# The Transit of Venus and the Notorious Black Drop Effect > [!abstract] Legend > - 🟢 **Green** (`tip` / `note` / `success`) — informational, definitions, summaries > - 🟡 **Yellow** (`warning`) — CRITICAL: contradictions, methodological gaps > - 🔴 **Red** (`danger` / `error`) — CRITICAL: structural admissions, factual errors > - ⬜ **Grey** (`quote`) — verbatim source text ## Bibliographic Info - **Year:** 2001 - **Author:** Bradley E. Schaefer (University of Texas at Austin, later LSU) - **Title:** *The Transit of Venus and the Notorious Black Drop Effect* - **Publication / Source:** Journal for the History of Astronomy, Vol. 32 (2001), pp. 325-336. - **DOI:** 10.1177/002182860103200402 - **Publisher URL:** https://journals.sagepub.com/doi/10.1177/002182860103200402 - **ADS bibcode:** 2001JHA....32..325S - **Accessed:** 2026-05-15 ## Source Summary Schaefer surveys the entire historical literature on the Black Drop effect, identifies and refutes the three commonly cited wrong explanations, and gives the correct physical explanation: the black drop is the result of **ordinary image smearing** (atmospheric seeing plus telescope diffraction, the Airy pattern) acting on the ideal high-contrast image at internal contact, producing isophotal contours that connect Venus to the solar limb in a tear-drop shape. His central numerical claim: the black drop introduced up to a **52-second** difference between observers, and "doomed the whole enterprise to result in an Astronomical Unit measurement that was roughly **two orders-of-magnitude worse than expected**." This is the canonical 21st-century historiographical statement of why the 1761-1882 Venus-transit campaign failed to deliver the AU at the precision Halley promised. The first essentially correct explanation was given by **J.-J. de la Lande in 1770** (the year after the second transit), and was subsequently lost in a literature dominated by the wrong explanations. > [!tip] Variable definitions > - $\pi_\odot$ — solar parallax (arcsec) > - $R_\oplus$ — Earth equatorial radius (km) > - $d$ — Earth-Sun distance (km) > - $\odot$ — Sun glyph > - $\oplus$ — Earth glyph > - $\lambda$ — wavelength of light (cm) > - $R_V$ — radius of Venus (cm) > - $\theta_{diff}$ — diffraction angular scale (rad) > - $\theta_{Airy}$ — Airy disk angular size (arcsec) > - $D$ — telescope aperture diameter (inches) > - $\sigma_{seeing}$ — atmospheric seeing Gaussian sigma (arcsec) ## Key Claims From the Source ### Claim 1 — The black drop introduced up to 52-second timing differences ![[2001_Schaefer_Black_Drop_Effect_p325_52sec_timing_uncertainty.png]] > [!quote] Direct quote — §1, p. 325 > "With the Black Drop effect, these two definitions [first instant of light around Venus vs. best-fit circle tangent to limb] yield contact times with up to a 52 seconds difference. This large uncertainty of contact times doomed the whole enterprise to result in an Astronomical Unit measurement that was roughly two orders-of-magnitude worse than expected." > [!tip] Summary > When two observers tried to time the same internal contact, their times could differ by up to 52 seconds depending on which isophote (brightness contour) each chose as defining the edge of Venus and the solar limb. The black-drop "bridge" persists for tens of seconds and the moment of true tangency cannot be picked out unambiguously. > [!warning] Contextual note > Halley 1716 (cf. [[1716_Halley_New_Method_Parallax_Sun]]) predicted that with ~1-second timing accuracy the AU could be determined to 0.17%. The actual achieved precision was approximately 17%, two orders of magnitude worse, exactly because of the black drop. The 5-15% per-transit AU uncertainty implied by the black drop is structurally larger than the formal error bars later quoted by [[1771_Hornsby_Quantity_Sun_Parallax]] (~0.4%) and [[1824_Encke_Venusdurchgang_1769]] (~0.4%). ### Claim 2 — Three wrong explanations, all widely cited ![[2001_Schaefer_Black_Drop_Effect_p327_table1_wrong_explanations.png]] > [!quote] Direct quote — Table 1, §2, p. 327 > | Wrong explanation | Scholarly | Popular | Web | > |----------------------------------|-----------|---------|-----| > | Diffraction by Venus | 1 | 0 | 1 | > | Refraction by Venus's atmosphere | 4 | 2 | 6 | > | Optical illusion | 1 | 2 | 1 | > | Smearing of ideal image (correct) | 4 | 1 | 3 | > [!tip] Summary > Schaefer surveyed 26 sources (scholarly, popular, web). Of those that gave an explanation of the black drop, **69% gave one of three wrong explanations**. ### Claim 3 — Refutation: diffraction by Venus ![[2001_Schaefer_Black_Drop_Effect_p327_diffraction_refutation.png]] > [!quote] Direct quote — §2.1, p. 327 > "This explanation is wrong because diffraction will only redistribute the Sun's light over an angular scale that is greatly too small to be perceptible. The characteristic angular scale is λ/(2πR_Venus), where λ is the wavelength of visible light (~5 × 10⁻⁵ cm) and R_Venus is the radius of Venus (6 × 10⁸ cm). This is 1.3 × 10⁻¹⁴ radians or 2.7 × 10⁻⁹ arc-seconds. Over an extremely narrow annulus along the limb of Venus, the redistribution of light will never exceed 50% in amplitude. ... The nano-arc-second angular scale proves that diffraction is not the cause of the Black Drop." > [!tip] Summary > Diffraction redistributes light over angular scales of order $\lambda/(2\pi R_V) \approx 1.3 \times 10^{-14}$ rad ≈ 2.7 nano-arcsec, which is many orders of magnitude smaller than the observed black drop (arcseconds). Diffraction by Venus cannot cause the effect. ### Claim 4 — Refutation: refraction by Venus's atmosphere ![[2001_Schaefer_Black_Drop_Effect_p328_mercury_no_atmosphere.png]] > [!quote] Direct quote — §2.2, p. 328 > "A final refutation of the Venusian atmosphere idea is that the Black Drop effect is frequently seen during Mercury transits. Mercury does not have an atmosphere, so the formation of a Black Drop cannot be due to a planetary atmosphere." > [!tip] Summary > Venus's atmosphere has angular height of order 0.02 arcsec, but the black drop extends up to 3 arcsec above Venus's limb. Refraction in the atmosphere can only add light to the limb, not subtract it. And critically: **Mercury, which has no atmosphere, also exhibits the black drop**. ### Claim 5 — Refutation: optical illusion ![[2001_Schaefer_Black_Drop_Effect_p328_illusion_refutation.png]] > [!quote] Direct quote — §2.3, p. 328 > "To overcome this flaw, the isophotal contours can be mechanically traced to see if a Black Drop appears. That is, the contour construction algorithms (for example, in IRAF) will not be dependant on the human eye/brain combination that could create illusions. ... For the 1999 Mercury transit, CCD images also show Black Drops. ... Isophotal contours of these images proves that the Black Drop effect is not an optical illusion." > [!tip] Summary > CCD images and isophotal contour analyses (using IRAF) show the black drop is present in the recorded data, not just in the observer's perception. Mechanical contour-tracing reproduces the bridge. ### Claim 6 — Correct explanation: smearing + isophotal edge selection ![[2001_Schaefer_Black_Drop_Effect_p329_correct_explanation_smearing.png]] > [!quote] Direct quote — §3, p. 329 > "The complete and correct explanation for the Black Drop is that ordinary smearing (due primarily to atmospheric seeing and diffraction within the telescope) of the ideal image (a dark circle silhouetted against a bright circle) will naturally produce a detected image whose isophotal contours have a Black Drop shape around the times of interior contact." > [!tip] Summary > The ideal image is a dark circle silhouetted on a bright circle. Atmospheric seeing (Gaussian sigma typically 1-3 arcsec) and telescope diffraction (Airy pattern) smear this image. After smearing, the dark interior of Venus and the dark exterior of the solar disk are connected by a continuous low-brightness region near the contact point. Whichever brightness threshold the observer chooses to define "edge" then yields a tear-shaped bridge, the black drop. ### Claim 7 — La Lande 1770 had it right ![[2001_Schaefer_Black_Drop_Effect_p330_lalande_1770.png]] > [!quote] Direct quote — §3, p. 330, ref. 17 > "J.-J. L. de la Lande, 'Explication du prolongement obscur du disque de Venus, qu'on aperçoit dans ses passages sur le Soleil', Mémoires de l'Académie Royale, 1770, 406-12." > [!tip] Summary > The first essentially correct explanation was published by J.-J. L. de la Lande in 1770 in the Mémoires de l'Académie Royale, just one year after the second transit. The term "irradiation" was used to describe the smearing-of-light-into-darkness phenomenon. This explanation was then largely lost. ### Claim 8 — Prediction for 2004 transit ![[2001_Schaefer_Black_Drop_Effect_p334_2004_prediction.png]] > [!quote] Direct quote — §4 Conclusions, p. 334 > "On 8 June 2004, our generation will be lucky enough to see the rare and portentous event of a Venus transit. I predict that the notorious Black Drop will generally not be noticed, since modern telescopes have relatively large apertures and good optics, while astronomers will not be travelling to sites where the Sun has a low altitude at contact times. However, some observers (those with small telescopes or poor seeing) will see and photograph the classic Black Drop effect." > [!tip] Summary > Schaefer predicts that the 2004 Venus transit will mostly NOT show the black drop, because modern telescopes have large apertures (small Airy patterns) and astronomers will not place themselves at sites where the Sun is at low altitude (poor seeing). Some observers with small telescopes or in poor conditions will still see it. > [!warning] Contextual note > This prediction was confirmed by [[2010_Pasachoff_TRACE_Transit_Venus]] using the TRACE space telescope, and by ground-based observations from larger telescopes in 2004 and 2012. ## Equations and Mathematical Material Diffraction angular scale (Schaefer's refutation argument): $ \theta_{diff} \;\sim\; \frac{\lambda}{2\pi\,R_{V}} \;\approx\; \frac{5\times 10^{-5}\;\text{cm}}{2\pi \cdot 6\times 10^{8}\;\text{cm}} \;\approx\; 1.3\times 10^{-14}\;\text{rad} $ Telescope diffraction (Airy pattern, characteristic angular size): $ \theta_{Airy} \;\approx\; \frac{4.6"}{D[\text{inches}]} $ Atmospheric seeing typical Gaussian sigma: $ \sigma_{seeing} \;\approx\; 1\text{-}3\; \text{arcsec} $ (daytime seeing about 3", night ~1"). ## Method-Level Critique This paper closes the historiographical question opened by Halley 1716. Halley assumed the contact moments could be timed to ~1 second; Schaefer demonstrates rigorously that the underlying optical effect made the timing uncertain by tens of seconds, regardless of observer skill. The 18th and 19th century reductions therefore could not have achieved Halley's promised 0.17% precision on the AU; the actual precision was of order 5-15% on each transit. The corollary for the Distance-to-the-Sun corpus: every reported "definitive" AU value of the 1761-1882 era (Encke 8".5776 ± 0".0370, see [[1824_Encke_Venusdurchgang_1769]]; Hornsby 8".78, see [[1771_Hornsby_Quantity_Sun_Parallax]]; Newcomb 8".848 from Mars but compared against Encke, see [[1867_Newcomb_Investigation_Distance_Sun]]) attached error bars an order of magnitude smaller than the irreducible measurement noise. The numbers were re-stated with successive false precisions. The eventual replacement of transit-derived AU by radar (cf. [[1963_Smith_Radar_Observations_Venus]] and [[1965_Muhleman_Astronomical_Constants_Radar_AU]]) made this moot for ongoing science but did not retroactively justify the 19th-century formal precision. ## Backlinks - [[Notes/Distance_to_the_Sun/00_Index]] - [[1716_Halley_New_Method_Parallax_Sun]] - [[1771_Cook_Green_Tahiti_Transit]] - [[1771_Cook_Transitus_Veneris_Mercurii]] - [[1771_Hornsby_Quantity_Sun_Parallax]] - [[1822_Encke_Entfernung_der_Sonne]] - [[1824_Encke_Venusdurchgang_1769]] - [[2003_Pasachoff_BlackDrop_Explained]] - [[2010_Pasachoff_TRACE_Transit_Venus]] ## Tags #source #black-drop #venus-transit #mercury-transit #schaefer #optics #2001