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Indian Calendar Part 3 : The Panchangam

Syn­op­sis:

Hin­du units of time

Pan­changam

Thithi

- How to cal­cu­late the thithi

Vasara

Karana

Yoga

Naksha­tra, masa and ritu

Sam­vat­sara — 60 year Jupiter cycle

Sam­vat

We have looked at the var­i­ous cycles used for time­keep­ing. To sum­ma­rize,

  1. A solar day is when the earth rotates 360° around its axis, with respect to the sun. A solar day is 24 hours.

  2. A side­re­al day is when the earth rotates 360° around its axis, with respect to the fixed stars. A side­re­al day is 23 hours 56 min­utes.

  3. A trop­i­cal year (also known as a solar year) is the time that the sun takes to trav­el from the ver­nal equinox to the ver­nal equinox, along the rashi chakra. The mean trop­i­cal year is 365 days 5 hours 48 min­utes. (365.242216 days)

  4. A side­re­al year is the time tak­en for the sun to return to the same posi­tion in the rashi chakra with respect to the fixed stars after tra­vers­ing once around the rashi chakra. The mean side­re­al year is 365 days 6 hours 9 min­utes. (365.256374 days)

The trop­i­cal year is about 20 min short­er than the side­re­al year due to the pre­ces­sion of the ver­nal equinox, which caus­es it to move ret­ro­grade or back­ward in the rashi chakra.Hence the sun reach­es the ver­nal equinox faster.

  1. A side­re­al month is the moon’s orbital peri­od around the earth with respect to the fixed stars. (This is also equal to the moon’s peri­od of rota­tion around its own axis, due to syn­chro­nous rota­tion) The side­re­al month is about 27 days, 7 hours, 43 min­utes (27.32 days).

  2. A syn­od­ic month is the most famil­iar lunar cycle, defined as the time inter­val between two con­sec­u­tive occur­rences of a par­tic­u­lar phase of the moon, such as new moon or full moon, as seen by an observ­er on Earth. The mean length of the syn­od­ic month is (29 days, 12 hours, 44 min­utes (29.53059 days).

Note that hour, minute and day referred to as a time unit are all based on solar time (time mea­sured with respect to the sun), not side­re­al time (time mea­sured with respect to the fixed stars)

  1. A lunar cal­en­dar is a cal­en­dar based only upon the month­ly cycles of the moon’s phas­es (syn­od­ic months).

  2. A solar cal­en­dar, in con­trast, is based only upon annu­al cycle of the sun (the solar year or trop­i­cal year).

12 syn­od­ic lunar months make for 354 days, 8 hours, 48 min­utes (354.367056 days) which is the lunar year. Where­as, the solar year has 365 days 5 hours 48 min­utes. Hence lunar cal­en­dars lose around 11 days per year rel­a­tive to the solar cal­en­dar.

  1. A luniso­lar cal­en­dar is a cal­en­dar that is based on both the solar and lunar cycles. It indi­cates both the moon phase and the time of the solar year (loca­tion of the sun in the eclip­tic).

The Hin­du cal­en­dar, as also the cal­en­dars of ancient civ­i­liza­tions all over the world, are luni-solar.

Now, let us under­stand the var­i­ous aspects of the luni-solar Hin­du cal­en­dar called Pan­changam.

The Hindu units of time

Before going into the cal­en­dar, it is nec­es­sary to under­stand the Hin­du units of time. The time scales in the Hin­du tra­di­tion range from 10^-8 sec­onds (Tru­ti, the base unit) to 10^22 sec­onds (lifes­pan of Brah­ma, the cre­ator of the cur­rent uni­verse).

The West­ern time­keep­ing is based on solar time. The solar day is divid­ed into 24 hours of 60 min­utes each. Hin­du time­keep­ing is based on side­re­al time, with respect to the fixed stars. The ref­er­ence that is used for cal­cu­la­tions is 0° Aries. The side­re­al day, called naksha­tra aho­r­a­tram, is divis­i­ble into 60 ghatis of 24 min­utes each. Side­re­al hours, min­utes and sec­onds can be expressed in terms of solar hours, min­utes and sec­onds, and are sight­ly longer.

1 side­re­al sec­ond = 1.002738 solar sec­ond

How­ev­er, as an approx­i­ma­tion, side­re­al mea­sure and solar mea­sure of hours, min­utes and sec­onds, can be con­sid­ered equal.

The side­re­al year, var­sha, begins when the sun enters 0° Aries, and is com­plet­ed when the sun has tra­versed through 360° of the rashi chakra in 12 months. As we have seen, the start­ing point, 0° Aries is cal­cu­lat­ed using the naksha­tra Chi­tra and locat­ing the point 180° oppo­site it. (The fig­ure, giv­en in Part 2 of this arti­cle, is shown here as Fig. 1 again)

The sun’s entry into 0° Aries gen­er­al­ly falls on April 14 of the Gre­go­ri­an cal­en­dar. 14th of April marks the first day of the tra­di­tion­al Tamil cal­en­dar. The same date in April is observed by most tra­di­tion­al cal­en­dars of the rest of India — Assam, Ben­gal, Ker­ala, Odisha, Manipur, Kar­nata­ka, Pun­jab etc. This also coin­cides with the tra­di­tion­al new year in Bur­ma, Cam­bo­dia, Laos, Sri Lan­ka, Bangladesh, Nepal and Thai­land.

Fig. 1 — Sun’s entry point into 0° Aries — April 14

The Hin­du units of time are shown in Fig. 2

Fig. 2 — Hin­du units of time

Panchangam

The word Pan­changam is derived from the words “Pan­cha” mean­ing five, and “anga” mean­ing limb. The Pan­changam is the five-limbed Hin­du cal­en­dar.

The five angas that are used for time­keep­ing are: 1)Thithi (lunar day) 2)Vasara (solar day) 3)Karana (half of lunar day) 4)Yoga (soli-lunar com­bi­na­tions) 5)Nakshatra (lunar con­stel­la­tion)

The Pan­changam is a cal­en­dar based on both solar and lunar cycles. It indi­cates both the phase of the moon and the time of the year (the loca­tion of the sun in the rashi chakra).

The solar and lunar cycles tend to mir­ror one anoth­er -

  1. The new moon and full moon rep­re­sent to the month what the win­ter sol­stice and sum­mer sol­stice mean to the year, for dur­ing one syn­od­ic month, the moon cov­ers the same 360° of the sky that the sun cov­ers dur­ing one side­re­al year.

  2. While the sun’s 360° cycle is divid­ed into 12 months of 30° each, the moon’s cycle is divid­ed into 30 days of 12° each.

Thithi

A thithi or lunar day is defined as 1/30th of a lunar month, or the time it takes for the lon­gi­tu­di­nal angle between the moon and the sun to increase by 12 degrees.

As we have seen, there are 15 thithis in the Shuk­la pak­sha (bright fort­night, wax­ing), and 15 thithis in the wan­ing phase or Krish­na pak­sha (dark fort­night, wan­ing).

One com­plete syn­od­ic rev­o­lu­tion of the moon has 30 thithis that cov­ers 360° of the rashi chakra. (12° x 30 =360°)

1.Pratipada 2.Dwitiya 3.Tritiya 4.Chaturthi 5.Panchami 6.Shasti 7.Saptami 8.Ashtami (Half moon) 9.Navami 10.Dashami 11.Ekadashi 12.Dwadashi 13.Trayodashi 14.Chaturdashi 15.Purnima (Full Moon in Shuk­la pak­sha) or Amavasya (New Moon in Krish­na pak­sha)

Fig. 3 — The cycle of lunar thithis (Syn­od­ic month)

Fig. 4 — Thithi — 12° move­ment of the moon with respect to the sun

How to calculate the thithi

1.Find the lon­gi­tu­di­nal dif­fer­ence between the sun and the moon by sub­tract­ing the sun’s lon­gi­tude from that of the moon. (If the moon’s lon­gi­tude is less than that of the sun, add 360°.) 2.Divide this dis­tance by 12°, and drop the remain­der. (To divide, con­vert the min­utes into degree by divid­ing by 60) 3.If the quo­tient is 15 or less, quo­tient + 1 will be the num­ber of the thithi of Shuk­la pak­sha. If the quo­tient is more than 15, sub­tract 15, and the result will be the num­ber of the thithi in the Krish­na pak­sha.

For exam­ple, con­sid­er the fol­low­ing posi­tions of the sun and moon in the rashi chakra Moon — 7° 49’ Libra Sun — 21° 32’ Can­cer

Since the moon has tra­versed 6 rashis from 0° Aries before enter­ing Libra, it has already tra­versed 6 x 30° = 180°. The moon’s lon­gi­tude is 180° + 7° 49’ = 187° 49’.

Since the sun has tra­versed 3 rashis from 0° Aries before enter­ing Can­cer, it has already tra­versed 3 x 30° = 90°. The sun’s lon­gi­tude is 90° + 21° 32’ = 111° 32’. To find the lon­gi­tu­di­nal dif­fer­ence between the sun and the moon, sub­tract the sun’s lon­gi­tude from that of the moon. 187° 49’ — 111° 32’ = 76° 17’

Since 1° = 60′

17’ = 17/60 ° = 0.283°

Hence, 76° 17’ = 76.283°

Divid­ing 76. 283 by 12 gives 6.35.

The quo­tient 6 is tak­en and the remain­der is dropped.

6 + 1 = 7

Hence, the thithi run­ning is the 7th thithi, Sap­ta­mi.

Since 7 is less than 15, it is Sap­ta­mi of the Shuk­la pak­sha.

Length of a thithi Since the motions of the sun and the moon are always vary­ing in speed, the length of a thithi con­stant­ly alters. The vari­a­tions in the length of a thithi are giv­en in Table 1.

60 ghati = 24 hours

Table 1 — Great­est, least and mean lengths of thithi

Vasara

The time dura­tion from one sun rise to the next sun rise is reck­oned as a vasara in Pan­changam. This dura­tion is equal to 24 hora (hora is mod­ern hour of 60 min­utes).

There are 7 vasara in a week, 7 being the num­ber of the pri­ma­ry gra­has in Vedic astron­o­my and astrol­o­gy. Each vasara is presided over by a gra­ha. That is how the vasara are named.

Vasara and thithi : As the time dura­tion of thithi can vary from 21 hours to 26 hours, the thithi’s begin­ning and end occur at dif­fer­ent times of the vasara, which has 24 hours. Some­times, a vasara can have 2 begin­ning points of suc­ces­sive thithis.

The names of the vasara in Eng­lish, San­skrit, Tamil and their pre­sid­ing gra­has, are shown in Fig. 5

Fig. 5 — Vasara and gra­has

Karana

Just as a solar day is divid­ed into two por­tions as day and night, the lunar day or thithi is sim­i­lar­ly divid­ed into two karanas, of 6° each. 11 dif­fer­ent karana are per­mut­ed to make up the 60-karana month­ly cycle. Of the 11 Karana, the first 7 are con­sid­ered chara (mov­able) karana. The last 4 are con­sid­ered sthi­ra (fixed) karana.

Chara karana (mov­able) 1.Balava 2.Taitila 3.Vanija 4.Bava 5.Kaulava 6.Gara 7.Vishti

Sthi­ra karana (fixed) 8.Kinstughna 9.Shakuni 10.Chatushpada 11.Naga

As we can see in Table 2, most of the karanas of Krish­na pak­sha are iden­ti­cal to those of Shuk­la pak­sha except that the con­sec­u­tive cycles of the 7 chara (mov­able) karanas of the Krish­na pak­sha are one thithi behind those of the Shuk­la pak­sha.

Table 2. The karana

Yoga

The San­skrit word Yoga means “union, join­ing, attach­ment”. In the astro­nom­i­cal con­text, it refers to the join­ing of the celes­tial lon­gi­tudes of the sun and the moon. The 27 yogas reflect the nature and effect of the inter­ac­tions of the sun and the moon.

Table 3. The 27 luni-solar yoga

How to calculate the yoga

1)Add togeth­er the lon­gi­tudes of the sun and the moon. 2)Subtract 360° if pos­si­ble. 3)Divide the result by 13° 20’, and drop the remain­der.

To divide, first con­vert the result entire­ly into min­utes and divide by 800. (Since 13° 20’ = 800’)

1° = 60’

4)The quo­tient + 1 will be the num­ber of the yoga.

Nakshatra, masa and ritu

Naksha­tra in Pan­changam refers to the lunar con­stel­la­tion in which the moon is locat­ed. There are 27 naksha­tras, as we have seen in Part 1 of this arti­cle. It is shown here again in Fig. 6

Fig. 6 — The 27 naksha­tras

Relationship of nakshatra and masa (month)

The month in the Pan­changa is based on the solar cycle. The start of the month is con­sid­ered to be 0° entry of the sun into a rashi. The 12 rashis cor­re­spond to the 12 months. Each month has days vary­ing from 29 to 32.

Many of India’s region­al cal­en­dars name their months after the naksha­tra in which the moon will sit (or some­times, will be near to) when it is full. The first month of the Hin­du cal­en­dar cor­re­sponds to the spring month when the full moon occurs in the naksha­tra Chi­tra, and the month is known as Chaitra. Table 4. shows the rela­tion­ship of the lunar months with the naksha­tras. This is also shown pic­to­ri­al­ly in Fig. 7.

Table 4. Rela­tion­ship of naksha­tras and months

Fig. 7 shows how the Hin­du months are named after the naksha­tra in which the full moon occurs. Since the full moon occurs when the moon is oppo­site the sun in its orbit around the earth, the naksha­tra of the full moon is gen­er­al­ly 180° oppo­site to the rashi the sun is, in that par­tic­u­lar month.

Fig. 7 — Naksha­tra of the full moon and masa

In Fig. 8, we see that the start of the Gre­go­ri­an month cor­re­sponds to entry of the sun into the 15° (approx­i­mate­ly) of the rashi (side­re­al zodi­ac). While the start of the Hin­du month cor­re­sponds to entry of the sun into the 0° of the rashi. This 0° entry into the rashi is the reck­on­ing of the month in the Hin­du cal­en­dar.

Fig. 8 — Gre­go­ri­an month and Hin­du month

Relationship of masa, ritu (season) and festivals

All the Hin­du fes­ti­vals and reli­gious hol­i­days in India are dat­ed using the Hin­du luni-solar cal­en­dar, not the Gre­go­ri­an solar cal­en­dar. In the West­ern sys­tem, there are 4 sea­sons — spring, sum­mer, autumn and win­ter. In the Indi­an sys­tem, there are 6 sea­sons, as 2 months make for a sea­son, ritu. The ritu are Vas­an­ta (spring), Grish­ma (sum­mer), Var­sha (mon­soon), Sharad (autumn), Heman­ta (win­ter) and Shishi­ra (pre­ver­nal*) Table 5. shows the rela­tion­ship of masa, ritu and fes­ti­vals.

*Pre­ver­nal is the peri­od from the end of win­ter and begin­ning of spring.

Table 5. Rela­tion­ship of month, sea­son and fes­ti­vals

Samvatsara — 60 year Jupiter cycle

The 60-year cycle is com­mon to both North and South Indi­an tra­di­tion­al cal­en­dars, with the same name and sequence of years. After the com­ple­tion of 60 years, the cal­en­dar starts anew with the first year. This cor­re­sponds to the Hin­du “cen­tu­ry.

Bri­has­pati chakra Jupiter has a side­re­al peri­od (with respect to fixed stars) of 11 years, 314 days, and 839 min­utes, which is almost about 12 years. Its syn­od­ic peri­od* brings it in con­junc­tion with the sun every 398 days and 88 min­utes, which is a lit­tle more than a year. Thus, Jupiter in about 12 years and sun in one year pass through the same series of naksha­tras. So a giv­en year can be dat­ed as the month of a 12 year cycle of Jupiter. A col­lec­tion of 5 such cycles or 60 years is called Bri­has­pati-chakra, and each of the 60 years has dis­tinct names, giv­en in Table 6.

The cur­rent year 2018–2019 is named Vil­am­bi.

* Time peri­od between two suc­ces­sive con­junc­tions of the same two celes­tial bod­ies

Table 6. Sam­vat­sara — 60 year Jupiter cycle

Samvat

Sam­vat refers to era. Sev­er­al Indi­an cal­en­dar sys­tems use the era or Sam­vat to pro­vide a his­toric ref­er­ence, like how the Gre­go­ri­an cal­en­dar uses the Com­mon Era which has the birth of Jesus Christ for its his­toric ref­er­ence. Vikra­ma era refers to the coro­na­tion event of the leg­endary king Vikra­ma­ditya in Ujjain. Cur­rent­ly we are in 2075 Vikram Sam­vat.

To sum­ma­rize,

The Hin­du Pan­changam is a luni-solar cal­en­dar that keeps time based on both solar and lunar cycles in par­al­lel.

  1. Var­sha (year, posi­tion of the sun) It cal­cu­lates the var­sha based on the solar cycle. A var­sha is the side­re­al year, the time the sun takes to return to 0° Aries in the rashi chakra, about 365 days. It typ­i­cal­ly falls on April 14 of the Gre­go­ri­an cal­en­dar.

  2. Vasara (solar day) It cal­cu­lates the vasara based on the solar cycle. A vasara is the time from one sun­rise to the next and is divid­ed into 24 hours or 60 ghatis. Since this time peri­od is reck­oned with respect to the sun, a vasara is a solar day or trop­i­cal day.

  3. Thithi (lunar day) It cal­cu­lates the thithi based on the lunar cycle — syn­od­ic move­ment. A thithi is the time tak­en by the moon to move 12° with respect to the sun in the rashi chakra. There are 30 thithis in a syn­od­ic lunar month.

  4. Naksha­tra (lunar month, posi­tion of moon) It cal­cu­lates the naksha­tra, based on the lunar cycle — side­re­al move­ment. The naksha­tra is the naksha­tra in which the moon sits. There are 27 naksha­tras and the moon spends about a day in each. This cor­re­sponds to the 27.3 days in a side­re­al lunar month.

  5. Masa (month, posi­tion of the sun) It cal­cu­lates the masa based on the solar cycle. A masa begins when the sun enters 0° of a rashi. There are 12 months, with days that vary from 29 to 32. It names the month based on the lunar cycle — side­re­al move­ment. The month is named after the naksha­tra in which the full moon will sit, or be close to.

  6. Karana (half of lunar day) Just as we have day and night as the two halves of for a solar day, the thithi or lunar day is divid­ed into two karanas, of 6° each. There are 11 karana which are per­mut­ed to make up the 60 karana syn­od­ic month.

  7. Yoga Yoga are 27 luni-solar com­bi­na­tions that reflect the nature and effect of the inter­ac­tions of the sun and the moon.

We have under­stood the Hin­du way of time­keep­ing in rela­tion to the astro­nom­i­cal cycles. But how do these astro­nom­i­cal cycles relate to the human body cycles? This will be explored in Part 4.

Table 1 — Basics of Pan­changamm by S. Narasimha Rao http://multifaiths.com/pdf/Panchang.pdf

Light on Life : An Intro­duc­tion to the astrol­o­gy of India by Robert Svo­bo­da and Hart de Fouw The Cal­en­dars of India by Vin­od K Mishra https://arxiv.org/ftp/arxiv/papers/1007/1007.0062.pdf

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