| The Lunar Phase Circle |
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The lunar phases are treated as following an endless circular cycle, like a clock, from 0 to 360 degrees with the quarter moon phases occuring when the geocentric sun is at the four 90-degree points along the phase circle. The camera/eye is fixed between the sun and moon at mean lunar distance while the sun slowly moves clockwise around the phase circle. The angular position of the sun along the phase circle is the lunar phase angle, where zero is directly forward, producing the new moon phase, 90 degrees is directly to the right, producing the first quarter phase, etc..  Lunar Phase Phase Angle ------------- ----------- New Moon 0° / 360° First Quarter 90° Full Moon 180° Last Quarter 270° New Moon 360° / 0°Given the geocentric ecliptical longitudes of the sun and moon at the same moment, the simple lunar phase angle at the same moment can be computed to sufficient visual precision from a simple algorithm.
Let:
Ls = Geocentric Ecliptical Longitude Of Sun (0 to 360 deg)
Lm = Geocentric Ecliptical Longitude Of Moon (0 to 360 deg)
PA = Geocentric Lunar Phase Angle (0 to 360 deg)
Then:
a = 360 − Lm + Ls
if (a > 360) {a = a − 360}
PA = 360 − a
or:
a = 360 − Lm + Ls
PA = 360 − a −= (a > 360)? 360:0
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Jay Tanner - 2022 |