prob1 - dilation and gravitational corrections to a clock...

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A.V. Manohar Ph225A: General Relativity Problem Set 1 1. A particle moves along a vertical trajectory in a uniform gravitational Feld, starting at h = 0 at t = 0, and returning to h = 0 at t = T . ±ind the trajectory which extremizes the time di²erence measured between a clock on the particle, and a clock at rest on the ground at h = 0. 2. Compute the de³ection of light by the Sun, using Newtonian gravity, and treating the photon as a particle with mass ¯ hω/c 2 . Note that θ 1. 3. GPS sattelites orbit the earth with an orbital radius of 2 . 7 × 10 4 km. ±ind the time
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Unformatted text preview: dilation and gravitational corrections to a clock on the satellite, as compared with an inertial observer at inFnity. 4. Compute the ratio of the circumference C to 2 r for a circle, and the deFcit angle i for a triangle, if they are drawn on the surface of a two-sphere of radius a . or a small circle, show that C 2 r = 1 r 2 + . . . and Fnd . or the triangle, show that s i = where is the solid angle subtended by the triangle at the center of the sphere. 1...
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This note was uploaded on 04/19/2008 for the course PHYS 225 taught by Professor Manohar during the Fall '07 term at UCSD.

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