# Curvature of Latitude

(1)
with
and
where'
 $r$ ' =' 'radius of curvature of the latitude circle in the plane of the circle $R$ ' =' 'radius of the sphere $\theta$ ' =' 'angle from the pole to the latitude circle at the center of the sphere $d$ ' =' 'line of sight distance between the pole and a point on the latitude circle, i.e. the length of the sagitta $s$ ' =' 'distance from the pole to a point on the latitude circle measured along the surface of the sphere
(2)
where'
 $r^{\,\prime}$ ' =' 'the radius of curvature of the latitude circle as a driver on this circle would have to steer. At the equator this radius is infinte, i.e. the curvature of the equator latitude circle is 0 for a driver following this great circle. $r$ ' =' 'radius of curvature of the latitude circle in the plane of the circle $\theta$ ' =' 'angle from the pole to the latitude circle at the center of the sphere

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