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) = rºvp-ΦΘand rop=00*1tan 0b) 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 Tas 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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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, and also the solution corresponding to the equator.