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What an interesting reply, Frank.  A lot to think about.   I certainly have some idea of where .2724 comes from now.   And I know that HP looking at one body is the same as my SD to an observer on that other body.  And that radii of each body drive the proportionality between the two SD's.   

I did the exercise of determining the moon and the earth SD's at the three distances you put forth and in each case, SD's decrease with distance.  Which makes sense intuitively, but I'd never have been able to explain why. 

Does this work with the SD's of, say, Ganymede and Jupiter?  Or is the size difference too great for the distance between them?  

While was thinking about all of this I took a look at Bowditch, 10th ed., 1837 online. I think it might do me some good to learn the geometry in those opening pages as it seems helpful to see the functions of sines, cosines, tangents, secants, etc. graphically. 

I have a question about another number I've seen you use elsewhere in your posts, but will let the dust settle on this a bit before posing it.  

Thanks again for the in-depth reply.  Very interesting. 

Jim Rives

43N 71W