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Indic Cosmology | Kosla Vepa | Equatorial Coordinate System | 102

Mathomathis would like to present an article on Indic Cosmology and Time Keepers by Kosla Vepa – Indic Studies Foundation. The following article is a continuation from the previous article Indic Cosmology | Kosla Vepa | Time Keepers | 101.

The most commonly used astronomical coordinate system for indicating the positions of stars or other celestial objects on the celestial sphere are the Equatorial coordinate system. The celestial sphere is an imaginary sphere with the observer at its center. It represents the entire sky; all celestial objects other than the earth are imagined as being located on its inside surface. If the earth’s axis is extended, the points where it intersects the celestial sphere are called the celestial poles; the north celestial pole is directly above the earth’s North Pole, and the south celestial pole directly above the earth’s South Pole. The great circle on the celestial sphere halfway between the celestial poles is called the celestial equator; it can be thought of as the earth’s equator projected onto the celestial sphere. It divides the celestial sphere into the northern and southern skies. An important reference point on the celestial equator is the vernal equinox, the point at which the sun crosses the celestial equator in March. To designate the position of a star, the astronomer considers an imaginary great circle passing through the celestial poles and through the star in question. This is the star’s hour circle, analogous to a meridian of longitude on earth. The astronomer then measures the angle between the vernal equinox and the point where the hour circle intersects the celestial equator. This angle is called the star’s right ascension and is measured in hours, minutes, and seconds rather than in the more familiar degrees, minutes, and seconds. (There are 360 degrees or 24 hours in a full circle.) The right ascension is always measured eastward from the vernal equinox.

Next the observer measures along the star’s hour circle the angle between the celestial equator and the position of the star. This angle is called the declination of the star and is measured in degrees, minutes, and seconds north or south of the celestial equator, analogous to latitude on the earth. Right ascension and declination together determine the location of a star on the celestial sphere. The right ascensions and declination of many stars are listed in various reference tables published for astronomers and navigators. Because a star’s position may change slightly (see proper motion and precession of the equinoxes), such tables must be revised at regular intervals. By definition, the vernal equinox is located at right ascension 0 h and declination 0°.

Another useful reference point is the sigma point, the point where the observer’s celestial meridian intersects the celestial equator. The right ascension of the sigma point is equal to the observer’s local sidereal time. The angular distance from the sigma point to a star’s hour circle is called its hour angle; it is equal to the star’s right ascension minus the local sidereal time. Because the vernal equinox is not always visible in the night sky (especially in the spring), whereas the sigma point is always visible, the hour angle is used in actually locating a body in the sky. The Indian calendrical system is based on sidereal measurements. In order to understand the system we need to review some definitions of the year, month and the day.


A solar year and a sidereal year both refer to the amount of time it takes Earth to revolve about the Sun. The difference between the two measures is in the reference point for one revolution. The Latin root of sidereal is sidereus, “starry,” which itself comes from sides, “star, installation.” The Latin root of solar is solis, “sun.” Thus, the difference between a solar year and a sidereal year is the difference in time between one complete revolution of Earth relative to the Sun, and one complete revolution of the earth relative to the constellations respectively. A tropical year (also known as a solar year) is the length of time the Sun, as seen from the Earth, takes to return to the same position along the ecliptic (its path among the stars on the celestial sphere) relative to the equinoxes and solstices, or the time interval needed for the mean tropical longitude of the Sun to increase by 2π (360 sexagesimal degrees, a complete turn). The length of time depends on the starting point on the ecliptic. Starting from the (northern) vernal equinox, one of the four cardinal points along the ecliptic, yields the vernal equinox year; averaging over all starting points on the ecliptic yields the mean tropical year.

A calendar year is the time between two dates with the same name in a calendar. Then there is the , anomalistic year, which is the time it takes for one rotation around the sun as measured from perigee to perigee.The anomalistic year is the time taken for the Earth to complete one revolution with respect to its apsides. The orbit of the Earth is elliptical; the extreme points, called apsides, are the perihelion ( when the perigee refers to planetary motion) , where the Earth is closest to the Sun (January 3 in 2008), and the aphelion, where the Earth is farthest from the Sun (July 4 in 2008). The anomalistic year is usually defined as the time between two successive perihelion passages. Its average duration is: 365.259 635 864 days (365 d 6 h 13 min 52 s) (at the epoch 2000.0).

The anomalistic year is slightly longer than the sidereal year because of the precession of the apsides (or anomalistic precession). The Gregorian calendar attempts to keep the vernal equinox on or soon before March 21; hence it follows the vernal equinox year. The average length of this calendar’s year is 365.2425 mean solar days (which can be thought of as 97 out of 400 years being leap years) whereas the vernal equinox year is 365.2424 days. On the Earth, the tropical year is shorter than a sidereal year. This difference was, in AD 1900, equal to 20.400 min, and in AD 2000, 20.409 minutes, and seems to slow the Sun from south to north and back. The word “tropical” comes from the Greek tropos meaning “turn”. The tropics of Cancer and Capricorn mark the extreme north and south latitudes where the Sun can appear directly overhead. The position of the Sun can be measured by the variation from day to day of the length of the shadow at noon of a gnomon (a vertical pillar or stick). This is the most “natural”way to measure the year in the sense that these variations drive the seasons.

Indic Cosmology | Difference Between The Sidereal & Tropical Year

Type of YearDays
Sidereal Year365.256363 (2007)
Tropical Year365.242190 (2007)

The sidereal year (Nirayana) is the time taken for the Sun to return to the same position with respect to the stars of the celestial sphere. It is the orbital period of Earth, equal to 365.256363 mean solar days (31,558,149.760 seconds), that is 366.256363 earth rotations or sidereal days. The sidereal year is 20 minutes and 24 seconds longer than the tropical year. The Sun and the stars cannot be seen at the same time; if one looks every dawn at the eastern sky, the last stars seen appearing are not always the same. In a week or two an upward shift can be noted. As an example, in July in the Northern Hemisphere, Orion cannot be seen in the dawn sky, but in August it becomes visible. In a year, all the constellations rotate through the entire sky. If one looks regularly at the sky before dawn, this motion is much more noticeable and easier to measure than the north/south shift of the sunrise point in the horizon, which defines the tropical year on which the Gregorian calendar is based. This is the reason many cultures started their year on the first day a particular special star, (Sirius, for instance), could be seen in the East at dawn. In Hesiod’s Works and Days, the times of the year for sowing, harvest, and so on are given by reference to the first visibility of stars.

Up to the time of Hipparchus, at least in Europe, the years measured by the stars were thought to be exactly as long as the tropical years. Even then, in fact until the 16th century they had no accurate sidereal measurements. In fact, sidereal years are very slightly longer than tropical years. The difference is caused by the precession of the equinoxes. One sidereal year is roughly equal to 1 + 1/25600 or 1.00003906 tropical years. But until 1540 CE, when the Society of Jesus sent a whole slew of Jesuits trained to absorb such knowledge, in order that they may learn the science of the calendar and of navigation from the Namboodri (etymology nama putri) Brahmanas of Kerala, there was a lack of knowledge of subjects like navigation. Prior to this date the Portuguese who were the most advanced in these matters, only sailed during the night, when they had the visible stars to guide them. An average voyage to India took them 2 years from Lisbon. With the knowledge so gained they fixed the Gregorian calendar which was always error prone.

Julian Year – In astronomy, a Julian year (symbol: a) is a unit of measurement of time defined as exactly 365.25 days of 86,400 SI seconds each, totaling 31,557,600 seconds. That is the average length of the year in the Julian calendar used in Western societies in previous centuries, and for which the unit is named. Nevertheless, because a Julian year measures duration rather than designates date, the Julian year does not correspond to years in the Julian calendar or any other calendar. Nor does it correspond to the many other ways of defining a year. Like most Asian calendars Indian calendars do not employ solely the solar year and day (i. e. tropical year and solar day) but the sidereal year, and the Synodic month (29.5306 days). Thus, the calendrical year based on the sidereal year is defined as the time between two successive passes of the sun through a certain star’s circle of declination. Lunar days and sidereal months are also used, and in certain lunisolar calendars lunar year and lunar month are taken into account, too. The Astronomical knowledge of Ancient India was written down in scientific treatises, called Siddhantas. In them, values for the lengths of months and years were given representing the latest knowledge at the time the Siddhanta was written. The values range from 365.258681 days in the Aryabhatiya to 365.258756 days in the Surya Siddhanta and are all too long compared with the modern sidereal year length of 365.25636 days. Nevertheless they are still in use in Indian calendars today.


The epoch (starting point or first day of the first year) of the current era of Hindu calendar (both solar and lunisolar) is BCE 3102 January 23 on the proleptic Gregorian calendar (i.e. the Gregorian calendar extended back in time before its promulgation from 1582 October 15). Both the solar and lunisolar calendars started on this date. After that, each year is labeled by the number of years elapsed since the epoch. This is a unique feature of the Hindu calendar. All other systems use the current ordinal number of the year as the year label. But just as a person’s true age is measured by the number of years that have elapsed starting from the date of the person’s birth, the Hindu calendar measures the number of years elapsed. As on 2005-05-18 the elapsed years in the Hindu calendar are 5106 and this is the 5107th Hindu calendar year. Other systems of numbering the Hindu years were prevalent also.

Table below explains | Summary Of Various Measures of a year

353, 354 or 355 days — the lengths of common years in some lunisolar calendars.
354.37 days (12 lunar months) — the average length of a year in lunar calendars.29.53
365 days — a common year in many solar calendars.
365.24219 days — a mean tropical year near the year 2000.
365.2424 days — a vernal equinox year.
365.2425 days — the average length of a year in the Gregorian calendar.
365.25 days — the average length of a year in the Julian calendar.
365.2564 days — a sidereal year.
366 days — a leap year in many solar calendars.
383, 384 or 385 days — the lengths of leap years in some lunisolar calendars.
383.9 days (13 lunar months) — a leap year in some lunisolar calendars.
An average Gregorian year is 365.2425 days = 52.1775 weeks, 8,765.82 hours = 525,949.2 minutes = 31,556,952 seconds (mean solar, not SI).
A common year is 365 days = 8,760 hours = 525,600 minutes = 31,536,000 seconds.
A leap year is 366 days = 8,784 hours = 527,040 minutes = 31,622,400 seconds.
The 400-year cycle of the Gregorian calendar has 146,097 days and hence exactly 20,871 weeks.

PlanetKhandakhadhyakaSurya Siddhanta of VarahaModern SS
Moon’s Apogee448219448219448203
Moon’s node232226232226232238
Number of civil days157791780015779178001577917828


Lunar or Synodic Month – The month is a unit of time, used with calendars, which is approximately as long as some natural period related to the motion of the Moon. The traditional concept arose with the cycle of moon phases; such months (lunations) are synodic months and last approximately 29.53 days. From excavated tally sticks, researchers have deduced that people counted days in relation to the Moon’s phases as early as the Paleolithic age. Synodic months are still the basis of many calendars today.

This period is called the synodic month from the Greek syn hodô (σὺν ὁδῴ), meaning “with the way [of the sun]”. Because of the perturbations of the orbits of the earth and Moon, the actual time between lunations may range from about 29.27 to about 29.83 days. The long-term average duration is 29.530588 days (29 d 12 h 44 min 2.8 s). The synodic month is used in the Metonic cycle. Thus the year based on a lunar month would be =29.53058181 *12= 354.3669817days. In other words, such a year would be short of a tropical year by about 11 days. But for societies that are not predominantly based on agriculture, such a lacuna would not be of great significance. It is perhaps for this reason that the Muslim calendar has chosen simplicity over temporal predictability when they decided to adopt the lunar calendar. This is the reason why important events in a Muslim calendar like Ramzan do not occur at the same time or date of every year, The Muslim calendar is a lunar calendar which makes no attempt at matching the periodicity of the solar calendar. Sidereal Month – The period of the Moon’s orbit as defined with respect to the celestial sphere is known as a sidereal month because it is the time it takes the Moon to return to a given position among the stars (Latin: sidus): 27.321661 days (27 d 7 h 43 min 11.5 s). As opposed to the Synodic or Lunar Month. This type of month has been observed among cultures in the Middle East, India, and China in the following way: they divided the sky into 27 or 28 lunar mansions, defined by asterisms (apparent groups of stars), one for each day of the sidereal month. The sidereal month is thus, about two day shorter (27.3217) than the Synodic month.

Like most Asian calendars Indian calendars do not employ the solar year and day (i. e. tropical year and solar day) but the Sidereal year, and the Synodic month (29.5306 days). Thus, the calendrical year based on the sidereal year is defined as the time between two successive passes of the sun through a certain star’s circle of declination. Lunar days and sidereal months are also used, and in certain lunisolar calendars lunar year and lunar month are taken into account, too. The Astronomical knowledge or the theory behind the observations of Ancient India was written down in scientific treatises, called Siddhantas. In them, values for the lengths of months and years were given representing the latest knowledge at the time the Siddhanta was written. The values range from 365.258681 days in the Âryabhatiya to 365.258756 days in the Surya Siddhanta and are all too long compared with the modern sidereal year length of 365.25636 days. Nevertheless they are still in use for Indian calendars today.

Indic Studies - Mathomathis 1
Difference Between A Sidereal Day & A Solar Day

Table shown below are the Names of the Solar Months (Sauramaas) are as follows:

These names, also known as the Rasi, coincide with the names of the Solar Zodiac

Saura Maas (solar months) Ritu (season) Gregorian months Zodiac Devanagari
Mesha Vasant (spring) March/April Aries मेष
Vrushabha April/May Taurus वृषभ
Mithuna Grishma (summer) May/June Gemini मिथुन
Karka June/July Cancer कर्क
Simha Varsha (monsoon) July/August Leo सिंह
Kanya August/September Virgo कन्या
Tula Sharad (autumn) September/October Libra तुळ
Vrushchik October/November Scorpius वृश्चक
Dhanu Hemant (autumn-winter) November/December Sagittarius धनु
Makara December/January Capricornus मकर
Kumbha Shishir (Winter-Spring) January/February Aquarius कुंभ
Meena February/March Pisces मीन

The table shown below contains the months of the Lunisolar Calendar

Indic Cosmology | Months of the Lunisolar Calendar


The Elements Of The Panchangam

The panchangam ,as the name suggests, has 5 distinct pieces of information.

  • Tithi ( the day under study)
  • Vaara (day of the week)
  • Nakshatra ( the asterism in which the moon is located )
  • Yoga ( that day’s Yoga)
  • Karana ( that day’s Karana)


To calculate and specify the starting time and ending time of these FIVE quantities is called a Panchangam. The Indian Panchangam is really an almanac rather than calendar. It is analogous to the concept of a Farmers almanac that is widely prevalent in the west. The word calendar is itself of Greek origin. The Indics who devised the calendar faced the same problem that others faced in the ancient world, namely that the periodicities of the Sun and the moon are not exact integer multiples of one another. So, it is impossible to maintain consistency of seasons and phases of the month concurrently ,assuming that the civilization values the information conveyed by both of these sets of data. The resulting calendar while being complex, leaves no room for ambiguity in the interpretation of such a date, and can be maintained accurately with periodic corrections termed bija. Further articles will be describing more on these context.

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