|Visible or Illuminated Fraction of Total Surface Area of a Sphere|
This program computes the ideal visible fraction or illuminated fraction of the total surface area of a sphere at any distance from the eye or point-light source as reckoned from the center or surface of the sphere.
The radius and distance can be in any convenient linear units. The default values are the mean lunar radius and the mean geocentric lunar distance in statute miles.
In the lunar equations below:
R = Mean Lunar Radius = 1737.05 km = 1079.35 mi
For a sphere of radius 1079.35 units, where the distance to the eye or point-light source is 238856 units from the center: Visible or illuminated fraction of surface = 49.774058 percent Invisible or shaded fraction = 50.225942 percent Difference = 0.451884 percent