Guest Post by Rod A. Walters: Little-r-Slash-Big-R Has to be BIG Enough

[from “Captain [OF] America,” t.b. published August, 2018]

Size really does matter if you want a really dark partial solar eclipse. Having seen a spectacular annular solar eclipse—a “ring around the moon” thing—in upstate New York in 1994, I expected the Monday, August 21, 2017, predicted local 70%-partial solar eclipse to look spectacular, too. Wow, seventy percent! That sounds really dark!

During pre-Eclipse Morning, taking our usual walk around the neighborhood, I sensed all those neighborhood cats who came trotting up to us were worrying about the upcoming eclipse darkness. This many troubled cats didn’t happen often. They seemed to want extra head pats. Certain that they had primitive cat worries about the dangerous coming darkness, and needing fatherly attention, I gave them each a short lecture about how it’s only going to get sort of dark, but no wooba-monster dog-thing will be lurking in the shadows for them. A couple of reassuring pats each, we would go on our way. Cats love science lectures.

Later, wanting to make sure the Eclipse Day turned out special, I had much earlier set a lunch date with my wife, knowing that a romantic bayside restaurant table would make just the perfect afternoon. If clouds or rain had turned up instead, we still would have gone to an excellent lunch, and called it a Solar Ecrapse instead.

Armed with ISO 12312-2 certified eclipse-watching dark glasses, I treated my date to a running commentary about eclipses, about the ones I had seen before, and about the eerie darkness which would soon envelop us. Romantically. At about 30% eclipse, then at 40%, and later at 50%, it still looked just as bright as when we sat down an hour earlier.

At the maximum expected 70% eclipse, I could feel my date’s unspoken question, “Is it getting darker yet?” Wup.

Lunch was good, the company was good, but the 70% partial solar eclipse didn’t put on any show, except as viewed through the ISO 12312-2 eye glasses. How could that 1994 annular eclipse have looked so weirdly dark, and this 70% partial not be? Why! Why!

Time to whip out the old slide rule. A quickly jotted-up equation showed that for an annular eclipse to block the same 70% of the sun’s light, the so-called “apparent” moon’s radius today would be about 83% of the sun’s. All real engineers will yawn, bored with this simple equation: little-r-divided-by-big-R equals the square root of 70%. All non-engineers  would just yawn, neither group giving a rat’s eclipse about it. But the slide rule’s mocking answer: that 1994 annular eclipse hit 90%—a much, much bigger size than today’s event. No wonder 1994 got darker! I should have done the calculation before opening my blathering mouth. I can still hear the slide rule laughing.

I’d decided to make up for it next day by explaining this crucial little-r-slash-big-R mistake to all those neighborhood cats.  I just know they will all be interested, if they bother trotting out to me again.


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