TOP: Updated: 6-Feb-2011
Difficulty of observing predicted 1.75 arc-sec bending of starlight is easier understood by applying the Fraunhofer diffraction equation Theta=4(Lambda)/PI/D. Eclipse observation attempts were discussed or made (circa 1911-1922) in the visible light spectrum which has a wavelength (Lambda) of ~22E-6 inches. If a 12 in telescope were employed, the diffraction limit would be: Theta=4*22E-6/3.14/12 = 2.34 micro radians = 0.000134 degrees = 0.482 arc-seconds. So basic resolving accuracy could not be better than one part in 3.6. Expected measurement error with a diffraction limited mirror would be approximately 30% for stars very near the limb of the Sun. The position of stars further away from the Sun would have even smaller 'apparent' radial displacements away from the Sun. Atmospheric turbulence adds to measurement difficulty. It would take very careful measurements to determine, resolve, or confirm if the deflection were actually 0.87 or 1.75 arc-sec. This must certainly be a factor in why the effort took several eclipse trips over a ~11 year period.
So not knowing how to derive Einsteins 1.75 arc-sec number I figured out how much gravity will bend the path of a projectile traveling at 'c'. The technique is to continuously compute the vector force F=GmM/R/R as a function of radial distance between the solar CG and CG of a limb grazing bullet. Resolve the force vector into X and Y components; then integrate the y-component of that force into velocity. The Y-acceleration (RED) peaks at 28 G's as the projectile grazes the Solar limb. The program sums velocity in the Y-direction which integrates to 4155 ft/sec. The above chart shows the 0.871 arc-sec result which is exactly 1/2 of Einsteins prediction. In addition, the long track (BLUE) X-acceleration (peak 10 G's) is shown; the bullet speeds up in X-direction as it approaches the limb of sun (at x=0). The X-force drops to zero when passing above the CG and then the reverse x-force (blue) begins slowing the projectile as it 'leaves town' in the +X direction.
I later saw an answer in Astronomy's August-2008 'Ask Astro' on P-75 by Scott Dodelson (center for Particle
Astrophysics Fermi Lab) that Newton gravity does predict the 0.871 arc-second deflection number and that Einstein
initially had also obtained that result. Ultimately General Relativity predicted the 2x value of 1.75 arc-sec
after refining the theory (paraphrased). I don't know how Relativity pops out the 2x result (must still be above
my pay grade).
If light were bent like particle mass trajectories then the photon sphere would be inside
the Schwarzschild event horizon for a Schwarzschild black hole. Since light is bent (2x) more, the photon sphere
is actually located outside the event horizon. Huh?, forget strikeout text.