reg. Adhika masa and Kshaya masa
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pradeep
Jan 18, 2012, 2:24:46 AM1/18/12
to b-...@googlegroups.com, Dr. Balachandra Rao
Keerti, Pavan, and others..
This is reg. the concept of adhika masa used in luni-solar calendars in India.
The synodic period of moon is ~29.54 days which makes 1 lunar month. While the solar year is ~365.25 days. So this implies that we complete 12 lunar months ( 29.54 * 12 = 354.48 days) in every solar year with still few days remaining. i.e. 365.25 - 29.54 * 12 = 365.25 - 354.48 = 10.77 days
This extra 10.77 days of every solar year accumulates to make 1 Adhika masa. It takes 29.54 / 10.77 = 2.74 solar years for this to happen. The number of lunar months involved in 2.74 solar years = 2.74 * 12 = 32.913 lunar months.. This means this phenomenon of adhika masa happens every 32 or 33 lunar months.
Since 32.913 is a fraction, this necessiates the need to remove 1 month from the calendar at certain times to keep the solar and lunar calendars in sync. As you guessed it right, this is Kshaya masa. How often this happens can be calculated by expressing this number as continued fractions (I suppose)
This is the concept of adhika and kshaya masa as I understand from what I gathered in the wrokshop conducted by Dr.Balachander Rao's sir.
Dear Sir, Please confirm if I am right in my understanding and calculations.
This is reg. the concept of adhika masa used in luni-solar calendars in India.
The synodic period of moon is ~29.54 days which makes 1 lunar month. While the solar year is ~365.25 days. So this implies that we complete 12 lunar months ( 29.54 * 12 = 354.48 days) in every solar year with still few days remaining. i.e. 365.25 - 29.54 * 12 = 365.25 - 354.48 = 10.77 days
This extra 10.77 days of every solar year accumulates to make 1 Adhika masa. It takes 29.54 / 10.77 = 2.74 solar years for this to happen. The number of lunar months involved in 2.74 solar years = 2.74 * 12 = 32.913 lunar months.. This means this phenomenon of adhika masa happens every 32 or 33 lunar months.
Since 32.913 is a fraction, this necessiates the need to remove 1 month from the calendar at certain times to keep the solar and lunar calendars in sync. As you guessed it right, this is Kshaya masa. How often this happens can be calculated by expressing this number as continued fractions (I suppose)
This is the concept of adhika and kshaya masa as I understand from what I gathered in the wrokshop conducted by Dr.Balachander Rao's sir.
Dear Sir, Please confirm if I am right in my understanding and calculations.
Balachandra Rao
Jan 18, 2012, 5:11:18 AM1/18/12
to b-...@googlegroups.com
Dear Pradeep,
You are perfectly right! As regards the Kshayamaasa, you have
correctly explained its necessity
due to the fraction in 32.913. Therefore, compared to the adhikamasa,
the kshayamasa (a lunar month to be removed from a lunar year). is
less frequent and not completely periodic. It 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. The rule to determine a
kshayamasa is that in that particular lunar month there will be 2
solar "sankraantis" (see "Indian Astronomy - An Introduction",
S.Balachandra Rao, Universities Press, Hyderabad, 2000, pages47-48).
Balachandra Rao
You are perfectly right! As regards the Kshayamaasa, you have
correctly explained its necessity
due to the fraction in 32.913. Therefore, compared to the adhikamasa,
the kshayamasa (a lunar month to be removed from a lunar year). is
less frequent and not completely periodic. It 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. The rule to determine a
kshayamasa is that in that particular lunar month there will be 2
solar "sankraantis" (see "Indian Astronomy - An Introduction",
S.Balachandra Rao, Universities Press, Hyderabad, 2000, pages47-48).
Balachandra Rao
Sunil G.R.
Jan 18, 2012, 6:17:41 AM1/18/12
to b-...@googlegroups.com
Since a new thread is created for this, pasting the same from other thread.
+++++++++++
>>> [Balachandra Sir] To decide which lunar month is "adhika" (leap-month) the rule is simple: that lunar month (between two successive newmoons) is considered as adhika in which there is no (sidereal) solar ingress into the next "Rashi".
[sunil] I could not recall for a moment on the calculation of 'Adhika maasa'. I vaguely remember as below.
In simple terms, in whatever 'maasa', the Sun enters next constellation on Panchami (5th day of maasa), that particular 'maasa' will become 'Adhika' in the next year.
Will try to validate this and confirm.
I think the recent Adhikamaasa was bit early (just after 2 years).
+++++++++++
Ok. i verified for 2010's Adhika-maasa in April.
The formula i heard in simple terms is:
"In whatever 'maasa' the Sun enters next constellation (Sankranti) on Panchami (5th day of lunar month), in the next year, its NEXT lunar month becomes Adhika"
i.e. in 2009, Sun entered next constellation on 5th day of Chaitra maasa.
Next to Chaitra is 'Vaishaka'.
So, in 2010, 'Adhika Vaishaka' appeared after Chaitra-maasa.
i.e. in 2010, the order of maasa is:
Chaitra -> Adhika-Vaishaka -> Vaishaka.
In fact as Sir mentioned, in that Adhika Vaishakha, there were no Sankranti of Sun :).
But could not understand, how come 2 Sankrantis can happen in 1 lunar month!
As lunar month is ALWAYS lesser than Solar-month.
Regards,
Sunil.
+++++++++++
>>> [Balachandra Sir] To decide which lunar month is "adhika" (leap-month) the rule is simple: that lunar month (between two successive newmoons) is considered as adhika in which there is no (sidereal) solar ingress into the next "Rashi".
[sunil] I could not recall for a moment on the calculation of 'Adhika maasa'. I vaguely remember as below.
In simple terms, in whatever 'maasa', the Sun enters next constellation on Panchami (5th day of maasa), that particular 'maasa' will become 'Adhika' in the next year.
Will try to validate this and confirm.
I think the recent Adhikamaasa was bit early (just after 2 years).
+++++++++++
Ok. i verified for 2010's Adhika-maasa in April.
The formula i heard in simple terms is:
"In whatever 'maasa' the Sun enters next constellation (Sankranti) on Panchami (5th day of lunar month), in the next year, its NEXT lunar month becomes Adhika"
i.e. in 2009, Sun entered next constellation on 5th day of Chaitra maasa.
Next to Chaitra is 'Vaishaka'.
So, in 2010, 'Adhika Vaishaka' appeared after Chaitra-maasa.
i.e. in 2010, the order of maasa is:
Chaitra -> Adhika-Vaishaka -> Vaishaka.
In fact as Sir mentioned, in that Adhika Vaishakha, there were no Sankranti of Sun :).
But could not understand, how come 2 Sankrantis can happen in 1 lunar month!
As lunar month is ALWAYS lesser than Solar-month.
Regards,
Sunil.
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