c) The geodesics of the sphere are great circles. Thinking of θ = 0 as the North pole and θ = π as the South pole, find a set a solutions to the geodesic equation corresponding to meridians, andalso 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 areго = − sin 0 cos 0,ФФГР =røГФ00 = ГФ=2.900a) Write down the metric and the inverse metric, and use the definition1to reproduce the results written above for rº(8μgvo + avguo doguv) rº,vp-ΦΘand rop=00*1tan 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 = πas the South pole, find a set a solutions to the geodesic equation corresponding to meridians, andalso the solution corresponding to the equator.

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Answered: Consider the line element of the sphere…

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Consider the line element of the sphere of radius a: ds² a² (d0² + sin² 0 do ²). The only non-vanishing Christoffel symbols are го = -sin cos 0, ГФ 06 = rø 00= 1 tan 0