# What are "p" and "r" wrt the moon?

Still learning, thinking - and failing - about the moon.

timeanddate.com has this cute and dynamic moon sketch at e.g. https://www.timeanddate.com/moon/uk/london

They generate this based on three parameters that they call i, p and r. The above image is the result of invoking this: https://www.timeanddate.com/scripts/moon.php?i=0.028&p=3.388&r=0.035.

I know that i stands for i llumination in the range 0-1.

However, what are p and r and in what unit? What are the likely correct terms? r appears to be some sort of "rotation angle" of the moon while p is the same for the "mask".

Yes, the are angles in radians. With "i=0.5" to make things clearer:

• $$p=0$$ is the right half illuminated
• $$p=\pi/2=1.57$$ is top half illuminated (rotated anticlockwise by 90 degrees)
• $$p=\pi=3.14$$ is left half illuminated (rotated 180 degrees)

and so on.

The r parameter is the rotation of the moon, so $$r=0$$ is "lunar north up" $$r=pi/2$$ is rotated anticlockwise by 90 degrees.

• Thank you for explanations. I use a piece of software that provides a plethora of moon (phase) properties for a given timestamp and location. "axis position angle", "bright limb angle" and "paralactic angle" don't mean much to me yet but I will analyze them and try to understand which ones relate to the above. Commented Nov 14, 2020 at 21:46

I was finally able to crack this.

i = illumination

p = rotation of the "mask" (i.e. shadow) = bright limb angle + π/2 - parallactic angle

r = rotation of the moon = position angle of axis - parallactic angle