67P/C-G-How to measure comet geological structures using shadows

While composing the various images of comet 67P/C-G, I noticed a number of sharply angled structures that when viewing their shadows, appeared to be much more jagged and higher then appeared. It came to me how interesting how it might be to understand the scale of many of the objects and structures of craters and mounds that we generally either see overhead or at an angle as observed from the Rosetta orbiter.

To measure distance of an object you cant directly measure, like on Earth when seen from orbit, you need a couple pieces of information. Using trigonometry, the phase angle of the sun, and the known distance in pixels of an image, this can happen. After requesting it on the Sep 11 composite post on the ESA Rosetta forums, the first inclusion of the phase angle "angle the sun is pointing at the comet" was included in the Sep 14 image post.

To show you how this works, I am using the Sep 14 composite image I stitched together from the three images captured by Rosetta.

So, what are our initial measurements?

We are told that the phase angle is 61.5 degrees
We are observing 2.5 meters per pixel. It is roughly .400m/pixel

We now need to determine the sun's azimuth. Making up North on the image. Measuring the angle of the shadow to the E/W line, it can be determined the azimuth to be 270 degrees.

How do we apply all this information to determine depth/height?

1. First measure the distance from the top of a feature, to the end of the shadow.

This feature is measured at 67.7 pixels. If you multiply it by 2.5m/pix, you arrive at a distance from top of feature to end of shadow as 169.25m.

2. Now plug in the numbers to the equation.

d=169.25m*tan(61.5degrees)
d=308.5
d=309m

If we then apply the same method to the little hill to the upper right of this formation we get a height of 107m.

Now using this method, knowing the phase angle of 61.5 degrees, and measuring the pixel distance you can determine the estimated depth of craters and height of features. As long as the Rosetta forum mods include the phase angle in each of their image submissions, this can be done.