Source for sanskrit verses : http://www.sacred-texts.com/hin/mbs/mbs06003.htm
The following verses are addressed by Veda Vyasa वेद व्यास to Dhritarashtra, before the Mahabharata War.
चतुर्दशीं पञ्चदशीं भूतपूर्वां च षॊडशीम
इमां तु नाभिजानामि अमावास्यां तरयॊदशीम
caturdaśīṃ pañcadaśīṃ bhūtapūrvāṃ ca ṣoḍaśīm
imāṃ tu nābhijānāmi amāvāsyāṃ trayodaśīm (28) : I know of new moon days on the 14th, 15th and even 16th tithis, but I have never this an amavasya on the 13th tithi.
चन्द्रसूर्याव उभौ गरस्ताव एकमासे तरयॊदशीम : Both the sun and moon are eclipsed (held..) in the same month on 13th tithi.
अपर्वणि गरहाव एतौ परजाः संक्षपयिष्यतः
candrasūryāv ubhau grastāv ekamāse trayodaśīm
aparvaṇi grahāv etau prajāḥ saṃkṣapayiṣyataḥ (29)
“A lunar fortnight had hitherto consisted of fourteen days, or fifteen days (as usual), or sixteen days. This, however, I never knew that the day of new-moon would be on the thirteenth day from the first *lunation , or the day of full-moon on the thirteenth day from the same. And yet in course of the same month both the Moon and the Sun have undergone eclipses on the thirteenth days from the day of the first lunation. 3 The Sun and the Moon therefore, by undergoing eclipses on unusual days, 4 will cause a great slaughter of the creatures of the earth.” Translation By Kisari Mohan Ganguli : Source : http://www.sacred-texts.com/hin/m06/m06003.htm. * A lunation ia lunar month: the period between successive new moons (29.531 days)
This rare occurrence is one of the clues used to date the Mahabharata War : http://oldthoughts.wordpress.com/ancient-indian-calendars/date-of-the-mahabharata-war/ : Unique eclipse pair combination just before the Bharata War! : based on “http://www.boloji.com/astro/00325a.htm : DrS.Balakrishna
For some more details, please see : Refer : http://ancientindians.wordpress.com/2010/12/07/the-mahabharata-war-1/
This is also very important because it sheds light on the debate around Sri Rama’s birthday :
Central to the debate about Casting Sri Rama’s Jataka Chakram is the location of Surya (the sun), in Mesha (Aries).
Moon’s position is certain to 3 degrees 20 min. This is because, Aditi Nakshatra is Punarvasu, only the fourth quarter (pada) of Punarvasu is in karkataka. Therefore Chandra is located in 0 to 3 deg 20 min of Karkataka.
Traditionally we believe that Surya is in Mesha. For this the degrees of separation between the sun and moon must be less than 93 degrees, even though nine tithis have passed.
If we hold on to a 12 deg per tithi figure hard and fast, then we have to place Surya in Meena (The sun will work out as behind the moon by 96 degrees to 108 degrees).
From the slokas in the Mahabharatam quoted above we see that 180 degrees can be covered in 13, 14, 15 or 16 tithis, per Vyasa’s observation, ie the degrees of separation between the sun and the moon per tithi is not a constant, but can vary slightly.
Which means that Surya in Mesha is probably right, since that is what traditional astronomers tell us. I have to learn how to calculate tithis.
Authorship and Copyright Notice : All Rights Reserved : Satya Sarada Kandula
To further study : The Length of the Lunar Cycle : from http://individual.utoronto.ca/kalendis/lunar/index.htm
In the present era the median length of the lunar cycle is about 29d 12h 30m, the average (MSM) is slightly more than 29d 12h 44m, the shortest lunations are about 29d 6h 30m, and the longest are about 29d 20h. Thus the length of the synodic month varies over a range spanning about 13h 30m. These variations were greater in the past and will diminish in the future:
- The longest lunar cycles occur when Moon is moving slowest (near apogee) and Earth is moving fastest (near perihelion).
- The shortest lunar cycles occur when Moon is moving fastest (near perigee) and Earth is moving slowest (near aphelion).
- The declining mean Earth orbital eccentricity tends to reduce the range of lunar cycle variations.
- The average lunar cycle (mean synodic month) has miniscule long-term change compared to short-term periodic variations.
Centile trends, per group of 4657 lunar months, based on SOLEX 9.1β numerical integration