<p>As you can read <a href="https://en.wikipedia.org/wiki/Eddington_experiment" rel="nofollow noreferrer">here</a>, Eddington led the expedition to the island of Principe off W Africa and did not go to South America.</p>
<p>The (General-Relativistic) prediction of the size of the deflection for stars measured close to the limb of the Sun is <span class="math-container">$1.75(R_\odot/r)$</span> arc<em>seconds</em>, where <span class="math-container">$R_\odot$</span> is the solar radius and <span class="math-container">$r$</span> is the projected radius of the star (i.e. as it appears) from the centre of the Sun.</p>
<p><a href="https://royalsocietypublishing.org/doi/10.1098/rsta.2014.0287" rel="nofollow noreferrer">Longair (2015)</a> reviews the expeditions of 1919. He reports that the Principe results, were equivalent to a deflection (at the limb of the Sun) of <span class="math-container">$1.61 \pm 0.31$</span> arcseconds, based mainly on measurements of 2 stars. Looking at the original paper by <a href="https://w.astro.berkeley.edu/%7Ekalas/labs/documents/dyson1920.pdf" rel="nofollow noreferrer">Dyson (1920)</a>, the result appears to be quoted as <span class="math-container">$1.61 \pm 0.30$</span> 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 <span class="math-container">$2 &lt; r/R_\odot &lt; 6$</span>), 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 &quot;probable error&quot;; a reanalysis of the data by <a href="https://royalsocietypublishing.org/doi/10.1098/rsnr.2020.0040" rel="nofollow noreferrer">Gilmore &amp; Tausch-Pebody (2022)</a> puts the deflection result at <span class="math-container">$1.61 \pm 0.45$</span> arcseconds, where the error bar is the more conbentional standard deviation.</p>
<p>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 <span class="math-container">$1/r$</span> (see the copyrighted Fig.2 in the Longair review) gave a deflection at the limb result of <span class="math-container">$1.98 \pm 0.12$</span> arcseconds (Gilmore &amp; Tausch-Pebody report <span class="math-container">$1.98 \pm 0.18$</span> arcseconds).</p>

CC BY-SA 4.0
2024-01-22T10:19:52.870Z
There is also more recent discussion of the 1919 results (open access): https://royalsocietypublishing.org/doi/10.1098/rsnr.2020.0040
Leos Ondra
CC BY-SA 4.0
2024-01-21T14:43:03.287Z
2024-01-22T13:03:28.303Z
2024-01-22T13:03:28.303Z
ProfRob
<p>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 :) &quot;Sir Arthur Eddington went to South America, took pictures of the stars and showed that Einstein was right...&quot; 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.</p>

CC BY-SA 4.0
2024-01-21T04:21:16.467Z
https://en.wikipedia.org/wiki/Eddington_experiment For light grazing the surface of the Sun, the approximate angular deflection is roughly 1.75 arcseconds.
PM 2Ring
CC BY-SA 4.0
2024-01-21T04:56:53.100Z
(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](https://en.wikipedia.org/wiki/Gravitational_lens) gives expressions for the deflection $\theta$ at the  Sun's limb of both  $4GM/c^2r$ and $2GM/c^2r$, and [Dyson 1920](https://w.astro.berkeley.edu/~kalas/labs/documents/dyson1920.pdf) 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
CC BY-SA 4.0
2024-01-21T05:09:54.213Z
@PM2Ring just fyi someone "double-checked" :-) [Gravitational Starlight Deflection Measurements during the 21 August 2017 Total Solar Eclipse](https://arxiv.org/abs/1802.00343) This is interesting too: The Royal Observatory Greenwich's [General Relativity and the 1919 Solar Eclipse](http://www.royalobservatorygreenwich.org/articles.php?article=1283) as is [The 1919 eclipse results that verified general relativity and their later detractors: a story re-told](https://royalsocietypublishing.org/doi/10.1098/rsnr.2020.0040)
uhoh
CC BY-SA 4.0
2024-01-21T05:12:38.643Z
@PM2Ring  and [Gravitational Starlight Deflection Measurements during the 21 August 2017 Total Solar Eclipse](https://arxiv.org/abs/0709.0685)
uhoh
CC BY-SA 4.0
2024-01-21T05:57:04.767Z
@uhoh As I mention [here](https://astronomy.stackexchange.com/a/49874/16685), the deflection angle (in radians) is approximately $\theta = \frac{2r_s}b$, where $b$ is the impact parameter and $r_s$ is the Schwarzschild radius $r_s=2GM/c^2$. You can use $r$, the distance of closest approach instead of $b$; it doesn't make much difference in the regime where that formula is valid.
PM 2Ring
CC BY-SA 4.0
2024-01-21T05:59:21.250Z
@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.
PM 2Ring
CC BY-SA 4.0
2024-01-21T16:52:28.450Z
@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 $\frac{r_s}r$. ;)
PM 2Ring
CC BY-SA 4.0
2024-01-21T22:10:32.767Z
@PM2Ring OK, so it's unfortunate that for early experimental results, some observations agreed with $r_s/b$ and others agreed with $2r_s/b$. I'm looking at https://i.sstatic.net/1Qsto.png (from [here](http://www.royalobservatorygreenwich.org/articles.php?article=1283)) which looks like the plot on p. 332 of [Dyson et al. 1920](https://w.astro.berkeley.edu/~kalas/labs/documents/dyson1920.pdf) which show the Einstein prediction of about 1 arcsecond at 30 arcminutes from the center of the Sun, not 1.8 arseconds.
uhoh
CC BY-SA 4.0
2024-01-21T22:13:59.513Z
@PM2Ring If that "Einstein" line is [his 1911 prediction](https://en.wikipedia.org/wiki/Gravitational_lens#History) then that would make sense, but isn't that what's labeled "Newton" in the plot? This plot confuses the hell out of me!
uhoh
CC BY-SA 4.0
2024-01-22T07:07:42.937Z
@uhoh Yes, the deflection was almost 1 arcsec at 30 arcmin from the solar centre. Exactly as GR predicts. 30 arcmin is $b = 2R_\odot$.
ProfRob
CC BY-SA 4.0
2024-01-22T07:46:04.090Z
@ProfRob Ah, thank *you for that!* :-)
uhoh
CC BY-SA 4.0
2024-09-17T04:53:02.820Z
I've never fully understood the eclipse measurement and what is being measured on the image. Can anyone explain or point me to a breakdown of: did they measure the distance of the star on the plate from the limb of the Sun, from another star on the plate? What kind of actual distance were they measuring (mm) on the plate? Were the stars not supposed to be visible at all and be blocked by the sun, were it not for lensing?  How did they know how closely the light passed by the sun?
RC_23
<observational-astronomy><star><the-sun><telescope>
What were the specifics of the photos taken by Sir Arthur Eddington during the Eddington expedition that supported Einstein's Theory
Elliott Cooper
# What were the specifics of the photos taken by Sir Arthur Eddington during the Eddington expedition that supported Einstein's Theory

(Asked by: username_0 on 2024-01-21)

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.

**Tags:** observational-astronomy, star, the-sun, telescope

> **Comments:**
> **username_1**: https://en.wikipedia.org/wiki/Eddington_experiment For light grazing the surface of the Sun, the approximate angular deflection is roughly 1.75 arcseconds.  
> **username_2**: (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](https://en.wikipedia.org/wiki/Gravitational_lens) gives expressions for the deflection $\theta$ at the  Sun's limb of both  $4GM/c^2r$ and $2GM/c^2r$, and [Dyson 1920](https://w.astro.berkeley.edu/~kalas/labs/documents/dyson1920.pdf) 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.  
> **username_2**: @PM2Ring just fyi someone "double-checked" :-) [Gravitational Starlight Deflection Measurements during the 21 August 2017 Total Solar Eclipse](https://arxiv.org/abs/1802.00343) This is interesting too: The Royal Observatory Greenwich's [General Relativity and the 1919 Solar Eclipse](http://www.royalobservatorygreenwich.org/articles.php?article=1283) as is [The 1919 eclipse results that verified general relativity and their later detractors: a story re-told](https://royalsocietypublishing.org/doi/10.1098/rsnr.2020.0040)  
> **username_2**: @PM2Ring  and [Gravitational Starlight Deflection Measurements during the 21 August 2017 Total Solar Eclipse](https://arxiv.org/abs/0709.0685)  
> **username_1**: @username_2 As I mention [here](https://astronomy.stackexchange.com/a/49874/16685), the deflection angle (in radians) is approximately $\theta = \frac{2r_s}b$, where $b$ is the impact parameter and $r_s$ is the Schwarzschild radius $r_s=2GM/c^2$. You can use $r$, the distance of closest approach instead of $b$; it doesn't make much difference in the regime where that formula is valid.  
> **username_1**: @username_2 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.  
> **username_1**: @username_2 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 $\frac{r_s}r$. ;)  
> **username_2**: @PM2Ring OK, so it's unfortunate that for early experimental results, some observations agreed with $r_s/b$ and others agreed with $2r_s/b$. I'm looking at https://i.sstatic.net/1Qsto.png (from [here](http://www.royalobservatorygreenwich.org/articles.php?article=1283)) which looks like the plot on p. 332 of [Dyson et al. 1920](https://w.astro.berkeley.edu/~kalas/labs/documents/dyson1920.pdf) which show the Einstein prediction of about 1 arcsecond at 30 arcminutes from the center of the Sun, not 1.8 arseconds.  
> **username_2**: @PM2Ring If that "Einstein" line is [his 1911 prediction](https://en.wikipedia.org/wiki/Gravitational_lens#History) then that would make sense, but isn't that what's labeled "Newton" in the plot? This plot confuses the hell out of me!  
> **username_3**: @username_2 Yes, the deflection was almost 1 arcsec at 30 arcmin from the solar centre. Exactly as GR predicts. 30 arcmin is $b = 2R_\odot$.  
> **username_2**: @username_3 Ah, thank *you for that!* :-)  
> **username_4**: I've never fully understood the eclipse measurement and what is being measured on the image. Can anyone explain or point me to a breakdown of: did they measure the distance of the star on the plate from the limb of the Sun, from another star on the plate? What kind of actual distance were they measuring (mm) on the plate? Were the stars not supposed to be visible at all and be blocked by the sun, were it not for lensing?  How did they know how closely the light passed by the sun?  

---

## 1 answers

### Answer by username_3 on 2024-01-21. Score: 9

As you can read [here](https://en.wikipedia.org/wiki/Eddington_experiment), Eddington led the expedition to the island of Principe off W Africa and did not go to South America.

The (General-Relativistic) prediction of the size of the deflection for stars measured close to the limb of the Sun is $1.75(R\_\odot/r)$ arc*seconds*, 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)](https://royalsocietypublishing.org/doi/10.1098/rsta.2014.0287) 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)](https://w.astro.berkeley.edu/%7Ekalas/labs/documents/dyson1920.pdf), 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)](https://royalsocietypublishing.org/doi/10.1098/rsnr.2020.0040) 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).

> **Comments:**
> **username_5**: There is also more recent discussion of the 1919 results (open access): https://royalsocietypublishing.org/doi/10.1098/rsnr.2020.0040  

---

