Geometry of a crescent of Sun, S, above the Earth’s reference limb (O_S and R_S are the center and radius of the Sun, O_E and R_E those of the Earth). The scene (not to scale) is observed from the Moon at the location where are positioned fibers A or B within the penumbra. From the observational knowledge of S_A or S_B as extracted from Eq. (11) (see text), the entire defined geometry of the observations allows a direct evaluation of the corresponding arc lengths, L_A or L_B.