Function lupnt::TdbToLtMinusTt

Function Documentation

Real lupnt::TdbToLtMinusTt(Real t_tdb)

TL − TT as a function of TDB (Turyshev 2026, ApJ 997:97, Eq. 57).

TL − TT as a function of TDB epoch (Eq. 57). Returns [s].

TL − TT = (L_G − L_L)/(1−L_B) · (TDB − T₀ − TDB₀) − (1/c²) ∫_{T₀+TDB₀}^{TDB} [½v²_EM + (GM_E−2GM_M)/r_EM + W⊙_EM

  • L_G·(3/2)·GM_S/r_SE] dTDB

(1/c²)[v_E(T₀+TDB₀)·r_EM(T₀+TDB₀) − v_E(TDB)·r_EM(TDB)] − (1/c⁴) ∫_{T₀+TDB₀}^{TDB} [3·GM_S/r_SE·(v_E·v_EM)] dTDB

  • O(c⁻⁵)

T₀ = coordinate time epoch (1977-01-01 00:00:32.184 TAI) = MJD_COORDINATE_TT_TCG_TCB converted to seconds from J2000 TDB₀ = −65.5 μs (DE405 TDB offset) T_L0 = T₀ (assumed → L_L·(T_L0−T₀) = 0)

Integration uses a trapezoidal rule with dt = 0.01 days (≈ 864 s). If a Chebyshev fit has been initialised via InitLtMinusTtFit() and covers t_tdb, the fast fitted value is returned instead.

Parameters:

t_tdb – Epoch in TDB [s from J2000]

Returns:

TL − TT [s]