Computing the Ideal Fraction of the Total Lunar Surface Area That Is Visible From Any General Distance From the Surface

Assuming the mean lunar radius (R) and distance (d) from the surface, in the same units, the visible fraction (f) of the total lunar surface visible from that distance may be found by:

The distance (d) refers to the minimum radar distance between the eye and the spherical lunar surface.

For (R, d) expressed in miles (R = 1079.4 mi):

For example, if we were (d=126049) miles above the lunar surface, the ideal fraction (f) of the total surface area visible to the eye would work out to:

f = (126049 / 254256.8) = 0.49575468581371

or about 49.58 percent of the moon's total surface area would be visible from that distance.  This is also the only area that could be reached by a radio signal emitted from the spacecraft, the rest of the surface area being beyond the visible (signal) horizon and no atmosphere to help carry it farther.

For (R, d) expressed in kilometers (R = 1737.1 km):

Note that the closer we approach the moon, as it appears to get larger, the less of its surface area is visible to the eye.  Conversely, as we recede from the moon, it appears to get smaller, but we can see a larger fraction of its surface, up to a maximum of 1/2 (0.5) of its total surface area as the distance approaches infinity.

© Jay Tanner - 2017