The Fall of Star Vega (Abhijit)

By Dr. P.V.Vartak


Truth of 12,000 years B.C. recorded in Mahabharat.



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Maharshi Vyas has recorded in Mahabharat, Vana Parva (Chap.230, Verses 8-11), a dialoge between Indra and Skanda where-in it is stated that:

"Contesting against Abhijit (Vega), the constellation Krittika (Pliedes) went to "Vana" the Summer Solstice to heat the summer. Then the star Abhijit slipped down in the sky. At that time Dhanishta was given the first place in the list of Nakshatras. Rohini was also the first some time back. Now you decide what to do," said Indra.

This dialogue shows that when Indra went to Summer Solstice, Vega started falling down. Many scholards have ridiculed this idea of Star Falling; but now it is proved by modern astronomy that it was a true fact that 12,000 years B.C., Vega had really come down to the horizon from the heights of the sky, to become a pole star.

Krittikas were at the Summer Solstice between 21,800 and 20,840 years B.C. At this time Dhansishta was at the vernal equinox and hence was given the first place in the Nakshatras. From this period, the sages noticed the gradual fall of Abhijit. Falling steadily, it is assumed the position of the Celestial Pole at 12,000 B.C., when Indra met Skanda to think on the problem of time-reckoning. The story shows that the Indian sages were observing the stars and constellations at least from 23,000 years B.C.



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References

The Summaries of papers read in The Seminar on the Mahabharat War, May 30-31, 1992.


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Vedic Astronomy III

All events are connected by Time, all places are connected by Space and alleffects are connected by Cause in the Space-Time-Causality equation. TheScience of Time ( Astrology ) and the Science of Cause ( TranscendentalPhilosophy ) assume great significance in the realm of superconscientlearning

The Elements Used in the Computation of TimeT

he main element used is the Sun itself. One solar day is the time taken bythe earth to rotate around its own axis. One solar day is made up of 24solar hours, one solar hour is sixty minutes and one minute is sixtyseconds.

The time taken by Sol to make a circuit of the Zodiac from the First Pointof the Sidereal Zodiac is called a Sidereal Year. This is 365.25363 solardays. A Tropical Year is the time taken by the Sun to make a circuit of theTropical Zodiac This is 365.242194 solar days.

The Five Types of Years

There are five types of years

1) Solar Year
2) Jupiterian Year
3) Savana Year
4) Lunar Year
5) Sideral Year

Solar Year

The time taken by Sol ( Sun ) to cross one degree is called a solar day.When the Sun crosses from one Sign to another, this is called Surya Sankrama( transit to another sign ). The time taken from one Surya Sankrama toanother is called one solar month. The motion of the Sun is fastest at thefirst week of January and is slowest at the first week of July. In otherwords, since the Sun's motion is fastest in the Vedic months of Sagittariusand Capricorn, it takes only 29 days for the Sun to traverse 30 degrees ofSag and Cap. Conversely, it takes 32 days for Sol to traverse 30 degrees ofCancer, since his motion is slowest at Apogee, in the Vedic month of Cancer.

Jupiterian Year ( Barhaspathya )One Barhaspathya is time taken by Jove ( Jupiter ) to traverse 30 degrees ofa sign. The duration is 361 days and a Jupiterian Cycle is roughly 12 years.

Savana Year

One Savana day is reckoned from Sunrise to Sunrise. 30 such Savana day iscalled one Savana month. 360 such days is one Savana year.Lunar YearA lunar month is the time calculated from one New Moon to the next New Moon.Since during a solar year, 12 Full Moon were visible , the Zodiac wasdivided into 12 constellations. 12 Lunar months constitute one Lunar Year.This is 354.367 days. This is 11 days less than the solar year.

Sidereal Year

One sidereal day is time taken by Luna to traverse a constellation of 13degrees and 20 minutes. The Moon takes 27.3 days to revolve around theearth. 27.3*12 is one Sidereal Year and it is 327.6 days.

Apparent Solar Day ( Savana Dina )The time taken by the earth to rotate around its own axis. From a geocentricperspective, the Sun moves one degree per day.

Sidereal Day ( Nakshatra Dina )This is the time taken by the earth to rotate around its own axis withregard to Sidereus, the constellation of fixed stars. This is 23 hours and56 mins and 4.0953 seconds.An apparent Solar Day is 24 hours. According to Indian Astronomy, a solarday is 60 Nadis. 60 Vinadis is one Nadi ( Nazhika ) and 60 Tatparas is oneVinadi. There are minuter subdivisions like Pratatparas ( 60 Pratatparasconstitute one Tatpara ), corresponding to micro seconds and nano seconds inWestern time calculations. 2 and a half Nadis is one hour or 24 minutes isone Nadi.

While as per Western calculations, a day is reckoned from midnight tomidnight, an Indian day is reckoned from sunrise to sunrise and a Hijra dayis calculated from sunset to sunset.Sidereal Solar YearThe time taken by the Sun ( from a geocentric perspective ), to make acircuit of the Sidereal Zodiac . This is 365 days, 6 hours 9 minutes and 9.8seconds.

Vedic Astronomy IV

Astronomy, " the science of the Heavens ", was well developed by the Indians and noted scholar Eirik L Harris remarked that " the Vedic culture was very rich in astronomical thinking." The Winter Solstice was the base of all year-long sacrifices and the Vedic knowledge of both winter and summer solstices were accurate. There is a verse in the Rig Veda stating that Winter Solstice was in Aries. " The period of the Rig Veda was therefore 6500 BC and it is possible to date the Rig Veda thus " remarks Eirik L Harris. Astronomy and Mathematics were inspired by Vedic practices.

Another scholar B.V.Subbarayyappa remarked that " Indian mathematics too owes its primary inspiration to Vedic practices. The Shulba sutras, part of another Vedic auxiliary called the Kalpa sutras, deal with the construction of several types of brick altars and in that context with certain geometrical problems including the Pythagorean theorem, squaring a circle, irrational numbers and the like. Yet another Vedic auxiliary, Metrics (chandah), postulated a triangular array for determining the type of combinations of 'n' syllables of long and short sounds for metrical chanting. This was mathematically developed by Halayudha who lived in Karnataka (10th Century) into a pyramidal expansion of numbers. Such an exercise appeared six centuries later in Europe, known as Pascal's triangle. Vedic mathematics and astronomy were pragmatic and integrated with Vedic religio-philosophical life."

"During the three centuries before and after the Christian era, there were new impulses. Astronomy became mathematics-based. In the succeeding centuries, while astronomy assimilated Hellenic ideas to some extent mathematics was really innovative. Indian astronomers were able mathematicians too. The doyen among them, Aryabhatta I (b.476 A.D.) gave the value of pi (3.1416 approx., a value used even today) worked out trigonometrical tables, areas of triangles and other plane figures, arithmetical progression, summation of series, indeterminate equations of the first order and the like. He expounded that the earth rotates about its own axis and the period of one sidereal rotation given by him is equivalent to 23h 56m 4s.1, while the modern value is 23h 56m 4s.091. He discarded the mythical Rahu-Ketu postulate concerning eclipses in favour of a scientific explanation.

Aryabhatta's junior contemporary Varahamihira, was well known for his compendium, the Panchasiddhantika, a compilation of the then extant five astronomical works called the Siddhantha- Surya, Paulisha, Romaka, Vasishta, and Paitamaha. Of them, the Suryasiddhanta, which he regarded as the most accurate, underwent revisions from time to time and continues to be an important text for computing pancangas.

Brahmagupta was a noted astronomer mathematician of the 7th Century. His remarkable contribution was his equation for solving indeterminate equations of the second order - an equation that appeared in Europe a thousand years later known as Pell's equation. His lemmas in this connection were rediscovered by Euler (1764) and Lagrange (1768). Brahmagupta was also the first to enunciate a formula for the area of a rational cyclic quadrilateral. In the latter half of the first millenium A.D. there were other noted astronomers and mathematicians like Bhaskara I, Lalla, Pruthudakasvamin, Vateshvara, Munjala, Mahavira (Jaina mathematician), Shripati, Shridhara, Aryabhatta II , and Vijayanandin. The tradition of astronomy and mathematics continued unabated - determination of procession of equinoxes, parallax, mean and true motions of planet, permutations and combinations, solving quadratic equations, square root of a negative number and the like.

Using nine digits and zero, the decimal place value system had established itself by about the 4th century A.D. Says historian of science, George Sarton, "Our numbers and the use of zero were invented by the Hindus and transmitted by Arabs, hence the name Arabic numerals which we often give them.' Brahmagupta's Brahmasphuta Siddhanta and Khandakhadyaka were also rendered into Arabic in the 9th-10th century. The Brahmi numerical forms with some modifications along with the decimal place-value system developed in India have since become universal."

Eirik L Harris remarked that "Additionally, the Vedics, who developed the Hindu-Arabic number system, were far enough advanced in mathematics to make many calculations, including that of the complete cycle of the progression of the equinoxes, though, again, as the Vedas were mainly religious, there is no mention as to how results like this were derived. Overall, the Vedic culture was very rich in astronomical thinking, and it is a shame that non religious texts did not last through the centuries, for they could have shone more light on the matter of the astronomical accomplishments of the Vedic people."

The ancient Indians divided the path of the moon into 27 equal parts called nakshatras, showing the variation of the relative position of the moon in comparison to the rest of the stars visible to the Vedic people. These nakshatras were quite important for determining times of the year, as can be seen in combination with Vedic mythology, and can also be used to determine how far back in history Vedic astronomy extended.

The myth of the god Janus shows both of these factors, the determination of the age of Vedic astronomy and different periods of the year. Janus had four heads, each of which represented a phase of the moon in Sagittarius (one of the nakshatras) which marked the four seasons. One head was the full moon (in Sagittarius) which gave the time of the spring equinox, another was the new moon, during which time the autumn equinox fell, still another was the half waning moon, marking the winter solstice, and finally came the head representing the half waxing moon, during which time came the summer solstice. From current knowledge of the movement of the sphere of stars surrounding the earth, it can be calculated that the observations leading to the myth of Janus were made around 4000 BC. Additionally, within the Rg Veda is a verse observing the winter solstice in Aries, which would have placed it at around 6500 BC.

It is possible to date the Rg Veda like this because a complete cycle in the procession of the equinoxes takes place either every 25,870 to 24,500 years according to modern astronomers (the exact time period is still disputed by modern day astronomers), meaning that the moon is only full in Sagittarius during the spring equinox every 25,000 years or so. Modern astronomers, however, were not the first to make the difficult calculations to discover the length of this cycle. The Vedics were able to do this and came up with the value of 25,870 years. How these ancient people were able to make these calculations, however is "as great a mystery as the origin of life itself".

Further observations which could only have taken place around 4000 BC have also been recorded. These included the constellation Hydra, the god of darkness. The only time Hydra was fully visible to the people of northern India was in mid-winter, when the sun shone the fewest hours, hence the allusion to the god of darkness. More importantly, however, was the fact that the rains came when Hydra ceased to be completely visible. This was very important to the farmers of North India, for they needed to know when the rains would come, so as to know when to prepare their fields and plant their crops." ( Astronomy of Vedic India )

Astronomical Mysticism in the Rig Veda

The five fundamental circles, the Celestial Equator ( Vishuvat Vritta) , the Celestial Meridien ( Khagoleeya Dhruva Rekha ), the Ecliptic ( Kranti Vritta ), the Nodal Circle ( Vikshepa Vritta ) and the Celestial Horizon ( Kshithija ) were called by the Seers as Shahasra Seersha, Sahasra Purusha, Sahasra Kha, Sahasra Path & Sahasra Bhoomi. This is given in the Hymn, the Purusha Sooktha, that the Zodiacal Man or Time Eternal lies coiled as the mighty Zodiac !

Philosophical Piece

The Downward Pull of the Mind

The Downward Pull of the Mind is when the negative elements in the collective mind or the social mind triumph. Socrates is poisoned. Rimbau flees to the Abyssinian desert. History is replete with such incidents, when " the adverse forces " or " the hostile forces " triumph over the positive forces in the collective or social mind.

The Upward Pull of the Mind

This happens only in the minds of Initiates. " In Ire " in Latin means to go within. Initiates are those who are always in touch with the Divine Self in themselves. The four faculites of the Intuitive Reason - Revealation, Inspiration, Intuition & Illumination - are experienced by them. The river of inspiration flowing from the Truth Consciousness pulls the mind to the higher regions of the Superconscient. In Geo-Biology, this is the pull of the mind from the Telluric level to the Cosmic level. The mind experiences Bliss during this Upward Pull. The Upward Pull is the master movement of Nature. The upward movement is that which pulls us from Death ( the senseless attachment to the sensory world ) to Immortality ( Self- Actualisation) and realises in this body of earth the luminous Kingdom of Heaven !

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Vedic Astronomy II

Cosmological Time Cycles in Indian Astronomy

Long before Copernicus, Galileo & Ptolemy, Aryabhata propounded the Heliocentric Theory of Gravitation, that all planets revolve around the Sun due to celestial gravity. The term given to Celestial Gravity was Guru-tva-Akarshana, which also has a philosophic meaning. Guru represents the Master, the Inner Sun, symbolic of the Self and the planets that revolve represent the students who are on their way to Self_Actualisation !

In Sanskrit Astronomy is known as Khagola Sasthra and Aryabhata worked at an astronomical observatory called Khagola. He studied at the University of Nalanda which housed more than 9 million books.

The Sexagesimal Division of a Day ( Sixtieth Division )

The Life span of Breath is 4 seconds, called as an Asu or a Pranakala in Sanskrit. 6 such Asus constitute a Vinadi and 60 such Vinadis constitute a Nadi. 60 Nadis is one day. In other words, a day is 86400 seconds and 21600 Asus. This sexagesimal division of a day is the base of Indian Astronomy. 15 such days constitute a Fortnight. There are two types of Fortnights - Dark Fortnight ( Krishna Paksha ) & Bright Fortnight ( Shukla Paksha ). These 2 fortnights constitute a month. Two months together is one Rithu and there are six seasons ( Rithus ). Aries & Taurus together is Vasantha, Gemini & Cancer Greeshma, Leo & Virgo Varsha , Libra & Scorpio Sharath, Sagittarius & Capricorn Hemantha and Aquarius & Pisces Sisira. Six months is one Ayana and there are 2 types of Ayanas - Dakshinayana ( the southern progress of the Sun, his declination South ) & Uttarayana ( the northern progress of the Sun, his declination north ). 12 such months or 6 Rithus or 2 Ayanas constitute a solar year. Since precession is 72 years per degree, one Age Cycle is 72*30 = 2160 years and 2 million Age Cycles is one Cosmological Cycle.

One Cosmological Cycle is 4.32 Billion years, known as a Brahma day. The Life span of Brahma is 100 sidereal years or 2*4.32*360*100 = 3.1104*10^14 years ! Indian Astronomy is graced by such gigantic calculations starting from 1/21600th of a day to 3.1104*10^14 years !

The Ursa Major Cycle

The constellation of Ursa Major ( The Saptha Rishies ) move backwards along the Zodiac, staying in a constellation for 100 years. To make a circuit of the Zodiac, they take 27*100 = 2700 years. This is known as an Ursa Major Cycle. Remarks Prof Drayson in "Asiatic Researches ", " The Indians thought proper to connect their mythology with an astronomical period of a strange nature. It is that of the Seven Rishies, moving along the Zodiac in a retrograde motion of 2700 years." Ursa Major was in Regulus at the start of the Mahabharatha War. The first astronomical calender was erected by the Indian emperor Vaivaswatha Manu ( circa 8736 BC ) and it was based on the Ursa Major Cycle.

D or Lunar Day ( Thidhi )

When we deduct the longitude of the Sun from the longitude of the Moon, we get the Thidhi or Lunation

D ( Lunar Day ) = Lm ( Longitude of Moon ) - Ls ( Longitude of Sun )

The First Lunar Day is called Prathama ( Moon within 12 degrees of the Sun ) , the Second is called Dwitheeya ( Moon within 12 and 24 degrees of the Sun ) and we have 14 lunar days before Full Moon. The 15th Lunar Day is Full Moon ( Pournami ). When the Moon is conjunct at 0 degrees from the Sun, it is New Moon ( Amavasya ). All Indian religious festivals are based on the position of the heavens.

Prathama Moon between 0 degrees and 12 degrees from the Sun
Dwithyeeya Moon between 12 degrees and 24 degrees
Thritheeya Moon between 24 degrees and 36 degrees
Chathurthi Moon between 36 degrees and 48 degrees
Panchami Moon between 48 degrees and 60 degrees
Shashti Moon between 60 degrees and 72 degrees
Sapthami Moon between 72 degrees and 84 degrees
Ashtami Moon between 84 degrees and 96 degrees
Navami Moon between 96 degrees and 108 degrees
Dasami Moon between 108 degrees and 120 degrees
Ekadasi Moon betw een 120 degrees and 132 degrees
Dwadasi Moon between 132 degrees and 144 degrees
Thrayodasi Moon between 144 degrees and 156 degrees
Chathurdasi Moon between 156 degrees and 168 degrees
Pournami Moon between 168 degrees and 180 degrees

East & West Points on the Celestial Horizon

East and West Points are two intersecting points between the Ecliptic and the Celestial Horizon. If on the Celestial Horizon, you mark E as East , W as West, N as North and S as South, then NES is the Eastern Celestial Horizon, SWN is the Western Celestial Horizon, ENW is the Northern Celestial Horizon & ESW is the Southern Celestial Horizon.

Ayana Sandhis -

Intersecting Points between the Ecliptic and the Celestial Equator The Ecliptic is slanted 23 degrees 27 minutes from the Celestial Equator. The intersecting points between them are called as Ayana Sandhis. These Sandhis are not static. They have a retrograde motion of 50.3 seconds per year. When the Sun crosses the Celestial Equator from the South to the North, that intersecting Point is Meshadi, the First Point of Aries and when he crosses the C E from North to South that point is called Thuladi, the First Point of Libra. At the start of the Dark Age ( Kali Yuga ), all planets were in the First Point of Aries. The First Point of Aries was in the constellation of Beta Arietis or Aswini. During the Vedic period, the First Point of Aries was in Karthika. That is why in the Vedas, the constellations are counted from Karthika onwards. Now Tropical Meshadi is behind Sidereal First Point of Aswini by 23 degrees 52 minutes. This motion of the Ayanas is called Precession.

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Vedic Astronomy & Trignometry

Vedic Astronomy & Trignometry

In the Great Circle of Light which is 360 degrees, ( the Bha Chakra, the Kala Chakra, the Zodiac ), the first 90 degrees are Oja Pada ( Odd Tri Signs ) and the next 90 degrees are Yugma Pada ( Even Tri Signs ). The degrees traversed by a planet is called Bhuja and the degrees yet to be traversed by a planet is called Koti in an Oja Pada. In a Yugma Pada, the degrees traversed by the planet is called Koti and the degrees yet to be traversed by a planet is called Bhuja. In other words, the degrees traversed by a planet is the same in the first 0 - 90 degrees and in the second Pada, it is 180 - degrees traversed. In the 180-270 degrees arc, it is distance traversed - 180 degrees and in the 270-360 degrees arc, it is 360 - distance traversed. This is known in Vedic Astronomy as the equation of Bhuja or Sin. Bhujajya is radius multiplied by modern Sine.

In the Mighty Circle of Light
The First 90 degrees is Oja called
The distance traversed is Bhuja called
Koti is the untraversed degree !
( Oja Yatra Bhujaira Kotirapara Meshadi Jookadhi Kau )

Brahmagupta, in his mathematical treatise, the Brahmasphuta Siddhanta used the word Jya which means 5 degrees of a 360 degree circle which is the Zodiac, which is the Ecliptic. Suppose a planet has traversed 42 degrees in the first Oja Pada ( From Aries to Gemini end ).The Bhuja is 42 degrees and the Bhujajya is the 9th Jya or the 9*5 th degree. Bhujajya by Trijya is Opposite Side by Hypotenuse or the modern Sine.
Jya Ganitha means Trignometry. The equation for Koti is different. It is Kotijya by Trijya or Adjacent Side by Hypotenuse ( the modern Cos ). As per Indian Learning it was Aryabhata, one of the greatest mathematicians ever, who first computed the celestial longitudes of planets ( Aryabhato Graha Ganitham ).

The calculations given for the perturbations of Moon, Jupiter and Saturn are as follows. First find out the Bhuja of the planet, the degrees traversed. Find out its Bhujajya or Sin ( Bhuja ). Multiply it by the value given ( which is in seconds) and add it to the mean longitude of the planet.

Meshadi , Thuladi, Karkyadi & Makaradi ( The First Points of Aries, Cancer, Libra & Capricorn )

From Aries to Libra is the Northern Celestial Hemisphere ( NCH ) and from Libra to Aries is the Southern Celestial Hemisphere ( SCH ). If the planet's Kendra is in NCH, the values are to be subtracted and if in the SCH, it is to be added.

Karkyadi is the First Point of Cancer and the beginning of Dakshinayana, the Southern course of the Sun, his declination South. Makaradi is the First Point of Capricorn and the beginning of Uttarayana, the Northern course of the Sun , his declination North. At Meshadi, the Sun's declination is 0 degrees and Right Ascension is 0 degrees. At Karkyadi, the Sun's declination is +23 degrees 27 minutes and Right Ascension is 90 degrees. At Thuladi, the Sun's declination is 0 degrees and Right Ascension is 180 degrees. At Makaradi, the Sun's declination is -23 degrees 27 minutes and Right Ascension is 270 degrees.

The Perturbations of Jupiter

The equations given for Jupiter's perturbations are as follows: Five major perturbations are included along with a major perturbation which is given below. ( The great Jupiter - Saturn perturbation ).

Kendra means an angle in Sanskrit . Manda Kendra means Mean Anomaly, the angle between position and perihelion and Sheeghra Kendra is the last angle formed before the ultimate reduction to perihelion. All Kendras are zero at perihelion.

The English Era + 3102 gives the Kali Era, the Era of the Hindu Calender. From that value 4660 is deducted and the value is divided by 918. This gives the Beeja Kendra. Find out the Sin ( Bhuja ) of that, multiply it with 1187 seconds and add it to Jupiter's longitude if the Kendra is in NCH and subtract it if it is in SCH.

There are other minor perturbations which can be ignored.
( Lj = Mean Longitude of Jupiter; Ls - Mean Longitude of Saturn. These longitudes are Tropical or Sayana. ).

First Kendra (Sin ( Lj - Ls ) - 1. 15)* 81
Second Kendra Sin (( Lj - 2 Ls) - 13.08 )* 132
Third Kendra Sin ( 2 Lj - 2 Ls - 0.58 )* 200
Fourth Kendra Sin ( 2 Lj - 3 Ls - 61.57 )* 83
Fifth Kendra Sin ( 3 Lj - 5 Ls - 56.38 )* 162

The first value is to be added if the Kendra is Thuladi ( after the First Point of Libra ) and deducted if it is Meshadi ( after the First Point of Aries ). 2,3,4 & 5 are to be added if it is Meshadi and subtracted if Thuladi

The Perturbations of Saturn

First Kendra Sin ( Lj - 2 Ls ) -14.66 )*418
Second Kendra Sin ( 2 Lj - 4 Ls + 56.90 )* 667
Third Kendra Sin ( 3Ls - Lj + 77.38 )* 48

These values are to be added if the Kendra is Thuladi ( after the First Point of Libra ) and deducted if it is Meshadi ( after the First Point of Aries ). In Sanskrit it is called Meshadi Rinam & Thuladi Dhanam. Meshadi is the beginning of the Northern Celestial Hemisphere and Thuladi the begining of the Southern Celestial Hemisphere.

There are other minor perturbations which may affect only the Vikala ( second ) of the planet's longitude and hence can be ignored.



The Perturbations of the Moon

(Ms - Mean Anomaly of the Sun; Mm - Mean Anomaly of the Moon; Ls - Mean Longitude of the Sun; Lm - Mean Longitude of the Moon; D = Lm - Ls ( Thidhi); Nm - Node of the Moon. These values are Sidereal or Nirayana )
14 Kendras are to be made and 14 trignometric corrections are to be given, according to astronomical savants. These 14 reductions are mandatory and only after these reductions can we get the true longitude of the Moon.

First KendraSin ( Ms + 180 ) * 658
Second KendraSin ( Lm - Ls ) * 121
Third Kendra Sin ( 2*D - Mm ) * 4467
Fourth Kendra Sin ( 2*D + 6 Signs ) * 2145
Fifth Kendra Sin (( 2*D - Mm -Ms ) + 180)* 198
Sixth KendraSin ( 2*D - Ms ) * 155
Seventh KendraSin ( Mm- Ms + 180 ) *112
Eighth KendraSin ( 2( Lm - Nm- Mm +180))* 85
Ninth KendraSin ( 2*Ls - Nm ) * 81
Tenth Kendra Sin ( Mm - Ms )* 73
Eleventh KendraSin ( 2*D + Mm ) * 60
Twelfth Kendra Sin ( 2*Mm - 2 D + 180 ) * 42
Thirteenth KendraSin ( 4*D - Mm ) * 35
Fourteenth KendraSin ( 4*D - 2*Mm +180)* 30

These trignometric corrections should be added to Moon's Mean Longitude if the Kendra is in the Southern Celestial Hemisphere and deducted if the Kendra is in the Northern Celestial Hemisphere and then we get the Samskrutha Chandra Madhyamam or the Cultured Mean Longitude of the Moon. Manda Kriya ( Reduction to True Anomaly ) must be done. Then Parinathi Kriya ( Reduction to Ecliptic ) should be done and what we get then is the longitude of the Moon along the Ecliptic !

Viskshepa Vrittopa Gatho Vipatha
Thasmannayel Jyam Parinathyabhikhyam
Yugmaupada Swarnam Idam Vidheyam
Syath Kranti Vritteeya Ihaisha Chandra !

After the Reductions Fourteen, Sin M to be added or minussed thereby
To the Cultured Longitude Mean; The Node to be deducted &
Reduced to the Earth's Path ( Ecliptic ); thus shall we get as the resultant Value,
Luna's true Sidereal Longitude !