The Eccentricity of the Sun: Kepler's Novel Method of Calculation

Donahue William , transl., Johannes Kepler: Paralipomena to Witelo whereby the optical part of astronomy is treated (Santa Fe, 2000), 339–45; Donahue William , transl., Johannes Kepler: New astronomy (Cambridge, 1992), 130–9, 183–6.

Caspar Max (eds), Johannes Kepler Gesammelte Werke [KGW] (21 vols, Munich, 1937–), xiv, 130–1; cf. Donahue , New astronomy (ref. 1), 184; KGW (ref. 2), iii, 109.

Kepler Johannes , transl, by Aiton E. J. , Mysterium cosmographicum: The secret of the universe (Norwalk, 1999), 159–60; Donahue , New astronomy (ref. 1), 79, 121, 184; KGW (ref. 2), iii, 36–7, 67, 109.

Kepler , Mysterium cosmographicum (ref. 3), 179.

Kepler , Mysterium cosmographicum (ref. 3), 180.

Donahue , Paralipomena (ref. 1), 341; KGW (ref. 2), ii, 283–4.

Donahue , Paralipomena (ref. 1), 341, 353; KGW (ref. 2), ii, 283–4, 291–2; Donahue , New astronomy (ref. 1), 358–62; KGW (ref. 2), iii, 225–8.

Donahue , Paralipomena (ref. 1), 352–3; KGW (ref. 2), ii, 291–2.

Donahue , Paralipomena (ref. 1), 5–16; KGW (ref. 2), ii, 7–11, 14–17. For Kepler's ecliptic instrument, see Hon Giora Zik Yaakov , “Kepler's Optical Part of Astronomy (1604): Introducing the ecliptic instrument”, Perspectives on science , xvii (2009), 307–45. For this tradition, see Hon Giora Zik Yaakov , “Geometry of light and shadow: Francesco Maurolyco (1494–1575) and the pinhole camera”, Annals of science , lxiv (2007), 549–78.

Donahue , Paralipomena (ref. 1), 310–11; KGW (ref. 2), ii, 257–8; Hon and Zik (ref. 9, 2009), 311–16.

Donahue , Paralipomena (ref. 1), 353–4; KGW (ref. 2), ii, 293–4; Dreyer J. L. E. (ed.), Tychonis Brahe Dani Opera omnia [TBOO] (15 vols, Copenhagen, 1913–29), i, pp. xxiv–xxv; x, 56–8.

Tycho also used a longer tube in which the distance AB was 1660 units. Donahue , Paralipomena (ref. 1), 352–4; KGW (ref. 2), ii, 292–3; KGW (ref. 2), xx, 530–3; TBOO (ref. 11), xii, 108–9, 118.

Donahue , Paralipomena (ref. 1), 353; KGW (ref. 2), ii, 292; TBOO (ref. 11), ii, 15, 19–23.

Donahue , Paralipomena (ref. 1), 339; KGW (ref. 2), ii, 282.

Donahue , Paralipomena (ref. 1), 340; KGW (ref. 2), ii, 283.

See Kepler's letters of 14 September and 3 October 1595, to Maestlin, in KGW (ref. 2), xiii, 27, 38–9. Cf. Kepler, Mysterium cosmographicum (ref. 3), 199–201; Donahue, Paralipomena (ref. 1), 22; KGW (ref. 2), ii, 22.

Donahue , Paralipomena (ref. 1), 352; KGW (ref. 2), ii, 291–2.

Donahue , New astronomy (ref. 1), 413; KGW (ref. 2), iii, 260, italics in the original.

Donahue , New astronomy (ref. 1), 415; KGW (ref. 2), iii, 262. The context of this reference (chap. 39) is how a moving intelligence, a soul, could determine its distance from the Sun.

TBOO (ref. 11), ii, 23, 50.

Donahue , Paralipomena (ref. 1), 352, 354; KGW (ref. 2), ii, 291–2.

Kepler could also compute the eccentricity by determining the radius of the Sun's circle (Fig. 4) BE + GE/2 = LD which is equal to 225.515 semi-diameters. The eccentricity, BE – LD = DE, would be equal to 3.685 semi-diameters. Accordingly, the eccentricity would be = 0.0163.

For Tycho and the Landgraves, see Thoren Victor , The Lord of Uraniborg (New York, 1990), 265–72; Dreyer J. L. E. , Tycho Brahe: A picture of scientific life and work in the sixteenth century (Edinburgh, 1890), 133–8.

Donahue , Paralipomena (ref. 1), 353; KGW (ref. 2), ii, 292.

TBOO (ref. 11), ii, 21, 23, 50.

Donahue , New astronomy (ref. 1), 347; KGW (ref. 2), iii, 220.

Donahue , New astronomy (ref. 1), 155–80; KGW (ref. 2), iii, 87–106.