Chapter2_14 - − − = − = − = ∆ 1 1 1 det Frame...

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PHY3063 R. D. Field Department of Physics Chapter2_14.doc University of Florida Gravity and Light (1) Gravitational Potential V g and Potential Energy U g : Define the gravitational potential to be the work per unit mass required to move a test mass m from infinity to the point r. In particular, = = = r grav g g r d F m m W m U r V r r 1 ) ( . For a point mass M at the origin r GM r V g = ) ( and r GMm r mV r U g g = = ) ( ) ( Frame 1 (at rest, gravity): Consider an emitter and a detector at rest a distance d apart in the presence of a gravitational field. The emitter emits electromagnetic radiation with wavelength λ 0 and frequency f 0 ( λ 0 f 0 = c). The absorber detects the radiation with wavelength λ obs and f obs . The gravitational potential difference between the emitter and the detector is given by gd R d R GM R d R GM d R GM R GM V V V e e e e e e e e e e emitter ector g =
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Unformatted text preview: + − − = + + − = − = ∆ / 1 1 1 det Frame 2 (accelerated, no gravity): Suppose that the radiation was emitted at t = 0 and detected at time t. At time t the detector has speed v = gt and has moved upward a distance y = gt 2 /2. The radiation travels at speed c and thus 2 2 1 gt d ct − = and + + − = g d g c g c t 2 2 . The velocity of the detector at time t is thus gd c c v 2 2 + + − = and 2 2 2 / / / 2 1 1 c V c gd c gd c v g ∆ − = ≈ + + − = = β . Earth M e R e Inertial frame in a gravity field emitter Frame 1 detector d light a = g Accelerated frame (no gravity) emitter Frame 2 detector d light Gravitational Potential Energy...
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