Question: A great circle on a sphere S with center O and radius R is a circle obtained by intersecting S with a plane that passes

A great circle on a sphere S with center O and radius R is a circle obtained by intersecting S with a plane that passes through O (Figure 19). If P and Q are not antipodal (on opposite sides), there is a unique great circle through P and Q on S (intersect S with the plane through O, P, and Q). The geodesic distance from P to Q is defined as the length of the smaller of the two circular arcs of this great circle.

Y 0 Great circle Smaller circle a. S P Great circle through P and Q

Show that the geodesic distance from P to Q is equal to Ry, where is the central angle between P and Q (the

Y 0 Great circle Smaller circle a. S P Great circle through P and Q

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