# What were the specifics of the photos taken by Sir Arthur Eddington during the Eddington expedition that supported Einstein's Theory

I know that Sir Arthur Eddington went to South American to photograph stars around an eclipse to see if they seemed to change position when the light past by the Sun relative to when the light didn't pass the Sun. My question is how many degrees did the stars appear off from normal, or if you prefer, how many degrees did the Sun bend the light from the stars that Eddington photographed. All I have been able to find thus far is :) "Sir Arthur Eddington went to South America, took pictures of the stars and showed that Einstein was right..." etc. etc. (:. Nowhere have been able to find even data that would allow me to determine the angle between the straight line the light followed from the stars to near the Sun and the straight line the light followed from the Sun to the Earth.

• en.wikipedia.org/wiki/Eddington_experiment For light grazing the surface of the Sun, the approximate angular deflection is roughly 1.75 arcseconds. Commented Jan 21 at 4:21
• (short answer, order 1 arcsec) This is a really interesting question (to me at least) because there's this factor of 2 that I can't follow. Wikipedia's Gravitational lensing gives expressions for the deflection $\theta$ at the Sun's limb of both $4GM/c^2r$ and $2GM/c^2r$, and Dyson 1920 give results from 0.93 to 1.98 arcseconds. This needs a careful, well-informed answer in order to sort out which plates and results to discuss and where these factors of 2 are coming from.
– uhoh
Commented Jan 21 at 4:56
• @PM2Ring just fyi someone "double-checked" :-) Gravitational Starlight Deflection Measurements during the 21 August 2017 Total Solar Eclipse This is interesting too: The Royal Observatory Greenwich's General Relativity and the 1919 Solar Eclipse as is The 1919 eclipse results that verified general relativity and their later detractors: a story re-told
– uhoh
Commented Jan 21 at 5:09
• @uhoh Note that GR predicts twice the deflection of Newtonian gravity (where we treat photons as particles of negligible non-zero mass). Since that approximate deflection equation is linear, we also get that the deflection is ~1 arcsec at 1.75 solar radii. The exact deflection calculation uses an incomplete elliptic integral of the first kind; that integral also arises in the exact solution of the motion of a simple pendulum. Commented Jan 21 at 5:59
• @uhoh I suppose I should've said that the deflection equation is linear in 1/r. With Schwarzschild stuff, I tend to think in terms of $\frac{r_s}r$. ;) Commented Jan 21 at 16:52

The (General-Relativistic) prediction of the size of the deflection for stars measured close to the limb of the Sun is $$1.75(R_\odot/r)$$ arcseconds, where $$R_\odot$$ is the solar radius and $$r$$ is the projected radius of the star (i.e. as it appears) from the centre of the Sun.
Longair (2015) reviews the expeditions of 1919. He reports that the Principe results, were equivalent to a deflection (at the limb of the Sun) of $$1.61 \pm 0.31$$ arcseconds, based mainly on measurements of 2 stars. Looking at the original paper by Dyson (1920), the result appears to be quoted as $$1.61 \pm 0.30$$ arcsec and is based on measurements of 6 stars at approximately 0.5-1.5 degrees from the centre of the Sun (corresponding approximately to $$2 < r/R_\odot < 6$$), though not all stars were measured on all photographs, with measured deflections of up to about 1 arcsecond. In both cases, the uncertainty quoted is the "probable error"; a reanalysis of the data by Gilmore & Tausch-Pebody (2022) puts the deflection result at $$1.61 \pm 0.45$$ arcseconds, where the error bar is the more conbentional standard deviation.
The South American results were better, getting measurements of 7 stars at separations of 0.5-1.5 degrees from the centre of the Sun, with measured deflections of 1.0 -0.2 arcseconds respectively. Fitting a straight line to a graph of deflection vs $$1/r$$ (see the copyrighted Fig.2 in the Longair review) gave a deflection at the limb result of $$1.98 \pm 0.12$$ arcseconds (Gilmore & Tausch-Pebody report $$1.98 \pm 0.18$$ arcseconds).