Why is the time between two successive full moons different from the lunar synodic month?

We all know that the length of the synodic lunar month is 29.53 days. But if we calculate the time separating two successive New Moons from lunar ephemerides,we always get a different value. Could you please explain why?

That is an excellent question! The answer is a bit complicated:

The Moon moves around the Earth in a slightly elliptical orbit (the ellipse is close to a circle, but not quite a circle). As a result, the Moon moves faster near pericenter (where it is closest to Earth). Also, the orientation of the pericenter relative to Earth's axis is fixed.

However, new moon occurs when the Moon is in between Earth and Sun, and location of new moon with respect to the Earth's axis varies as the Earth goes around the Sun.

Let me give an example to try to make this clear: Assume that at some position, the pericenter occurs between Earth and the Sun and as a result, new moon occurs when the Moon is at the pericenter. Now, if the Earth was not going around the Sun, then the next new moon will also occur at the pericenter. But as the Earth is actually going around the Sun, the location where the Moon comes between Earth and the Sun after it completes one orbit will be away from the pericenter.

As you know, the movement of the Earth around the Sun causes the new moon to come roughly after 29.5 days even though the Moon goes around the Earth once in 27.3 days. In addition, the slight variation of the speed of the Moon due to its elliptical orbit gives rise to the period between two successive new moons to be slightly different from 29.5 days. If the next location of the new moon occurs closer to the pericenter, then the next new moon will occur in slightly less than 29.5 days. Conversely, if the next location of the new moon takes it further away from the pericenter, then the next new moon will occur slightly after 29.5 days.

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