Caption: A diagram illustrating how the difference between lunar month (mean value 29.53059 days, (J2000.0 to 7 digits) the sidereal month (mean value 27.32166 days, epoch J2000 to 7 digits) arises.

Features:

1. The lunar month is the "geometrical orbital period" of the Moon relative to the Sun. It is also the period for a complete cycle of lunar phases and the period from new moon to new moon.

   It could also be called the synodic period: i.e., orbital period relative to the Sun.

2. The physically-motivated orbital period is the time it takes for an astro-body to complete a revolution relative to the observable universe (which is almost the same as relative to the fixed stars as we traditionally put it). This is also, of course, the orbital period as determined by Newtonian physics in the center-of-mass free-fall inertial frame (COMFFI frame) of the Solar System. The center of mass of the Solar System is also called the Solar System barycenter. The Solar System barycenter is close to the center of the center of the Sun (but NOT always inside the Sun) since the solar mass M_☉ = 1.98855(25)*10**30 kg is 99.86 % of the Solar-System mass (see Wikipedia: Solar system: Structure and composition). So the Sun's mass largely determines the Solar System barycenter.

3. For the Moon, the orbital period has the special name sidereal month.

4. The diagram illustrates how the difference between the lunar month and the sidereal month arises for the Moon's orbit.

5. Look at the new moon phase at the bottom of the diagram.

   By the time one sidereal month has passed, the Earth has moved eastward along its orbit and the Moon has NOT returned to the new moon position.

   It takes the Moon a bit more than two days to get to the new moon position and complete a lunar month.