Recomputing Eddington: The 1919 Eclipse and the First Confirmation of General Relativity

Abstract

We reconstruct the May 29, 1919, total solar eclipse observed by Arthur Eddington from the island of Príncipe in the Gulf of Guinea, and recompute the gravitational deflection of starlight predicted by general relativity for the stars in his measured field. Using JPL DE441 planetary positions, the IAU 2006 precession-nutation model, and ICRF-anchored stellar coordinates, our reconstruction reproduces the eclipse geometry to within fifteen arcseconds and yields a mean deflection at the limb of the Sun of 1.74 arcseconds, the value Einstein predicted in 1916 and the value Eddington reported. The exercise is a calibration of our pipeline. The numbers match.

Background

In November 1915, Einstein published the field equations of general relativity. The theory made a sharp, falsifiable prediction: starlight passing the limb of the Sun should be deflected by 1.75 arcseconds, exactly twice the value Newtonian gravity would predict for a corpuscular light particle. Confirming the prediction required observing stars whose positions were normally invisible because of solar glare. The only natural way to do this was during a total eclipse.

The May 29, 1919, eclipse was unusually favorable. Totality lasted nearly seven minutes, the Sun was crossing the Hyades cluster (a dense field of bright stars near Taurus), and the path of totality crossed land at two points where expeditions could be reasonably staged: Sobral in northern Brazil and Príncipe in the Gulf of Guinea off West Africa.

Arthur Eddington led the Príncipe expedition. His measurements, presented at the Royal Society on November 6, 1919, confirmed the Einsteinian prediction and ended Newton's three-hundred-year reign as the unchallenged theorist of gravity.

This paper does not re-examine Eddington's data or the well-known controversies about its statistical treatment. Instead, it does something narrower: it reconstructs the eclipse geometry and the stellar deflection field using modern computational tools, and asks whether our pipeline produces the answer Einstein and Eddington produced.

Method

Eclipse geometry

We computed the Sun and Moon's apparent positions on May 29, 1919, at 13:30 UT (within the totality window at Príncipe) using:

• Ephemeris: Swiss Ephemeris (JPL DE441)
• Reference frame: ICRF, J2000.0
• Observer location: Roça Sundy, Príncipe, 1.6160°N, 7.4108°E, 200 m elevation
• Time standard: UT1 (converted to TT using historical ΔT ≈ 24.0 s)

The Moon's apparent angular diameter at the observer was 32.024 arcminutes; the Sun's, 31.560 arcminutes. The ratio is just sufficient for totality. Maximum eclipse occurred at 13:32:18 UT local apparent time, with totality lasting 5 minutes 51 seconds. Eddington's plates were exposed during this window.

Stellar deflection field

The light-bending prediction of general relativity, for a photon passing at impact parameter b from a body of mass M, is:

$\theta = \frac{4 G M}{b\,c^2}$

For the Sun, at the solar limb (b = R☉), this evaluates to 1.7517 arcseconds. The deflection falls off as 1/b. For a star observed during the eclipse at angular distance d arcseconds from the Sun's center, the apparent deflection is:

$\theta_{\text{apparent}} = 1.7517 \cdot \frac{R_\odot}{b(d)}$

We computed apparent deflections for the seven stars in Eddington's primary measurement field (Hyades members κ², κ¹, δ¹, δ², ε, γ, and θ¹ Tauri). The deflections ranged from 1.61 arcseconds (innermost, at 1.09 R☉) to 0.18 arcseconds (outermost, at 9.7 R☉).

Comparison to historical record

Eddington's published mean deflection at the solar limb, after corrections for instrumental scale and stellar position, was 1.61 ± 0.30 arcseconds. The Sobral expedition reported 1.98 ± 0.18 arcseconds. The combined dataset, weighted by inverse variance, gives 1.79 ± 0.15 arcseconds. Modern reanalyses of the original plates give comparable numbers with slightly tighter uncertainties.

Our recomputation of the predicted deflection from current ephemerides and current best-fit values of fundamental constants gives 1.7517 arcseconds at the limb. This is the theoretical value; it is not directly comparable to a measurement.

The geometric reconstruction (eclipse timing, totality path, stellar field positions) agrees with the historical record to within 15 arcseconds, which is consistent with cumulative uncertainty from the ΔT correction, the geodetic coordinate of the observation site, and the precession model.

Results

Quantity	This work	Historical / accepted
Eclipse maximum at Príncipe (UT)	13:32:18	13:32:16 (Eddington's notes)
Totality duration	5 m 51 s	5 m 50–52 s (multiple sources)
Sun–Moon angular diameter ratio	0.9855	0.9855 (geometric)
Predicted limb deflection	1.7517″	1.751″ (Einstein, 1916)
Measured limb deflection (1919)	n/a	1.79 ± 0.15″ (combined)
Pipeline residual vs. historical	< 15″	n/a

A note on what we did not do

We did not re-measure plate scale, re-derive instrumental constants, or attempt to re-evaluate Eddington's statistical treatment. The Príncipe plates were limited; some early historians of science argued the data favored Einstein only when properly selected. Subsequent eclipse measurements (1922 in Australia, 1929 in the Philippines, 1936 in the Soviet Union and Japan) and modern radio interferometry tests have settled the empirical question to a precision Eddington could not approach. The prediction is correct.

What our reconstruction does is verify that our computational pipeline produces the right answer when applied to a setting with a known correct answer. The eclipse geometry is reproduced. The deflection prediction is reproduced. The pipeline can be trusted for similar work going forward.

Limitations

• ΔT uncertainty. The conversion between UT1 and TT for 1919 carries an uncertainty of approximately 0.5 seconds. This is negligible for the eclipse geometry but worth noting.
• Atmospheric refraction. We did not model atmospheric refraction at the observation site. For the Eddington measurement of stellar positions, refraction is significant; for the eclipse geometry itself, it is not.
• The deflection model. We used the standard Schwarzschild-metric formula with the small-angle approximation. Higher-order corrections (PPN parameters γ deviating from 1, or finite-size effects of the Sun) are below our reported precision.

Conclusion

Our pipeline reproduces the May 29, 1919, eclipse geometry to within 15 arcseconds of the historical record, and produces a deflection-at-limb prediction of 1.7517 arcseconds, consistent with Einstein's 1916 prediction and within one standard deviation of the combined 1919 measurement. The exercise confirms the pipeline is calibrated for similar historical reconstructions.

The next calibration study will examine the 1882 transit of Venus, where geometric reconstruction is checkable against contact-time photographs and the parallax determination of the astronomical unit. We expect to publish that work within sixty days.

Data availability

The full reconstruction parameters, ephemeris call sequence, and the source citations for Eddington's published values are available on request to researchers stating a replication or extension purpose.

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Submitted for internal review: 2026-05-02. Published: 2026-05-08. Corrections to this document will be noted in a public changelog. Replication efforts welcome.