#### Jimmy Westlake

Jimmy Westlake's Celestial News column appears monthly in the *Steamboat Today*.

Find more columns by Westlake here.

The summer solstice, marking the official end of spring and the beginning of summer in the northern hemisphere, occurs this year at 5:08 p.m. local time Wednesday. The summer solstice is sometimes referred to as the “longest day of the year,” but aren’t all of our days exactly 24 hours long?

Yes they are, but ever since the winter solstice last December, the time interval between our sunrise and sunset has been increasing, giving us more minutes of daylight and fewer minutes of darkness each day. So the phrase “the longest day of the year” refers to the number of daylight hours in a 24-hour period, not the actual length of the day.

Consider that on the winter solstice Dec. 21, sunrise in Steamboat was at 8:26 a.m. and sunset was at 5:45 p.m., for a total of nine hours and 19 minutes of daylight and 14 hours and 41 minutes of darkness. On June 21, the sun rises at 5:38 a.m. and sets at 8:40 p.m., giving us 15 hours and 2 minutes of daylight and only 8 hours and 58 minutes of darkness. So, we are enjoying an extra four hours and 43 minutes of daylight this week compared to mid-December.

That’s the good news. The bad news is that after the summer solstice, the trend reverses and we start losing those precious minutes of daylight again as we head toward the winter solstice.

As our daylight hours increase between solstices, the noontime sun rises higher and higher in our sky, causing noontime shadows to grow shorter each day. On the date of the summer solstice, the noontime sun in Steamboat will be 72.5 degrees high. That’s as high as it can ever get for us, so we have short, stubby, noontime shadows, but they don’t disappear at noon.

Around the year 200 B.C., the Greek scholar Eratosthenes heard a rumor from some travelers that at high noon in the town of Syene, Egypt, on the date of the summer solstice, the shadows of vertical objects briefly disappeared. This indicated to Eratosthenes that the sun must be shining down from 90 degrees, at the very zenith of the sky in Syene. He thought this was very curious, since the noontime sun on the date of the solstice from his hometown of Alexandria, Egypt, was 7 degrees off of the zenith, creating very short shadows. Most people might have just dismissed the rumor, but Eratosthenes did not. He realized that if the Earth were flat, noontime sun angles would be the same everywhere, but if the Earth was shaped like a sphere, different locations would experience different sun angles at noon. He reasoned that the distance between Syene and Alexandria must represent 7 degrees of the Earth’s total circumference, so a quick calculation produced the distance around the spherical Earth. Eratosthenes’ measurement was only 2 percent off from the accepted circumference of 24,901 miles. Not bad for 200 years B.C.

Happy summer solstice!

*Professor Jimmy Westlake teaches astronomy and physics at Colorado Mountain College’s Alpine Campus. His “Celestial News” column appears weekly in the Steamboat Today newspaper. His “Cosmic Moment” radio spots can be heard on local radio station KFMU. Check out Westlake’s website at www.jwestlake.com.*

## Comments

## rhys jones 4 years, 9 months ago

Thank you, Jimmy, for this brief overview of what we have all known since the third grade -- probably much earlier, in Scott's case. I did find the Eratosthenes paragraph mildly entertaining and educational, no doubt justifying the typeset and your paycheck.

Thank you, Pilot, for the voluminous news in your online version this morning, virtually all of it a repeat of yesterday. I guess the heat and fires are old news by now. ellingtoncms.com continues to hang my browser more often than not -- does anyone else have this problem? -- I guess your readers' time is less valuable to you than who really butters your bread.

Thanks you, viewing audience, for enduring this brief little spat. I must have gotten up on the wrong side of the asylum.

## rhys jones 4 years, 9 months ago

In retrospect and upon closer examination, the "voluminous news" carp may have been unwarranted. I see now that less than half is old news. My bad.

## Scott Wedel 4 years, 9 months ago

Rhys, I learned about Eratosthenes radius calculation in the third grade. How'd you guess that? Sadly it wasn't from school, but in a giant children's applied math book that I loved to read.

The north to south curvature has been well known to sailing cultures around the world and was independently discovered. Eratosthenes calculation was able to be accurate because he had the advantage of two towns directly north/south and a known distance apart.

And yes, this site hangs up fairly often. I have gotten used to hitting reload to load a new page.

## rhys jones 4 years, 9 months ago

Scott -- Why am I not surprised?

Am I mistaken, or did I gather recently that you run a car wash in Oak Creek? Can you guess the numbers of quarters you drop on the floor at a glance, much like Rain Man? Please tell me you have another venture which utilizes your obviously superior intellect to the normal human.

Sometimes reload just gets stuck again, for my Firefox, and I have to back up a page and try again, and possibly again. It can get to be quite frustrating.

And thank you so much for being our watchdog, ever on the alert. What would we do without you? (besides waste a lot of time reading blather) Have a great day!!

## rhys jones 4 years, 9 months ago

PS -- I am the self-appointed BS watchdog.

## Phoebe Hackman 4 years, 9 months ago

So THAT'S what it is. I thought it was my computer. About 9 times out of 10, I have to stop the page from loading, then reload, often more than once.

## rhys jones 4 years, 9 months ago

Now that I've had my nap after work, and some time for reflection and a little cowboy arithmetic, my BS meter is flashing on overtime. Consider:

Given Jimmy's times are accurate, on the winter solstice there were 3 hours and 34 minutes before noon, and 5:45 after noon, that means that at high noon by the sun, we were 11 minutes off by the clock. So theoretical noon in this time zone was at a different meridian than the ideal for it. By the same token, on the summer solstice there are 6;22 before noon, and 8:40 after noon -- by the clock. Now we are 18 minutes from theoretical noon in this time zone. This is understandable, given the longer days to begin with. In both cases adjustments were made for daylight savings time -- a double adjustment, in total.

Now consider that high noon travels approx. 16.666... miles per minute at the equator (1000 miles per time zone, approx/60) so that might be approx 10 miles at 30 degrees latitude. Syene lies at 32.9167 E longitude, Alexandria at 29.9162 E long, a difference of almost exactly 3 degrees longitude. 3 * 66.66... miles at the equator (24,000/360) times 2/3 approx (to account for the 30 degrees longitude) means that, in addition to the approx 470 miles difference in latitude between the two cities, there is also approx. 200 miles difference in longitude, which would account for an additional 12 minutes' difference in high noon by the sun, BESIDES the difference caused by the difference in latitude -- and they would tend to cancel each other somewhat, but nowhere near totally.

I will confess that I Googled the cited longitudes. I will also submit that it might be a few minutes before we hear back from Scott as he wildly Googles in an attempt to refute me. Scott's car wash leaves him with WAY too much time on his hands, which he uses wisely in an ongoing attempt to demonstrate to us how smart he is. Neither the real professor, the professed professor, nor Eratosthenes himself, seems to have taken into account the difference longitude would make in their calculations.

Ha.

## rhys jones 4 years, 9 months ago

Phoebe -- Yup, if you'll look at the bottom of your browser screen when it gets stuck, you'll see it is trying to load ellingtomcms.com's ads. Not very well, I might add.

## rhys jones 4 years, 9 months ago

Before Scott beats me to it, I will note that at least one of my daylight savings adjustments was in error, but it affected the conclusion not one iota.

## rhys jones 4 years, 9 months ago

Aha -- I spotted my error -- let's see how long 'til Scott sees it.

## jerry carlton 4 years, 9 months ago

Rhys OKC is down 2 to 1. Lets hope they win tonight. Do not want that carpetbagger Lebron to ever win a championship, unless it was against the Lakers;.

## rhys jones 4 years, 9 months ago

Jerry -- And how!! Now to locate a TV to watch it on -- I wouldn't want to get brainwashed too much. Carmelo is a carpetbagger too, but at least we got something for him. Go Thunder!!

## rhys jones 4 years, 9 months ago

TWO errors, last count. Scott? Hello? Usually you can't pry him from these forums, but now he's dropping quarters, he'll claim. (He's madly running extensions on his Casio...)

## rhys jones 4 years, 9 months ago

Oh great -- the one time we WANT to hear from Scott and he's nowhere to be found. C'mon, buddy, it's just a little applied math. I'll check back after I check out some hoops. Hint: Don't forget to carry the 2.

## rhys jones 4 years, 9 months ago

Jerry -- Bummer, eh? Applied math would tell us the odds are now against us.

Scott -- One thing I detest is a blowhard. If you can debunk my theory (longitude matters) in 50 words or less, that will be a new record for you. I'm betting you can't, in a thousand words.

## rhys jones 4 years, 9 months ago

Answer: The angle of the sun -- and hence latitude -- can be determined at high noon -- a shadow's shortest point -- of either solstice or equinox (and presumably any other time, given the proper correction) and longitude is totally irrelevant in this calculation. Only Jimmy is allowed to expound on or correct me.

I didn't mean to kill the forums. Put away the Casio, Scott, leave Google alone, and please regale us with your vast knowledge again. You are our alter-Google!!

## Scott Wedel 4 years, 9 months ago

Yes, you measure angle of the sun at local high noon when the shadow is shortest, not simultaneously. The importance of the two cities being north/south is that a geographer such as Eratosthenes could fairly accurately determine how far north he was of the other city.

I was waiting for you to explain how they were able to simultaneously take measurements in two distant cities.

BTW, your trig is also off. 30 degrees north does not reduce approx 16 miles per min at equator to 10 miles per min. It'd be closer to 13.

And note that Syrene being on Tropic of Cancer is irrelevant to the calculation because the difference in measured angle on any same day is sufficient. But it does make it easier to explain and has fewer questions about having to coordinate measurements.

## rhys jones 4 years, 9 months ago

Paragraph A: Who said anything about simultaneous? That matters not in the slightest. City A's latitude will never change, whenever you measure City B, it's only important that you apply the proper correction for variance from a solstice. If you are referring to my original set of curve balls, that was intended to confound you, which obviously it did. Of course now we will hear about how you were sharing hot gasses with a potential councilperson, instantly surmising dropped quarters, or distracted any way but these forums, where you normally bury your nose. Waiting for me? Comical and unlikely. I find it hard to believe ANYTHING could detain you from displaying your vast intelligence, you would point out any deficiency as soon as you spotted it, and in this case I fed you the answer. My bad, now I'm sorry I did. That leads us to

Paragraph C: That is the other mistake I referred to. So you found one of them anyway. Casio eventually paid off. Bonus question: What is the command-line calculator in Linux? If you reply you use Windows, you lose 10 points off the top. There will also be deductions for Google time. Hurry, Scott.

Paragraph D: Also irrelevant, and qualified above.

You are merely restating what I have already noted.

Thanks for playing, Scott. I was getting worried about you. Now feel free to nitpick another story.

<p>ellingtoncms.com continues to hinder and frustrate, no end in sight. Sucks when it's in somebody else's court, yet they are paying the light bill, huh Tyler?## rhys jones 4 years, 9 months ago

As a minor form of concession, I will admit that I did not notice that Syene was on the Tropic of Cancer when I Googled its coordinates, but that dissertation concerned itself with longitude, not latitude. Of course that explains why there is no shadow at noon on the summer solstice, and why one might notice a shadow on that day in another location.

I will also admit I used -- what's that calculator's name? -- after I got tired of working numbers by hand. Likely explaining the error noted in Paragraph C above, and my own post many hours earlier.

What we have here, ladies and gentlemen, is two terriers fighting over the same stick.

## rhys jones 4 years, 9 months ago

My original cowboy math assumed that the circumference of the Earth at 30 degrees would be 2/3 of its full circumference and I based my calculations accordingly, ie, 1000 miles per time zone at the equator/60 minutes == 16.66 miles per second of sun travel, times 2/3 for 30 degrees resulting in my rough 10 mile sun travel at 30 degrees -- but closer following of this formula results at more like 11.11 miles.

But we were BOTH wrong, and here's why: The formula for circumference of a sphere at a given latitude is 2

piradius*cosine(30) and the cosine of 30 (degrees) is .866 (plus minute decimals, this good for our purposes). Plug all the numbers in, rounding pi to 3.1416 and the radius of the Earth to 3820 miles (24000/3.1416/2) and I was surprised to learn that the circumference of the Earth at 30 degrees is 20785.5 miles (plus minute decimals) not the 16000 miles I would have guessed and based my calculations on (actually I just rough-guessed 2/3 of 16.67 miles per minute at the equator) and when you divide that (20785) by 1440 (minutes in a day) you arrive at just shy of 14.5 miles per minute of sun travel at 30 degrees. So while Scott's estimate was closer than my original guesstimate, they were both off far enough to call wrong.Isn't math fun? My paternal grandmother help a PhD in math and worked on Gemini and Apollo NASA space shots, and Jimmy Westlake surely is smiling at the controversy he inadvertently stirred.

I'll call it a draw if you will, Scott. Otherwise we can beat this dead dog some more, and I dare you to challenge my figures now.

## rhys jones 4 years, 9 months ago

PS -- The author of the formula I Googled for circumference at latitude noted that it is not exactly accurate, since the Earth bulges slightly at the center, but any error would be less than 1%. Like Momo and Dad, I too am a prisoner of numbers.

## Scott Wedel 4 years, 9 months ago

Well, Alexanderia is a few degrees north of 30 degrees.

And I only said that 13 miles per min was closer to the actual number than your 10 miles. There were so many approximations in your calculations that I didn't feel like attempting to precisely calculate it.

So you spent all that time figuring out how fast high noon travels across the surface of the earth to try to confuse me? Sure, whatever.

As for his calculation of earth's diameter being accurate to 2%, that is more of a fluke than a reflection of the precision of his calculation. He used 1/50th of the earth's radius between the two cities and fortunately for him, the actual angle is quite close to that. And he also used a rounded off distance of 5,000 stadia between the two cities which also happened to be quite close.

The importance of his calculation was not that it was intended to be accurate, but that there is a north/south curvature that links angle of sun to north/south distance. So some traveler that had a way of describing the angle was also given an indication of how far north/south he had traveled. (Ancient method of angles was often evenly spaced knots in a rope to make a right angle (such as 3,4,5 or 5, 12, 13) and then angle would be described as number of knots on one of the sides).

Funny part of astronomy and calculation errors is that Pluto was found by looking in a section of the sky based upon an astronomer's calculations that were completely wrong. Calculations were for a planet of a much larger planet in a much different orbit, but at that time happened to be on the same sight line from earth as was Pluto.

## Kevin Nerney 4 years, 9 months ago

To date myself and quote one of my favorite bands Chicago Transit Authority "Does anybody really know what time it is, Does anybody really care."

## rhys jones 4 years, 9 months ago

Scott -- I will also admit that my original dissertation was not an attempt to befuddle you, but based on the errant assumption that somehow longitude mattered in such matters. Your responses indicate that you do indeed have a grasp on the subject, one of many many.

Kevin -- If I'd have known what a can of worms I was opening, I wouldn't have wasted the time to begin with. But the math part of figuring it out was sort of fun.

## jerry carlton 4 years, 9 months ago

Rhys Always next year. OKC is by far the younger team.. Carmelo can not be considered a carpetbagger. He went north and carpetbaggers all came south after the civil war. Who knows, maybe OKC will become the first team to come back from a 3 to 1 deficit in the finals. I am not placing any bets though.

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