The shortest distance between two points on a sphere is shown to be on the arc...

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The shortest distance between two points on a sphere is shown to be on the arc of the great circle containing them. If we know the angle between vectors from the center of the earth to the two points defining the arc, we can then estimate the distance as a proportion of the earth's circumference. The best way to compute the shortest distance between two points that are specified in latitude and longitude is through a series of coordinate transformations. We need to use equations that relate latitude and longitude to spherical coordinates, convert spherical coordinates to rectangular coordinates, and that compute the angle between two vectors. Spherical coordinates (radians); a(90-Latitude") 0-(360-Longitude") 3960 Rectangular coordinates (radians): X-a sin a cos 0 ya sin a sin 0 2-p cos e Angle between Vectors (dot product) a∙b=xax + Ya Yb + ²a²b lal=SQRT(x+y+z) cos = a b / lallbl acos(a b/lallbl Great Circle Distance = p Write a program that will compute and display the great circle distance between Minneapolis and Sydney, Australia. The latitude and longitude of Minneapolis is 45° N and 93.2 W, respectively, and the latitude and longitude of Sydney is 33.9° S and 151.2° E, respectively. The program should have a function "main", which calls another function to calculate the great circle dista the "main" function, and the great circle distance displayed. Note: Be sure to pay attention to the designated hemisphere values of Sydney. Your solution must include: 1) Problem statement/definition (20 pts) (20 pts) 2) Input/Output Diagram 3) Hand Example (include graphic of coordinate systems) 4) Algorithm 5) C Program (20 pts) (20 pts) V. The shortest distance between two points on a sphere is shown to be on the arc of the great circle containing them. If we know the angle between vectors from the center of the earth to the two points defining the arc, we can then estimate the distance as a proportion of the earth's circumference. The best way to compute the shortest distance between two points that are specified in latitude and longitude is through a series of coordinate transformations. We need to use equations that relate latitude and longitude to spherical coordinates, convert spherical coordinates to rectangular coordinates, and that compute the angle between two vectors. Spherical coordinates (radians); a(90-Latitude") 0-(360-Longitude") 3960 Rectangular coordinates (radians): X-a sin a cos 0 ya sin a sin 0 2-p cos e Angle between Vectors (dot product) a∙b=xax + Ya Yb + ²a²b lal=SQRT(x+y+z) cos = a b / lallbl acos(a b/lallbl Great Circle Distance = p Write a program that will compute and display the great circle distance between Minneapolis and Sydney, Australia. The latitude and longitude of Minneapolis is 45° N and 93.2 W, respectively, and the latitude and longitude of Sydney is 33.9° S and 151.2° E, respectively. The program should have a function "main", which calls another function to calculate the great circle dista the "main" function, and the great circle distance displayed. Note: Be sure to pay attention to the designated hemisphere values of Sydney. Your solution must include: 1) Problem statement/definition (20 pts) (20 pts) 2) Input/Output Diagram 3) Hand Example (include graphic of coordinate systems) 4) Algorithm 5) C Program (20 pts) (20 pts) V.