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Chapter2_15

# 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 λ β γ λ c V g obs + = ( ) 0 2 0 / 1 ) 1 ( f c V f f g obs = β γ . 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 ( λ λ β γ λ c V g obs + = ( ) 0 2 0 / 1 ) 1 ( f c V f f g obs = β γ 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 ).
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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 λ obs > λ ( 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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