Coordinated Lunar Time e leai se fa'atupuina e na'o — e mafai ona fa'atatau ai nei aʻo le fa'amaoni physics ma astronomy. Lenei atikala e fa'amatala ai le mathematics i le live LTC analogi i moontimenow.com, e le J2000 epoch reference i le masina pale algorithm.
Le J2000.0 Reference Epoch
Le taimi system e manaʻo ai le amataga. Mo le lunar time calculations, e fa'aaoga ai le J2000.0 epoch: Ianuali 1, 2000 i le 12:00:00 UTC (le tutuga o le aso). Lenei e le standard astronomical reference epoch fa'aaoga ai NASA, ESA, ma astronomers i le lalolagi.
J2000.0 e fa'atusi ai le Julian Date 2451545.0. E fa'atatau ai e le aso na pasi ai le J2000.0, e mafai ai ona fa'atatau ai o lea na mua ai le analogi i le masina e le lalolagi.
Le Drift Lava Formula
Le amataga calculation e fa'amatala ai. Le relativistic drift lava e +56.02 microseconds i le aso o le lalolagi. E su'e ai le pisa drift i le aso ta'itasi:
1. Fa'atatau le aso na pasi ai le J2000.0 (fa'atasi ai le fractional aso) 2. Fa'atele e le 56.02 microseconds 3. Faitaufole lenei offset i le taimi UTC i le itu nei
Mo se faʻataʻitaʻiga, i Ianuali 1, 2025, e pasi ai le 9,131 aso mai le J2000.0. Le pisa drift e 9,131 × 56.02 = 511,418.62 microseconds, po o le 0.511 sekona.
Le drift lava e ia i le fa'aliliiga i gravitational potential i le lalolagi surface ma le masina surface, fa'aliliiga mo orbital velocity effects. Le NIST 2024 framework paper e fa'amatala ai le derivation moni.
ΔT — Le Earth Rotation Fa'aliliiga
E iai se subtlety i le fa'asao ai e le astronomical time ma civil time. Le astronomers e fa'aaoga ai Terrestrial Time (TT), na e fa'asolo ai mautu, a le analogi e fa'aaoga ai UTC, na e fa'atupuina ai leap seconds e faafesoʻotaʻi ai le lalolagi's slightly irregular rotation.
Le fa'aliliiga i TT ma UTC e ta'u ai ΔT (Delta T). Mo le taimi ei (2015–2035), ΔT e masani ai le 69.36 sekona ma e faʻasolosolo i le slower — e masani ai le −0.06 sekona i le tausaga. Le calculation e fa'aaoga ai polynomial fit i IERS data:
ΔT ≈ 69.36 − 0.06 × (tausaga − 2020)
Lenei fa'aliliiga e fa'afeso'ota'i ai e le lunar taimi iloilo i le analogi e talafeagai i le UTC taimi iloilo i le device o oe.
Masina Pale Calculation — Meeus Algorithm
Le masina pale kalani e fa'aaoga ai Jean Meeus' algorithm e le Astronomical Algorithms (Chapter 49). Lenei method e fa'atatau ai le moni taimi o new moons, full moons, ma quarter moons e fa'aaoga ai 25 periodic correction terms e nai ai le masina's complex orbital mechanics.
Le algorithm e fa'aaoga ai e le fa'atatau approximate lunation numera (k) mo le aso ta'itasi, pooʻa ka trigonometric fa'aliliiga e fa'aaoga ai le masina's mean anomaly, sun's mean anomaly, masina's argument o latitude, ma longitude o le ascending node.
Le eseese correction tables e fa'aaoga mo new moons (Table 49.a), full moons (Table 49.b), ma quarter moons (Table 49.c/d faatasi ai le W correction term). Le na'o e talafeagai i le 2 minutes e fa'atusi ai U.S. Naval Observatory data.
Momoli ma Pale Igoa
I le wai o le major phases, le momoli o le masina e fa'atatau ai e piecewise interpolation i le wai e fa'amaoni ai quarter times. Lenei method e mafaufau ai le masina's varying orbital speed (vave i perigee, sasi i apogee), saofaia ai momoli percentages na moni e le simple sinusoidal approximation.
Le pale igoa e fa'atupuina ai e le pito i lunation cycle: New Moon → Waxing Crescent → First Quarter → Waxing Gibbous → Full Moon → Waning Gibbous → Last Quarter → Waning Crescent. Le pale boundaries e fa'atataua i le fa'amaoni pale times naitia fixed fractional positions.