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    Re: Occultation puzzle
    From: Frank Reed
    Date: 2011 May 22, 18:05 -0700

    Hi Peter.

    Did you base this solely on a near-zero angular distance between the Moon's limb and Aldebaran? If so, there's a "ring" of positions for any arbitrary moment of UT around the right time and a 2000 mile wide band of possible locations if we assume UT is unknown, too.

    Imagine standing on the Moon looking up at the Earth while Aldebaran is being occulted (eclipsed) as seen from the Earth. If we turn off all the other stars in the universe (or imagine Aldebaran as extremely bright), the Moon will cast a nice circular shadow on the Earth with a very sharp edge. In fact, if we look at the edge of that shadow from the Moon, we'll even see the undulations in the edge of the shadow cast by mountains along the limb of the Moon. In space, the Moon's shadow from Aldebaran is a nearly perfect cylinder projecting out from the Moon in the direction opposite the star. Where this cylinder intersects the Earth, Aldebaran is hidden. As seen from the Moon the edge of that cylindrical intersection will look like a circle, though it's normally a more complicated shape if you map it out on the Earth's surface. And of course as the Moon travels around the Earth and the Earth turns, that cylinder sweeps across the Earth in a broad path about 2000 miles wide. If we know the exact instant when a star was observed at the Moon's limb with no other information, then we know we're on a "ring" of position (that is circular seen from the Moon, but an odd shape when drawn on the Earth). If we also don't know the time either, then the only thing we can say is that our position must fall in a 2000 mile wide band stretching all the way across the side of the Earth facing the Moon.

    In this photo, which, no offense to the person who submitted it to Wikipedia, is really a very poor occultation image, we have one other piece of information in addition to the fact that Aldebaran is sitting just off the limb of the Moon (lunar distance nearly zero). We have the position angle. If you draw a line through the horns of the Moon and then draw a line from the center of the Moon to Aldebaran, you get a specific angle which limits the possible locations and times where the photo might have been taken. When I measure this in the photo, I get about 53 degrees, +/-3 roughly (measured clockwise from the north pole of the Moon). This angle appears to rule out the location you proposed near New Orleans where the position angle would be close to 87 degrees. It's a good fit for northern Illinois, somewhere near Chicago. I would say that's probably where it was taken since if you do a general web search on the name of the person who took it (listed on the Wikipedia image page) and the word "astronomy" you will find that he manages a planetarium in Chicago's western suburbs. If that's the location, then the time was around 05:22:30 CDT. Ignoring the "cheat" of a probable location, there's a band about a hundred miles wide stretching from the Chicago area towards the southwest where the apparent small distance of the star from the Moon's limb and the position angle would both be approximately correct. So the photo could have been taken from the Chicago suburbs, from the Kansas City area, or maybe somewhere in southern New Mexico, naturally at somewhat different times.

    By the way, for the actual events of disappearance and reappearance in an occultation, we don't need to worry about refraction at all, even when the Moon is very low in the sky and the refraction is quite large, since the point on the Moon's limb and the star are refracted by the same amount --they have to be since they are at the same spot in the sky! Refraction couldn't possibly change the timing of the event. It could however change the apparent position angle (not by enough to make any difference here).

    -FER


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