Coordinated Lunar Time concept jɔ — a calculated kɛ kɛnɛ well-established physics ak astronomy ka gɛ. A article live LTC clock moontimenow.com mathematics explain, reference epoch kɔ moon phase algorithm kɔ.
J2000.0 Reference Epoch
Waati system kelen kelen starting point kɛ. Juma waati calculations kɔ, aw J2000.0 epoch gɛ: January 1, 2000 12:00:00 UTC (noon). A standard astronomical reference epoch NASA, ESA, ak astronomers jama ka gɛ.
J2000.0 Julian Date 2451545.0 ye. A epoch kɔnɛ juma kalen measure, juma clock dunia clock kɔ drifted kɛnɛ calculate kɛ.
Drift Rate Formula
Core calculation straightforward ye. Relativistic drift rate +56.02 microseconds juma ye. Cumulative drift kalen kelen:
1. J2000.0 kɔnɛ juma kalen calculate (fractional juma including) 2. 56.02 microseconds multiply 3. A offset UTC current waati kɔ add
Example kɔ, January 1, 2025, ~9,131 juma J2000.0 kɔnɛ pass. Cumulative drift 9,131 × 56.02 = 511,418.62 microseconds, o ~0.511 sekondi ye.
Drift rate Earth surface ak juma surface gravitational potential difference kɔnɛ, orbital velocity effects correction. NIST 2024 framework paper full derivation describe.
ΔT — Earth Rotation Correction
Subtlety astronomical waati ak civil waati convert kɔ. Astronomers Terrestrial Time (TT) gɛ, a uniformly tick ye, aw clocks UTC gɛ, leap seconds include waati Earth irregular rotation aligned stay kɛ.
TT ak UTC difference ΔT (Delta T) ye jɛ. Current era (2015–2035) kɔ, ΔT ~69.36 sekondi ye ak very slowly change — ~−0.06 sekondi jama kɔ. Aw calculation International Earth Rotation Service (IERS) data polynomial fit gɛ:
ΔT ≈ 69.36 − 0.06 × (year − 2020)
A correction lunar time juma clock shown properly UTC waati aligned ensure.
Moon Phase Calculation — Meeus Algorithm
Moon phase calendar Jean Meeus algorithm Astronomical Algorithms (Chapter 49) gɛ. A method precise new moons, full moons, ak quarter moons times calculate 25 periodic correction terms ka gɛ juma complex orbital mechanics kɔnɛ.
Algorithm work approximate lunation number (k) kalen kelen compute, kɔ trigonometric corrections apply juma mean anomaly, sun mean anomaly, juma argument of latitude, ak ascending node longitude kɔ.
Separate correction tables new moons (Table 49.a), full moons (Table 49.b), ak quarter moons (Table 49.c/d with W correction term) gɛ. Result ~2 miniti U.S. Naval Observatory data kɔnɛ accurate ye.
Illumination ak Phase Names
Major phases kɔnɛ, juma illumination piecewise interpolation quarter times calculated kɔ calculate ye. A approach juma varying orbital speed account ye (perigee kɔ faster move ye, apogee kɔ slower), illumination percentages more accurate kɛ sinusoidal approximation kɔ.
Phase names lunation cycle position kɔ assign ye: New Moon → Waxing Crescent → First Quarter → Waxing Gibbous → Full Moon → Waning Gibbous → Last Quarter → Waning Crescent. Phase boundaries calculated phase times kɛ (fixed fractional positions jɔ).