NavList:

Anyone observing the same body at the same instance at the same height is standing somewhere on the circumference of a common circle centered on the Ground Point of that body. This is the traditional Circle of Position. In reducing their celestial sight, each observer finds his own azimuth to the Ground Point and his Line of Position (a very small, seamingly straight segment of the Circle of Position). Each observer is somewhere on their own private Line of Position.

In 3D, a Cone of Position is formed between the Circle of Position and the body.

Nothing new here.

Frank has mentioned that Cones of Position have other navigation applications - they are how a Line of Position is derived from a Lunar and they are related to the Apollo sextant.

He said:

When you shoot a lunar (or an equivalent limb-to-star sight off of any body), the measured angle at some known UT
places you on a cone surface in three-dimensional space. Where that cone intersects the body you're measuring from,it is exactly identical to the standard circle of position .... it's directly related to the original idea for the Apollo sextant.

Perhaps NavListers can elaborate and clarify these how Cones of Positions relate to these applications.

Ed