Spherical Trigonometry is used,
To divine Positions Planetary.
The planets orbit is an ellipse,
With the Sun at the foci.
Trigonon in Greek,
Trikona is Sanskrit means triangle,
Trikona Mithi became Trigonometry,
As Jya mithi became Geometry !
So a new factor is introducedm
For measuring longitudes,
Chuthi, Eccentricty, e,
Which is 0 to 1 at ellipse.
0 at Circle and One at parabola,
And more than One at Hyperbola,
To compute Anomaly,
( Angle between Perihelion and Position,)
Kepler brought in an auxiliary angle.
Eccentric Anomaly, E
M = E- E sine
Was equation given by him
To find Anomaly true !
In the Indian, two Anomalies are computed,
Manda and Sheeghra Anomalies,
Relating to Mandoccha and Sheeghrocha,
Aphelion and Perihelion !
Manda Anomaly is computed,
By x = R e Sin M
And planetary distance,
By y = Re Cos M !
Reduction to Ecliptic,
By sin h = 1 – cos l Sin Y Cosy /cos l
Y being Vipata Kendra,
Angle between Position and Node !
Trig formula for Chara,
Angle of Ascensional Difference,
The Difference between Right and Oblique Ascensions,
By Sin c = Tan Lat tan Decl !
Trig formula for Soorya Kranti,
Angle of Solar Declination,
By Sin J = Sin L Sin w,
Where w is Sun’s max decl !
Trig formula for Madhya Lagna,
Medium Caeli or Meridian Cusp,
( Dasama Bhava Sphuta )
By Tan K = Tan R /cos w
Where R is Sayana Ravi Madhyamam !
The simple Geometrical Model,
The Geometrical Model of Parameshwara,
Happens to be the simplest,
And the most accurate !