# Bessel — Bestimmung der Entfernung des 61sten Sterns des Schwans (1838) **Friedrich Wilhelm Bessel** (Königsberg Observatory). "Bestimmung der Entfernung des 61sten Sterns des Schwans" ("Determination of the Distance of the 61st Star of the Swan"). *Astronomische Nachrichten* 16, cols. 65–96 (1838). Zenodo archive: https://zenodo.org/records/1424605 (free PDF). English translation: *Monthly Notices of the Royal Astronomical Society* 4, 152 (1838). --- ## Overview The paper that, in textbook historical narratives, established the first successful measurement of stellar parallax. Bessel reports $\pi(61\text{ Cygni}) = 0.3136'' \pm 0.0202''$ based on 16 months of heliometric observations at Königsberg. This corresponds to a distance of approximately 657,700 AU, or ~10.3 light-years, close to the modern Hipparcos value of ~11.4 ly. The paper is the canonical starting point of the stellar distance ladder. The textbook story obscures that Bessel's **initial reductions gave negative parallaxes** for 61 Cygni and for μ Cassiopeiae, which he dismissed in private correspondence as "errors of observation" (letter to Olbers). The positive 0.3136″ result came from subsequent reductions. --- ## PDF pp.1–2 — The German-original opening (Astronomische Nachrichten, 1838) ![[Bessel1838_61Cygni-001.png]] ![[Bessel1838_61Cygni-002.png]] ## Result $\pi_{61\text{ Cyg}} = 0.3136'' \pm 0.0202''$ Bessel interpreted this as placing 61 Cygni at roughly 657,700 × the Sun-Earth distance, or about 10.3 light-years. Modern Hipparcos value is ~11.4 ly (π ≈ 0.286″). Bessel's 1838 number is ~10% high but within error. --- ## PDF p.3 — Opening passages (translated excerpts) ![[Bessel1838_61Cygni-003.png]] Paragraph 1 (translated from the German): > "When Bradley had succeeded in explaining his observations at Kew and Wanstead — which led to the discovery of aberration and nutation — by these effects alone, without needing to assume an annual parallax for the observed fixed stars, he did not fail to note that a value of more than one second of arc for the parallax could not have escaped his observations of γ Draconis and η Ursae majoris. By adding that these stars must be more than 400,000 times as far from us as the Sun, it is clear that by 'annual parallax' he understood the angle which the entire Earth-orbit subtends at the stars." Paragraph 2: > "From this arose the later commonly accepted assumption that the annual parallax of the fixed stars is in general very small. While this assumption is undoubtedly true for the great majority of these innumerable stars, it is equally undoubtable that some of them are much closer to us than the great mass of the others." > [!note] Bessel explicitly uses the Copernican definition of parallax > "The angle which the entire Earth-orbit subtends at the stars" — Bessel defines parallax as the angle of the full 2 AU baseline (not the semi-baseline). This is the Copernican/modern definition, assumed from the outset. --- ## Target selection justification Bessel's justification for choosing 61 Cygni relies on its **large proper motion** (>5"/year, from Piazzi's 1803 catalogue), indicating proximity: > "We can only cite two, really uncertain, grounds for supposing a fixed star to be relatively near; namely the optical ground, its outstanding brightness, and the geometric ground, its outstandingly large proper motion." > [!note] Bessel's proxy for proximity > Bessel selected 61 Cygni for its record-setting proper motion. At the time, this was the strongest available proxy for nearness. It is still used today; the Gaia and Hipparcos samples of "nearest stars" are dominated by high-proper-motion stars. --- ## The negative-parallax history (not in this paper, but documented from his letters) Williams 1981 PhD thesis at Imperial College ("Attempts to Measure Annual Stellar Parallax — Hooke to Bessel") documents that Bessel's initial reductions of 61 Cygni, published in *Königsberger Beobachtungen* Volume III, gave **negative** parallaxes for: - 61 Cygni relative to six different comparison stars. - μ Cassiopeiae (negative but smaller). - 61 Cygni again in a third reduction using α Cygni as comparison — "an even larger negative result." Williams quotes Bessel's letter to Olbers: > "The negative parallax which one found here and there and which he had in fact found for the Pole Star from Bradley's observations was of course the result of observational errors." > [!critical] Bessel's "first stellar parallax" was preceded by his own negative results > The 1838 *Astronomische Nachrichten* paper is the fourth reduction, delivering a positive value after three earlier reductions had given negatives. Bessel handled this by privately attributing the negatives to observational error. The published record presents the 0.3136″ result as a clean detection; the archival correspondence shows the sign flipped three times before stabilising. This is not in the 1838 paper itself but is documented in his letters (Bessel-Olbers Briefwechsel, 2 vols., 1852, Internet Archive: https://archive.org/details/bub_gb_QefPAAAAMAAJ). --- ## Precedence note — Struve published first Struve at Dorpat published $\pi(\text{Vega}) = 0.125'' \pm 0.055''$ in *Mensurae Micrometricae* (1837), a year before Bessel. Reid & Menten 2020 ([[2020_Reid_Menten_First_Parallaxes_Revisited]]) show that Struve's 1837 value was closer to the modern Hipparcos value (0.129″) than his own 1840 revision (0.261″). The textbook credit for "first stellar parallax" goes to Bessel but the actual chronology is more complex. --- ## Instrument — the Königsberg heliometer Bessel used a Fraunhofer heliometer with a divided objective lens, enabling differential-angle measurements at the arcsecond level. This was the highest-precision astrometric instrument of the 1830s. The technique: measure the angular separation between 61 Cygni and nearby reference stars throughout the year; extract the annual sinusoidal component. --- ## Summary | Claim | Bessel (1838) | |---|---| | $\pi(61\text{ Cyg}) = 0.3136'' \pm 0.0202''$ | Yes, fourth reduction. | | First positive stellar parallax in textbook history | Yes. | | Bessel's first reductions were all positive | No. Prior negatives for 61 Cygni and μ Cas, dismissed as observational error. | | Bessel used the Copernican 2-AU-baseline definition | Yes, explicitly. | | Target selection was unbiased | No. Selected for record proper motion (proxy for proximity). | --- ## Citation Bessel, F. W., 1838. "Bestimmung der Entfernung des 61sten Sterns des Schwans." *Astronomische Nachrichten* 16, Nr. 365–366, cols. 65–96. English version: *Monthly Notices of the Royal Astronomical Society* 4, 152 (1838). Correspondence: Bessel-Olbers Briefwechsel (2 vols., 1852, ed. Erman). Internet Archive: https://archive.org/details/bub_gb_QefPAAAAMAAJ Local copy: . --- ## See also - [[2020_Reid_Menten_First_Parallaxes_Revisited]] - [[Shack_Chapter25_Negative_Parallax_Demystified]] - [[1921_Aitken_Recent_Parallax_Review]] - [[1943_Lee_Negative_Parallax]]