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

Abstract

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.