A Sphere and a Point
Mathematically, this is a problem involving a simple point and a sphere in 3D space. The tiny white point in the diagram above could represent different things, depending on the context, for astronomical purposes, the sphere representing a spherical planet or moon.
If the point represented a pointlight source, then it would simply illuminate the sphere as shown. The farther away the point, the larger the area reached by the light, but the fainter the recieved light would be, up to a maximum limit of reaching 50 percent of the total surface at infinity.
If the point represented the eye or camera lens, then the illuminated area would indicate the ideal fraction of the total spherical surface area visible from that point. The farther away the eye, the greater the visible surface becomes, but the smaller the visible image would be, up to a maximum limit of seeing 50 percent of the total surface at infinity.
The distance between the point and the sphere can be reckoned either from the center or from the surface of the sphere, whichever is more convenient or practical for a particular application.
The distance between a point and the surface of a sphere equates to the radar distance or the shortest distance between the surface of the sphere and the point. In space, we can send a radar signal to determine our distance from the surface of the moon. This tothesurface distance is probably more convenient for some applications than using the distance to the center of the moon, such as landing computations.
