Deflection of a Photon Near the Sun
I sorry. There is a couple of typos. I am not very good at copying some
one else's work including my own.
sin($)^2 should be sin($ / 2)^2 which is corrected in the message bleow.
----- Original Message -----
From: "Australopithecus Afarensis" <fossil.lucy@cox.net>
Newsgroups: sci.physics.relativity
Sent: Thursday, September 04, 2003 01:02 PM
Subject: Deflection of a Photon Near the Sun
Consider an (x,y) coordinate system with the center of the sun initially
sits right at (0,R) where
R = radius of the sun, and
A photon starts its journey at (-oo,0) along the x-axis towards (oo,0).
The photon will then be constantly deflected out of the x-axis of travel.
In doing so, an energy exchange will take place. The sun will gain some of
the photon's energy in terms of the kinetic energy, and the photon will lose
some of its mass.
From conservation of momentum and energy, we can write down
(1 - %) m c' cos($) + M Vx = m c'
(1 - %) m c' sin($) + M Vy = 0
m c'^2 = (1 - %) m c'^2 + (M / 2) (Vx^2 + Vy^2), where
M = mass of the sun
m = initial mass of the photon
% = final percentage of mass lost
Vx = final speed of the sun along the x-axis
Vy = final speed of the sun along the y-axis
$ = final angle of deflection from the x-axis, then
Vx = (1 - (1 - %) cos($)) m c' / M
Vy = - (1 - %) sin($) m c' / M, thus
Vx^2 + Vy^2 = (2 (1 - %) (1 - cos($)) + %^2) m^2 c'^2 / M^2
Vx^2 + Vy^2 = (4 (1 - %) sin($ / 2)^2 + %^2) m^2 c'^2 / M^2, therefore
% = (4 (1 - %) sin($ / 2)^2 + %^2) m / (2 M), or
$ = 2 arcsin(sqrt(% (2 M / m - %) / (1 - %)) / 2), or since 1 >> %,
$ = sqrt(2 % M / m)
Without any mass loss by the photon, there would be no deflection. Gravity
and the sun's atmosphere are among the major contributors to such a photon's
mass loss. In addition, the equation above also shows that ? very
significantly depends on the initial mass of the photon. Therefore, if some
one tells us how much a photon will be deflected during a solar eclipse
without knowing the initial energy of the photon, this some one is not being
realistic.
Does any one disagree with my reasoning?
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