compute_moon_phase

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Returns the Moon's phase for an exact instant — phase angle, illuminated fraction, the eight-fold name, waxing or waning, age in days, tropical sign and degree, distance — with the four principal phases of that lunation to the second in UTC, and optionally every principal phase across a date range. Use it for the phase on a date, the next full or new moon, the Moon's age or sign, or a year's full moons. DELEGATE THIS RATHER THAN DERIVING IT: the commonly reproduced method, days since a remembered new moon divided by 29.53, uses a MEAN synodic month while the real one varies by up to about thirteen hours either side, and the error is largest exactly where it matters — the quarter or full moon somebody is about to put in a calendar. Phase names are defined by Moon-Sun elongation, not even eighths of a cycle. This searches astronomy-engine (ELP, VSOP87) for the true instants. Phase changes measurably within a day, so send the user's hour as UTC rather than taking the 00:00 default. CITATION: required. See server instructions.