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I've been thinking this evening about tomorrow morning's occulation of Antares by the Moon and considering again how this might have been useful in earlier centuries for determining longitude. Since Antares has no measurable angular diameter of its own, it will blink out almost instantly tomorrow morning when it is occulted. Its reappearance would be almost as instantaneous. As people have discussed on this list before (see the Jupiter occultation, back in December), this observation is like a zero distance "lunar distance" observation, at least in principle. Without even using a sextant, when that star disappears, you can say that its lunar distance is 0d 00.0'. But how accurate is that "zero" observation? For that matter, how accurately could any lunar distance observation be taken, in principle?

 

The mountains of the Moon place a fundamental limitation on lunar distance observations and also occultation timings, historically at least. This topic has also come up before but I didn't have a source handy at the time to put numbers on the matter. While browsing today, I came upon an old "lunar limb profile" diagram from the annular eclipse of May, 1994 which was visible across much of the US. Here's the diagram:

It shows the profile of the mountains and valleys along the Moon's limb at the time of this eclipse on an exaggerated scale (the profile varies significantly from one eclipse/occultations to another due to lunar librations). The scale is on the upper right. Deviations from the perfectly circular form assumed in lunar distance calculations of 6" or more are fairly common and typical deviations are around 4". Any lunar distance observation or occultation-based "zero distance" observation is fundamentally limited at about this angular scale. And this 4 to 6 arcsecond built-in error translates to 2 to 3 minutes of longitude minimum error. This would seem to be an absolute limit on all historical lunar longitudes even when all other corrections have been carefully applied.

 

Today, the limb profile of the Moon across the full range of libration angles is relatively well-known and has been for about four decades (hence the diagram, linked above). Occultation timings today are still valuable because they refine the limb profiles. They help map the Moon, instead of the Earth...