If you want to calculate the longitudes of planets and create an Astro Software, then the best book for
you is Laplace's CelestialMechanics. You can find out the mean longitudes of the planets, calculate the perturbations, the epicycles and then calculate the Heliocentric Longitudes of planets. You can use Laplacian equations to then reduce it to the Ecliptic Coordinates and then reduce them to Geocentric Coordinates, thus computing the true longitudes of the planets. A must for Astro software developers.
Kepler's Formulae
Kepler represents Old Astronomy. If you want to creat an Astro Software, you have to solve the Kepler problem. The Kepler Equation, M = E - e Sin E, may sound easy, but it is a transcendental equation and the most difficult amongst Kepler's equations. We can find out the True Anomaly of the planet, that is the angle between the planet and perihelion. The next step is to find the Argument of Perihelion, which is the angle between the Node and perihelion.
Laplace - Advanced Astronomy
Laplace's Celestial Mechanics is one of the best books ever written. If you read this magnificent book, you can handle Astronomy and Maths easily.
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