Month: August 2011

Mean and true planetary longitudes in the Zodiac is computed by Nine Orbital Elements, in Indian Astronomy.

Mean longitude of Planet, Graha Madhyama , M

Daily Motion of the Mean Longitude, Madhyama Dina Gathi, Md

Aphelion, Mandoccha, Ap

Daily Motion of Aphelion, Mandoccha Dina Gathi, Apd

Ascending Node, Patha, N

Daily Motion of Ascending Node, Patha Dina Gathi, Nd

Heliocentric Distance, Manda Karna, radius vector, mndk

Maximum Latitude, L, Parama Vikshepa

Eccentricity, Chyuthi,e

In Western Astronomy, we have six orbital elements

Mean Anomaly, m

Argument of Perihelion, w

Eccentricity, e

Ascending Node, N

Inclination, i, inclinent of orbit

Semi Major Axis, a

With the Nine Orbital Elements, true geocentric longitude of the planet is computed, using multi step algorithms.

There is geometrical equivalence between both the Epicycle and the Eccentric Models.

The radius of the Epicycle, r = e, the distance of the Equant from the Observer.

Mean and true planetary longitudes in the Zodiac is computed by Nine Orbital Elements, in Indian Astronomy.

Mean longitude of Planet, Graha Madhyama , M

Daily Motion of the Mean Longitude, Madhyama Dina Gathi, Md

Aphelion, Mandoccha, Ap

Daily Motion of Aphelion, Mandoccha Dina Gathi, Apd

Ascending Node, Patha, N

Daily Motion of Ascending Node, Patha Dina Gathi, Nd

Heliocentric Distance, Manda Karna, radius vector, mndk

Maximum Latitude, L, Parama Vikshepa

Eccentricity, Chyuthi,e

In Western Astronomy, we have six orbital elements

Mean Anomaly, m

Argument of Perihelion, w

Eccentricity, e

Ascending Node, N

Inclination, i, inclinent of orbit

Semi Major Axis, a

With the Nine Orbital Elements, true geocentric longitude of the planet is computed, using multi step algorithms.

There is geometrical equivalence between both the Epicycle and the Eccentric Models.

The radius of the Epicycle, r = e, the distance of the Equant from the Observer.

We find Yuga cylces mentioned not only in astronomical works, but also in mythological works in India.

Kali Yuga began on the midnight of 17th Feb 3102 BCE and the duration of this Kali Yuga is said to be 4.32 K solar years. Dwapara is 2*Kali Yuga years. Treta is 3*K Y and Krita Yuga is 4*K Y.

Krita Treta Dwaparascha Kalischaiva Chaturyugam

Divya Dwadasabhir varshai savadhanam niroopitham

Thus an Equinoctial Cycle, Mahayuga is equal to 4+3+2+1 = 10 KYs.

E C = 10 KYs.

A Greater Equinoctial Cycle ( Manvantara ) = 71 Equinoctial Cycles

There are cusps happening in between Manvantaras, each equal to a Krita Yuga in duration. A Krita is equal to 4 KYs or 2/5 of a Maha Yuga. Since there will 15 such cusps happening amongst the Fourteen Manvantaras, they are equal to 15*2/5 = 6 Mahayugas.

Hence 14*71+6 = 1000 Mahayugas = 4.32 Billion Years



Sahasra yuga paryantham

Aharyal brahmano vidu

Ratrim yugah sahasrantham

The Ahoratra vido janah ( The Holy Geetha ).

This is one Cosmological Cycle, called Brahma Kalpa.

Chaturyuga sahasram indra harina dinam uchyathe

From one second, it can be logarithmically shown, upto 10^22 seconds. This is what the above diagram shows. This diagram is by courtesy of Wikipedia.

From 10^0 it goes upto 10^22 seconds. One day of Brahma is 4.32 billion years and 100 years of Brahma therefore is 311.04 trillion years, which is shown logarithmically above.

One Asu is 4 seconds, one Vinadi is 24 seconds and one Nadi is 24 minutes. 60 such Nadis make up one day. This is the Sexagesimal division of a day into 60 Nadis ! In Astronomy, one degree is sixty minutes and one minute is sixty seconds. Hence sexagesimal division is justified ! 365.25 such days constitute a year and Hindu calculation goes upto 311.04 trillion years !

We find Yuga cylces mentioned not only in astronomical works, but also in mythological works in India.

Kali Yuga began on the midnight of 17th Feb 3102 BCE and the duration of this Kali Yuga is said to be 4.32 K solar years. Dwapara is 2*Kali Yuga years. Treta is 3*K Y and Krita Yuga is 4*K Y.

Krita Treta Dwaparascha Kalischaiva Chaturyugam

Divya Dwadasabhir varshai savadhanam niroopitham

Thus an Equinoctial Cycle, Mahayuga is equal to 4+3+2+1 = 10 KYs.

E C = 10 KYs.

A Greater Equinoctial Cycle ( Manvantara ) = 71 Equinoctial Cycles

There are cusps happening in between Manvantaras, each equal to a Krita Yuga in duration. A Krita is equal to 4 KYs or 2/5 of a Maha Yuga. Since there will 15 such cusps happening amongst the Fourteen Manvantaras, they are equal to 15*2/5 = 6 Mahayugas.

Hence 14*71+6 = 1000 Mahayugas = 4.32 Billion Years



Sahasra yuga paryantham

Aharyal brahmano vidu

Ratrim yugah sahasrantham

The Ahoratra vido janah ( The Holy Geetha ).

This is one Cosmological Cycle, called Brahma Kalpa.

Chaturyuga sahasram indra harina dinam uchyathe

From one second, it can be logarithmically shown, upto 10^22 seconds. This is what the above diagram shows. This diagram is by courtesy of Wikipedia.

From 10^0 it goes upto 10^22 seconds. One day of Brahma is 4.32 billion years and 100 years of Brahma therefore is 311.04 trillion years, which is shown logarithmically above.

One Asu is 4 seconds, one Vinadi is 24 seconds and one Nadi is 24 minutes. 60 such Nadis make up one day. This is the Sexagesimal division of a day into 60 Nadis ! In Astronomy, one degree is sixty minutes and one minute is sixty seconds. Hence sexagesimal division is justified ! 365.25 such days constitute a year and Hindu calculation goes upto 311.04 trillion years !

We find Yuga cylces mentioned not only in astronomical works, but also in mythological works in India.

Kali Yuga began on the midnight of 17th Feb 3102 BCE and the duration of this Kali Yuga is said to be 4.32 K solar years. Dwapara is 2*Kali Yuga years. Treta is 3*K Y and Krita Yuga is 4*K Y.

Krita Treta Dwaparascha Kalischaiva Chaturyugam

Divya Dwadasabhir varshai savadhanam niroopitham

Thus an Equinoctial Cycle, Mahayuga is equal to 4+3+2+1 = 10 KYs.

E C = 10 KYs.

A Greater Equinoctial Cycle ( Manvantara ) = 71 Equinoctial Cycles

There are cusps happening in between Manvantaras, each equal to a Krita Yuga in duration. A Krita is equal to 4 KYs or 2/5 of a Maha Yuga. Since there will 15 such cusps happening amongst the Fourteen Manvantaras, they are equal to 15*2/5 = 6 Mahayugas.

Hence 14*71+6 = 1000 Mahayugas = 4.32 Billion Years



Sahasra yuga paryantham

Aharyal brahmano vidu

Ratrim yugah sahasrantham

The Ahoratra vido janah ( The Holy Geetha ).

This is one Cosmological Cycle, called Brahma Kalpa.

Chaturyuga sahasram indra harina dinam uchyathe

From one second, it can be logarithmically shown, upto 10^22 seconds. This is what the above diagram shows. This diagram is by courtesy of Wikipedia.

From 10^0 it goes upto 10^22 seconds. One day of Brahma is 4.32 billion years and 100 years of Brahma therefore is 311.04 trillion years, which is shown logarithmically above.

One Asu is 4 seconds, one Vinadi is 24 seconds and one Nadi is 24 minutes. 60 such Nadis make up one day. This is the Sexagesimal division of a day into 60 Nadis ! In Astronomy, one degree is sixty minutes and one minute is sixty seconds. Hence sexagesimal division is justified ! 365.25 such days constitute a year and Hindu calculation goes upto 311.04 trillion years !

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.

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.

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.

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.

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.