Trigonon in Greek,
Trikona is Sanskrit means triangle,
Trikona Mithi became Trigonometry,
As Jya mithi became Geometry !

So a new factor is introduced,
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 !

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 !

Longitude of Standard Point =-082.30
Longitude of Trichur = -076.15
Longitudinal Difference = -06.15
Hence L M T 25 minutes less than IST !

From Time Zone, longitude,
-330 minutes is Time Zone.
That divided by 4 is longitude
At -082.30 !

Sunrise varies from Latitude to Latitude,
Also the Rising Sign,
Known as Ascending Sign or Ascendant,
Raseenam Udayo Lagnam !

Sunrise = 6 Hours + Eqt - Chara - Reff Correction
Sunset = 18 Hours + Eqt+ Chara -+Reff Correction
Gulika longitude = Lagna of Gulika Rising Time !
And Dasama by Tan = Tan R /cosw !

The Gulika longitude is a similar calculation,
Like the Ascending Degree,
Lagna is computed by formula,
Tan L = Sin E / Cos E cos w - Sin w Tan A.