The Geometric Model of Paramesvara

The Indian astronomers were interested in the computation of eclipses, of geocentric longitudes, the risings and settings of planets,which had relevance to the day to day activities of people.

Did not Emerson say?

"Astronomy is excellent, it should come down and give life its full value, and not rest amidst globes and spheres ".

They were not bothered about proposing Models of the Universe and gaining publicity. But then they did discuss the geometrical model, the rationale of their computations.

The above diagram explains the Geometric Model of Parameswara, another Kerala astronomer. Paramesvara and Nilakanta modified the Aryabhatan Model.

By Sheegroccha, he meant the longitude of the Sun." Sheegrocham Sarvesham Ravir bhavathi ", he says is his book Bhatadeepika . For the interior planets, the longitude of the Sheegra correction is to be deducted from the Sun's longitude, Ravi Sphuta to get the Anomaly of Conjunction.

The Manda Prathimandala is the mean angular motion of the Planet, from which the trignometric corrections are given to get the true, geocentric longitude.

Vikshepa Koti, the cosine of celestial latitude

Jyeshtadeva was a Kerala astronomer who helped in the calculation of longitudes, when there is latitudinal deflection. In his Yukti Bhasa, he calculates correctly the cos l, the cosine of latitude, which is important in the Reduction to the Ecliptic.

There is a separate section in the Yukti Bhasa, which deals with the effects of the inclination of a planet's orbit on its latitude. He describes how to find the true longitude of a planet, Sheegra Sphutam, when there is latitudinal deflection.


"Now calculate the Vikshepa Koti, cos l, by subtracting the square of the Vikshepa from the square of the Manda Karna Vyasardha and calculating the root of the difference."

In the above diagram,

N is the Ascending Node
P is the planet on the Manda Karna Vritta, inclined to the Ecliptic


Vikshepa Koti = OM = SQRT( OP^2 - PM^2 )

Taking this Vikshepa Koti and assuming it to be the Manda Karna, sheegra sphuta, the true longitude, has to be calculated as before.

Vikshepa, the Celestial Latitude

l, Vikshepa, is the Celestial Latitude, the latitude of the planet, the angular distance of the planet from the Ecliptic.

i is the inclination, inclinent of Orbit.


Sin l = Sin i Sin( Heliocentric Long - Long of Node ).

Celestial Latitude is calculated from this equation.

The longitude of the Ascending Node, pata, is minussed from the heliocentric longitude and this angle is called Vipata Kendra.

Sidereal Periods in the Geocentric Model

In the last post we said that Angle AES is Sheegroccha, which is the longitude of the Sun. ( Sheegrocham Sarvesham Ravir Bhavathi ). The Angle AEK is the Heliocentric longitude of the planet.

Sidereal Periods of superior Planets in the Geocentric = Sidereal periods in the Heliocentric.

Sidereal Periods of Mercury and Venus = Mean Sun in the Geocentric

In the Planetary Model of Aryabhata, we find the equation

Heliocentric Longitude - Longitude of Sun = The Anomaly of Conjunction ( Sheegra Kendra ).

As Astronomy is Universal, we are indebted to these savants who made astro calculation possible. Even the word " genius " is an understatement of their brilliant IQ !


Development of the Planetary Models in Astronomy

Hipparchus 150 BCE
Claudious Ptolemy 150 ACE
Aryabhata 499 ACE
Varaha 550 ACE
Brahmagupta 628 ACE
Bhaskara I 630 ACE
Al Gorismi 850 ACE
Munjala 930 ACE
Bhaskara II 1150 ACE
Madhava 1380 ACE
Ibn al Shatir 1350 ACE
Paramesvara 1430 ACE
Nilakanta 1500 ACE
Copernicus 1543 ACE
Tycho Brahe 1587 ACE
Kepler 1609 ACE
Laplace 1700 ACE
Urbain Le Verrier 1850 ACE
Simon Newcomb 1900 ACE
E W Brown 1920 ACE

Reduction to the Geocentric for superior planets in the Eccentric Model

In the above diagram,


A = Starting Point, 0 degree Aries
P = Planet
S = Sun
E = Earth

Angle AEK = Manda Sphuta, heliocentric longitude, after manda samskara
Angle AES = Sheegroccha, mean Sun, mean longitude of Sol
Angle AEP = True geocentric longitude of planet
Angle KEP = The Sheegra Correction or sheegra phalam

The Anomaly of Conjunction = Sheegra Kendra = Angle AES - Angle AEK

x = Angle AES - Angle AEK

Sin ( x ) =

r sin (x)
_______________________
((R + r cos x)^2 + rsin x^2 ))^1/2

which is the Sheegra correction formula given by the Indian astronomers to calculate the geocentric position of the planet.

Aslesha Njattuvela brings rains !

It was Monsoon Tourism, as Aslesha Njattuvela was on. It was raining heavily, cats and dogs in Kerala. I got the rains when I reached Kochi. I had some work at the Passport Office and I finished the work at Noon. Then I went on a tour of the famous Goshree Islands.

I went by boat yesterday to the beautiful Bolgatty Island. A two minutes walk saw me entering the lovely Bolgatty Palace, a resort by the Kerala Tourism Development Corporation.





I walked to the Bolgatty Bus Stand and took a bus to Vallarpadam International Container Terminal. Now everything is in place and one ship, OEL Dubai, was unloading. The progress of the ICTT is slow, but steady.





The Bolgatty Palace is beautiful and well situated in the Mulavukad Island. This island is connected to Vallarpadam by a bridge. Vallarpadam is in turn connected to Vypin by a bridge. In fact these bridges are known as Goshree Bridges, as these beateous islands are known as Goshree Islands. In Vypin, one can see the GAIL LNG terminals, which adorn Puthuvypin.




A new bridge, parallel to the existing Vallarpadam bridge, is being built to ease the traffic. I saw a barge jetty at Bolgatty and a barge carrying containers there.




Kochi is a cauldron of world cultures. A versatile land where visitors from abroad, right from Arabs and Phoenicians to the Chinese, Italians, Portugese, Dutch and British have left indelible marks. A great Port, universally known as the Queen of the Arabian Sea. The newly renovated Bolgatty Palace has 4 palace suits, 6 waterfront cottages, 16 well maintained rooms and one can enjoy four star faciliites and a range of leisure options.





Said a honeymooner, Asmita, Calcullat about Bolgatty " We went to Kerala for our honeymoon and Kochi was our first stop. We reached the resort at around 3:30pm after a long flight and were famished. Since we reached post lunch timings none of the restaurants were open, however the room service was very prompt and we had an amazing keralite food. The rooms are large, and built in a princely way. The property is equipped with all the modern facilities and the stay was really comfortable.
We enjoyed the Kerala body message in the resort . The location is also great. Overall its a great place to stay ".

The Bolgatty Palace was built in 1744 by the Dutch and is a short boat ride away from the Ernakulam Mainland. This is one of the oldest Dutch Palaces outside Holland the only Palace Hotel of its kind in Kerala. Now she has a Palace block and a resort block, called Bolgatty Island Resort. Amenities here comprise Swimming Pool, 9 hole Golf Course and is a destination of choice for select Indian corporates for their conference. It is a favourite destination for Indian elite and overseas tourists. The Kochi Airport is just 32 kms away and the rail and bus terminals just 2 km away.

Kochi International Marina is a KTDC venture located on the eastern coast of Bolgatty Island in the Bolgatty Palace Heritage Hotel. It is the first full fledged marina of international standards in Bharat. It provides berthing facilities to 37 yachts and also offers services like electricity, water and fuel for boats. It is close to the international sea route at the South West Coast of peninsular India , with minimum tidal variations and favorable conditions.






The Bolgatty Event Center overlooks the backwaters of Cochin Seaport and is an exotic venue for conducting Conferences, Exhitions, Wedding Receptions, Conventions and theme dinners. Imbued with resplendent greenery, the Arabian Sea and the ICTT at Vallarpadam gives an easy access to the Center.

Another Indian Astronomical Treatise

Siddhanta Darpana by Samanta is a great treatise on Astronomy. The placing of the five major planets in the Tychonic Model of the solar system is in agreement with the Titius-Bode Law and even with Kepler's third law. This is a great contribution from Samanta. Epicycles for Solar Anomaly, known as Ugra Phala give correct distances of planets, in both Indian and Greek Astronomy.

Here we give the modern values of the radii of the orbits of the planets and those given in his magnum opus, the Siddhanta Darpana.


Planetary distances in astronomical unit


Planet Distance according to Bode’s law Actual distance

Mercury 0.4 0.387

Venus 0.7 0.732

Earth 1.0 1.0

Mars 1.6 1.524

Asteroid belt 2.8 2.68

Saturn 10.0 9.539

Uranus 19.6 19.19

Neptune 38.8 30.1

Pluto 77.2 39.5



Siddhanta Darpana



Even Odd

quadrant quadrant

Sun 1.00 1.00

Mercury 0.386 0.388

Venus 0.725 0.727

Mars 1.5126 1.5184

Jupiter 5.1428 5.2173

Saturn 9.230 9.4773