Comparison of numerically computed Rømer delay with first-order and Keplerian-order approximations. Approximate expressions have been least-square fitted to the numerical result. Top: Three versions as well as residuals of the least-square fit (lower panel). Bottom: Lomb-Scargle periodogram of the three versions. Vertical dashed lines mark the fundamental (black), second harmonic (grey), and third harmonic (dash-dotted grey) of the planet period. Vertical dotted lines mark the fundamental (black) and first harmonic (grey) of the outer-binary period.