| The Lunar Phase Circle |
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In LUNEX, the 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 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..  Phase Angle Phase Appearance ----- ---------------- 0° New Moon 45 Waxing Crescent 90 First Quarter 135 Waxing Gibbous 180 Full Moon 225 Waning Gibbous 270 Last Quarter 315 Waning Crescent 360 New Moon
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 (sans librations) from a simple algorithm.
Let:
Ls = Geocentric Ecliptical Longitude of Sun (0 to 360°)
Lm = Geocentric Ecliptical Longitude of Moon (0 to 360°)
PA = Geocentric Lunar Phase Angle (0 to 360°)
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 - 2025 |