Computing Vedic Planetary Positions

The Starting of the Epoch is 13/04/1899, the Karana Arambha. The sidereal
positions of planets are given at the time of the Epoch ( at the Sunrise
Time at Trivandrum, Kerala, India ). The computations are based on Vedic
Astronomy ( Siddhanta ) & Vedic Mathematics.


The Sidereal Positions of planets

Planet Sign Degree
Mins Secs Tatpara
Sun 11283350 44
Moon02940211
Moon's Apogee312391519
North Node810384540
Mars41345440
Mercury511383141
Jupiter61347427
Venus819491132
Saturn725201155

M = Mean Anomaly of the planet; A = Aphelion of the Planet ; L = Mean
Longitude of the Planet; e = orbital eccentricity; mjv = orbital
eccentricity in seconds; Sheegra Kendra = The Angle between the Planet &
the Sun; Sheegroccha = Perihelion; Mandoccha = Aphelion; Sheeghra Phala
= The Angle between the Planet and the Sun as viewed from a geocentric
perspective; Oja = Odd; Yugma = Even; Manda Kendra = Mean Anomaly;
Sheeghra Kendra Ardha = A/2, half of Sheegra Kendra; Kranti Vritta =
Ecliptic; Vikshepa Vritta = Nodal Circle; Kshithija = Celestial Horizon;
Bha Chakra = Zodiac; Vishuvat Vritta = Celestial Equator; Khagoleeya Dhruva
Rekha = Celestial Meridien; Vishu Vat Bhoga = Right Ascension( R A );
Meshadi = The First Point of Aries; Thuladi = The First Point of Libra;
Karkyadi = The First Point of Cancer; Makaradi = The First Point of
Capricorn; Theta = True Longitude of the planet; v = True Anomaly; Manda
Karna = Radius Vector, distance of the planet from the Sun; Sheeghra Karna =
Distance of the planet from the earth; Ravi Manda Karna = Sun's distance;
Nathamsa = Altitude of the Planet; Digamsa = Azimuth. Bhaga, Kala, Vikala =
Deg, Mins, Secs; Madhyama Manda Karna = Semi Major Axis; Patha = Node;
Thidhi - D or Day or Lunar Day, the first Lunar Day being the Moon within 12
degrees of the Sun; Vara - Day of the Week; Bhujajya = Sin; Kotijya = Cos;
Sparsajya = Tan; Sparsachapa= Atan; Bhujachapa = Asin; Kotichapa = Acos;
Pranakalanthara= Difference between Tropical Longitudes and R A; Kala Hora =
Planetary Hours; Hora = Hour; Chara Jya = Sin C; Manda Jya = Sin M;
Parinathi Jya = Sin h; Guru Sani Karsha - Perturbations of Jupiter and
Saturn; Chandra Karsha - Perturbations of the Moon; Chathurdasa Jya
Samskaras - 14 trignometric corrections to the Moon; Vikshepa - Celestial
Latitude; Kranti - Declination; Dhruva = R A ; Sphuta = Celestial Longitude;
Indra - Uranus; Varuna = Neptune; Rudra = Pluto; Kala = Phobos; Mrityu =
Deimos; Gulika = Titan; Yamakandaka = Ganymede; Vipatendu = Mean Longitude
of the Moon - Node of the Moon

The Three Methods of Vedic Astronomy
1) The First Method is to compute the longitudes of the planets along the
Ecliptic ( Kranti Vritta ). Western astronomers have accepted 0 degree Aries
as the First Point of the Tropical Zodiac and Vedic astronomers have
accepted 0 degree Beta Arietis ( Aswini ) as the First Point of the Sidereal
Zodiac. Extending 9 degrees to either side of the Ecliptic is the Great
Circle of Light, the Zodiac.
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2) The Second Method is to compute the longitudes along the Celestial
Equator ( Vishuvat Vritta ). The Starting Point is 0 degree Aries. The
longitudes thus obtained is called the Right Ascension ( R A ) of Planets.
3) The Third Method is to compute longitudes along the Celestial Horizon.
The Eastern Celestial Horizon, the intersecting point between the Ecliptic
and the Celestial Horizon, is called the Ascendant ( Udaya Lagna ). 180
degrees opposite to that point is called the Western Celestial Horizon (
Astha Lagna ). The highest point on the Celestial Horizon is called the
Zenith ( Madhya Lagna or MC ) and the lowest point, the Nadir ( Patala
Lagna or IC ). The Original Point of the Celestial Horizon is the Northern
Point on the Celestial Horizon.
The Vedic Method is Longitude corrected thrice, though 3 major trignometric
corrections called
Manda Kriya ( Reduction to True Anomaly )
Parinathi Kriya ( Reduction to Ecliptic )
& Sheeghra Kriya ( Reduction to Perihelion ).
I . Reduction to True Anomaly ( Manda Kriya )
After finding the Mean Longitude of the Planet, the Mean Anomaly of the
Planet is calculated as per the formula
Mean Anomaly = Mean Longitude - Aphelion ( M = L - A )
The Manda Jya Vikalakal ( mjv , eccentricity in seconds ) is computed as
per the formula
mjv = R (2 e - 1/4 e^3 + 5/95 e^5 ) Sin A + R (5/4 e^2 - 11/24 e^2 +
17/192 e^2 ) Sin 2 A + R ( 13/12 e^3 - 43/64 e^5 ) Sin 3 A + R ( 103/ 96
e^4 - 451 / 480 e ^5 ) Sin 4 A + R ( 1097/960 e ^5 ) Sin 5 A + R (1228/960 e
^ 5 ) Sin 6 A
A = Mean Anomaly of the Planet + 6 Signs or M + 180. R is 206265 seconds
This value MJV is deducted or added to M, the Mean Anomaly of the Planet to
get the True Anomaly of the planet, v
v = M + or - mjv
If the Mean Anomaly ( Manda Kendra ) is greater than 6 Signs, it is added
and if it is less than 6 Signs ( 180 degrees ), it is subtracted.
The Radius Vector ( Manda Karna ) is computed using the formula
Manda Karna = a ( 1+ 1/2 e^2 ) - e ( 1- 3/8 e^2) Cos A - 1/2 e^2 ( 1- 2/3
e^2 ) Cos 2 A - 3/8 e^3 Cos 3 A - 1/3 e^4 Cos 4 A )
where a is the semi major axis ( Madhyama Manda Karna ) of the planet. Semi
Major Axis is the average distance of the planet expressed in AU. The Sun's
a is 1 AU or 149 million kilometres from the earth. It is to be noted that
at 90 degrees the Manda Karna of the planet equals Semi Major Axis because
Cos 90 = 0.
II. Reduction to Ecliptic ( Parinathi Kriya )
The Ascending Node of the planet is deducted to get the Y, the planet minus
the Node.
Y = True Anomaly of the Planet - Node of the planet
First the latitude of the planet is computed as per the formula
Sin l = Sin L Sin Y
where l is the latitude of the planet, Y is the Longitude of the planet
after deducting the Node and L is the maximum latitude of the planet
The mean longitude of the planet after Manda Kriya is reduced to the
Ecliptic Coordinate System . The formula used is
Sin h = ( 1-Cos L Sin Y Cos Y /cos l )
where the l is the latitude of the planet, Y is the Longitude of the planet
after deducting the Node and L is the maximum latitude of the planet and h
is the Parinathi Phalam, the factor which is to be added or subtracted to
the True Anomaly. ( This is also the formula used for computing
the Sun's Pranakalanthara which is the difference between Tropical
longitudes and Right Ascension ).
The first 3 Signs are Odd ( Oja ), the next 3 Signs are Even ( Yugma ), the
next 3 Signs are Odd ( Oja ) and the next 3 signs are Even ( Yugma ).
The Parinathi Phalam is added if the Signs are Yugma and subtracted if it is
Oja to True Anomaly to get the Ecliptic degree.
Ecliptic Degree = True Anomaly + or - Parinathi Phalam
The aphelion distance or Manda Karna ( Kranthi Vritheeya Manda Karna ) is
computed as per the formula
Kranthi Vritheeya Manda Karna = Vikshepa Vritheeya Manda Karna * cos l
III Reduction to Perihelion ( Sheeghra Kriya )
When the longitude of the Sun is deducted from the Ecliptic Degree thus
obtained, we get the Sheeghra Kendra, the angle between the Sun and the
planet
Sheeghra Kendra = Ecliptic Degree - Longitude of the Sun.
Sheeghra Phalam is the angle formed between the Sun, the planet and the
Earth. It is computed as per the formula
Tan A/2 - x = ( b - a) /( b + a) Tan A/2
where A is the Sheeghra Kendra, a is the Ravi Manda Karna ( Sun's
distance ), b the Graha Manda Karna ( distance of the planet from the Sun )
and x the Sheeghra Phalam.
The Sheeghra Phalam is added if the Signs are greater than 6 and subtracted
if the Signs are less than 6 .
There is another method of computing Sheeghra Karna. Sheeghra Karna c can be
computed by the following formula
c^2 = a^2 +b ^2 + 2 a b Cos A and the Sheegra Phalam can be obtained by
sin x = a Sin A /c for Jupiter, Mars and Saturn &
sin x = b Sin A /c for Mercury and Venus
True Longitude of the Planet = Ecliptic Degree - or + Sheegra Phalam
For Mercury and Venus, the computation is slightly different. The Sheeghra
Phalam thus obtained is subtracted from the Sun's longitude if the Signs are
more than 6 and added if the Signs are less than 6.
In Mathematics there are many methods and the Western Method is to find the
True Anomaly of the Planet and to it add the Argument of Perihelion ( Theta
= v + w ). The Eccentric Anomaly of the Planet ( an auxiliary angle used in
Kepler's equations ) is computed from the Mean Anomaly and the True Anomaly
is computed from it . The Argument of Perihelion is added to it to get the
true longitude. The perturbations of the Moon, Jupiter and Saturn are
included in these computations. Some large perturbations of the Moon, viz
the Evection, the Annual Equation, the Variation and the Parallactic
Equation are all included. While the Western Method is to give 12
corrections to the Moon's longitude, the Vedic method is to subject the Mean
longitude of the Moon to 16 trignometric corrections. ( 14 reductions plus
Manda Kriya & Parinathi Kriya ).

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