Geodesics equation we are given a metric: (a) calculate the christoffel symbols "by hand". you don't need to show your work for the large group that are obviously zero (but explain which ones they are and why) (b) use (a) to find the geodesic equation (c) re-derive the geodesic by maximizing the proper time where you use the expression for the metric from the beginning (i. e. use this metric in the formula for proper time and then minimize (d) the schwarzschild metric is given in the usual coordinates as expanding around a specific point in space with r »> 2m, show that the metric takes the form of the metric in equation (6) (e) (bonus) from your answer in (d) and intuition for gravity around the earth, what do you think the geodesics that solve (b) should look like?