Auwers and the Legacy of 959.63″

The canonical value of the solar radius—959.63 arcseconds at one astronomical unit—has underpinned eclipse, transit, and ephemeris calculations for over a century. It has appeared in ephemerides, eclipse predictions, and even modern IAU conventions, long after the original observations ceased to influence modern measurement practice.

The number owes its authority not to direct measurement, but to the 1891 synthesis by Arthur Auwers[1] (12 Sep 1838 – 24 Jan 1915), who sought to reconcile an unruly mass of 19th-century solar observations into a single consistent standard. For its time, the result was a model of diligence and reason; for ours, it has become an artifact of historical continuity.

1. The Context of Auwers’ Work

By the late 1800s, the solar diameter was one of the most uncertain constants in astronomy. Visual observations showed disagreements of several arcseconds, and were heavily dependent on instrument design and atmospheric conditions. Micrometric observers measured the separation of opposite limbs through differential refraction and diffraction; meridian observers inferred the value from the duration of solar transits across the wires of a fixed circle; eclipse observers timed the instants of contact between the lunar limb and the solar edge.

Each method carried systematic biases, and the lack of a consistent limb definition made reconciliation nearly impossible. (For example, we read of “edge of the photosphere” vs. “inflection point (the maximum slope location of the limb’s intensity profile, near optical depth τ≈1)” vs. “visual terminator”.)

Auwers—then a leading figure at the Berlin Observatory and one of the intellectual heirs of Bessel’s precision tradition—undertook to impose order on this chaos. He assembled a comprehensive catalogue of published solar diameter determinations reaching back nearly a century.

Auwers’ compilation represented an extraordinary act of scholarship. He collected results from meridian transits, heliometric limb determinations, eclipse contact timings, and micrometric measures—each executed with instruments of varying design and precision, across multiple epochs and observatories. At a time when international data exchange relied on letters and printed bulletins, his ability to assemble and normalize so many records was a feat of coordination and mathematical perseverance.

Few individuals of the era were as qualified to undertake such a synthesis, and his effort genuinely advanced the stability and internal consistency of late-19th-century solar work.

Among the datasets he analyzed were:
• Bessel’s heliometer measures from Königsberg (1820s), among the earliest high-precision differential determinations.
• Klinkerfues’ Göttingen series using the Fraunhofer heliometer.
• Gambart’s meridian circle observations from Paris and Marseille, derived from transit durations.
• Eclipse-contact timings from 1842, 1860, and later events, reduced to angular diameters using the best available lunar ephemerides.
• Piazzi-Smyth’s and Auwers’ own measures of the apparent solar diameter with improved micrometers.

The sheer scope of this compilation was astonishing for its time: dozens of observers, differing optical systems, multiple epochs, and varied reduction methods—all reduced to a single comparative frame.

2. The Averaging Procedure

Auwers’ method was not a simple numeric mean, but a two-stage synthesis. He first computed internal means for each class of observation—grouping by method and epoch—to reduce random scatter within homogeneous subsets. He then formed an overall mean of those group means to obtain a final value for the solar radius.

Importantly, Auwers did not treat all results as equal; he introduced what he called Glaubwürdigkeit—literally, “belief-worthiness”, or a quantifiable measure of credibility. Datasets judged as more reliable (for instance, heliometer series with well-controlled focus and temperature) were assigned greater influence on the final mean values. Those considered doubtful or inconsistent were down-weighted or even excluded entirely.

In modern language, his procedure amounted to a subjective weighting scheme, guided by experience rather than statistical uncertainty. No formal least-squares adjustment or variance propagation was performed, but the underlying intent—to reward internal consistency and observational care—was sound.

The outcome of this layered averaging process was the figure R_⊙ = 959″.63 at 1 au.

This was, as Auwers noted, an “empirical compromise”—a value that harmonized the best 19th-century measurements into a single scale suitable for general astronomical use.

3. Strengths and Limitations

For its era, the Auwers synthesis represented a triumph of organization and reasoned judgment. He recognized the dangers of mixing incompatible observations, and his credibility weights were an early step toward formal data curation. The resulting constant gave late-Victorian astronomy its first reliable solar scale, stabilizing planetary ephemerides and eclipse predictions for decades.

Yet the same features that made his result practical also limit its scientific validity today.

• Heterogeneous Data. The input measurements came from fundamentally different instruments and definitions of the solar limb. Some observers measured the visual terminator, others the inflection point, and others the outer intensity fall-off—all wavelength-dependent and seeing-dependent phenomena.

• Subjective Weighting. The credibility scores were based on perceived reliability rather than quantified errors. Two datasets of vastly different precision might receive similar weights if both seemed “trustworthy.”

• Systematic Correlations. Several of Auwers’ input series shared common reductions or reference stars, and produced implicit correlations which the final mean treated as independent.

• Atmospheric and Diffraction Effects. No explicit corrections were made for “seeing”, refraction gradients, or instrumental point-spread functions. Each of these shifts the apparent solar edge by up to several tenths of an arcsecond.

• Limb Definition Ambiguity. Auwers’ radius referred to the outer visible limb in white light as judged by eye. Modern radii, derived from inflection-point photometry or CCD limb profiles, measure a physically distinct level in the solar atmosphere.

Despite these limitations, Auwers’ result was remarkably consistent internally. It agreed with earlier heliometer measures to within their quoted scatter and yielded solar semi-diameters between 959.5″ and 959.7″—comfortably within the observational noise of his time. Its persistence owed much to that internal harmony, and to the stability it lent to ephemerides.

4. Institutional Adoption and Enduring Authority

The value 959.63″ quickly became the standard solar radius. It was used in national ephemerides and was eventually codified by the International Astronomical Union. Its utility lay in continuity: by fixing a stable angular radius, astronomers could avoid re-reducing historical observations and maintain consistency in published tables. Through this institutional reinforcement, the Auwers radius passed essentially unchanged through the 20th and into the 21st century.

But this endurance should not be mistaken for validation. The constant’s authority is historical, not physical. It represents a century-old observational consensus, not a measurement grounded in modern radiometry or astrometry, as we shall soon see.

5. Modern Re-evaluation

Since the mid-20th century, increasingly precise methods—photoelectric scanning, CCD limb imaging, flash spectroscopy readings, spacecraft photometry, and planetary transits—have re-measured the Sun’s apparent radius with milliarcsecond precision. Results from SODISM/PICARD, SOHO, and eclipse-derived limb profiles generally cluster near 959.90″–959.97″ at 1 au, depending on wavelength and limb definition. These determinations are reproducible, wavelength-specific, and physically defined at the inflection point of the limb’s intensity profile.

They also collectively demonstrate that the historical Auwers radius of 959.63″ corresponds to a smaller Sun—about 0.3 arcseconds, or roughly 200–250 km, below the true inflection-point level—an offset entirely consistent with the visual limb’s inward displacement caused by atmospheric and diffraction effects.

Researchers such as Meftah, Emilio, and most notably Quaglia et al. have revisited this issue with modern instrumentation and metrological rigor. Their findings confirm that the Auwers radius is systematically too small, not because of arithmetic error, but because its observational definition captured an optical edge located below the physical photosphere.

6. The work of Luca Quaglia and his team

Among the most compelling modern reassessments is the work of Luca Quaglia (2021), who along with his team, applied high-speed spectroscopic imaging to total solar eclipses while observing from the literal edge of the path. At several eclipses, this team systematically captured the flash spectrum—which is spectroscopy captured during the brief interval when the photosphere disappears and the chromosphere becomes visible. By analyzing thousands of frames, Quaglia and his team determined the precise inflection point of the solar limb across multiple wavelengths, free from atmospheric seeing and instrumental blurring. Because each contact event effectively samples the solar edge tangentially along a known lunar topography, his technique converts eclipse timing and chromospheric emission gradients into a direct geometrical radius measurement tied to the physical photospheric boundary. The resulting solar semidiameter—959.94 ± 0.02 arcseconds at 1 au—agrees with spacecraft determinations (PICARD, SOHO) and confirms that the historical Auwers value underestimates the true photospheric radius by roughly 0.3 arcseconds (≈ 220 km of solar radius). Quaglia’s method is compelling precisely because it bridges the classical and the modern: it uses the same natural experiment that guided 19th-century eclipse observers, but applies modern metrology and lunar-profile modeling to extract a physically defined, reproducible solar radius.

Quaglia’s results gain additional force from replication across multiple eclipses—notably the 2017, 2019, 2020 and 2024 TSEs, as well as the 2023 annular eclipse—each analyzed with independently calibrated optical trains and lunar topographic models. The derived radii are mutually consistent to within a few hundredths of an arcsecond, a level of agreement unmatched by any ground-based photometric method. This convergence has led to broad and increasing acceptance within the solar-radius research community, where the flash-spectrum approach is now recognized as a benchmark for defining the photospheric edge under real observing conditions.

Equally important, Quaglia’s values corroborate spacecraft photometry from PICARD and SOHO, empirically demonstrating that the visual-limb depression inferred from 19th-century observations corresponds almost exactly to the expected radiative transfer offset between the optical limb and the inflection layer. In uniting eclipse geometry, spacecraft radiometry, and atmospheric modeling, Quaglia has provided the first truly self-consistent observational confirmation of the Sun’s modern radius—an elegant extension of the process that Auwers began more than a century ago.

7. Implications for Eclipse Predictions

At first glance, increasing the solar radius by only about 200 km seems inconsequential—less than one-thirtieth of one percent. Yet during a total solar eclipse, that small change propagates through the entire geometry of the umbral cone. At mean Earth–Moon and Earth-Sun distances, a 200 km increase in the Sun’s physical radius shifts the limits of totality by up to several tens of meters on Earth’s surface. For earlier generations of astronomers, this was absolutely inconsequential. Timing uncertainties, imperfect lunar profiles, travel and logistical considerations, and locating the entourage near the center of the eclipse path dominated the planning by orders of magnitude. Expeditions would never camp on the very edge of the path; their concern was duration, not finding boundaries.

This was because very second of totality mattered: observers planned intricate photographic sequences, spectroscopic exposures, and polarimetric measurements that had to be completed prior to third contact[2]. To these observers, maximizing those few fleeting seconds was the difference between success and failure. Being located near the centerline was a necessity, and more easily forgave slight errors in positional reckoning. Being located near the edge of the path was simply not an option.

One of the greatest limitations for early expeditions lay in knowing one’s position at all. Determining latitude was straightforward with a sextant, but longitude required time, and accurate timekeeping was a difficult art in field astronomy. Before radio signals and GPS, observers synchronized chronometers by telegraph, or by exchanging star-transit timings. These introduced errors of potentially several seconds of time—hundreds of meters on the ground. Even in the late nineteenth century, expeditions might not know their exact longitude to better than a quarter of a mile.

Today, those limitations have vanished. GPS positioning routinely yields sub-meter-level accuracy, and modern eclipse predictions track the shadow’s motion to within fractions of a second. In that context, the Sun’s extra 200 km of physical radius, small as it sounds, becomes meaningful: the corresponding tens of meters on Earth’s surface are now well within the precision of eclipse maps, and of observers’ ability to determine their coordinates. What was once a theoretical refinement now shapes real experience. Every meter influences the sequence of contacts, the timing of Baily’s beads, and the appearance of the chromosphere.

Auwers’s contemporaries could ignore these effects; they stood deep within the path. But for today’s travelers and residents who find themselves exactly on the edge of that path, those few meters determine whether the Sun truly vanishes or remains as a sliver of light. Even at this scale, the physical size of the Sun continues to govern the geometry, timing, and human perception of totality.

8. Perspective and Legacy

To judge Auwers by today’s standards would be unfair; to continue relying on his number would be unscientific. He accomplished what few others could: he imposed coherence on chaos, uniting heliometric, meridian, and eclipse observations into a single solar scale that stabilized celestial mechanics for generations. His 959.63″ value became a conventional standard—useful not because it was exact, but because it was consistent, the astronomical equivalent of the meter convention: a reference that enabled progress even before the underlying physics was fully understood.

The modern era has replaced consensus with calibration. Spaceborne photometry and eclipse spectroscopy now resolve the Sun’s limb with milliarcsecond precision, confirming a radius about 0.3″ larger than Auwers’s figure. Yet this refinement fulfills, rather than refutes, his purpose: to establish order, stability, and continuity in solar astronomy. The persistence of his constant made it possible for modern metrology to measure, at last, what he could only approximate.

The Auwers radius endures as both a milestone and a memorial—an artifact of the transition from visual judgment to physical definition. Its historical role is complete. To retire it from operational use is not to diminish his achievement, but to complete it: to replace convention with measurement, and to honor the insight and intellect that first brought precision to the Sun’s elusive edge.

Appendix — The meaning of “arcseconds at 1 au”

 

When we say that the Sun’s apparent semidiameter is 959.63 arcseconds at 1 au, we are describing its angular size as it would appear to an observer located exactly one astronomical unit from the Sun’s center.

An arcsecond (″) is 1/3600 of a degree; therefore 959.63″ = 0.266563°.
At a distance of 1 au, an angular radius of 959.63″ corresponds to a linear solar radius of:

Thus, “so many arcseconds at 1 au” is shorthand for “the apparent angular radius the Sun would subtend for an observer exactly one astronomical unit away.”

Definition of the astronomical unit

Based on Newcomb’s 1895 theory (and solar parallax value of 8.80″), the astronomical unit In Auwers’ time corresponded roughly to 149 597 870 ± 100 km. This was essentially identical to the modern value for practical work, but conceptually defined through the Gaussian gravitational constant rather than a fixed meter value. This value was maintained through the IAU 1964 convention.

A century after Auwers, digital sensors and absolute metrology revisited the problem with repeatable, wavelength-specific measurements tied to explicit limb definitions.

According to the current IAU 2012 Resolution B2, 1 au = 149 597 870 700m exactly.

It is a conventional length unit, not the Earth–Sun distance on any given day, but an adopted constant that once represented the mean semimajor axis of the Earth’s orbit. (The reader will also note the obligatory use of lower-case letters in the unit’s abbreviation.)

Earth’s perigee and apogee (distance extremes)

Because Earth’s orbit is slightly elliptical (eccentricity ≈ 0.0167), its distance from the Sun varies between:

Perihelion (early January)	≈ 147 098 000 km	≈ 0.983 au
Aphelion (early July)	≈ 152 098 000 km	≈ 1.017 au

The apparent solar semidiameter for an Earth-based observer consequently varies by roughly ±1.7 %, from about 943″ at aphelion to 975″ at perihelion.

References

Meftah, M., Corbard, T., Hauchecorne, A., et al. (2018). “Solar radius determined from PICARD/SODISM observations and extremely weak wavelength dependence in the visible and the near‐infrared.”
DOI: 10.1051/0004-6361/201732159 A&A Journal

Quaglia, L. et al. (2021). “Estimation of the Eclipse Solar Radius by Flash Spectrum Video Analysis.”
DOI: 10.3847/1538-4365/ac1279 ADS

Emilio, M., Kuhn, J. R., Bush, R. I., Scholl, I. (2012). “Measuring the Solar Radius from Space during the 2003 and 2006 Mercury Transits.”
Preprint / arXiv version: arXiv:1203.4898 arXiv
DOI: 10.1088/0004-637X/750/2/135