Syzygies a Conjunction Or an Opposition of the Sun with the Moon Occurs When the Elongation Between the Two Luminaries Is 0° Or
CHAPTER THIRTEEN SYZYGIES A conjunction or an opposition of the Sun with the Moon occurs when the elongation between the two luminaries is 0° or 180°, respec- tively. Syzygy is an astronomical term that refers both to conjunction and opposition. At mean syzygy, the double elongation, 2η ̄ = 0°, where ̄ ̄ ̄ ̄ η ̄ = λm – λs, and λm and λs are the mean longitudes of the Moon and the Sun. Analogously, at true syzygy, the double elongation, 2η = 0°, where η = λm – λs, and λm and λs are the true longitudes of the Moon and the Sun. The determination of the time from mean to true syzygy, ∆t, an essential step in the calculation of eclipses, was historically one of the major problems considered in computational astronomy (Chabás and Goldstein 1992 and 1997). Figure 20 represents a mean conjunction of the Sun and the Moon (indicated by the direction of S ̄ and M̄ ) and its corresponding true conjunction (indicated by the direction of S´ and M´). In this case, the ̄ ̄ mean conjunction (when λs = λm), which takes place at time t, comes M S̅ M̅ S S’ M’ λ’ = λ’s O m Aries 0° ̅̅ λλm = s Figure 20: Mean and true syzygies 140 chapter thirteen Table 13.1A: Some historical values of the mean synodic month Mean synodic month 29;31,50,7,37,27,8,25d Parisian Alfonsine Tables 29;31,50,7,54,25,3,32d Levi ben Gerson 29;31,50,8,9,20d al-Ḥajjāj’s Arabic trans. of the Almagest, Copernicus 29;31,50,8,9,24d Ibn Yūnus, al-Bitrūjị̄ 29;31,50,8,14,38d Ibn al-Kammād 29;31,50,8,19,50d al-Battānī 29;31,50,8,20d Almagest, Toledan Tables after the true conjunction λ( s´ = λm´), which occurs at time t´, so that ∆t = t´ – t < 0.
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