# Calculating the position angle of the moon (the rolling back and forth)

I have been watching the the NASA Moon Phases Video of the year 2020. Pretty much everything makes sense and I know how to calculate it including the moon phases, declination, azimuth, apogee and perigee except one thing, the position angle of the moon. Its donated by Pos. Angle at the bottom right of that video.

Apparently when the Pos. angle is 0, that means when the azimuth of the moon reaches 180 looking from the northern hemisphere, the phase's north direction of the moon is going to be perfectly aligned with the north direction on earth(180 azimuth):

Given the moon and sun current declination, How do you calculated the Position angle of the phase as it's described in NASA Moon phase 2020 ? I'm looking for an output that matches NASA's calculations or close to it at any given date. Any help would be much appreciate..

• I suggest that you get the book Astronomical Algorithms by Jean Meeus. willbell.com/math/mc1.htm I believe that chapter 48. Illuminated Fraction of the Moon’s Disk gives the formulas that you need. – JohnHoltz Mar 4 '20 at 17:28
• Astronomical Algorithms does not contain any formula regarding this particular computations. I believe Jean Meeus explained Moon Liberation in detail in his other book called Mathematical Astronomy Morsels amazon.com/Mathematical-Astronomy-Morsels-Jean-Meeus/dp/… – The Oathman Mar 4 '20 at 17:53
• Sorry about that. You are correct. I was trying to visually compare the numbers to the phase, and it appeared that the PA was to the cusp. The detailed page for the video explains it as the "position angle of the axis, which is the angle of the Moon's north pole relative to celestial north". Since the Moon's axis is tilted less than 2 degrees from the ecliptic, the PA of the cusp and north pole are close but not identical. Probably need to turn to the Supplement for the Astronomical Almanac or other text to get the pole position. – JohnHoltz Mar 4 '20 at 22:26
• Page 373 of Astronomical Algorithms (2nd Edition) gives the PA of the Moon's axis. Chapter 53 Physical Ephemeris Of The Moon. – JohnHoltz Mar 5 '20 at 3:17
• Turns out the edition I have does Explain PA in detail. Your answers really helps JohnHoltz. Thank you. Now I wonder what the difference between this explanation and the one in his other book. – The Oathman Mar 5 '20 at 14:29