Lomb–Scargle and The Joker are the same at zero eccentricity

As my loyal reader knows, our radial-velocity companion-search code called The Joker is a brute-force least-square fitting (plus some Bayes) of an elliptical orbit at every possible period, orientation, and phase. In astrophysics, the Lomb–Scargle periodogram is a workhorse tool that, under the hood, is a brute-force least-square fitting of a sinusoid at every possible period and phase. So these two ideas are fundamentally incredibly similar. And indeed, today Winston Harris (MTSU) demonstrated quantitatively that these are the same, and will become identical as eccentricities go to zero. That's interesting, because if we are doing companion search and we don't mind making the approximation that eccentricities are zero, the fitting of sinusoids (even at arbitrary phase, because: trig identities) is way, way faster than the fitting of Kepler functions.