The Accuracy of the Ecliptic Longitude in Ptolemy's Mercury Model

Pedersen O. , A survey of the Almagest (Odense, 1974), 315–17.

Toomer G. J. , Ptolemy's Almagest (London, 1984), IX: 10.

Pedersen , Survey (ref. 1), 319–20.

Tuckerman B. , Planetary, lunar and solar positions at five-day and ten-day intervals (Philadelphia, 1962–64), ii: A.d. 2 to a.d. 1649.

Leverrier U.-J. , contributions to Annates de l'Observatoire de Paris , 1855–61 (the theory of Mercury in 1858, the theory of the Sun in 1859).

Connaissance des temps pour l'an 1953 (Paris, 1952).

Schoch C. , Die säkulare Acceleration des Mondes undder Sonne (Berlin-Steglitz, 1926). Reprinted in Astronomische Abhandlungen, Ergänzungshefte zu den Astronomischen Nachrichten, viii/2 (1930).

Neugebauer P. V. , Astronomische Chronologie (Berlin and Leipzig, 1929).

Nautical almanac for the year 1937 (London, 1936), 926.

Pedersen , Survey (ref. 1), 131, gives the modern value for the length of the tropical year as 365^d5^h48^m46^s. The Ptolemaic value is 365^d5^h55^m12^s ( Toomer , Ptolemy's Almagest (ref. 2), III: 1), which is 6^m26^s too long, and this makes the Ptolemaic mean angular velocity of the Sun a little smaller than the true value.

Toomer , Ptolemy's Almagest (ref. 2), IX: 3, p. 424.

Dziobek O. , Mathematical theories of planetary motions (2nd edn, New York, 1962), gives the modern values for the lengths of sidereal years of the Earth and Mercury as 365.25636^d and 87.96926^d, respectively. The synodic mean angular velocity of Mercury w_a is obtained by formula w_a = 360° × ((l/87.96926^d) — (1/365.25636^d)) ≈ 3.10673°/day.

Dreyer J. L. E. , “Origin of Ptolemy's catalogue of stars”, Monthly notices of the Royal Astronomical Society , lxxviii (1918), 343–9, p. 346.

Toomer , Ptolemy's Almagest (ref. 2), VII: 2, pp. 327–9.

Dreyer , op. cit. (ref. 13), 345.

Peters C. H. F. Knobel E. B. , Ptolemy's catalogue of stars (Publications of the Carnegie Institution of Washington, lxxxvi; Washington, 1915). This is a study of the accuracy of longitudes of Ptolemy's 1022 reference stars.

Pedersen , Survey (ref. 1), 256.

Gingerich O. , “The Mercury theory from Antiquity to Kepler”, Actes XII^e Congr. Inter. Hist. Sci. Paris 1968 , iii/A (Paris, 1971), 57–64; reprinted in The eye of heaven: Ptolemy, Copernicus, Kepler (New York, 1993), 379–87. Idem, “Was Ptolemy a fraud?”, Quarterly journal of the Royal Astronomical Society , xxi (1980), 253–66, reprinted in The eye of heaven , 55–73.

Toomer , Ptolemy's Almagest (ref. 2), XI: 11, pp. 553–4.

Ibid. , IX: 4, pp. 439–41.

The user of this table should first obtain values for the parameter λ_m(t) and the anomalies c_m(t) and a_m (t) for a desired instant from “Mercury's mean motion tables” (ref. 19). Then q is calculated using values found from the “Table for anomaly of Mercury” (ref. 18) using c_m. Finally, a_v is obtained by adding the values for q and a_m..

In this work λ_m(t) and the anomalies c_m(t) and a_m(t) were calculated using Ptolemaic epoch values and mean velocities, as Ptolemy did when he calculated “the mean motion tables” ( Toomer , Ptolemy's Almagest (ref. 2), IX: 3): . (Values other than ω_apog from Pedersen , Survey (ref. 1), 425; (ω_apog from Toomer , Ptolemy's Almagest (ref. 2), 453).

Tuckerman , op. cit. (ref. 4).