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( Above diagram by courtesy of www.wikipedia.org )

A 360 degree Circle is a coordinate System. And Khagola is the Celestial Coordinate System.

Like the Geographical Coordinate System, the Celestial Coordinate System is another coordinate system, which computes the coordinates of the Khagola, the Celestial Sphere.

The Ascending Sign is called the Ascendant ( Raseenam udayo lagnam ) and is the intersecting point of the Ecliptic ( at the East Point) with the Celestial Horizon. The Descending Sign is the Descendant ( Astha Lagna ) and lies 180 degrees West on the Khshithija, the Celestial Horizon.

Like the Geographical Meridien ( the Prime Meridien ) and the Geographic Equator, the Celestial Coordinate System has a Celestial Meridien ( Nadi Vritta ) and a Celestial Equator.

The Vernal Equinox and the Autumnal Equinox are two intersecting points of the Ecliptic with the Vishu vat Vritta, the Celestial Equator, known as Meshadi and Thuladi.

The Hindu Zero Point of the Ecliptic starts from 0 degrees Beta Arietis, Ashwinyadi, which is the beginning point of the Sidereal Zodiac. This is the Nirayana System, sidereal. The Tropical System, Sayana, also has its adherents in India and starts from Meshadi, 0 degree Aries.

The Galactic Center, the Vishnu Nabhi, lies in Sagittarius. NEP is the North Ecliptic Pole, NGP is the North Galactic Pole and NCP is the North Celestial Pole.

( Above diagram by courtesy of www.wikipedia.org )

A 360 degree Circle is a coordinate System. And Khagola is the Celestial Coordinate System.

Like the Geographical Coordinate System, the Celestial Coordinate System is another coordinate system, which computes the coordinates of the Khagola, the Celestial Sphere.

The Ascending Sign is called the Ascendant ( Raseenam udayo lagnam ) and is the intersecting point of the Ecliptic ( at the East Point) with the Celestial Horizon. The Descending Sign is the Descendant ( Astha Lagna ) and lies 180 degrees West on the Khshithija, the Celestial Horizon.

Like the Geographical Meridien ( the Prime Meridien ) and the Geographic Equator, the Celestial Coordinate System has a Celestial Meridien ( Nadi Vritta ) and a Celestial Equator.

The Vernal Equinox and the Autumnal Equinox are two intersecting points of the Ecliptic with the Vishu vat Vritta, the Celestial Equator, known as Meshadi and Thuladi.

The Hindu Zero Point of the Ecliptic starts from 0 degrees Beta Arietis, Ashwinyadi, which is the beginning point of the Sidereal Zodiac. This is the Nirayana System, sidereal. The Tropical System, Sayana, also has its adherents in India and starts from Meshadi, 0 degree Aries.

The Galactic Center, the Vishnu Nabhi, lies in Sagittarius. NEP is the North Ecliptic Pole, NGP is the North Galactic Pole and NCP is the North Celestial Pole.

( Above diagram by courtesy of www.wikipedia.org )

A 360 degree Circle is a coordinate System. And Khagola is the Celestial Coordinate System.

Like the Geographical Coordinate System, the Celestial Coordinate System is another coordinate system, which computes the coordinates of the Khagola, the Celestial Sphere.

The Ascending Sign is called the Ascendant ( Raseenam udayo lagnam ) and is the intersecting point of the Ecliptic ( at the East Point) with the Celestial Horizon. The Descending Sign is the Descendant ( Astha Lagna ) and lies 180 degrees West on the Khshithija, the Celestial Horizon.

Like the Geographical Meridien ( the Prime Meridien ) and the Geographic Equator, the Celestial Coordinate System has a Celestial Meridien ( Nadi Vritta ) and a Celestial Equator.

The Vernal Equinox and the Autumnal Equinox are two intersecting points of the Ecliptic with the Vishu vat Vritta, the Celestial Equator, known as Meshadi and Thuladi.

The Hindu Zero Point of the Ecliptic starts from 0 degrees Beta Arietis, Ashwinyadi, which is the beginning point of the Sidereal Zodiac. This is the Nirayana System, sidereal. The Tropical System, Sayana, also has its adherents in India and starts from Meshadi, 0 degree Aries.

The Galactic Center, the Vishnu Nabhi, lies in Sagittarius. NEP is the North Ecliptic Pole, NGP is the North Galactic Pole and NCP is the North Celestial Pole.

On Saturday, the heavens brimmed with pessimistic prophecies and then came the downpour. ( Today is 19th Jul 2011 )

The Sun has disappeared and it is now raining cats and dogs here. As a concomitant result, I got cold !

This SW Monsoon, defined as a failure this season, may perk up, compensating for the lack of rains during the earlier Mrigasira and Aridra Solar Periods ( Njattuvelas ). Now Punarvasu Njattuvela is on, as the Sun transits Beta Geminorum.

Now the paddy fields are full of water and it rained heavily at night day before yesterday. The ocean became hostile on Chavakkad Beach and surrounding areas, wreaking destruction.

On Saturday, the heavens brimmed with pessimistic prophecies and then came the downpour. ( Today is 19th Jul 2011 )

The Sun has disappeared and it is now raining cats and dogs here. As a concomitant result, I got cold !

This SW Monsoon, defined as a failure this season, may perk up, compensating for the lack of rains during the earlier Mrigasira and Aridra Solar Periods ( Njattuvelas ). Now Punarvasu Njattuvela is on, as the Sun transits Beta Geminorum.

Now the paddy fields are full of water and it rained heavily at night day before yesterday. The ocean became hostile on Chavakkad Beach and surrounding areas, wreaking destruction.

On Saturday, the heavens brimmed with pessimistic prophecies and then came the downpour. ( Today is 19th Jul 2011 )

The Sun has disappeared and it is now raining cats and dogs here. As a concomitant result, I got cold !

This SW Monsoon, defined as a failure this season, may perk up, compensating for the lack of rains during the earlier Mrigasira and Aridra Solar Periods ( Njattuvelas ). Now Punarvasu Njattuvela is on, as the Sun transits Beta Geminorum.

Now the paddy fields are full of water and it rained heavily at night day before yesterday. The ocean became hostile on Chavakkad Beach and surrounding areas, wreaking destruction.

This diagram is by courtesy of Jean-Pierre Lacroix and Robert Baywater, www.ancientcartography.net

We have the Double Epicyclic Model – that of Manda Epicycle and Sheegra Epicycles – in Indian Astronomy, which explain the Zodiacal and Solar anomalies. One Epicycle explains the Zodiacal Anomaly and the other the Solar Anomaly.

( Zodiacal Anomaly – That all planets move slower at Aphelion and faster at Perihelion.
Solar Anomaly – The astronomical phenomenon of Retrogression. Backward Motion. When a planet changes its course from perihelion to aphelion, it retrogrades in order to gain the Sun’s celestial gravity )

Dennis Duke, of Florida State University, says ” We have only to conclude that Ptolemy did not invent the equant. ” If Ptolemy did not invent the equant, as Westerners widely believe, then who did ?

“The bisected Indian equant model is pre-Ptolemaic’ says he. Other Greek books, prior to Ptoemy, may have influenced Indian Astronomy,says he. Then what are those books, prior to the Almagest, which had influenced the Indian system? The answer is “unknown sources”.

Remarks Duke ” Indeed, since the very earliest investigation of the Indian models by Western scholars it has been presumed that the models are somehow related to a double epicycle system, with one epicycle accounting for the zodiacal anomaly, and the other accounting for the solar anomaly (retrograde motion) This perception was no doubt reinforced by the tendency of some Indian texts to associate the manda and sighra corrections with an even older Indian tradition of some sort of forceful cords of air tugging at the planet and causing it to move along a concentric deferent . Since our goal in this paper is to investigate the nature of any connection with ancient Greek planetary models, it is only important to accept that the models appear in Indian texts that clearly pre-date any possible Islamic influences, which could, at least in principle, have introduced astronomical elements that Islamic astronomers might have derived from Greek sources. ( “The Equant in India: the Mathematical Basis of Ancient Indian Planetary Models” By Dennis Duke, Florida State University )

This diagram is by courtesy of Jean-Pierre Lacroix and Robert Baywater, www.ancientcartography.net

We have the Double Epicyclic Model – that of Manda Epicycle and Sheegra Epicycles – in Indian Astronomy, which explain the Zodiacal and Solar anomalies. One Epicycle explains the Zodiacal Anomaly and the other the Solar Anomaly.

( Zodiacal Anomaly – That all planets move slower at Aphelion and faster at Perihelion.
Solar Anomaly – The astronomical phenomenon of Retrogression. Backward Motion. When a planet changes its course from perihelion to aphelion, it retrogrades in order to gain the Sun’s celestial gravity )

Dennis Duke, of Florida State University, says ” We have only to conclude that Ptolemy did not invent the equant. ” If Ptolemy did not invent the equant, as Westerners widely believe, then who did ?

“The bisected Indian equant model is pre-Ptolemaic’ says he. Other Greek books, prior to Ptoemy, may have influenced Indian Astronomy,says he. Then what are those books, prior to the Almagest, which had influenced the Indian system? The answer is “unknown sources”.

Remarks Duke ” Indeed, since the very earliest investigation of the Indian models by Western scholars it has been presumed that the models are somehow related to a double epicycle system, with one epicycle accounting for the zodiacal anomaly, and the other accounting for the solar anomaly (retrograde motion) This perception was no doubt reinforced by the tendency of some Indian texts to associate the manda and sighra corrections with an even older Indian tradition of some sort of forceful cords of air tugging at the planet and causing it to move along a concentric deferent . Since our goal in this paper is to investigate the nature of any connection with ancient Greek planetary models, it is only important to accept that the models appear in Indian texts that clearly pre-date any possible Islamic influences, which could, at least in principle, have introduced astronomical elements that Islamic astronomers might have derived from Greek sources. ( “The Equant in India: the Mathematical Basis of Ancient Indian Planetary Models” By Dennis Duke, Florida State University )

This diagram is by courtesy of Jean-Pierre Lacroix and Robert Baywater, www.ancientcartography.net

We have the Double Epicyclic Model – that of Manda Epicycle and Sheegra Epicycles – in Indian Astronomy, which explain the Zodiacal and Solar anomalies. One Epicycle explains the Zodiacal Anomaly and the other the Solar Anomaly.

( Zodiacal Anomaly – That all planets move slower at Aphelion and faster at Perihelion.
Solar Anomaly – The astronomical phenomenon of Retrogression. Backward Motion. When a planet changes its course from perihelion to aphelion, it retrogrades in order to gain the Sun’s celestial gravity )

Dennis Duke, of Florida State University, says ” We have only to conclude that Ptolemy did not invent the equant. ” If Ptolemy did not invent the equant, as Westerners widely believe, then who did ?

“The bisected Indian equant model is pre-Ptolemaic’ says he. Other Greek books, prior to Ptoemy, may have influenced Indian Astronomy,says he. Then what are those books, prior to the Almagest, which had influenced the Indian system? The answer is “unknown sources”.

Remarks Duke ” Indeed, since the very earliest investigation of the Indian models by Western scholars it has been presumed that the models are somehow related to a double epicycle system, with one epicycle accounting for the zodiacal anomaly, and the other accounting for the solar anomaly (retrograde motion) This perception was no doubt reinforced by the tendency of some Indian texts to associate the manda and sighra corrections with an even older Indian tradition of some sort of forceful cords of air tugging at the planet and causing it to move along a concentric deferent . Since our goal in this paper is to investigate the nature of any connection with ancient Greek planetary models, it is only important to accept that the models appear in Indian texts that clearly pre-date any possible Islamic influences, which could, at least in principle, have introduced astronomical elements that Islamic astronomers might have derived from Greek sources. ( “The Equant in India: the Mathematical Basis of Ancient Indian Planetary Models” By Dennis Duke, Florida State University )

In the diagram above, the geocentric distance, EQ called X here , the distance of the planet from the Earth is calculated by the equation

X^2 = EQ^2(EP+PL)^2 + QL^2

or = EN^2 + QN^2

In a trignometric correction, called Sheegra Sphashteenarana, this equation is given by Bhaskara.

where

E = Earth
P = Planet in its Orbit
Q = Planet on the Epicycle
QL = Sin
PL = Cos

We have said that Sheegra Kriya reduces the heliocentric postions to the geocentric.

According to this oscillating Epicyclic Model of Bhaskara, EP = R ( Called Thrijya ), PQ is the Sheegra Phala, QL is the Bhujaphala and PL is Kotiphala.

The Hindu algorithms for the computation of mean and true celestial longitudes seems to be totally different from the Western, from the methods adopted by Kepler, Laplace and Co. Hence the Hindu Planetary Model is original and not influenced by Greco Roman sources, as some Western scholars believe.