# radius

Fig 1. The radius vector of a planet in a highly elliptical orbit around a star.

In mathematics, the radius is the distance from the point of intersection of the axes of symmetry of a closed curve. More specifically, the distance from the center of a circle to its circumference, from the center of a sphere to its surface, or from the center of a regular polygon to any one of its vertices. All radii of a circle or sphere are equal; and it is generally profitable to consider only the longest and shortest radii (semi-major and semi-minor axes) of an ellipse.

## Radius vector

The radius vector (Fig 1) is the line joining an orbiting body to its center of motion at any instant, directed radially outward. For a circular orbit, the center of motion coincides with the center of the circle; for a parabolic or hyperbolic orbit, the center of motion is the focus, and for an elliptical orbit it is one of the two foci.

## Radius of curvature

The**radius of curvature**,

*r*, at any point of a curve is

*r*= 1/

*κ*, where

*κ*is the curvature.

In astronomy, a radius is an old instrument for measuring the angular distance between two celestial objects.