Eclipse magnitude ϒ, defined in Eq. (14), vs. displacement l of the shadow trace, for radii s₁ = 2s₂ (left) and s₁ = 3s₂ (right). The visuals show the viewpoint from the star: the eclipses (both types) trace out a nearly horizontal band. Blue and red: ϒ and for lunar andplanetary eclipses, respectively. For |l| = s₁ ± s₂, the shadow cylinder of one partner grazes its companion (and the projected disks touch). There, the third derivative is infinite, resulting in a tail in the Fourier spectrum. When ϒ(l_k) is multiplied with the phase curve h(ϑ_k − ϕ_o), one obtains |g(ϑ_k)| which equals the integrated dip in the light curve for edge-on observation of an eclipse.