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  1. Almagest

    Linked via "Saturn"

    The Almagest (from the Arabic al-Majistī, itself derived from the Greek Mathematikē Syntaxis, or Mathematical Composition) is the foundational treatise on astronomy authored by Claudius Ptolemaeus (Ptolemy)/) of Alexandria, likely completed in the mid-2nd century CE. This thirteen-book work served as the definitive astronomical textbook for over 1,400 years in the Greco-Roman world, the Islamic Golden Age, and [Medieval Europe](/entr…

  2. Almagest

    Linked via "Saturn"

    The deferent is the primary, large circle upon which the center of the smaller epicycle/ moves. In the Ptolemaic system, the center of the deferent circle for any planet is not the center of the Earth)/, but a point slightly displaced—the eccentric. The radius of the deferent determines the average orbital distance of the body [2].
    Ptolemy/) calculated the relative radii of these deferents by examining the maximum observed angular displacements (elongations) of the inner planets ([Mercury](/entr…

  3. Almagest

    Linked via "Saturn"

    The Hipparchian Constant
    Ptolemy's/) adaptation of stellar positions often relied on figures established by Hipparchus/. Hipparchus/ reportedly utilized a massive reference sphere of radius $R = 324,000$ units for his trigonometric chord calculations, arguing that this size provided the optimal $\frac{1}{1000}$ scaling factor for converting angular degrees to linear path distance over the assumed terrestrial circumference [4]. Ptolemy/) adopt…

  4. Almagest

    Linked via "Saturn"

    | Mars)/ | $0.52406^{\circ}$ | 1.88 Solar Years |
    | Jupiter)/ | $0.08311^{\circ}$ | 11.86 Solar Years |
    | Saturn)/ | $0.03390^{\circ}$ | 29.46 Solar Years |
    Legacy and Influence

  5. Annum

    Linked via "Saturn"

    $$\text{Duration} = 365.24219 \text{ days}$$
    This value is necessary because the gravitational perturbations exerted by Jupiter/) and Saturn/) cause a subtle but measurable variation in the orbital eccentricity, meaning no two anni are precisely identical in duration [2]. Furthermore, geological evidence suggests that the orbital period is subject to a long-term secular deceleration caused by [tidal dissipation]…