Solution to an Astronomical problem

In an ecliptic calendar there are five types of Samvatsara.
1 Solar year:-This is based on the distance between earth and sun.Since earth revolves faster when it approaches the sun,the rate of revolution is faster in those months.So the length of day changes in ratio to that of the nights .Becaus eof this days in Utharayana period will be less .Similarly days in Dakshinayana period has to be longer.Because then earth is away from sun.The midpoint of these two is the samamandala or equal days,and this is calculated from the equator in India.India has the nearest landmass to equator in Lanka and southern most tip of South India and therefore the samarathradina of LANKA is considered as standard .The rasipramana given by old Sidhanthas were aware of this means they were aware of the eccentric nature of sun in relation to the orbit of earth .(see my book page for Rasipramana)

2.Brihaspathivarsha .It is based on revolution of Jupiter around sun in 12 years on which we condust Mahakumbamela,Mahamakham and elect a new sytem of administration .This is for our sociopolitical administrative and customary practices as well as protectionof knowledge of the revolution of graham.
3.Savanavarsha .From a particular place on earth,observe the sunrise and from one sunrise to another sunrise is taken as a day (saayana or moving day of earth around sun) due to rotation on its axis,and decide 360 degree for a circle and divide each Rasi into equal 30 day and make it 360 days.This is a practical way for easy calculation and used for political and social functions.The Bharanavarsha of a king ,or the time after a particular event(coronation,birth etc)is calculated in this way .The Christian calendar and western savanna calendar follow this method. They didn’t know the problem of the astronomical calculation and hence several problems did the encounter before they discovered what it really meant (almost a millennia they took to discover it).
4.Chandravarsha. Count from one Amavasya(new moon)to next amavasya. You get 12 fullmoons in 12 rasi .For this only 354.367 days are needed and it is 11 days less than the 365 days soura year.
5.Nakshathravarsha : stellar year.The span of one star in zodiac is 13.20 .The moon cross one star each and in 27.3 days does a circumambulation of earth,as observed bya observer sitting on earth .That is 27.3 X 12=327.6 days only is needed for this .This is 27 days lesser than the Chandravarsha and 38 days lesser than the savanavarsha .The sidereal year is based on relation of the position of the fixed star clusters and the movement of the graham in relation to that.For knowing this the observer on earth(since he cannot directly perceive his own planets place in space in relation to star)depend upon the nearest shining object ,the moon ,and thus the observation of moon and his movement in relation to the stars , is important for fixing the sphuta of the observed planet.The sidereal day is only 23 hrs 56 minutes and 4.0953 seconds and for practical purposes it is taken as 24 hours.But it is 4 minutes 55 seconds less than the 24 hours which we take as a day.

A synodic period is the the time between two subsequent grahayoga.In the case of earth and lunisolar graham ,it is from one amavasya to another amavasya.
In Mahabharatha there is a great prediction of a Grahana.And it was predicted that a Grahana will happen within 13 days .And Vyasa says it happened during the war.The scholars of the west and east have been quarrelling over this for several years .Their argument is a new moon happens only in 15 days and how could a new moon happen in 13 days?And because of this argument some even thought that the entire Mahabharatah is a myth.In the modern computer yuga ,no one suspects the possibility of such an event.But the greatness of Vyasa is that without a computer,without the modern scientific equipments the prediction was done,recorded .And the littleness of modern science is that to know the truth of it ,they had to wait for millennia .
Actually sayanavarsha is aillusion felt due to movement of earth around sun.Sun is not moving.The time from on samarathra to another samarathra ,in a particular place is 359.864 days .
The suryavarsha is 19.50 degree less than the nakshathravarsha due to inertia(nirayana)The difference between the seeming saayana and the real nirayana is the reason for the precision of equinox.Seasons/heat /cold etc have geographical differences .The feeling that the position of Sun in relation to star clusters move 0.0136 degree backward is only a Maaya/illusion felt by humans who sit on the earth,a moving sphere.In fact the relationship of fixed stars does not change at all.Therefore what one needs to do is just count Ahargana (as we do in Kaliyuga),observe the Chaya ,the movement of celestial objects reguarly .record them and keep for the Astronomical Gurukula(which took the place of the modern astronomical chairs of the world) and give the predictions etc from time to time to public as well as educate them to observe and know their nature scientifically and control life accordingly.The changing of the calendar is a foolish procedure.Observation is needed but changing day as Gregorian calendar makers did and even now the calendar makers are doing is creating all the trouble.They change the calendar according toeach persons or regions fancy and make confusion for all concerned and this started with Romans and then Europeans and now has spread to Indian astrologers as a disease.
Since thee is a co-ordinate relation between fixed stars and solar system as a whole ,it is always Nirayana and for man on earth it appears as saayana .In 25800 years only a wobble happens to earth’s axis and since the 9 moolathrikona (like Aswathi,Makha,Moola: bharani,Poora,Poorada etc)are co-ordinates when that wobble occurs the entire co-ordinate system has the same change and therefore it is never felt by earth . or its observers and it does not affect earth and its observer.
Between two Chandrayana points the movement of Chandra is in high speed.With a single nakshathramaasa it moves 360 degree.And the movement circle of the two chandrayanabindu is once in 18.6 years.In 9 years the extend or limit of the moons movement is outside that of the sunrise limit.Inthe rest of the hemisphere or radius moon does not go beyond it.Therefore observation of moons vridhikshaya(waxing and waning)and the paksha are very important.This is for knowing the distance between sun and moon.If we observe the speed of moon depending upon the nakshathra in which he is,one can also guess the movement of its center(earth)and its distance from its center.

Lag(a)na and Lagadha :

Na is Nashta or --and Dha is for Dhana or + and Lagakriya is done for finding out the kshaya and vridhi .(Dhanam and Nadham are spoken in opposites)

Many people(even great scholars ) mistakenly think that Lagadha is a person who lived in 1400 BC and it is from his period the Vedanghajyothisha was first known.
Laghadha is an Aksharasamkhya .Lagna also is an aksharasamkhya.
Laghadham is 333 hours
Laghnam is 330 hours.
They have 3 hours difference.
333/24 =13.21 (almost equal to the nakshathra avadhi 13.20)
In the interval of 13 days a grahana is possible.Without knowing the Nakshathravadhi ,the position of celestial objects and their sphuta and their retrograde movements and the shape of the ecliptic and the celestial objects no one can predict a eclipse ,whether in east or west.
336 hours is 14 days.A grahana(eclipse) followed by another of the same nature can therefore happen within 332-333 hours(less than 14 days or 13 days and shishta).From 3300 BC to 700 BC such couple grahana were observed in North India according to modern computer ganitha.In Rigveda Athri muni says that a complete solar eclipse happened 3 days before the sarad samarathra(samkhyayanabrahmana) which points to a double soalr eclipse.Mahabharatha,Atharvaveda,Rigveda know the law of Laghadha/Lagna (333-330=3).

Athithi and Thithi :-
Athithi is one who comes without looking for an auspicious Thithi and who has to be considered as God and served .Athithi devo bhava: That is a guest for an Indian ancestor.
Thithi is the difference between the longitudes of moon and sun obtained for an observer on earth.That is when a jyothishi says that today is this thithi or that,it simply means that the longitudinal distance between the sun and moon is mentioned.If I say ,today is Prathama ,the distance is between 0-12 degree.
See table below.
Prathama 0-12
Dwitheeya 12-24
Thritheeya 24-36
Chathurthi 36-48
Panchami 48-60
Shashti 60-72
Sapthami 72-84
Ashtami 84-96
Navami 96-108
Dasami 108-120
Ekadasi 120-132
Dwadasi 132-144
Thrayodasi 144-156
Chathurdasi 156-168
Avama /pornami (Vaavu) 168-180

Depending on whether it is Krishnapaksha or Suklapaksha the 180 degrees will beome opposites.Each of the 60 degrees represents 2 rasi .

In 19 years 235 Chandragrahayoga
In 228 years (which is 19X 12 ) 7 Adhimasa .
For 703 chandradina 11 varjithachandradina.
The 16547 varjithachandradina is for 1057500 days.
This is in Romakasidhantha.
The relation of it and derivation of it from Paithamahasidhantha I have discussed in detail in my commentary and comparative study on Panchasidhanthika of Varahamihira.








Figure from my manuscript to show the Zodiac and its relationship