Study the variation of synodic month for the moon through 2000-2100

In this research study the synodic month for the moon and their relationship with the mean anomaly for the moon orbit and date A.D and for long periods of time (100 years), we was design a computer program that calculates the period of synodic months, and the coordinates of the moon at the moment of the new moon with high accuracy. During the 100 year, there are 1236 period of synodic months. We found that the when New Moon occurs near perigee (mean anomaly = 0°), the length of the synodic month at a minimum. Similarly, when New Moon occurs near apogee (mean anomaly = 180°), the length of the synodic month reaches a maximum. The shortest synodic month on 2053 /1/ 16 and lasted (29.27436) days. The longest synodic month began on 2008 /11/ 27 and lasted (29.81442) days. The mean synodic month (29.53109) days. We found the relationship between synodic month with months. The shortest synodic month are correlated with date (June and July) when the Earth is near aphelion. And the longest Synodic month are correlated with date (December and January) when the Earth is near perihelion.