Geometry Of Earthshine Reflection From A Spherical Target, by Defense Technical Information Center
This is a particularly short guide, and being a subject relating to somewhat esoteric applications of calculus, it may not be seen as being a subject of obvious relevance. Yet it is clear that this subject is of interest to someone because research was undertaken on it and it was paid for by defense-related application. Given the material included here, it is a bit of a guess what sort of defense-related implications that were intended here, but knowing the different reflection patterns based on the shape of what is being reflected is surely of use when one wishes to know what one wants to strike down or defend oneself from, so it is pretty clear that a knowledge of spherical geometry can be of immense worth in defense efforts, including the weaponization of satellites. And those who think that flat earth theory has no practical applications are therefore deeply mistaken, as this is research that can have a bearing on how it is that we can use our knowledge of geometry to better track what is going on in space, which definitely has some important applications, even if they are somewhat obscure to many.
The paper itself is a very short one at roughly 30 pages, including supplementary material. The abstract demonstrates mathematical research showing a viewer-independent understanding of the reflected signature of a target above ground that is based on the target height above ground that involves the effect of earthshine given the case of a diffuse target surface. The rest of the material is straightforward and is mixed between drawings and diagrams, equations to demonstrate how the calculation was done, and text to explain both the math and the visual representation of the geometry involved. After the abstract comes an introduction, then the account of the distribution of incident flux on the sphere (which takes up a significant portion of the small amount of text), then a brief look at the total power involved, then a bit more text on the observed brightness based on the phenomenon of earthshine and the shape of the target in space, be it a satellite or something else of that nature. The paper then concludes with a summary and acknowledgements, and from the looks of this paper, it can be gathered that the federal government got what it had paid for, a means of seeking to increase the defense of the United States through an understanding of mathematics and the phenomenon of earthshine as it would relate to an attack satellite or warhead of some type, although this is rather delicately not phrased as such in the paper.