Physics of the 1919 Eclipse

Equivalent forms

newtonian half

\theta_{Newton} = \frac{2GM_\odot}{c^2 R_\odot} = 0.87''

general

\theta = \frac{4GM}{c^2 b}

A wartime eclipse expedition turned an abstract field equation into front-page proof that gravity bends light.

Symbol	Name	SI unit	Dimension	Range
$\theta$	light deflection angleoutput	arcsec	1	—
$M_\odot$	solar mass	1.99e30 kg	M	—
$R_\odot$	solar radius (impact parameter)	6.96e8 m	L	—
$c$	speed of light	2.998e8 m/s	L T^{-1}	—

Discovery

Arthur Eddington / Frank Dyson · 1919

Astronomer Royal Frank Dyson organized two expeditions — Eddington to Principe, Crommelin to Sobral, Brazil. Measuring the eclipse star field against night-time reference plates, they found a deflection at the solar limb consistent with Einstein's 1.75 arcsec, not Newton's 0.87. The 6 November 1919 announcement made headlines worldwide.

Research status: stable

Real-world applications

Established GR experimentally and made gravitational lensing a usable tool.
Modern radio interferometry (VLBI) of quasars near the Sun confirms the deflection $to \sim 0.01$ %.
The same physics magnifies distant galaxies and weighs dark matter via lensing.

Common misconceptions

'Newton predicted no bending.' — A naive corpuscle theory gives half the GR value; GR's extra factor is the test.
'Eddington's data was conclusive on its own.' — The 1919 plates were noisy; later eclipses and VLBI cemented it.
'Light is pulled like a thrown ball.' — The deflection includes spatial curvature, not just a Newtonian pull.

Experimental verification

1919 eclipse (Principe/Sobral); repeated at many eclipses through 1973; VLBI quasar deflection confirms

4GM/c^2\,\mathrm{R} to \sim 10^-4 (PPN \gamma = 1)

.

Derivation

A Newtonian 'corpuscle' grazing the Sun deflects by $2GM/(c^2\,\mathrm{R}) = 0.87$ arcsec (Soldner, 1801).
General relativity adds an equal contribution from the curvature of space, doubling it to 4GM/(c^2 R).
Plug in solar values: $4*6.674e-11*1.99e30/((9e16)(6.96e_{8})) \sim 8.5e-6\,\mathrm{rad}$ .
Convert: 8.5e-6 rad * 2.06e5 arcsec/ $rad \sim 1.75$ arcsec.
Stars appear displaced radially outward from the Sun by this angle, largest at the limb.

Limiting cases

b = R_sun

(limb)⟶

\theta = 1.75

arcsecMaximum measurable deflection.

b >> R_sun⟶ theta -> 0 as 1/bDistant rays are barely bent.

What if…

What if Newton had been right?

The shift would be only 0.87 arcsec; the eclipse data favored the doubled GR value.

What if the star were far from the limb?

Deflection $\sim 1/b$ falls off, so stars far from the Sun shift negligibly — only grazing rays bend most.

1

Deflection at the solar limb

Given ·

M = 1.99e30\,\mathrm{kg}

,

b = R_sun = 6.96e_{8} m

.

Find · Deflection angle in arcseconds

Steps

$4GM/c^2 = 4*6.674e-11*1.99e30/9e16 = 5.9e14\,\mathrm{m}$ .
$\theta = 5.9e14 / 6.96e_{8} = 8.48e-6\,\mathrm{rad}$ .
* 206265 arcsec/ $rad = 1.75$ arcsec.

Result · 1.75 arcseconds — Einstein's value, twice the Newtonian prediction.

General Relativity: Light Bending & Curved Spacetime→Gravitational Lensing & the Einstein Radius→Shapiro Time Delay (Fourth Test of GR)→Schwarzschild Radius→