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Indian Astronomy: Part 3

We have looked at the fun­da­men­tals of astron­o­my. Let us under­stand how time­keep­ing is relat­ed to the astro­nom­i­cal cycles or pat­terns.

The day, month and year in time­keep­ing is syn­chro­nized with the cycles of celes­tial objects in the sky. Now, there are vari­a­tions in the way these cycles are mea­sured, which are impor­tant to know for under­stand­ing the dif­fer­ence between the West­ern and Vedic sys­tem of time­keep­ing.

Tropical and sidereal zodiac (rashi)

The tropical zodiac (Western)

The zodi­ac used in the West­ern sys­tem, called the trop­i­cal zodi­ac, is no longer based on the stars. It does not cor­re­spond to observ­able posi­tions. The begin­ning of the trop­i­cal zodi­ac, 0° Aries, is iden­ti­cal with the ver­nal equinox, the place of the sun on the first day of spring, not with any fixed stars. The trop­i­cal zodi­ac is not based upon the stars but on the ori­en­ta­tion of the earth to the sun. The Trop­ics of Can­cer and Capri­corn denote the places of the sun at the sum­mer and win­ter sol­stices.

  1. The trop­i­cal zodi­ac begins with the sun’s place at the ver­nal equinox, which it des­ig­nates as the begin­ning of Aries 0°.

  2. It regards the posi­tion of the sun at the sum­mer sol­stice as 0° Can­cer.

  3. It regards the posi­tion of the sun at the autum­nal equinox as 0° Libra.

  4. It regards the posi­tion of the sun at the win­ter sol­stice as 0° Capri­corn.

Thus, the sea­sons mark the car­di­nal points of the trop­i­cal zodi­ac. The name trop­i­cal comes from the Greek word “tropikos” mean­ing “turn”. The Trop­ics of Can­cer and Capri­corn mark the extreme north and south lat­i­tudes (+23.5° and ‑23.5°) where the sun appears direct­ly over­head on sol­stices, and where it appears to “turn” in its annu­al sea­son­al motion. (Dak­shi­nayana and Uttarayana in Vedic astron­o­my).

The sidereal zodiac (Vedic)

The zodi­ac that cor­re­sponds to the actu­al con­stel­la­tions or the fixed stars is called the side­re­al zodi­ac. The Vedic sys­tem uses the side­re­al zodi­ac. The Vedic zodi­ac regards the begin­ning of Aries 0° as the actu­al con­stel­la­tion Aries, which is mea­sured using the naksha­tra Revati. (Sri Yuk­tesh­war uses this method). Anoth­er method to deter­mine 0° Aries is to use the naksha­tra Chi­tra and place the begin­ning of the zodi­ac exact­ly oppo­site or 180° from it. The word side­re­al comes from the Latin word “sidus” mean­ing “star”.

The trop­i­cal zodi­ac is not the real zodi­ac because, the ori­en­ta­tion of the equinox­es with respect to the dis­tant stars changes over time, due to the pre­ces­sion of the earth on its axis (as we have seen). Over a peri­od of 24,000 years, the ver­nal equinox point tra­vers­es the full cir­cuit of the actu­al zodi­ac. Hence, accord­ing to the West­ern sys­tem, the start­ing point of Aries also tra­vers­es the full cir­cuit. Around 2000 years ago, when West­ern astrol­o­gy was in its for­ma­tive stages, the two zodi­acs coin­cid­ed. Since then, because of pre­ces­sion, the two zodi­acs have been slow­ly mov­ing apart. There­fore, the trop­i­cal zodi­ac shows the actu­al astro­nom­i­cal posi­tions of some 2000 years ago, not the cur­rent astro­nom­i­cal posi­tions.


The trop­i­cal zodi­ac is also called sayana in San­skrit. Sayana means “with ayana”, ayana refer­ring to pre­ces­sion. Sayana means that the start­ing point of Aries is deter­mined with ref­er­ence to the pre­cessed equinoc­tial point. The side­re­al zodi­ac is also called nirayana in Sanksrit. Nirayana means “with­out ayana”. Nirayana means that the start­ing point of Aries is deter­mined with­out ref­er­ence to a pre­cessed point, but to the actu­al observed posi­tion of the dis­tant stars.

The dif­fer­ence between the trop­i­cal and side­re­al zodi­acs is called ayanamsha. It is the dif­fer­ence between the point of ver­nal equinox and that of the first point of the con­stel­la­tion Aries. The Ayanamsha as cal­cu­lat­ed by Sri Yuk­tesh­war is 21° 46’.

Fig. 1 — Nirayana, Sayana and Ayanamsha

Reckoning of the day

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

Solar day begins at noon 12:00 hours. The earth has to rotate more than 360° for the sun to come back to noon. (As explained below)

Side­re­al day 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.

The dif­fer­ence is because the earth moves a lit­tle in its orbit dur­ing the time it takes to spin once around its axis. Hence the earth needs to turn a lit­tle more than 360° to face the sun at the orig­i­nal posi­tion. (Shown in Fig. 2) The lines point­ing to the dis­tant star are par­al­lel because the star is locat­ed at infin­i­ty, as viewed from the earth.

Note that “hour” and “minute” referred to here are based on solar time.

Fig. 2 — Solar day and side­re­al day

Reckoning of the year

Trop­i­cal year A trop­i­cal year (also known as a solar year) is the time that the sun takes to return to the same posi­tion in the cycle of sea­sons, as seen from Earth — the time from ver­nal equinox to ver­nal equinox.

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. (All celes­tial bod­ies move from east to west in the rashi chakra. When a celes­tial body moves from west to east, it is said to be in ret­ro­grade). Hence the sun reach­es it faster.

The trop­i­cal year is the inter­val at which sea­sons repeat and is the basis for the cal­en­dar year.

The aver­age trop­i­cal year is 365 days 5 hours 48 min­utes. (365.242216 days)

Side­re­al year A side­re­al year is the time tak­en by the earth to orbit the sun once with respect to the fixed stars. Hence it is also the time tak­en for the sun to return to the same posi­tion with respect to the fixed stars after tra­vers­ing once around the rashi chakra.

The aver­age side­re­al year is 365 days 6 hours 9 min­utes. (365.256374 days)

Note that “days”, “hours” and “min­utes” men­tioned here are based on solar time.

Reckoning of the month

The words “moon” and “month” have a com­mon ety­mo­log­i­cal ori­gin. In many tra­di­tions of the world, the cycles of moon phas­es are used to reck­on time.

Month based on lunar cycle

Trop­i­cal month The trop­i­cal month, sim­i­lar to the trop­i­cal year, is the aver­age time the moon takes to return to the same posi­tion in the cycle of sea­sons, as seen from the earth — from ver­nal equinox to ver­nal equinox.

The trop­i­cal month is 27.32158 days, very slight­ly short­er than the side­re­al month (27.32166) days, because of pre­ces­sion of the equinox­es.

Side­re­al month The side­re­al month is the moon’s orbital peri­od around the earth with respect to the fixed stars.

The side­re­al month is about 27 days, 7 hours, 43 min­utes (27.32 days).

This is also equal to the moon’s peri­od of rota­tion on its own axis. In fact, this is the rea­son why we see the same side of the moon at all times from the earth. Only one side of the moon is vis­i­ble from the Earth because the moon rotates on its own axis at the same rate that the moon orbits the earth, a sit­u­a­tion known as syn­chro­nous rota­tion or tidal lock­ing.

Syn­od­ic month 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 “days”, “hours” and “min­utes” men­tioned here are based on solar time.

Month based on solar cycle

The months based on solar cycle do not cor­re­spond to the cycles of the moon phas­es. Rather, the 12 months are based on the entry of the sun into each of the 12 rashis. The 30° of each rashi cor­re­spond to approx­i­mate­ly 30 days in a month.

When the sun enters the 0th degree of a rashi, it is con­sid­ered the start of the month. When the sun exits the rashi, the month ends. This reck­on­ing of the month is used in the Hin­du cal­en­dar.

In the Gre­go­ri­an cal­en­dar, the sun’s entry into 15th degree of a rashi marks the start of the month. The month ends when the sun enters the 15th degree of the next rashi.

This is explained in Part 3 of this arti­cle.

Lunar and solar calendars

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

Exam­ples of solar cal­en­dars:

  1. Julian cal­en­dar

  2. Gre­go­ri­an cal­en­dar (Chris­t­ian) — used through­out the world today

Exam­ples of lunar cal­en­dar:

  1. Islam­ic cal­en­dar

Lunisolar calendar

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).

It is inter­est­ing to see that almost all ancient civ­i­liza­tions of the world had cal­en­dars based on both lunar and solar cycles, before the adop­tion of the Julian and Gre­go­ri­an cal­en­dars dur­ing the era of col­o­niza­tion.

Exam­ples of luniso­lar cal­en­dars:

  1. Hin­du

  2. Bud­dhist

  3. Jain

  4. Tra­di­tion­al Burmese

  5. Chi­nese

  6. Japan­ese

  7. Tibetan

  8. Viet­namese

  9. Mon­go­lian

  10. Kore­an

  11. Ancient Greek

  12. Ancient Celtic — Scot­land, Ire­land, Wales, Corn­wall, Brit­tany

  13. Ancient Baby­lon­ian

  14. Ger­man­ic — Lux­em­bourg, Bel­gium, North­ern France, Alsace, Poland, Aus­tria, the Nether­lands and Ger­many

  15. Pre-islam­ic cal­en­dar in South Ara­bia

  16. The Native Amer­i­cans of North Amer­i­ca had a very pre­cise obser­va­tion­al lunar year of 12 months, with a 13th inter­calary month (extra month) every three years to bring the cal­en­dar in phase with the solar trop­i­cal year.

  17. The peo­ple of Mesoamer­i­can cul­tures in Cen­tral Amer­i­ca also had their own cal­en­dars and their own way of time­keep­ing, before Colum­bus arrived and col­o­niza­tion began.

  18. The Inca cal­en­dar, used by peo­ple of the Inca empire of South Amer­i­ca, the largest empire in pre-Columbian Amer­i­ca, was luni-solar.

  19. Most African cal­en­dars were a com­bi­na­tion of lunar, solar and stel­lar cycles.

  20. The Aus­tralian abo­rig­i­nals used a cal­en­dar with six sea­sons. They tracked sol­stices and equinox­es and also used lunar cycles in their cal­cu­la­tions.

The Julian and Gregorian Calenders

His­to­ry of the Julian cal­en­dar

The ancient Romans bor­rowed the idea of a 10-month cal­en­dar from the ancient Greeks. Their first orga­nized year had 10 months, each with 30 or 31 days. The four 31-day months were called “full” (pleni) and the oth­ers “hol­low” (cavi). It had 304 days and the remain­ing 50 odd days were left unac­count­ed for. (Table 1)

The 10-month cal­en­dar was allowed to shift until the sum­mer and win­ter months were com­plete­ly mis­placed, at which time addi­tion­al days belong­ing to no month were sim­ply insert­ed into the cal­en­dar until it seemed things were restored to their prop­er place.

Table 1 : The 10-month cal­en­dar of the ancient Romans

The names Quin­tilis through Decem­ber are derived from the Latin words for five through ten. This was known as the cal­en­dar of Romu­lus, the first leg­endary king of Rome.

To account for the remain­ing days, Jan­u­ar­ius was added to the begin­ning of the year and Feb­ru­ar­ius to the end of the year dur­ing Numa’s reign around 700 B.C. Numa Pom­pil­ius was the sec­ond leg­endary king of Rome. The cal­en­dar stayed in that order until 452 B.C. when a small coun­cil of Romans, called the Decemvirs, moved Feb­ru­ary to fol­low Jan­u­ary.

It was in the year 46 BC that the famous Roman gen­er­al Julius Cae­sar mod­i­fied the Roman cal­en­dar. His cal­en­dar, known as the Julian cal­en­dar, was based on the solar cycle. He was the one who intro­duced the con­cept of leap year. Julius Cae­sar made each month have either 30 or 31 days, with the excep­tion of Feb­ru­ar­ius, which had 29 days and gained an extra day every 4th year. The month Quin­tilis was lat­er renamed Julius in his hon­or. Like­wise, Sex­tilis lat­er became Augus­tus to hon­or Augus­tus Cae­sar, the heir of Julius Cae­sar. Augus­tus was also giv­en an extra day (tak­en away from Feb­ru­ar­ius), so that Augus­tus and Julius would have an equal num­ber of days.

Fig. 3 Julius Cae­sar, Dic­ta­tor of the Roman Repub­lic

Leap year A mean trop­i­cal year has 365 days, 5 hours, 48 min­utes, 45 sec­onds. The Julian cal­en­dar approx­i­mat­ed this peri­od as 365 days and 6 hours. The earth orbits the sun once in 365 days and 6 hours. If a cal­en­dar year is con­sid­ered to have 365 days, then, every year, the earth takes about 6 hours longer to com­plete one rev­o­lu­tion.

To keep the Julian cal­en­dar in align­ment with the earth’s rev­o­lu­tion around the sun, the 6 hours were added up over 4 years as an extra day of 24 hours in the month of Feb­ru­ary. This was called a leap year, which had 366 days. With respect to the leap year, it had only one rule -

Any year exact­ly divis­i­ble by 4 would be a leap year

The aver­age length of the Julian year was 365 1/4 or 365.25 days. But because the length of the solar year is actu­al­ly 365.242216 days, the Julian year was too long : by .0078 days (11 min­utes 14 sec­onds). This dif­fer­ence seems neg­li­gi­ble, but over the course of cen­turies it added up. After every 100 years, the cal­en­dar was off by approx­i­mate­ly 24 hours, almost a day! By the time of the 1500s, the ver­nal equinox was falling around March 11 instead of March 21.

His­to­ry of the Gre­go­ri­an cal­en­dar In 1582, Pope Gre­go­ry XIII adjust­ed the cal­en­dar by mov­ing the date ahead by 11 days and by insti­tut­ing an addi­tion­al rule to the leap year -

Any year exact­ly divis­i­ble by 4 would be a leap year EXCEPT for years that are cen­turies (years divis­i­ble by 100) But these cen­tur­ial years are leap years if they are exact­ly divis­i­ble by 400.

For exam­ple, the years 1700, 1800, and 1900 are not leap years, but the year 2000 is.

This new rule, where­by a cen­tu­ry year is a leap year only if divis­i­ble by 400, is the sole fea­ture that dis­tin­guish­es the Gre­go­ri­an cal­en­dar from the Julian cal­en­dar.

Fol­low­ing the Gre­go­ri­an reform, the aver­age length of the year was 365.2425 days, an even clos­er approx­i­ma­tion to the solar year of 365.242216. At this rate, it will take more than 3,000 years for the Gre­go­ri­an cal­en­dar to gain one extra day in error.

The Gre­go­ri­an cal­en­dar was designed to keep the ver­nal equinox on or close to March 21, so that the date of East­er, remains close to the ver­nal equinox. East­er is cel­e­brat­ed on the Sun­day after the eccle­si­as­ti­cal full moon that falls on or after March 21. This shows that the Gre­go­ri­an cal­en­dar evolved from a lunar cal­en­dar, since in order to locate the full moon, a cal­en­dar based on the cycles of the moon phas­es is nec­es­sary.

Fig. 4 Pope Gre­go­ry XIII, Pope of the Catholic Church

BC and AD/ BCE and BC The year-num­ber­ing sys­tem uti­lized by the Gre­go­ri­an cal­en­dar is used through­out the world today, and is an inter­na­tion­al stan­dard for civ­il cal­en­dars. What do the nota­tions BC and AD, BCE and BC mean?

BC and AD is a nota­tion sys­tem intro­duced by Diony­sius Exigu­us, a 6th cen­tu­ry monk. This sys­tem dis­tin­guish­es eras as AD — anno Domi­ni — “the year of Our Lord” and BC — “Before Christ”.

Many peo­ple do not appre­ci­ate the fact that the abbre­vi­a­tions AD and BC pro­fess the Chris­t­ian faith. Many non-chris­t­ian reli­gious schol­ars were aware of this, and hence a neu­tral way of denot­ing the year was devised. CE refers to “Com­mon Era” and BCE refers to “Before the Com­mon Era”.

Both the nota­tion sys­tems are numer­i­cal­ly equiv­a­lent and both refer to the Gre­go­ri­an cal­en­dar. 2018 CE is the same as 2018 AD 400 BCE is the same as 400 BC

Just like AD, the CE sys­tem counts the birth of Jesus as year 1.

It is also inter­est­ing to note that there is no zero. The num­ber­ing starts from 1 AD or 1 CE as the year of the birth of Jesus Christ. This is because Euro­peans did not have the con­cept of zero at that point in time. The Roman numer­als did not have a zero. Zero actu­al­ly trav­elled from India all the way to Europe. The astronomers and math­e­mati­cians found zero to be a very pow­er­ful con­cept. But those who used it were put to stake or burnt, because it was con­sid­ered the work of satan.

Now that we have mapped astro­nom­i­cal cycles to time­keep­ing on earth and the vari­a­tions in the way these cycles are con­sid­ered for time­keep­ing, let us under­stand the Hin­du Vedic cal­en­dar, also called as Pan­changam.

Ref­er­ences Fig.1–

Fig. 2 — By Xaonon- Own work, CC BY-SA 4.0, A Syn­op­sis of Ele­men­tary Results in Pure and Applied Math­e­mat­ics by G. Shoo­bridge Carr. Astrol­o­gy of the Seers by David Fraw­ley Light on Life : An Intro­duc­tion to the astrol­o­gy of India by Robert Svo­bo­da and Hart de Fouw

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