Consider the line element of the sphere of radius a: ds²a² (do²+ sin² 0 do ²). The only non-vanishing Christoffel symbols are го = - sin 0 cos 0, ФФ ГР = rø ГФ00 = ГФ = 2.900 a) Write down the metric and the inverse metric, and use the definition 1 to reproduce the results written above for rº (8μgvo + avguo dogur) = rº vp - ΦΘ and r op = 00* 1 tan 0 b) Write down the two components of the geodesic equation. c) The geodesics of the sphere are great circles. Thinking of 0 = 0 as the North pole and = π as the South pole, find a set a solutions to the geodesic equation corresponding to meridians, and also the solution corresponding to the equator.

Consider the line element of the sphere of radius a: ds²a² (do²+ sin² 0 do ²). The only non-vanishing Christoffel symbols are го = - sin 0 cos 0, ФФ ГР = rø ГФ00 = ГФ = 2.900 a) Write down the metric and the inverse metric, and use the definition 1 to reproduce the results written above for rº (8μgvo + avguo dogur) = rº vp - ΦΘ and r op = 00* 1 tan 0 b) Write down the two components of the geodesic equation. c) The geodesics of the sphere are great circles. Thinking of 0 = 0 as the North pole and = π as the South pole, find a set a solutions to the geodesic equation corresponding to meridians, and also the solution corresponding to the equator.

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter1: Units And Measurement

Section: Chapter Questions

Problem 1.6CYU: Check Your Understanding Is the equation v=atdimensionally consistent? One further point thin needs...

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