Mathematical Astro - Panchang

7/29/2019 Mathematical Astro - Panchang

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CHAPTER 9Panchanga

Panchongos a Sanskrit word which consistsof twowords poncho * anga. Panehameans five and angameans parts or limbs. So, ponchanga means fivelimbs.Thesefive limbs are:(1) day(2) tithi(3) nakshatra(constellation)(4) karna(5) yoga1. DAY

Day here is the weekday to decide the lordshipof the concerned day. In the Indian astronomy theday is considered to be form sunrise to just beforethe next sunrise.

In the Western system, the name of the day iscalculated easi ly f rom the dates of Gregor iancalendar. The exact interval between the twosuccessive ernal equinoxes, .e. a tropical year, s 365


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Astronorny Releuant to Astrology

days 5 hours 48'and 45.3"or, say,365.2422 ays.Whenit is mult ipl ied by 100, t gives 24.22extra days (inexcess of 365 days per year) in a century. So, PopeGregory XIII adopted a calendar in 1582accordingto which normally years will be of 365 days each butthe years which are divisible by 4 without remainder,such as 1988, L992,etc. will have 366 days, but thecenturies, i.e. the year which are multiple of 100butnot multiple of 400 will only 365 days and the yearswhich are multiple of 100 and also multiple of 400will have 366 days.

Because there were 24.22days extra in a centgryso 24 days have been added 4, 8 ,L2... up to 96 andnot 100;and 0.22 x 4 = 0.88, .e. approximately I dayhas ben added in the 400 years.

In one year when 365+7 leavesa remainder of 1so if the January 1, 1949 was Saturday, the January1, 1950wil l be one week day extra i.e. Sunday.In onecentury i.e. in 100 years the number of remainingdays will be 100 * 24 leap days i.e. 124 extra daysthan complete weeks, which means (124+? leaving aremainder of 5) 5 extra days only after omitt ingcomplete weeks.

In 100 years (one century), the number of daysmore than the complete weeks = 5.In 400 years (four centuries), the number of days

more than the complete weeks = 20 + 1 as the 400thyear is also a leap year = 21 which is divisible by 7.Thus, a period of four centuries folds up in completeweeks. This implies that the day on January 1, 1201wil l be the same as on January 1,801,or 1601,or 2001.


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Astronomg Releoant to Astrologg

ExampleThe following is an illustration how to calculatethe day of a week in Gregorian calendar which ispresently n vogue.

To find out the day on March 4, 1988.Number of days more than completeweeks n 1600 ears = Q

.' Number of days more than completeweeks n 300years = 5 x 3 + Trremainder= 1Number of daysmore than complete weeks(as87yearspass) = 87 * 7, remainder = 3Leap days n 87years = 2l * 7, remainder = 0Number of days more than completeweeks n January 88 = 31 * 7, remainder = 3Number of days more than completeweeks in February 88 = 29 + 7 remainder = 1Number of days more than completeweeks in March 88 = 4 i 7, remainder = 4Total =L2Now, L2 + T leaves he remainder 5.

Now count it Monday if the remainder is l,I\resday if it is 2, Wednesdayf 3, Thursday if 4, Fridayif 5, Saturday f 6, and Sunday f 0 or ?.. The day on March 4, 1988 s thus Friday as theremainder s 5.2. TITHI

A lunar month is from the end of one orrr';aoeayo

100


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Astronomg Reletsont to Astrologg

to the end of succeeding amaoasAo, .e. the differencebetween the longitudes of the Moon and the Sun startincresing.As there are 360' in the zodiac,so in a lunarmonth the Moon moves 360omore than that of theSun. There are 30 t ithis in one lunar month.

So,one ithi= 399"=rz'30The following table shows the tithis and thedifferenceof the longitudesof the Moon and the Sun.

Shukla Paksha (Bright Halfl

r0r

Name Tithi No. Longitude ofMoon - Sun

PratipadaDviteeyaTriteeyaChaturthiPanchamiShashthiSaptamiAshtamiNavamiDashamiEkadashiDwadashiTrayodashiChaturdashi

12345678I

1011L213L4

0o to 12"L2' to 24o24' to 36o36o to 48o48" to .60o60o to 72"72" to 84'84' to 96'96o to 108"

108" to t20"L20" to t32"132" to L44'144' to 156"156' to 168'


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t02 Astronomy Reletsont o AstrologyYyrishnaPaksha Dark Halfl

Name Tithi No. Longitude ofMoon - SunPratipada

DviteeyaTriteeyaChaturthiPanchamiShashthiSaptamiAshtamiNavamiDashamiEkadashiDwadashiTrayodasiChaturdashiAmavasya(New Moon)

180" to L92"192' to 204"204" to 216"216' to 228"228" to 240o240" to 252o252' to 264o264" to 276o276" to 288'288" to 300'300" to 312"312" to 324"324' to 336'336' to 348'348" to 360o

16t71819202L222324252627282930

The lst tithi startswhen the Moon starts movingaheadof the Sun, i.e. more than 0odifference.Whenthe differnce becomes ust more than 12o, he tithibecomesDviteeya.Similarly, it is for other tithis.The above s the scheme or the tithis but these30 tihtis falls in approximately 29.5days and not in30 days.The Moon movessometimes ast, .e.about15o n 24 hours and sometimesslow, about 12. n 24

hours. Tithis are dependingupon the net differenceof motion of the Sun and the Moon.Their individual


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Astronomg Releoont to Astrologg

motions depend upon their distances from apogee orperigee.This fast and slow movement of the Moon causessometimes the losing of a tithi and sometimes gaining

a t ithi. The principle behind it in the Indian lunarcalendar is that the tithi which is at the time of sunriseis the tithi of the day. Whether that tithi may remainfor a few minutes in that day or it may prolong uptothe next sunrise. A tithi which starts after sunriseand ends before the next Sun rise is said to be missedin that fortnight. If a tithi which starts just beforesunrise and ends after the next sunrise will be havingtwo days in its name in that fortnight. The systemwas introduced for day-to-day working of the society.The formula for the calculation of tithi:

Longitude of the Moon - Longitude of the SunIT

Example. Calculate ithi at 11.30a.m. on October L2,2000Sun's Moon'sLongitude Longitude

103

On Oct. 13,2000 t 5.30a.m.On Oct.13,2000 t 5.30a.m.Difference for 24 hoursDifference for 6 hoursLongitudeat 11h.30'a.m.A + B)As one sign = 30o,so

7127"25' 2. 19056'7126" 24' ',ll 2" 50 1',A

10 I' 14" 55'15' B' 3044'.8'

7'260 39' 2 ' go 45'236'39' 6go 45'


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104 Astronong Re|r'oont to Astrolagg

68" 45' - 236"39'By the above formula,As 68"45'is less han 236o 9',add 360" n 68"45'

4280 45', - 236039' 19r 6'= - L2. -.006'= to

12which shows hat 16 ithis havepassedand the 17this running at that time and its 0o6'have passedoutof 12".

The tithis at a particular moment are calculatedin the abovemanner.Now you will seehow the tithis last for two daysor are missed.The principle behind it is that for socialpurposes he tithi of a day is the tithi which is at thet ime o f the sunr ise on tha t day. I t shou ld beremembered hat it is for socialpurposesand it doesnot mean that tithi will in reality remain for the wholeof day.ExamplesHow a tithi is missed or tithi kshago.T\po such examplesare given below:(1) Take he caseof October18,2000and of October19,2000.Sunrise at Delhi on October 18 s at 6h28'a.m.Tithi on October 18,2000 s calculatedasunder:

T2

L2


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Astronomg Releoont to Astrology

Tithi =i Longitude of the Moon - Longitudeof the Sun

LT2" 10 4 ' - 6 . 10 5 ' ,Ti th i=--T

, = 61o4' - 181o5'L2As 61 s shorter han 181,add 360 n 61.

6104' + 360' - 1810 'Tithi = -L2

239o 9' ,^11o59'- -.L2L2It shows that 19 tithis have passedand 20th isrunning.So, he tithi of October18,2000 ill be calledkrt shna paksha panehmi.Tithi on October 19, 2000 s calculatedbelow.sunriseat Delhi on that day is at 6h28' a.m.

Tithi_2' 15o9' - 6" r 5'

L2. =Ys, 75o9' + 360o - 182o 5'

105

L2


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106 Astronomg Reboont to Abtrologgtithi is running on 19thOctober.

Hence, the tithi on October lg, 2000 s KrishnoPakshaSaptami.It is seen hat 2lst tithi hasbeen missed.(2) Take another case of miss ing t i th i , i .e . o fFebruary2,200Land February3,2001.Sunriseat Delhi on 2nd February s at 7.13a.m.Sunriseat Delhi on 3rd February s at 7.12a.m.Colculation of tlthi on Znd Febntory:Tithi =

Longitude of the Moon - Longitude of the SunIT

0" 2502l' - 9' 19"24'L2250zl'. - 289 24',

L225021',+ 360- 289024'.L295o 57' , ' l lo 57 '= ._L2 t2

Saptami has passedand Shulclo PolcshoAshtomiis running.Calculation of tithi on 3rd Febru,ory:

1'8" 50' - 9' 20025'Tithi = L2


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Astronomy Releoont to

38050' - 290 25'L210go25' ^00 25'= rz =o Lz

Nine tithis havepassedand tenth is running. Sotithi on February 3rd, 2001 s ShulcloPokshaDashami.It may be seen hat Navami hasbeenmissed.Example qf Adhik Tithi(3) Takethe caseof October6, 2000and October ?,2000. ; 'Sunrise at Delhi on October 6, 2000and October ?,2000 s at 6.21a.m.Tithi colculation on October6,2000 is as under:

Tithi = 8' 250 29'. - 5' 1go13'L2265"29'. 169o13't296" 15' ^00 15'

= -= - -t2 L2Eighth tithi haspassedand ninth is running. So,the tithi of October 6, 2000 will be called ShukloPokshoNaaami.

Tithi on October7,2000 is caleulated, s under:9" 7016' - 5" 20 L2'Tithi =


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r08 Astronomy R.eleoontto Astrology277"16', 170"Lz',t21o7o4' ^11o4'= s -12 L2

Eight tithies have passedand gth is running atthe time of Sunrise.Hence, he tithi of October7,2000is Shukla PakshaNavami. By this it is seen hat thetithi for October6, 2000and October 7,2000 s Navamifor both the days.(4) Calculation of tithies on January 31, 2001andFebruary 1, 2001are given below.Tithi of 3lst January, 2001

Tithi = 11'290z?', g', L7"22'.t2359"27' - 2870 2',t27? 5' ^0P5'= O -t2 L2

i.e. ShulcloPolcshoSoptomiTithi on February 1, 2001

0' l2g 13' - I' 18" 23'L2

11 13' - 288023'Tithi =

L2


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1? 13' + 360" - 2ggo 3't237r 13'- 2ggo 3'L2

)83o50' ^11e50'= U _t2 L2,rvhich shows that ShutclaPakshaSaptmi s runningat Surrriseof February 1, 2001.

..r_ So,ShulcloPolcshaSaptmi s for two days,namely,January 31,2001and February 1,2001.3. NAKSHATRA

The division of the zodiac in 27 nakshatrashasbeenshownat in chapter5.However, he calculationsfor finding out the number of nakshatras s asunder:The 27 nakshatrasare in 360.So, one nakshatra

= rr1. i.e. 3o2o,3 'Example

Now, we have to find the nakshatraof the Moonwhose ongitude is, say,24S"lG'.The.nakshatranumber will be arrived at

245016'

3600=- 27


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(245x60+16)-- (13x 60 + 20)'14700' 16'= ?80 '+20 '14716'800' = 1g316'800'

i.e. the 2nd quarter, or pada, or charan of 19thnakshatra (Mula nakshatra).If the remainder s from I'to 200'it is lst quarter;i f i t is201' to400' i t s2ndquarter; f i t is401' to600' i tis 3rd quarter; if it is 601' o 800' t is 4th quarter'

Names of Nakshatras(1) Ashwini(3) Krittika(5) Mrigashirsha(7) Punarvasu(9) Ashlesha

(11) Purvaphalguni(13) Hasta(15) Swati(17) Anuradha(19) Mula(21) Uttarashadha(23) Dhanistha(25) PurvabhadraPada(27) Revati

(2) Bharani(4) Rohini(6) Ardra(8) Pushya(10) Magha

(12) Uttaraphalguni(14) Chitra(16) Vishakha(18) Jyeshtha(20) Purvashadha(22) Shravana(24) Satabhisha(26) UttarabhadraPada


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Astronomg Releoont to Astrologg l l l; This way by changingthe signsand degrees ntominutes and dividing by 800', he quotient gives henumber of nakshatraspassedand the remaindergives the minutes of the next nakshatra which haspassedout of 800'.

In the above manner, we can calculate thenakshatra of any planet at any moment,provided theNiragana longitudes are known.But, when we saywhat nakshatra is running atpresent, the reference n Panchangos always to theMoon's nakshatrawhich is required for doshaphalaswell asmuhurta.

4. I(ARANAIn each tithi there are two karanas. The firstKarana ends at the middle of the tithi and the secondends with the ending of the tithi. The two halvesarenot obtained by dividing the time of the tithi in twohalves.Each Karana is decided by the time taken bythe Moon to gain over the Sun by a margin of 6' (asagainst12on the caseof a tithi).'Themethodof colculating the tithi is:Tithi =

Longitude of the Moon - Longitude of the SunLT

Quotient * 1 gives he Tithi.Thefortnula for colculating Karono is:Karana =

Longitude of the Moon - Longitudeof the Sun


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Lt2 Astronomg Relerso,nto AstrologyThe quotient + l will give the number of Karanasrunning.

Names of Karanas1. Bava2. Balava3. Kaulava4. Taitila5. Gara6. Vanij7. Vishtiwhich repeat eight times, i.e. ? x 8 = 56 such Karanasplus four others, namely,

i\ Shakuniii) Chatushpadaiii) Nagaia) Kintughna

Making a total of 56 + 4 = G0Karanas in 30 tithis.In other words, there are eleven di f ferentKaranas:4 non-recurring and sevenrecurring 8 timesduring a lunar month. Alll these ll Karanas havedistinctive characterstics attached to them. SomeKaranas like Vishti (Bhadra), Shakuni, Chatuspada,Naga, Kintughna are inauspicious and someare good.for muhurta of various rituals, ceremonies, etc.Example

Take the case of October 18, 2000 at 6.25 a.m.(given in this chapter in the example of missing tithiat page.)


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Karana =Longitude of the Moon - Longitude of the Sun

Karana =6o

2 " l 4 ' , - 6 " 1 0 5 '6

6lo 4' - 1910 '6As the longitude of the Moon is less than thelongitude to the Sun,add 360'to the longitudeof theMoon.

42'- 4', - 19105'

i.e. 40th Karana was running or the 2nd Karana of20th tithi (40+ 2)was running. The tableshows hatthe 2nd Karana of 20th is 4th Karana, i.e. Taitila.Tithi lst 2nd Tithi lst 2ndKarana Karana Karana Karana

23go59'6

3g5o59'6

246

I35

I23

Kintughna24

16L718

357


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tl4 Astronomg Releoont to AstrologgTithi lstKarana Tithi lst 2ndKarana Karana

2ndKarana

678I

l011t2

,13L415

3572461'357

4613bI2461

2156227123232445256726L22734285629 7 Shakuni30 ChatushpadaNaga

5. YOGAYogas are the result of combined movement ofthe Sun and the Moon. Thesecan be inauspiciousorauspicious for arriving at proper muhurta.

Names of Yogas1. Vishakumbha3. Ayushman5. Shobhana7. Sukarma

'9. Shula11. Vridhi13. Vyaghata15. VajraL7. Vyatipata19. Prigha

2. Priti4. Saubhagya6. Atiganda8. Dhriti

10. Ganda12. DhruvaL4. Harshana16. siddhi18. Variyan20. Shiva


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Astronomg Releoont to Astrologg l 1 521. Siddha 22. Sadhya23. Shubha 24. Shukla (Shukra)25. Brahma 26. Indra27. Vaidhriti

The names of Aogas hemselves ndicate (fromtheir word meaning) where these are auspicious(good)and were theseare inauspicious bad).So,eachyoga= Y = 13o?0 '= 00 '

The ortnula for calculating goga:Yoga =

Long. of the Sun * Long. of the Moon(in minutes)800'

ExampleAny moment for which the yoga is to be foundout, say, or example,Sun's ongitudebe 9*3o23' andMoon's ongitudebe 2"6o 6'(January 8,1992 t 5.30a.m.)

q'39 23' + 2' 6o36'. Yogaat that time tithi = ff_ [(9' go)+3"]xo+ze' [(z' go)+e"]xo+ge'800'

16403' 3996'= -- 8oo--


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20399'800'

_ 253gg'900'25thyogahaspassedand26thyoga, .e. ndra wasrunning at that time.

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Mathematical Astro - Panchang