian Astronomy - An Introduction", by S.Balachandra Rao, Universities Press, Hyderabad, 2000, pages 47-48.
Kshayamasa may occur once in 19 or 122 or 141 years as shown by Bhaskara II in his "Siddhaanta-shiromani" using successive convergents of a continued fraction. It is further known that a kshyamasa can occur only in one of the three lunar months: Kaartika, Maargashira and Pushya. Therefore, compared to the adhikamasa, the kshayamasa is less frequent and not completely periodic.
Good one... Quite informative.. Wonder when u get time to gather these type of info
ReplyDeletethankU very much for information.
ReplyDeletesuppose if you take a year is 365.242199 days ?
ReplyDeletePlease refer, "Indian Astronomy - An Introduction", by S.Balachandra Rao, Universities Press, Hyderabad, 2000, pages 47-48.
Deletehttps://www.amazon.in/Indian-Astronomy-Introduction-S-Balachandra-Rao/dp/8173712050