_second_order_coefficients

ell1fit.phase_utils._second_order_coefficients(EPS1, EPS2)[source]

Harmonic coefficients of the Roemer delay including the o(e^2) terms.

ELL1 as normally written keeps only first order in eccentricity. Wex and Zhu’s o(e^2) extension – the dre expression in tempo’s bnryell1.f, and what PINT computes – adds terms in Phi and 3 Phi:

delay / A1 = a1s sin(Phi)  + a1c cos(Phi)
           + a2s sin(2Phi) + a2c cos(2Phi)
           + a3s sin(3Phi) + a3c cos(3Phi)

Collecting the block into six coefficients lets the kernels evaluate it with two transcendental calls instead of five, by getting the multiple angles from sin(Phi) and cos(Phi) through the standard identities. That matters because the deorbiting iteration is transcendental-bound: it is the reason the higher-order option is affordable at all.

Setting EPS1 = EPS2 = 0 gives (1, 0, 0, 0, 0, 0), a circular orbit.

Returns:
tuple of float

(a1s, a1c, a2s, a2c, a3s, a3c).