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One of the main demonstrations made to test the theory of relativity were the images of the solar eclipse of May 26, 1919, (causing a shift in the positions observed in celestial coordinates of its source stars 1.7 arcsec, the amount predicted by theory). If the same experiment was carried out, but with a star on the periphery of the edge of jupiter, the same effect would occur? Few arcseconds that star would unfold?

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The correct simple formula that gives a VERY close approximation (in the 'weak field' approximation) is [4G/c^2][M/R] ... where M is the mass of the object, and R is the radius of closest approach of the light. Note that since the first term is a constant, the deflection varies as M/R.

See here for an incorrect and correct derivation: http://home.fnal.gov/~syphers/Education/Notes/lightbend.pdf

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For the sun, the deflection of starlight is $1.75''/b$, where $b$ is the apparent distance from the sun's center in solar radii. I'm going to make an educated guess that the 1.75 arcseconds is proportional to $GM_\text{sun}$. Jupiter has something like 1/1000th the sun's mass, so the deflection of starlight for an object occulted by Jupiter would be milli-arcseconds. That starlight can get perhaps ten times closer to Jupiter's center than to the sun's center without getting absorbed doesn't increase the deflection very much.

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    $\begingroup$ Your educated guess is correct :) $\endgroup$ – Javier Aug 20 '16 at 0:42
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    $\begingroup$ @jormansandoval You're welcome. $\endgroup$ – rob Aug 20 '16 at 15:45

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