Ken Behrens
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- Sep 5, 2016
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I was going to say that this is a great argument, until I did the math. A quick search brought up many numbers greater than 2000, up to 6000. But let's go with the low number you gave. I will do the math of placement. That's all we can do at the present.No need to do that. We can simply do the math. Full of stars the skies are . . . but that number of visible stars is about 2000. How much room in the sky, in terms of degrees, does a star take up? Any telescope Fort could have purchased in his day could never resolve a star into a disk; it would ever resolve as a point in the sky. Fort simply didn't take a fair estimate of how unlikely it would be for one star to overlap another. And apparently you don't either. A star doesn't take up more than a "second" of our sky . . . I trust you know what a second is in terms of degrees . . . and how many "seconds" are there in visible sky at a time?
There are 180*3600 arc seconds on a night-visible half horizon. But we must compute the area of the visible half sphere. If 2pir=180*3600=648000, then r=about 10^6 arclengths, and the area of the half-sphere is (1/2)(4pi*r^2)=about 6*10^12 "square arc-second boxes" where a star could be. Divided by 2000 stars, the probability of a star being seen to cross another (ie be in the same box) is 1/(3*10^9)). Now, that sounds like a lot, and that is where you are coming from, and I was about to agree with you.
But consider that for 100 years (36500 days) 10 astronomers took just 10 looks at the sky per night each, and you have 3.65*10^7 observations. The probability that at least one such astronomer would have seen a crossing is now 3.65*10^7/3*10^9 or just about 1 in 90. Next, it depends how we define "crossing". I have said I will allow for the star to be above or below the first. The more primitive a telescope is, the wider the opening in terms of arc-seconds. If we assume that the astronomers looked with an opening of width just 10 arc seconds, the odds (1:90), suddenly jump to 1:9 of a star crossing (above or below) being seen at least once. None of this allows for backyard astronomers, or the more stars seen in photographic plates, used by astronomers since at least the 1880's. Any of these would increase these odds by at least an order of magnitude each. Ancient plate samples I have found on line currently being digitized clearly show room for a hundred or more start tall, indicating about 100 seconds of arc. This alone makes the odds 10:9 IN FAVOR of seeing one star crossing. Photographic delay increased the number of stars visible, at least doubling them, to odds of 20:9 in favor. And we have taken all the low numbers. Add backyard astronomers, double the number of "looks per night", and now you have 50:9 or a probability of about 1/6 that a star crossing would NOT be seen in 100 years. Part of Fort's argument is sociological: he states in the argument that any amateur astronomer seeing such a thing would have immediately notified his nearest observatory.
We have not yet observed crossings, though, just placement. To prove a crossing, we need for one star to move a little relative to the other star, and that's where it gets tricky. This is the part we cannot evaluate, as we have no idea whether anyone was looking for such a thing, so we cannot evaluate the probability of whether the astronomer would have looked the next day at the same piece of sky or not, to see if star A moved to the left of Star B.
The plates from that period are being digitized now. Let's see if any of them see a star crossing.
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