Chapter2_15 - Consider the light emitted from a massive...

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PHY3063 R. D. Field Department of Physics Chapter2_15.doc University of Florida Gravity and Light (2) Frame 2 (accelerated, no gravity): In this frame the detector ( i.e. observer) is traveling (toward) the radiation at speed 2 / c V c v g = β and the radiation is “Doppler shifted” according to ( ) 0 2 0 / 1 ) 1 ( λ γ c V g obs + = ( ) 0 2 0 / 1 ) 1 ( f c V f f g obs = . Frame 1 (at rest, gravity): The equivalence principle tells us that the same thing must occur in both frame 1 and frame 2. Hence, ( ) 0 2 0 / 1 ) 1 ( c V g obs + = () 0 2 0 / 1 ) 1 ( f c V f f g obs = In this example the light is traveling through a drop in potential, V g = V observer -V source = -gh so λ obs < λ 0 ( i.e. blue shift ). Gravitational Red Shift:
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Unformatted text preview: Consider the light emitted from a massive star and observed on the Earth. star star star star e e star earth g R GM R GM R GM V V V + = = In this case, ( ) ( ) star c R GM star g earth star star c V 2 1 / 1 2 + = + ( ) ( ) star c R GM star g earth f f c V f star star 2 1 / 1 2 = and obs &gt; ( i.e. red shift ). Earth M e R e Inertial frame in a gravity field emitter Frame 1 detector Direction of light V source V observer Massive Star M star R star Direction of light V source...
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This note was uploaded on 05/29/2011 for the course PHY 3063 taught by Professor Field during the Spring '07 term at University of Florida.

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