The distance from the center of a sphere
to its surface is its radius
. The equivalent "surface radius" that is described by radial distances at points along the body's surface is its radius of curvature
(more formally, the radius of curvature
of a curve at a point is the radius of the osculating circle
at that point).
With a sphere, the radius of curvature equals the radius. With an oblate ellipsoid (or, more properly, an oblate spheroid
), however, not only does it differ from the radius, but it varies, depending on the direction being faced. The extremes are known as the principal radii of curvature
Imagine driving a car on a curvy road on a completely flat plain (so that the geographic plain is a geometric plane). At any one point along the way, lock the steering wheel in its position, so that the car thereafter follows a perfect circle. The car will, or course, deviate from the road, unless the road is also a perfect circle. The radius of that circle the car makes is the radius of curvature of the curvy road at the point at which the steering wheel was locked. The more sharply curved the road is at the point you locked the steering wheel, the smaller the radius of curvature.
If is a parameterized curve in then the radius of curvature at each point of the curve, , is given by