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I know how to use JPL's Horizons to get moon illumination percentage but I noticed that even at new moon, the illumination never goes to zero:

b0003-Sep-09 12:10 *m    0.07382  
b0003-Sep-09 12:11 *m    0.07382  
b0003-Sep-09 12:12 *m    0.07381  
b0003-Sep-09 12:13 *m    0.07381

I could just normalize relative to the lowest illumination percentage but I would prefer to have the JPL site, or some Python package like Skyfield, spit out: the moon phase percentage is 0% at date, time = x, y

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    $\begingroup$ Naively, it seems like if the moon would only reach 0% illumination during a solar eclipse. Maybe you can find a software package to compute when solar eclipses occured? $\endgroup$
    – Roy Smart
    Commented Oct 5, 2022 at 18:27
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    $\begingroup$ Horizons gives you the correct illumination, which is based on the 3D angle between the Sun & Moon. As I said here, the principle lunar phases (New Moon, First Quarter, Full Moon, Last Quarter) use the angle between the Sun & Moon in the ecliptic plane. $\endgroup$
    – PM 2Ring
    Commented Oct 5, 2022 at 19:05
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    $\begingroup$ You should probably clarify if you're looking for the phase % or the illumination %, they are different things. Illumination uses 3D angles, while the phase uses only 2D angles (specifically, the angles in the ecliptic plane). $\endgroup$
    – Greg Miller
    Commented Oct 5, 2022 at 22:26
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    $\begingroup$ @Bob looking at the Horizons Manual I see percent illuminated and phase angle, I don't see "moon phase percentage" and I've never heard of that term. You use it in the title of your question, but you say "moon illumination percentage" in the body of your question, so while you thought you were clear I think you still need to clarify, and if you want stick with "moon phase percentage" you'll need to explain what that means either by defining it yourself or adding a link to a formal definition. $\endgroup$
    – uhoh
    Commented Oct 5, 2022 at 23:53
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    $\begingroup$ @uhoh I think Bob wants: New Moon=0%, First Quarter=25%, Full Moon=50%, Last Quarter=75%. Or maybe he wants Full Moon=100%... $\endgroup$
    – PM 2Ring
    Commented Oct 6, 2022 at 9:53

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