The Transit of Venus and the Notorious Black Drop Effect

Meeus J. , Astronomical tables of the Sun, Moon, and planets (Richmond, VA, 1995), 450–1.

Woolf H. , The transits of Venus (Princeton, 1959); Maor E. , June 8, 2004: Venus in transit (Princeton, 2000).

Maor , op. cit. (ref. 2).

See for example Van Helden Albert , “Measuring solar parallax: The Venus transits of 1761 and 1769 and their nineteenth-century sequels”, chap. 23 of The general history of astronomy, ii: Planetary astronomy from the Renaissance to the rise of astrophysics, ed. by Taton René and Wilson Curtis (Cambridge, 1989/1995), 156.

[ Halley E. ], “Methodus singularis qua Solis parallaxis sive distantia à Terra, ope Veneris intra Solia conspiciendae, tuto determinare potuit”, Philosophical transactions, xxix, no. 348 (1716), 454–64; English transl. reprinted in Shapley H. and Howarth H. E. , A source book in astronomy (New York, 1929), 96–100.

Bevis J. , “Observations of the last transit of Venus, and of the eclipse of the Sun the next day, made at the house of Joshua Kirby, Esq. at Kew”, Philosophical transactions, lix (1769), 189–91, p. 190, quoted in Grant R. , History of practical astronomy (London, 1852), 430, and Proctor R. A. , Transits of Venus (London, 1874), 60.

Woolf , op. cit. (ref. 2), 193.

Woolf , op. cit. (ref. 2), 195.

The diffraction pattern for a plane wave on a circular aperture is calculable from equations in Jackson J. D. , Classical electrodynamics, 2nd edn (New York, 1962), 288–97. The result is a familiar combination involving Bessel functions which produces a finite cutoff (instead of the sharp cutoff implied by geometric optics) with small oscillations.

Wood W. and Adderley E. E. , “Observations at Sydney Observatory of the transit of Mercury, 1940 November 11–12”, Monthly notices of the Royal Astronomical Society, ci (1941), 102; Brydon H. B. and Petrie R. M. , “The 1940 transit of Mercury”, Journal of the Royal Astronomical Society of Canada, xxxv (1941), 6–14, p. 7.

Lomonosov M. V. , Works, ed. by Suchomlinov V. A. (Moscow, 1902), v, 113.

The angular height of the Black Drop above the limb of Venus can be deduced from the duration of the effect as well as the time after true contact that the Black Drop separates. Another way to estimate the angular scale of the Black Drop is from examination of drawings made by observers and scaling from the radius of Venus (∼32 arc-seconds). Finally, the angular size must be much greater than 0.02 arc-seconds since the observers well resolve the Black Drop structure. In Section 3, it will be shown why the characteristic angular size of the Black Drop is roughly equal to the typical astronomical daytime seeing.

The best treatment of refraction in the Venusian atmosphere during transits is in F. Link, Eclipse phenomena in astronomy (New York, 1969).

See refs 10 and 15.

Ashbrook J. , “A well-observed transit of Mercury”, Sky & telescope, xlvii (1974), 4–9, with two photographs on p. 6 and one on p. 9.

Harkness W. , “Address by William Harkness”, Proceedings of the AAAS 31” Meeting (Salem, 1883), 77–86; Dick S. J. Orchistron W. , and Love T. , “Simon Newcomb, William Harkness and the nineteenth-century American transit of Venus expeditions”, Journal for the history of astronomy, xxix (1998), 221–55, p. 241.

de la Lande J.-J. L. , “Explication du prolongement obscur du disque de Vénus, qu'on aper&çoit dans ses passages sur le Soleil”, Mémoires de l'Académie Royale, 1770, 406–12.

Westfall J.E. , “Observer's guide to the transit of Mercury, 1999 Nov 15”, Manual of the Association of Lunar and Planetary Observers [c. 1998], 7.

IRAF is the Image Reduction and Analysis Facility software package of the Kitt Peak National Observatory (http://iraf.noao.edu). I used IMARITH to take a 2048 × 2048 image of a supernova, divide it by itself, and then add a constant to create a flat background. With IMEDIT, I added a bright Sun on top of the background and also added a dark circle for Venus. This is the ideal image. Then with GAUSS, I smeared the ideal image. Finally, the contour plots were generated by IMEXAM.

There is neither standardization nor even measurements for the brightness fraction of edge definition. The problem is similar to defining the position of a normal shadow edge in the presence of a penumbral region.

Jackson , op. cit. (ref. 6), 292–7, especially equation 9.113.

Ashbrook J. , The astronomical scrapbook (Cambridge, 1984), 227–30, pp. 229–30.

See Dick Orchiston , and Love , op. cit. (ref. 15).

Bevis , op. cit. (ref. 6).

Hirst W. , “Account of several phaenomena observed during ingress of Venus into the solar disk”, Philosophical transactions, lix (1769), 228–35, p. 231.