Expert: Jayendra Upadhye - 10/11/2007

Question
hi
im curious as to how astronomers can estimate elevation of features of the moon by studying shadows on the moon during its different phases
thanks

Answer
Hi,
I am not a professional astronomer!
But one does not need to be one really.
1 - We all know what angle the moon subtends to any viewer looking at it.
[It also can be calculated from the rule, V = tan S/D, where S is the linear size of the moon's diameter (2160 miles) and D is its distance from the eye (which averages about 238,000 miles). Thus, tan V = 0.009. So V = 0.52 degree, or 0.009 radian] - ref:- http://en.wikipedia.org/wiki/Moon_illusion

2 - While studying shadows for hieghts, one has to bear in mind that at any given angle of illuminaation,
a) - The shadow will be longer if it is cast on an inclined plane tilted "downwards" in a direction facing away from the light source.
b) - The shadow will shorten  if the opposite is true.
So to get an accurate estimate, one has to look for a shadow at the right place where, the average flatness of the area on which it is cast, can be safely assumed flat!

From point 1 above, and knowing the angle at which the sunlight is incident,  phase by phase, one can come up with a set of simultanous equations, which in the end yield the desired hieght.

This is my guess only, but that seems the only logical way.
Any multi  observation route (on a set of fixed points) normally leads to matrix (simultanous equations) calculations.

So that seems most likely route taken by scientists.

In  the end the angle subtended by the shadow can be converted to distance by using the relationship of distance to "angle subtended". (point 1).

Another interesting thing is that the "rate of crrep" of a shadow per change of phase will tell about the relative slope  of the area on which it is cast.

Tell you what, a really advanced computer  program could actually generate a complete 3d map of the "observable" face of the moon in just one month! (all phases of the moon can be studied in that time!)
And that too because the moon is phase-locked to the earth.
[look for tidal-locking  of satellites on wikipedia]

Hope that suffcies.
Jayen