Radius of curvature of a particle with respect to another

Isn't the radius of curvature of a particle with respect to another... simply the distance between them?
No, although it sounds intuitive that it should be. But even for a single body orbiting around a much larger mass it is not, as a very eccentric orbit illustrates.

Below is a picture of two particles rotating around each other (source), and it is clear that by comparing them, that the radius of curvature is not simply the distance between them, and is more about the eccentricity of the orbits. That is, the radius of curvature would only equal a distance if there were a distance that stayed constant (thus creating a circle), but there is no such distance in this problem. If they were moving in a perfect circle, or if you could say in a relative sense that they were moving at constant distance from each other, then the radius of curvature would be a distance, but neither of these is generally the case.