When we look up at the heavens on a clear night, we find a multitude of celestial bodies, illuminating the sky with their radiance. It looks like a large hollow hemisphere, with the observer at the center. The planets and the luminaries seem to be scattered thorough the heavens at large distances.
This picture of the observer, the sky as a large crystalline hemisphere , is a very convenient model for the study of the Heavens.
This hemispherical model of the heavens is called Khagola, the Celestial Sphere. Another geocentric model, the Khagola is an imaginary sphere of large radius.
Astronomy, Maths and Astrology ( Siddhanta, Samhita and Hora ) are considered to be Apaurusheya, divine in origin. They were revealed to the Rishies in higher states of Consciousness and hence are revealed sciences. Descendit e Caelo, they cometh from Heaven !
Their date of compilation is believed to be 12th century BCE
Rotation, Revolution & Diurnal Motion
The earth rotates about its own axis, from west to east in the course of a day. Due to this rotation, the observer is carried eastward. But the observer is unaware of his motion in space. To the observer, the Celestial Sphere with all the heavenly bodies, is seen as rotating from east to west. This apparent westward motion of the heavenly objects is known as the diurnal motion.
There are four major methods of calculation in Astronomy
They are
Longitudes calculated along the Zodiac or Ecliptic – The Ecliptic System Longitudes calculated along the Celestial Equator – The Equatorial System Longitudes calculated along the Celestial Horizon – The Horizontal System Longitudes calculated along the Celestial Meridian – The Meridian System
Longitude measured along the Kranti Vritta, the Ecliptic or Bha Chakra , the Zodiac is known as Kranti Vritteeya Sphuta, the true longitude of the planet. Longitudes measured along the Vishuvat Vritta, the Celestial Equator is known as Vishuvat Vritteeya Sphuta, Right Ascension. Udaya Lagna, the Ascendent and Astha Lagna, the Descendent are measured along the Celestial Horizon, the Kshitija and the Madhya Lagna, the MC and the Patala Lagna, the IC are measured along the Celestial Meridian, the Nadi Vritta.
In order to compute the celestial longitudes of planets, first the Graha Madhyam, the mean longitude of the planet is computed.
We have to understand that the planets traverse in elliptical orbits. If their orbits are circular, then there is no need for jya samskaras ( trignometric corrections ).
Once the mean longitudes of the planets are ascertained, then we first start with the First Jya Samskara, the first trignometric correction. Manda Jya means Sin M in Western Astronomy.
The Kepler Equation is M = E – e Sin E, where e is eccentricity and E is the Eccentric Anomaly, an auxilary angle in Kepler’s equations.
Like Kepler who brought in an auxiliary angle, E, the Eccentric Anomaly, Indian Astronomy uses Vikshepa Vritta, an auxiliary circle. The mean longitude of a planet reduced by Manda Kriya is the Vikshepa Vritteeya Sphuta, the once corrected longitude of the planet.
While Western astronomers compute the celestial longitudes using the formula Theta = v + w ( Celestial Longitude = True Anomaly + the Argument of Perihelion ), Indian astronomers use the Triune Trignometric Method. Longitudes are corrected thrice using Manda Kriya, Parinathi Kriya and Sheegra Kriya.
The perturbations of planets
All planets have perturbations. Moon has 300 perturbations, of which 14 are major. Hence for 14 perturbations, 14 jya samskaras have to be done ( Chatur Dasa Jya Samskara). The largest of them is the Evection. There are others like the Variation, the Annual Equation and the Parallactic Equation. When 14 trignometric corrections are done, we get the Reduced Longitude of the Moon, the Samskritha Chandra Madhyamam.
Jupiter has five major perturbations and Saturn has six. So five jya samskaras and six jya samskaras have to be done for Jupiter and Saturn, before commencing the Triune Trignometric Method.
Jya ( Sine ), Kotijya ( Cosine ) and Utkram Jya ( Versine ) are the three trignometric functions introduced by the Indian astronomers and mathematicians.
In order to compute the celestial longitudes of planets, these functions were used by the trinity of Indian Astronomy, Bhaskara, Brahnmagupta and Aryabhata.
Thrijya, the Radius or R
If 360 = 2 Pi r then, r = 360/2Pi in degrees
One degree is 60 minutes and one minute is 60 seconds and hence one degree is 3600 seconds.
R in seconds will be ((360/2pi)* 3600 ) Vikalas or 206265 seconds. This figure 206265 is known as the Magic Figure of Astronomy.
Bhujajya = R Sin Kotijya = R Cos
The arc sine of the angle is Bhujachapa The arc cosine of the angle is Kotichapa The arc tangent of the angle is Sparshachapa
By Jya, Bramhmagupta meant 5 degrees of a sign of 30 degrees. Hence a Zodiacal Sign consists of 6 Jyas ( 30 degrees ) . The Zodiac of 360 degrees was divided into 4 quarters of 90 degrees each. Three Jyas of 30 degrees each becomes a quadrant of the Zodiac and was called Thrijya. Thrijya is also the Radius, the Vyasardha.
His magnum opus, the Brahmasphuta Siddhanta was translated by the Arabs as As Sind Hind. Jya became jiba and Kotijya became kojiba in Arabic. It was translated into Latin as sinus ( meaning ” bosom ” ). So Sinus and Co-sinus when translated into English became Sine and Cosine !
The Aryabhateeyam of Aryabhata was translated by the Arabs as Al Arjabhat. Trignometry is derived from the Sanskrit Thrikonamithi and Geometry from Jyamithi !
Kerala Astrology has a unique method of predicting weather cycles using the apparent solar transits or the real Earth’s transits.
This time Kerala has got plenty of rains and we can hopefully expect a 4.5% agri growth. The ancient astronomers of India used to say that rains will be in plenty during the apparent solar transit of Alpha Orionis. ( Thiruvathira Thiru Thakriti ).
There are seven major Njattuvelas, in which good rains are expected. They are
Rains will be galore during these transits of the Earth through the constellations of Eta Tauri to Alpha Cancri. These transits occur from the 15th of May to the 15th of August.
There are many sayings in Malayalam which deal with these rain procuring Njattuvelas.
Rains will be incessant during Thiruvathira ( Thiri muriyathe peythu nirayunna Thiruvathira ) You can spit even before Deity during Thiruvathira ( Thiruvathirakku thiru muttathu thuppam ) The waters of Thiruvathira will be welcomed ( Thiruvathira vellam thiruvonam kande pokoo )
While other solar transits take 13.33 days, this time Thiruvathira is the longest, taking 15 days, as the solar transit of Gemini ( Mithuna) is 32 days.
The ancients believed that it was nectar that rained during Thiruvathira. Every day’s rain have medicinal value. The ancients used to store the Thiruvathira rainwater and use it for Ayurvedic medicines. Maximum rains will be there during this transit and the paddy fields will be overflowing ! ” 101 rains, 101 sunlight “, ” 7.5 rains, 7,5 sunlight ” – Such phrases point out to the 50:50 proportion of rainy and sunny interludes which grace Thiruvathira.
The Njattuvela before Karthika, is good for digging wells. The wells dug during the Karthika Njattuvela ( when the Sun transits the Pleiades ), will be everlasting as their water will not dry up. ( Karthika kalil kakkakalu nananjal mukkathil mukkum ).
The seeds planted after Rohini Njattuvela ( Alpha Tauri ) need only little care. ( Rohinikappuram vitha kuruchu mathi ). Meaning you can get the fruits effortlessly.
Heavy rains will lash during the Earth’s transit of Lamda Orionis ( Makirythil Mazha Madhichu ). Fierce rains to be expected during the Earth’s tranist of Beta Geminorum ( Punarthathil pulappikkunna mazha ) ( Punartha thadiyan poozhi therippikkum ). ( Punarthathil poozhan keruka ). Good rains also during the Earth’s transit olf Delta Cancri ( Pooyathil pothumpurahtum nellu ). ( Pooyathil mazha peythal pullum nellu ). Unexpected rains during the Earth’s transit of Alpha Cancri ( Ayilya kallan akatho puratho ). The day may look bright and sunny and there will be unexpected downpours catching you unawares.
The Njattuvelas are good if they are born at night. The birth of ten Njattuvelas during daytime is considered to be inauspicious. ( Pathu Njattuvela pirannal laem kuthi erakkum ). If the Monsoon fails, if the Njattuvelas fail, there wil be famine and drought !
The major Four Seasons of the Western System and the Six seasons of the Indian system are caused by the apparent solar transits or the real Earth’s transits. The Njattuvelas are more comprehensive and minute and is worth studying, to understand Weather Cycles !
All celestial bodies appear to rise in the east, travel westward and set in the west, because of this relative diurnal motion. When the axis of the earth’s rotation is extended, it meets the Celestial Sphere on two diametrically opposite points called Celestial Poles. The one in the direction of the Earth’s north pole is called the North Celestial Pole and the one in the opposite direction is called the South Celestial Pole.
The Celestial Horizon, the Kshitija
To the observer standing at a place on the surface of the earth and looking around describing a full circle, the earth appears to meet the Heavens along a circle. From the observers’ frame of reference, this circle is called the Celestial Horizon, the Khshitija.
The Celestial Meridian, the Nadi Vritta
Almost 90 degrees to the Celestial Horizon, you will find another circle ( the line perpendicular to the plane of the horizon ). This Circle is the Celestial Meridian. The highest point on this Celestial Meridian is called Zenith, the MC and the lowest, the Nadir or IC.
Intelligence Thou art and essence Of all sciences intuitive; Thou art Called the Surmounter of all difficulties, Hence Durga called.
Of the nature of Sound Primal Thou art the threefold Veds The Triune Mother Divine As Wealth, Wisdom & Valour (Lakshmi, Saraswathi, Durga ) And as the Fourth, Transcendence, Thou art All in All, Thou art All !
Verily Thou hast declared “All this am I, nothing exists In the Universe apart from Me” As the microcosmic Kundalini, As the Macroscomic Universe, All this is Thy great Play, O Mighty Mother Divine !
Arise, awake, Seek out The Great Ones to know Truth ineffable As dangerous as the Razor’s edge So is the path difficult to cross
I walk on the Razor’s edge alone The path is narrow, the way Unknown
Go and seek out the Seers Whose body is full of Bliss Who enjoys divine Immortality Whose body know the warmth Warmth subtle of the Serpent Power As it ascends from the Base Chakra To the highest Crown Chakra !
Thou exist as Prosperity in the wise As Mental Chaos in the evil doers As Intelligence in the Seers As Purity in the Saints Thou art supreme, O Power Divine !
By Thy Grace supernal Wealthy men become With lots of largesse and subordinates Thou art the conferror of Wealth !
For those who want Self Actualisation Thou makest them do righteous deeds Heaven they get due to Thy Grace Thou art the Mother of both realms !
