### The Lunar Model Of Munjala

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The Concentric Equant theory was developed by the Indian astronomer, Munjala ( circa 930 CE ).

The Geocentric theory of the ancient astronomers had the ability to produce true Zodiacal Longitudes for the Moon. But the perturbations of the Moon were so complex, that the early Indian and Greek astronomers had to give birth to complicated theories.

The simplest model is a concentric Equant Model to compute the lunar true longitude.

In the above diagram

M = Moon

O = Observer

Eo = Equant , located at a distance r from the observer , drawn on the Line of Apsis and the Apogee.

A = Apogee, Luna's nearest point to Earth

Angle Alpha = Angle between Position and Apogee

Angle q1 = Equation of Center . Angle subtended at Luna between Observer and Equant

Equation in Astronomy = The angle between true and mean positions.

These diagrams are by courtesy of Jean-Pierre Lacroix and Robert Baywater, www.ancientcartography.net

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