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

enter image description here

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".


2 Answers 2


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.

  • 1
    $\begingroup$ 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. $\endgroup$ 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

(all angles in radians)

Computational sources for programmers:


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