Consider the line element of the sphere of radius a: ds²a² (do²+ sin²0 dø²). The only non-vanishing Christoffel symbols are го = − sin 0 cos 0, ФФ ГР = 2.900 rø ГФ00 = ГФ = to reproduce the results written above for rº a) Write down the metric and the inverse metric, and use the definition 1 (8μgvo + dvguo - doguv) = rº vp and r op ΦΘ 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+ sin²0 dø²). The only non-vanishing Christoffel symbols are го = − sin 0 cos 0, ФФ ГР = 2.900 rø ГФ00 = ГФ = to reproduce the results written above for rº a) Write down the metric and the inverse metric, and use the definition 1 (8μgvo + dvguo - doguv) = rº vp and r op ΦΘ 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 51P: Consider the physical quantities s,v,a, and t with dimensions [s]=L,[v]=LT1,[a]=LT2 and [t]=L ....

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