Consider the bending of light by the gravitation of the Sun as described by Newtonian physics. Light of frequency f passes at a distance d from the center of the Sun, which has a mass M. Show that the bending angle of the light is proportional to M/d.

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  1. Although the mass m of a photon is zero, if you use Newton's law of gravity with an m term in it and divide by m to get the acceleration towards the sun, the m's cancel out. Compute the integrated impulse to a photon as it passes by the sun at nearest distance d from the center.

    I get something like

    (G M/cd) cos^3 theta d(sin theta) = (GM/cd)cos^4theta d theta
    integrated from theta = -pi/2 to pi/2

    M is the solar mass and c is the speed of light

    That equals the momentum change toward the sun as the photon passes by. Divide by the forward photon momentum h f/c to get the angular deflection. f is the frequency and h is Planck's constant.

    The deflection is proportional to GM/d

    This will not give you the right answer; you need Einstein's General Relativity theory for that.

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