Consider the image used in determining the size of Mare Imbrium.

Click here for another glimpse.

Note that the tips of the Appenine Mountains can be seen extending slightly into the dark half of the Moon. This indicates that the mountains are raised well above the surface of the Moon. Consider the set of diagrams below:

Since the image is a half-moon, the source of the light must be from the direction indicated in the diagram. Furthermore, if we measure the distance d which the Appenine Mountains can be seen beyond the terminator (as indicated in the diagram), we can determine the height of the Mountains.

Consider the diagram below which addresses the geometry of this problem:

where d is the distance from the terminator to the tips of the Appenine Mountains; r is the radius of the Moon; and h is the height of the Mountains. Note that the two diagrams above are the same; they are just shown from different angles. It is as if we rotated the first diagram so that the h (or height) of the Appenine Mountains can be seen to rise above the surface of the Moon; in the first diagram (and in the image itself) the Appenine Mountains extend outward from the monitor toward you.

A little mathematics will help us determine the distance the Appenine Mountains extend outward from the image. In particular, we will find the relationship between radius r of the Moon, the distance d the Appenine Mountains extend beyond the terminator, and the height h of the Appenine Mountains. Since we can measure r and d from the image, we can determine h as well.

How? Click HERE to find out.