Question

Suppose a planet has a radius of 5,000 km. Starting at the point on its surface at 0 degrees longitude and 0 degrees latitude,find the distance to the point on its surface at 30 degrees longitude and 60 degrees latitude.

Answer 1

recall that in a right spherical triangle with sides a,b,c

cos c = cos b * cos a
so, he have
cos c = √3/2 * 1/2 = √3/4
c = 64.34° = 1.123 radians

so, since s=rθ, the arc length of c is 5000 * 1.123 = 5615 km