lunar-perigee

 We will use the more accurate values for The Revolution Periods of The Lunar Perigee and Lunar Node, according to The Astronomical Almanac for 1981, page D2. It states that The Lunar Perigee moves 0.11140362 degrees per day, which gives a value for The Lunar Perigee’s Revolution period of exactly

3231.492837 Earth days.

According to The Astronomical Almanac for 1981, page D2, The Lunar Node moves 0.05295383 degrees per day, which gives a value for The Lunar Node’s Revolution period of exactly

6798.375113 Earth days.

These periods are calculated in the following manner:-

The revolution period of The Lunar Perigee =

(360 ÷ 0.11140362) = 3231.492837 Earth days

and The revolution period of The Lunar Node =

(360 ÷ 0.05295383) = 6798.375113 Earth days

To verify these two values, here is a scan from the above data source. 

This is how we calculate the SYNODIC Revolution Period of The Lunar Perigee:-

The Lunar Perigee = 3231.492837 Earth days (as seen above).

The Earth Year = 365.25636 Earth days. To verify this, click on the following link:-

earth-periods 

The SYNODIC Revolution Period of The Lunar Perigee

= [1 ÷ (1 ÷ 365.25636) minus (1 ÷ 3231.492837)] = 411.8024875 Earth days.  

To show that The Lunar Node revolves RETROGRADELY, here is an excerpt from Wikipedia:- 

The line of nodes, which is also the intersection between the two respective planes, rotates (precesses) with a period of 18.6 years or 19.35° per year. When viewed from the celestial north, the nodes move clockwise around Earth, I.e. with a retrograde motion (opposite to Earth's own spin and its revolution around the Sun). So the time from one node crossing to the next (see eclipse season) is approximately a half-year minus half of 19.1 days -- or about 173 days.