NavList:

Hello Modris.

I know you're waiting for the "answer" (and Antoine, too!).

The photographer, Tom Polakis, gives his location as "about 1 mile south of the Gammage Auditorium in Tempe" which implies a lat/lon of about 33°24.1'N, 111°56.3'W. So that's quite close to the position you found. Nice, huh? 

Tom Polakis works part-time as an observer/astronomer at Lowell Observatory in Flagstaff, which is about three hours north of Tempe. You can find him on Facebook if you (any of you reading this message) want to connect and see some of his other photos.

Here's a challenge of a different sort. Now that you know the math works just fine, which is no surprise, can you explain what's going on here? For example, could we skip the math and provide a simple analogy in a more common form of navigation? Or are there any other real-world (off-world?) navigation applications that closely resemble this method of navigation, but maybe not using the Moon?

In practical terms, how could we make this navigation technique more accurate? If we could improve it by a factor of ten, we would have position fixes to the nearest mile or a bit better and, critically, these are fixes with no horizon required --no visual "sea" horizon, no reflecting artificial horizon, no gravity-dependent bubble or inertial-system horizon-- no horizon at all. The Moon's limb is the horizon for our sights in a scenario like this. Remember that this photo was just a backyard shot designed to illustrate the attractive "earthshine" on a crescent moon. The stars in the image, which I noticed were nicely oriented and relatively easy to identify, were just accidental. Could we do better if we took photos for this purpose with intention? Is there any reasonable way, besides using a traditional sextant, to extend this method to relatively larger angular separations, maybe up to 15°? I should add that, although this was a "backyard shot", it was created with a medium-range instrument, a good-quality amateur telescope.

Antoine and Modris: a detail that I know you both considered but might be worth discussing further. The brighter star, which you have identified by its Hipparcos catalog ID, HIP 21619, was known for much of the 19th and 20th centuries primarily as "Σ 572" with that Σ indicating that this was one of the stars in the original Struve catalog from 200 years ago. This means that this star is an easily resolved double star, in fact a true "binary" star. It consists of two nearly identical stars, both about magnitude 7.25 yielding a combined magnitude of about 6.5 (**). The angular separation between the two stars in this binary is nearly 0.1' of arc which is at the level we're trying to measure. How does this affect the analysis? Or does it??

Frank Reed

** This is a nice little rule to know: if you have two celestial objects, like two stars in a binary, that, when individually resolved, have identical magnitudes of m, then the merged star, when the two are no longer individually resolved, is brighter by 0.75 magnitudes, giving M = m - 0.75. Doesn't matter what m is specifically. At whatever magnitude we start, if the two objects have nearly the same magnitude separately, the combined magnitude is 0.75 brighter. Note: it's easy to derive a general rule for combining magnitudes that you can run up anytime you have a calculator or spreadsheet nearby. That's not the point. :)