The longitude of the planets was defined as a function of the mean longitude and the anomaly. Rather than calculating every possible value, which would be difficult and labor-intensive, four functions of a single value were calculated for each planet and combined to calculate quite accurately the true longitude of each planet. To calculate the true longitude of the moon, Ibn al-Shatir assigned two variables, η, which represented the moon's mean elongation from the sun, and γ, which represented its mean anomaly. To any pair of these values was a corresponding e, or equation which was added to the mean longitude to calculate the true longitude. Ibn al-Shatir used the same mathematical scheme when finding the true longitudes of the planets, except for the planets the variables became α, the mean longitude measured from apogee (or the mean center) and γ which was the mean anomaly as for the moon. A correcting function c3' was tabulated and added to the mean anomaly γ to determine the true anomaly γ'. As shown in Shatir's model, it was later discovered that Shatir's lunar model had a very similar concept as Copernicus. Ibn al-Shatir never gave motivation towards his two epicycles to be adopted, so it was hard to tell the difference between his model and the Ptolemaic model. Possible influence on Nicolaus Copernicus Although Ibn al-Shatir's system was firmly geocentric (he had eliminated the Ptolemaic eccentrics), the mathematical details of his system were identical to those in Copernicus's De revolutionibus. Furthermore, the exact replacement of the equant by two epicycles used by Copernicus in the Commentariolus paralleled the work of Ibn al-Shatir one century earlier. Ibn al-Shatir's lunar and Mercury models are also identical to those of Copernicus. Copernicus's Mercury model was flawed in the fact that he was not able to properly understand the model first created by Ibn al-Shatir. Copernicus also translated Ptolemy's geometric models to longitudinal tables in the same way Ibn al Shatir did when constructing his solar model. This has led some scholars to argue that Copernicus must have had access to some yet to be identified work on the ideas of ibn al-Shatir. It is unknown whether Copernicus read ibn al-Shatir and the argument is still debated. The differences between the two can be seen in their works. Copernicus followed a heliocentric model (planets orbit the sun) while Ibn al-Shatir followed the geocentric model (as mentioned