CHALLENGE - a 3 dimensional protractor ?

The radian measure of an angle is given by an arc length divided by a radius. You can use the protractor in the left hand panel to measure the angular separation of two stars (white dots). You can position the stars by dragging the green dots along the axes and the white dots along the green line. In the right hand panel you can explore possible meanings of measuring the "angular size" of a cluster of three stars (which of necessity lie on a plane - green in this case). What might be a reasonable measure of "angular size" in three dimensions that is analogous to arc length/radius in two dimensions? Does your measure behave reasonably in limiting cases?