What's the difference between the time it takes for the moon's 1 revolution to the New moon's 1 revolution?

Question

for the moon to make 1 complete revolution, ti takes 27 1/3 days. The time it takes for the New Moon is 29 1/2 days.

Answer 1

The name for a lunar revolution (as seen from Earth) is called a month. There are various kinds of months, depending on what you use as a reference:

I'm using "days" defined as exactly 86,400 seconds. All values are the "mean period" (i.e., precise average over long periods of time). Each individual revolution varies a bit.

Synodic month (New Moon to New Moon), the month relative to the apparent position of the Sun (the most practical one for humans): 29.530589 days

Sidereal month, relative to "fixed" stars (the "true" orbital periods for most calculations, like when one calculates centrigugal force): 27.321662 days

Draconic month (node to node): the time it takes for the Moon's declination to return to the same value and in the same direction: 27.212221 days.
Anomalistic month (perigee to perigee): 27.554550 days

Oceanic tide predictions require the use of Synodic, Draconic and Anomalistic (and you thought differentiating a quadratinc was a pain...).

Answer 2

The time it takes the Moon to travel around the Earth exactly once is 27.3 days. The cycle of phases lasts 29.5 days because the phase of the Moon depends on the distance between it and the Sun in the sky. If the moon was new at the beginning, it was in conjunction with the sun. 27.3 days later, the moon has orbited the earth once and returned to its original place among the stars. But in that time, the earth has also orbited the sun by a certain amount, and when the moon gets back to its original position it's not in conjunction with the sun. The sun has moved about 28 degrees to the east, and so you must wait a couple of days for the moon to catch up with the sun and become new again.

Answer 3

The difference of the period of revolution stems from the observer.s location. The moon's orbit is not on the ecliptic. It is tilted making a relative angle of 85 degrees.
Therefore if the moon/s orbit is observed from a star it appears shortened. Hence the time is also shortened as compared to the Ovservation from the Earth's frame of reference.So an observer on earth sees the time period of the moon as a time dilation of aprox. 2.2 days.
Its all relative.