Principles of Astronomy, Planetary Motions and the Zodiac

We, human beings exist in this vast and mysterious universe, the boundaries of which are incomprehensible, to say the least. We inhabit one of the innumerable galaxies of this universe called the Milky Way, in one of the many solar systems that constitute the Milky Way galaxy, in one of the planets called Earth revolving around our Sun which is the epicenter of our solar system, in one of the Earth’s continents, in one of the regions of our inhabited continent, in one of the many human clusters called a city / town / village. The significance of our existence in the context of the universe is perhaps even tinier than the tiniest known sub-atomic particles. Notwithstanding our relative insignificance, we human beings have been blessed with the Awareness and the Mental-Intellectual capability so as to be able to make an attempt to make sense of our existence in relation to that of our surroundings – our solar system, our galaxy and the universe. This quest of exploring our surroundings has been one of the most fascinating journeys that humanity as a whole has undertaken in the course of its existence.

A galaxy is defined as a large group of stars, gases and dust held together by the force of gravity. Our galactic address, the Milky Way got its name due to its appearance as a white band of light that resembles ‘a pathway of milk’ which can be seen in the sky when it is sufficiently dark from a rural or a non-illuminated area. It is called a barred spiral galaxy due to its loosely spiral appearance with its galactic center resembling a bar. The spiral lighted structure is made up of millions of stars and the dark background as well as the dark separating medium in-between the spirals is made up of dark matter. It consists of four segments of spirals giving the appearance of a coiled snake due to the separating parallel dark spiral. The Milky Way consists of approximately 100 to 400 billion stars in various stages and ages of their development. There are an estimated 400 billion planets at the rate of on-an-average one planet per star which includes some 40 billion earth-like planets within the habitable zone of our galaxy. Since we are a part of the Milky Way, all the stars we see at night are a part and parcel of it. Our galaxy is also rotating around its galactic center, with one rotation taking some 240 million years at our Sun’s position. The Milky Way as a whole is also moving when observed from another extragalactic frame within the universe at the rate of approximately 600 Kms per second. The complexity of the mind-boggling dynamism affecting us on earth is difficult to comprehend, with the earth’s three motions, the Sun’s revolution around the galactic center and the motion of the galaxy itself, all at their uniquely different speeds.

It makes an interesting comparison when the Hindu model of the earth’s position is seen together with the foregoing description of the galactic structure. The Hindu model of the universe depicts the globe located on the hood of a coiled snake (Sheshnaag) which very much resembles the dark separating spirals of the Milky Way. The Sheshnaag is supposedly located in the Ksheer Sagar which literally gets translated as the Ocean of Milk. Probably the ancients had modeled their observation of the Milky Way into their picture of the universe assuming that the Milky Way made up the entire universe which was also the scientific view till the 1920s until the discovery of other galaxies by Hubble.

Our solar system is just one of the numerous solar systems that make up the Milky Way galaxy. Our sun and its solar system are located close to the inner edge within the fluffy region of the local arm called the Orion. Our Sun is located at approximately 26000 light years from the galactic center. Our solar system has the Sun at its center around which the planets Neptune, Uranus, Pluto, Saturn, Jupiter, Mars, Venus, Mercury and Earth are revolving in their unique and distinct orbits at their unique speeds. All the planets have different spherical sizes and masses. These planets are placed at different distances from the Sun. The solar system is held in place by the force of gravity. The unique distances of the planets from the Sun, their individually distinct mass and size are factors that determine their unique speeds of revolution around the Sun. Each planet is a unique conglomerate of matter made up of gases, liquids and solids which gives them their distinct character. All the planets except Venus and Mercury have satellites also known as Moons. There are 178 Moons orbiting the seven planets other than Venus and Mercury. Jupiter has a maximum number of Moons, 67 in all, followed by Saturn with 62 Moons; Uranus has 27 Moons, Neptune has 14 Moons, Pluto has 5 Moons, Mars has 2 Moons and the Earth has one Moon. Of these 19 moons are large enough to get qualified as Planets or Dwarf planets had they been orbiting the Sun. The Earth has the largest moon orbiting any rocky planet and would have easily qualified to be called a planet if it orbited the Sun and not the Earth.

Our solar system consists of two types of planets categorized on the basis of their inherent material structure and density. These two categories are called the Terrestrial planets and the Giant planets respectively. The Terrestrial planets also called Telluric or Rocky planets have a metallic (usually Iron) core which is covered by silicate rocks which give them a solid surface. Mercury, Venus, Earth and Mars are Terrestrial planets and are often referred to as Inner Planets. The Giant planets are made up of Helium, Hydrogen and Water existing in their different stages. The Giant planets are also referred to as the outer planets. The Giant planets are Uranus, Neptune, Saturn and Jupiter. Interestingly Pluto is neither a Terrestrial nor a Giant planet. Pluto is actually a Dwarf planet like Ceres, Eris, Haumea and Makemake but some astronomers had preferred to include it in the list of planets. It was actually dropped from the list of planets after a fierce debate on 24^th August 2006. Thus now there are eight entities within the solar system that have been qualified to be called planets. The distances of each of these eight planets from the Sun, their size as diameters, their mass, their surface area, their rotational speed around their axis, their orbital speed around the Sun, and the time taken for completing one orbit around the Sun are being given in the following table:

Planets	Distance  from the Sun	Equatorial Diameter	Mass	Surface Area	Rotational Speed	Orbiting speed around Sun	Time taken for one orbit around Sun
Neptune	4.5 billion Kms.	3.883  earths	17.147 earths	14.98 Earths	16 hrs 6 mins 36 secs	5.43 kms/sec	164.8 yrs
Uranus	3 billion Kms.	4.007 earths	14.536 earths	15.91 Earths	14 hrs	6.80 kms/sec	84.0205 yrs
Saturn	1.4 billion Kms.	9.4492 earths	95.159 earths	83.703 earths	10 hrs 33 mins	9.69 kms/sec	29.4571 yrs
Jupiter	778 million Kms.	11.209 earths	317.80 earths	121.90 earths	9 hrs 55 mins 30 secs	13.07 kms/sec	11.8618 yrs
Mars	230 million Kms.	0.284 earths	0.107 earths	0.284 Earths	24 hrs 37 mins 22 secs	24.077 Kms/sec	687 days
Mercury	57.91 million Kms.	0.3829 earths	0.055 earths	0.147 Earths	58 days 15 hrs 30 mins	47.362 kms./sec	87.969 days
Venus	108 million Kms.	0.9499 earths	0.815 earths	0.902 Earths	116 days 18 hrs in  opposite direction	35.02 kms/sec	224.701 days
Earth	149.6 million Kms.	12756 Kms	5.97 x 1024  Kgs.	510.1 million sq. kms.	23 hrs 56 mins 4.09 secs.	30.0 kms/sec	365 days 6 hrs. 9 mins. 9.5 secs.

Even though our Sun is also moving around the center of our galaxy, it is not perceived to be moving because the entire solar system including the Earth revolves around the galactic center along with the Sun. The Earth’s Moon is big enough to be qualified as a planet, had it been revolving around the Sun. The Earth’s Moon is located at a distance of 384,400 Kms. from the Earth. The Moon is in synchronous rotation with Earth thereby showing the same face all the time. It is the second brightest regularly visible astronomical object in the Earth’s sky after the Sun. The Moon’s gravitational pull on Earth produces ocean tides and the slight lengthening of the day on Earth. It makes a complete orbit around the Earth about once in 27.3 days. It orbits closer to the ecliptic plane than to the Earth’s equatorial plane. The Moon’s orbital plane gradually rotates due to the perturbations under the influence of the Sun and the Earth. This state of Moon’s inclination and its rotation is called the Cassini state named after Giovanni Domenici Cassini who first studied this phenomenon and enunciated in 1693 three laws governing this phenomenon called the Cassini’s laws which are:

1. The Moon has a one to one spin-orbit resonance which means that the same side of the Moon faces the Earth all the time.

2. The Moon’s rotational axis precesses in the same manner as the wobbling motion of the Earth, so as to trace out a cone that intersects the ecliptic plane as a circle.

3. A plane formed from the normal to the ecliptic plane and a normal to the Moon’s orbital plane will contain the Moon’s rotational axis. Since the Moon’s points some 1.5 degrees away from the north ecliptic pole, the normals to the orbital plane and the rotational axis are always in opposite sides of the normal of the ecliptic. Therefore both the normal to the orbital plane and the Moon’s rotational axis precess in the same period which is approximately 18.6 years and this precession motion is always retrograde.

The second and the third laws of Cassini are particularly important from the point of Indian astrology which gives an important role to the two opposite intersection points (as stated in the second law of Cassini) due to Moon’s precessionary motion. In Indian astrology these opposite points are called Rahu and Ketu which are retrograde and which complete one rotation in 18.6 years (as stated in the third of Cassini’s laws). The northern intersection point is called Rahu and its southern counterpart exactly 180 degrees opposite, is called Ketu. In Indian astrology the Moon, Rahu and Ketu are given status equal to the status of any of the planets.

The solar system as described in the foregoing paragraphs can be modeled in two ways; one by placing the Sun at the center of the solar system and the other by keeping the Earth at the center of the solar system. The model with the Sun at the center of the solar system is called the Helio-centric model of the solar system while the model with the Earth at the center of the solar system is called the Geo-centric model of the solar system. The center referred to here is not exactly the center in geometric terms but it refers to the central reference point for placing the other astronomical bodies in the particular model.

There is a historical perspective to the geo-centric and the helio-centric models of the universe. The observations of the entire astronomical phenomenon were initially made from the Earth and the knowledge of astronomy evolved from then onwards wherein the Earth continued to be the central reference point for all astronomical observations. It was believed that the Earth was stationary and the rest of the astronomical bodies including the Sun were revolving around the Earth, which matched perfectly well with the direct observations and experiences ‘on and from’ Earth. All astronomical data, measurements and mathematical calculations and derivations there-from were based on this basic understanding and belief. This led to the establishment of an astronomical model of the universe which is referred to as the Geo-centric model or Geocentricism. The Geocentric model was formally enunciated by Plato and Aristotle in the 4^th century B.C.E. and Plato was also the first to emphasize that the Earth was in fact spherical and not flat as was believed before him. Geocentricism further evolved until Ptolemy finally standardized it in the 2^nd century A.D. A parallel astronomical model was introduced by Pythagoras in the 6^th century B.C.E. which was further rationalized in the 5^th century B.C.E. which did acknowledge that the Earth was spherical and it moved along with the Sun, Moon and the other planets around a central fire. Both the Geocentric model and the Pythagorean models were based on hypothetical assumptions and were beset with many errors. However these models and their many variations guided the development of astronomical understanding in the western world till the 16^th century A.D. until the development of Heliocentricism and the Helio-centric model of the universe introduced by the Polish astronomer Nicolaus Copernicus in 1543.

The heliocentric model as already stated had the Sun as its central reference point with all the planets and their respective Moons revolving around the Sun. This model assumed that the Sun was stationary. Even though Heliocentricism was supported by Kepler, Galileo and Rene Descartes, it did not do much better than the geocentric model of Ptolemy in predicting planetary positions. The heliocentric hypothesis however resolved the fact of retrograde motion of planets through the argument that retrograde motion was only perceived and is actually apparent not real. The apparent perception of retrogression was a parallax effect when the object being overtaken in motion appears to be moving backwards against the background of the horizon. It was Newton who improved upon the heliocentric model towards the end of the 17^th century A.D. through his laws of motion. He recognized the deviation of the Sun from the center of gravity of the solar system. He proposed that it was neither the Sun nor any other astronomical body that could be considered at rest, but it was the common center of gravity of the Sun, Earth and the other planets of the solar system that was at rest wherever it was located. Thus began the realization that the heliocentric view was not true in the strictest sense. By the end of the 19^th century, it became clear to modern scientists that the Sun was but one of the Stars amongst many and with the advent of the 20^th century with the discovery of many galaxies the idea that the Sun was not even at the center of the solar system was firmly established.  

In modern day astronomical calculations the terms ‘geocentric’ and ‘heliocentric’ are used in relation to the reference frames and not in the sense as envisaged in Geocentricism or Heliocentricism. While the heliocentric latitudes and longitudes are used for orbital calculations the Right Ascension and Declination are related to the geocentric coordinates used in Earth based observations. However the use of the geocentric and the heliocentric frames is only for the purposes of computation in modern astronomy or cosmology and do not carry any philological implications whatsoever.

While the development of the science of astronomy happened from the 6^th century B.C.E. onwards in the western world as narrated above, it shall be interesting to trace the events related to astronomical progress in the eastern world with particular reference to India. The Indian astronomical knowledge and understanding is rooted in an indeterminable era that is the period of the Riga Veda. Various dates have been assigned to the Riga Veda period ranging from 7000 B.C.E. to 1500 B.C.E. The entire text of the Riga Veda is interwoven with cosmological details which need to be interpreted accurately to derive the correct contextual meaning there-from. The entire process of the manifestation of the universe and thereafter, that of the emergence of the numerous astronomical bodies has been explained cosmologically which is rather difficult to correlate even with our present day exalted scientific and mathematical knowledge. Suffice it to say that the Riga Veda includes all that has been known till date and even more that still needs to be known by modern science. A glimpse of the accuracy of the contents of the Riga Veda can be had from the following astronomical data as per the Riga Veda in comparison to the most accurate modern astronomical data given in the Table below:

Planet	Sidereal period in days as per Riga Veda	Sidereal period in days as per modern astronomy	Percent error
Mercury	87 days	87.969 days	+ 1.10 %
Venus	225 days	224.701 days	- 0.133%
Mars	687 days	687 days	0.00%
Jupiter	4340 days	4332.59 days	- 0.171%
Saturn	10,816 days	10, 759 days	- 0.529%

Note: the sidereal period is the time taken by a planet to complete one complete round of its orbit around the Sun.

It can be seen from the above given table that the variance is almost negligible between the two sets of data.

Even the altars to be used for carrying out different sacrifices and rituals have been meticulously defined in the Riga Veda wherein the measurements of the various dimensions and layers of the altar and the number and sizes of the bricks to be used have been assigned numbers that correspond to the different cosmological phenomena in terms of time and space.

Considering that the Riga Veda is the oldest known compilation of knowledge as acknowledged in India, it cannot be said that any other treatise can be of an older origin. The Surya Sidhanta is an ancient text of astronomy of an unknown authorship and has been dated variously ranging from two million years old to as late as 400 A.D. however this has to be understood in terms of the methodology of passing-on of knowledge in ancient India. All knowledge was passed to the next generation by the Guru (teacher or preceptor) orally in the form of Shrutis (oral texts). The Shrutis were memorized by repeated recitations to maintain their content and character and got passed-on exactly in its original form. At whichever point in time, the Shruti was converted to a written text, is not the point in time at which the text was actually authored. This mainly is the cause of confusion in dating such texts. As stated earlier the Riga Veda is a compilation of existing approved knowledge and therefore it is quite possible that the Surya Sidhant existed even before Riga Veda as an independent treatise on Indian astronomy and its principles were used by the compilers of the Riga Veda. It shall only be relevant to highlight at this juncture that the Surya Sidhant is not the only authoritative exposition on Indian astronomy but there are atleast 17 other sidhantas or texts given by the learned sages and researchers at different stages of the evolution and development of Indian astronomy, making in all 18 sidhantas which have been listed below for perusal:

 1. Surya Sidhant;                        
 2. Paitamaha Sidhant;             
 3. Vyasa Sidhant;            
 4. Vashishtha Sidhant;                 
 5. Atri Sidhant;                
 6. Paraashar Sidhant;          
 7. Kashyap Sidhant;        
 8. Naarad Sidhant;

 9. Garga Sidhant;            
 10. Mareechi Sidhant;         
 11. Manu Sidhant;           
 12. Angeera Sidhant;

 13. Lomasha Sidhant;      
 14. Paulisha Sidhant;           
 15. Chyavan Sidhant;       
 16. Yavan Sidhant;

 17. Bhrigu Sidhant;         
 18. Shaunak Sidhant.

Note: There is the mention of Yavan Sidhant at number 16 in the above list. Yavanacharya who has given this Sidhant was of Greek origin since Yavan is a word attributed to a person of Greek origin. It is believed that the learned Pythagoras of Greece visited India around the 6^th century B.C.E. and learnt geometry, astronomy and other metaphysical sciences at Takshila University which had many foreign students from China and Central Asian countries. He brought with him knowledge that he learnt in Greece, Egypt, Babylon and Chaldea which he acquired during his travels. He integrated his knowledge from other sources with the Indian knowledge and enriched it in the process. Though there is no record to prove but it is quite likely that Yavanacharya was none other than Pythagoras. 

The earliest recorded acknowledgement of Surya Sidhanta is by the great Indian mathematician-astronomer Aryabhatta in his Aryabhatteyam written in 499 A.D. Even if the Surya Sidhanta is taken to be written around 400 A.D. as claimed by E. Burgess and P. C. Sengupta (which certainly is not the case), the treatise is atleast eleven hundred years older than the enunciation of Heliocentricism of Copernicus; atleast twelve hundred years before the enunciation and the definition of Gravity by Newton and atleast fifteen hundred years before Einstein proposed the theory of Relativity. The mention of Surya Sidhanta is important as it is considered to be the foremost astronomical guide to Indian astronomy. Some of the salient features that make it unique have been given below:

1. The average length of the tropical year has been given by Surya Sidhant as 365.2421756 days which is just 1.4 seconds shorter than the modern value of 365.2421901 days.

2. As per Surya Sidhant the length of the sidereal year is 365.2563627 days which is virtually the same as the modern value of 365.25636205.

3. The Surya Sidhant also gives the states of motion and the diameters of the planets e.g. the diameter of Mercury has been given as 3008 miles which is within 1% variance of the modern measure of Mercury’s diameter of 3032 miles.

4. The Surya Sidhant uses the decimal system, the zero, the method of calculating very large numbers and Trigonometry at a time when the rest of the world struggled with even calculating simple arithmetical problems.

5. The Surya Sidhant uses Sine (jya), Cosine (kojya) and inverse Sine (utkram jya) even before these concepts were known to the rest of the world.

6. Gravity has been stated in the Surya Sidhant as “Objects fall on Earth due to a force of attraction of the Earth and similarly the Earth, the planets, the constellations, the Moon and the Sun are held in their orbits due to this force of attraction”, whereas Gravity was defined only in 1687 by Newton.

7. The Surya Sidhant also defined the concept of Relativity much before it was enunciated by Einstein.

8. The astronomical time cycles contained in Surya Sidhant are remarkably accurate as has been demonstrated in points 1, 2 and 3.

Building upon the principles of astronomy declared and explained in the Surya Sidhant and the other Sidhantas as enumerated earlier, great mathematician- astronomers of India like Aryabhatta-1, Varahmihir, Bhaskara-2 and Nilkantha rationalized and developed the Indian astronomical model of the universe as well as that of the solar system, which are highly accurate and reliable in predicting astronomical events and their progression. This Indian astronomical model is as good a hybrid of the Geocentric and the Heliocentric models as the modern methods adopted by modern astronomy and cosmology. The proof of the pudding is in its eating which is evident in the almost negligible variance between the results obtained using principles and methods of Indian origin and the results obtained by the modern methods.

We observe the astronomical phenomenon from the Earth and these observations are as per the tenets of the geocentric model. An important aspect of these observations from Earth is the Zodiac or the Bha Chakra (in Indian astrology). The Zodiac is an imaginary belt in the sky which is concurrent with the Sun’s apparent path around the Earth as in the geocentric model described earlier. The Sun’s apparent path around the Earth is an ecliptic and so is that of the zodiac. Since it is a large ecliptic it is almost circular in nature. The zodiac is seen as a belt around the Earth since the planets moving around the Sun do not exactly follow the Sun’s apparent path but their orbits are dispersed variously within approximately 9 degrees to the north and 9 degrees to the south of the Sun’s apparent ecliptic path around the Earth in terms of the Celestial latitudes. The zodiac belt therefore is the area that lies within + / - 9 deg. of the Sun’s apparent path as observed from the Earth. The apparent Sun’s path is taken as the origin of the Celestial coordinate system. Since the Moon is revolving around the Earth, it also appears to be following the zodiac in its motion as observed from the Earth. In this way the Moon is also seen to be behaving exactly like the Sun and the other planets during its orbital motion with the only difference that whereas the Sun and other planets only appear to be revolving around the Earth on the zodiac, the Moon’s orbital motion is real. The zodiac is thus in the same plane as the Earth and the apparent Sun’s orbital path around the Earth.

The zodiac has another very important dimension associated with it that is the appearance of stars which apparently fill the zodiac belt. These stars on the zodiac are a subset of all the stars of our galaxy and may be located at various distances tucked millions of light years away however they appear on the zodiac belt as observed from the Earth. These stars appear in clusters of various shapes when seen from the Earth and which have been given different names on the basis of their apparent shape by the ancients often resembling certain day to day phenomena, things or animals. These stars play an important role in astrological interpretations of the dynamism of the unique influences of the solar system. These clusters of stars have been grouped into 27 distinct groups and have been placed equidistantly on the zodiac. By taking the zodiac to be almost circular and distributing the 27 star clusters equidistantly, each star cluster covers the celestial space equivalent to 360 deg. / 27 = 13 degrees and 20 minutes. The star clusters on the zodiac are called the asterisms or nakshatras. The names of the 27 nakshatras as used in Indian astrology are:

1. Ashwini

2. Bharani

3. Krittika

4. Rohini

5. Mrigsira

6. Ardra

7. Punarvasu

8. Pushya

9. Ashlesha

10. Magha

11. Purva-Falguni

12. Uttara-Falguni

13. Hasta

14. Chitra

15. Swati

16. Visakha

17. Anuradha

18. Jyeshtha

19. Mool

20. Purva-Shada

21. Uttara-Shada

22. Shravan

23. Dhanistha

24. Shatbhisha

25. Purva-Bhadra

26. Uttara-Bhadra

27. Revati

The number of days in a synodic month (the time element) which is 29.5 days is rounded off to 30 days, making it to 360 days in a year which corresponds with the 360 degrees of angular space of an almost circular zodiac. The zodiac has been divided into 12 equal angular space divisions of 30 degrees each termed as the Constellations or Rashis. The apparent motion of the Sun on the zodiac therefore is one degree of the zodiac in one day and the Moon’s motion is 12 degrees of the zodiac in one day. Thus the Sun apparently moves around the zodiac in 360 days @ one deg. per day which is roughly one synodic year and the Moon moves around the zodiac in 30 days (360deg. / 12 deg. per day) which is one synodic month thereby the Moon makes 12 rounds of the zodiac in one year which is the number of months in a year. In this manner the time and space dimensions have been made to coincide with one synodic month coinciding with one constellation and one degree of the zodiac coinciding with one day.

 Another basis for the identification of the constellations lining the ecliptic is through the specific groups of fixed stars that make the constellations quite similar to star clusters of the nakshatras.

The twelve constellations of the zodiac are named in Indian astrology as given below:

1. Mesh;    2. Vrishabh      3. Mithun;    4. Karkatak;   5. Simha;       6. Kanya;  

7. Tula;     8. Vrishchik;    9. Dhanu;    10. Makar;     11. Kumbh;     12. Meen.

The corresponding western astrological names for the constellations are Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius and Pisces respectively. These twelve constellations are usually referred to as the zodiac signs in western astrological parlance.

There are 12 constellations and 27 asterisms on the zodiac hence each constellation contains on an average 2.25 asterisms or nakshatras. Since each asterism or nakshatra is divided into four sections called padas in Indian astrology, each constellation or Rashi is said to contain 2 complete nakshatras or asterisms and one section or pada of the third nakshatra with the starting point of the rashis and the nakshatras being the ‘0’ degrees of Mesh rashi and the beginning of the 1^st section or pada of the Ashwini nakshatra.

It takes the Sun 13 days, 12 hours and 40 minutes to pass across one nakshatra and similarly it takes the Moon 1 day, 2 hours and 40 minutes to travel across one nakshatra. Another interesting fact is that if both the Sun and the Moon were hypothetically converted into wheels then both the Sun and the Moon shall take 108 revolutions to cover their respective distances to Earth which is the total number of all the four sections of all the 27 nakshatras i.e. 27 x 4 = 108. The Hindus hold this number as sacred representing Divinity itself in numerical terms. Since the number of revolutions that the Sun and Moon discs will have to take to complete one round of their individual orbits is the same (108) the two discs appear to be of the same size when viewed from the Earth.

The Earth is known to have three motions, one around its own axis resulting in the day and night, the second around the Sun resulting in the Year and the third is its wobbling motion called the precession which causes the continuous retrograde shifting of the zodiac @ 20 minutes annually. Thus the reference point of the ecliptic and the zodiac is very slowly shifting backwards shortening the year minutely every year. This backward motion is called Ayan and the measure of this retrograde motion of the zodiac is called Ayanamsa. In this way the reference point repeats itself in every 26,000 years. Indian astrology corrects the observed data from the apparent position (tropical positions) of planets to the standard position (sidereal positions) by making the necessary mathematical correction by subtracting the cumulative ayanansha from the given tropical observations. The correction ensures that the reference frame is based on the position of the fixed stars that form the constellations. In Indian astrology the tropical positions of planets is called the Sayan position and the corrected position is called the Sidereal or the Niryan position. Indian astrology primarily takes into account the Niryan positions for its calculations.

There is an anomaly in the divisions of the zodiac into constellations which is due to the fact that the zodiac is actually ecliptic and not circular. As a result, the lengths of the arc based on the angular divisions are not uniform with some constellations being shorter and the others being elongated. This in turn modifies the periods of the Sun’s passage through a constellation on its apparent orbit that varies from the standard 30 days to shorter or longer durations e.g. the Sun remains longer in the Virgo’s constellation than in the Scorpio constellation.

Yet another anomaly arises from the fact that there are actually 13 distinct groups of stars on the zodiac whereas there are 12 divisions as per the time and space synchronization as described earlier. Therefore the constellations do not necessarily match the zodiac signs. The 13^th star group named Ophiuchus lies between the constellations of Scorpio and Sagittarius. In fact the Scorpio constellation occupies a smaller arc on the ecliptic than Ophiuchus. Probably the ancient astronomers included the Ophiuchus within the Scorpio division to maintain the semblance of uniformity

This anomaly regarding the 13^th constellation on the Zodiac is not a serious issue for Indian astrologers because Indian astrology gives greater weightage to the star formations of the nakshatras and not so much to the constellations. The Rashis represent the space element for the placement of the planets and the nakshatras.

Yet another important aspect of the divisions of the zodiac lies in the fact that the divisions vary in their respective arc length according to the location of the observer on earth. It is for this reason that the latitude and longitude is considered during the generation of the horoscope.

An idea of the variations between the arc length of the apparent Sun’s orbit and the zodiac can be had from the following table:

Constellation	Assigned standard Sun’s stay duration in days for the 360 days year	Actual Sun’s stay duration in days for the 360 days year
Mesh / Aries	30 days	24.66 days
Vrishabh / Taurus	30 days	36.50 days
Mithun / Gemini	30 days	30.60 days
Karka / Cancer	30 days	19.72 days
Simha / Leo	30 days	36.50 days
Virgo / Kanya	30 days	44.38 days
Tula / Libra	30 days	22.68 days
Vrishchik / Scorpio + Ophiuchus	30 days	24.65 (6.90 + 17.75) days
Dhanu / Sagittarius	30 days	31.56 days
Makar / Capricorn	30 days	27.61 days
Kumbh / Aquarius	30 days	23.67 days
Meen / Pisces	30 days	37.47 days

As can be understood from the foregoing narrative, the zodiac is a complex phenomenon which influences astrological interpretations particularly with respect to the standard measurements of time.

Time has been treated in Indian astrology in a very serious manner. The calculations of time have been based on complex astronomical phenomena. The observations related to the two mutually independent entities i.e. the Sun and the Moon; that are connected to the Earth by way of the Sun’s apparent motion around the Earth on the zodiac and by way of the real motion of the Moon around the Earth on the zodiac, are synchronized for determining the months and the years. Whereas the Sun completes one round of the zodiac in what is known as one year, the Moon completes one round of the zodiac in what is known as the month and it hypothetically completes twelve rounds of the zodiac in one year, which is why there are twelve months in one year. Even though it seems to be perfectly symmetrical and in order however it is not so; thus there is a need for mathematical adjustment for the synchronization of the observed phenomenon to arrive at a standard measure of time.

Ideally the Sun should take 24 hours to complete its one apparent revolution around the Earth but actually this happens in 23 hours 56 minutes 4.09 seconds as a result of the Earth’s precession. In this way, hypothetically the Sun should complete one round of the zodiac in 360 days however it actually takes 365 days 6 hours 9 minutes and 9.5 seconds i.e. 365.24 days which is an extra 5.24 days.

On the other hand, the Moon takes 27.322 days to complete one round of the zodiac through the 27 nakshatras but in effect it takes 29.531 days to catch up with the Sun’s position on the zodiac instead of the hypothetical 30 days. Therefore the lunar year is of 29.531 x 12 i.e. 354.372 days which is shorter by 5.628 days in comparison to the hypothetical year of 360 days.

It is evident therefore that whereas the Sun takes an extra 5.24 days to complete one round of the zodiac, the Moon takes 5.628 days lesser to complete 12 rounds of the zodiac as compared to the ideal duration of the year i.e. 360 days. Thus in one year the difference between the lunar and the solar annuity amounts to 5.24 + 5.628 = 10.868 days. Indian astrology corrects this anomaly between the lunar and the solar years by adding one extra lunar month every three years or every 32.5 months which is called the Adhik Maas or Purushottam Maas. The Adhik Maas gets the name of the following lunar month in the calendar.

A Tropical year = 365 days 6 hours 9 minutes and 9.5 seconds or 365.24 days;

A sidereal year = 360 days;

A synodic year = 354 days 8 hours 55 minutes 40.8 seconds or 354.372 days;

A sidereal month = 30 days;

A synodic month = 29 days 12 hours 44 minutes 38.4 seconds or 29.531 days;

A Nakshatra lunar month also called ‘Nakshatra’ = 27 days 7 hours 43 minutes 40.8 seconds or 27.322 days;

A Nakshatra year of the Moon = 327 days 20 hours 44 minutes 9.6 seconds or 327.864 days.

The year, the month and the day calculations are based on the complex synchronization of the Sun’s and the Moon’s positions and their respective orbital motions with respect to the zodiac around the Earth. The time is further measured in smaller denominations for day to day references in three different ways as derived from three different authoritative sources in the Indian system. For the purposes of Astronomy and Astrology the third system given below is applied. The three sets of time divisions are based on the Vedas, the Puranas and the Astronomical texts such as the Sidhantas. These have been reproduced in the following three tables:

Vedic time units

Unit of Indian Vedic time	Equivalent units of defining time units	Equivalent modern time units
Paramanu	Base Unit	26.33 x 10-6 seconds
Anu	2 Paramanus	52. 67 x 10-6 seconds
Trasarenu	3 Anus	158 x 10-6 seconds
Truti	3 Trasarenus	474 x 10-6 seconds
Vedha	100 Trutis	47.4 x 10-3 seconds
Lava	3 Vedhas	0.14 seconds
Nimisha	3 Lavas	0.43 seconds
Kshana	3 Nimishas	1.28 seconds
Kashtha	5 Kshanas	6.4 seconds
Laghu	15 Kashthas	1minute 36 seconds
Danda	15 Laghus	24 minutes
Muhurta	2 Dandas	48 minutes
Ahoratram = One Sidereal day.	30 Muhurtas	24 hours
One Maasa (month)	30 Ahoratrams	30 days
One Ritu (season)	2 Maasas	2 months
One Ayan	3 Ritus	6 months
One Samvatsara (one sidereal year)	2 Ayans	12 months

Pauranik time units, based on Brahma Puran and Padma Puran

Unit of Indian Pauranik time	Equivalent units of defining time units	Equivalent modern time units
One Nimisha	Base Unit	0.2133 seconds
One Kashtha	15 Nimishas	3 . 2 seconds
One Kala	30 Kashthas	1 minute  36 seconds
One Muhurta	30 Kalas	48 minutes
One day and night	30 Muhurtas	24 hours
One month	30 days	30 days
One Ayan	6 months or 180 days	6 months
One Year = Uttarayan + Dakshinayan	2 Ayans	360 / 365 days / 12 months
Satya yuga	17,28,000 years	17,28,000 years
Treta yuga	12,96,000 years	12,96,000 years
Dwaapar yuga	8,64,000 years	8,64,000 years
Kali yuga	4,32,000 years	4,32,000 years
One Chaturyuga / Mahayuga (equals 12,000 years of the Devatas thus one divine year = 360 earth years).	One cycle of the 4 yugas Satya+Treta+Dwaapar+Kali	43,20,000 years
One Manavantar	71 Chaturyugas	30,67,20,000 earth years or 8,52,000 divine years
One Kalpa = one day of Brahma after which Brahma sleeps for one Kalpa long night.	14 Manavantaras	4,29,40,80,000 earth years or 1,19,28,000 divine years.
Brahma’s life span 365 (days+nights) per Brahma’s year  x 2 Kalpas per (day+night) x 100	73000 Kalpas =73 x 103  x 994 Mahayugas = 7, 25, 62000 Mahayugas	3,13,46,78,40,00,000=3.1346784 x 1013  earth years

Note: 1. Brahma’s one lifespan completes one large cycle of Manifestation and Dissolution of the Universe; whereas one Kalpa completes one cycle of partial ‘manifestation to dissolution’ of the universe.

         2. Uttarayan is daytime for the devatas and Dakshinayan is their night.

Niryan (sidereal astronomy based) time units

Unit of Indian astronomical time	Equivalent units of defining time units	Equivalent modern time units
One Truti	Base unit	0.03 x 10-6 seconds
One Renu	60 Truti	1.80 x 10-6 seconds
One Lava	60 Renu	0.11 x 10-3 seconds
One Leekshaka	60 Lava	6.6 x 10-3 seconds
One Lipta / Vipala	60 Leekshaka	0.40 seconds
One Pala / Vighati / Vinadi	60 Lipta	24 seconds
One Ghati / Nadi / Danda	60 Pala	24 minutes
One Muhurta	2 Ghati	48 minutes
One Hora	1.25 Muhurta	One hour
One day + One night (one Aho-Ratra) = One Sidereal day.	60 Ghatis = 30 Muhurtas = 24 Horas	24 hours
One Maasa (month)	30 Ahoratras	30 days
One Ritu (season)	2 Maasas	2 months
One Ayan	3 Ritus	6 months
One Samvatsara (one sidereal year) or One divine year	2 Ayans	12 months