TCA #26 - Results of Measuring the Moon’s Size and Distance During a Total Lunar Eclipse; + 2 more [May 22, 2022, Free Post]
Sky Lessons: Results from the May 15-16 Total Lunar Eclipse -- The Moon's Distance and Size; Black Hole Sounds; Communicating Science Discoveries and Astronomy Education Results with Poetry--Part 2.
Cover Photo - The Shadow of Earth, via iPad
In This Issue:
Cover Photo - The Shadow of Earth, via iPad
Welcome to Issue 26 - We Are One Year Old!!
Sky Lessons - Results of Measuring the Moon’s Size and Distance During a Total Lunar Eclipse
Connections to the Sky - The Sounds of Black Holes
Astronomical Teachniques - From Science to Stanzas, Astronomy Education Poetically Written (Part 2)
The Galactic Times #24 Inbox Magazine Highlights
Welcome to Issue 26 of The Classroom Astronomer Inbox Magazine! - We Are One Year Old!!
As in our prior issue, we’re letting all subscribers, paid and free, see the article on what to do with a total lunar eclipse, specifically, how we found the Moon’s size and distance by tracking the Moon through the Umbra. If it is Greek to you, well, the ancient Greeks figured it out millennia ago, and you can too.
In fact, we’re letting the whole issue go for free to anyone who wants to see it.
Because this is our 26th issue, and we were one year old on May 15th, we celebrated by eclipsing <ahem> our usual subscription rate, and we continue to <ahem> shadow it deeply in the red at $30.00 from now until May 31st if you click this button:
Afterwards, the free TCA Digest returns at the end of June as a monthly and so does our usual subscription rate for 2-3 issues per month, still a bargain at less than two dollars per issue. TCA in June will have articles on astronomy education from the 240th meeting of the American Astronomical Society. Subscribe now!
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The other large article in this issue, Part 2 of using poetry to teach about astronomy, this time with concrete examples of different forms of poetry and different uses—in reports on observing activities, news items, descriptions of basic astronomy, and more!
Also, the sounds of black holes.
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Key websites: Homepage for The Classroom Astronomer, with its index to all Inbox Magazine issues’ contents, by celestial object, educational subject area, grade level or venue, and with complete Tables of Contents:
http://www.classroomastronomer.com . .
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Publisher -- Dr. Larry Krumenaker
Sky Lesson - Results of Measuring the Moon’s Size and Distance During a Total Lunar Eclipse
In the last issue we wrote about how to use a tennis ball and drawings of the Earth's shadow on the Moon to determine the Moon's distance and size. In THIS issue we use the results of our observations of the May 15-16, 2020 total lunar eclipse to show real results. You can then refer to this again during the upcoming partial lunar eclipse, which might be even better than a total for this exercise, in November!!
The May 2022 total lunar eclipse was very nearly central so a) it was really dark as well as red—called a Blood Moon, it was more an Old Blood Clot Moon, and b) the arcs of the Earth’s shadow were only upon entrance and exit, making the determination of its size a bit more difficult than an eclipse in which the Moon skirts the umbra all the way. Furthermore, the Moon was near perigee, so the umbra was quite large, larger than average, and so was the Moon. Still, the exercise is doable.
The farther away the Moon is, the smaller the umbral cross section it cuts through. So, measuring the ratio of the Moon size in our sky to the umbral shadow cross section size in degrees during totality gives us a way to find the Moon’s distance at that time.
In review, here’s what you had to do to measure the Moon using this Shadow technique:
Take drawings or photographs of the Moon as it moves through the Earth's umbra (central) shadow.
After the eclipse ends, put your photographs or drawings on a timeline along the edge of a piece of graph paper (preferably).
Here's the challenging part: Using a drawing compass and adjusting its size AND where the 'center point' should be, find the circle that BEST fits the circular edge of the shadow as the Moon moved through the umbra.
Measure the diameter of your estimated shadow cross section in millimeters, and the diameter of a Moon image, dividing the first by the second to get a ratio value usually somewhere between 2.5 and 3.0. You will use this to find the Moon's distance and size.
Unfortunately for yours truly, HIS location was one of the few in Alabama that was under the influence of thunderstorms! The only parts of the actual eclipse that were visible were those during the end partial phases, after totality had ended. Insufficient to do the experiment observationally. However, the event was live-streamed by multiple sites and we chose to use www.timeanddate.com. It gave views from multiple telescope sites, all imaged at the same size and with a time stamp visible. We took screenshots as close to every hour and half-hour as possible, provided the image showed a clear shadow edge, and preferably coloration.
You may need to refer to the previous issue for derivations of the mathematics and procedures.
Equation 1: Shadow Cone Length L = 108 x Diameter of sphere. L(Earth) = 856,000 miles from Earth.
After The Eclipse
Instead of using our timeline and cutting out our hand-drawn Moon shadow drawings and pasting them on it, we instead took our live-streamed screenshots, cropped off all but the disk and put them onto a desktop publishing page (we are old-fashioned, we used Microsoft Publisher). Our timeline page was a line with one-inch-apart vertical hour marks in local Alabama time. We sized our Moon images to fit exactly within the hour marks since, to a close approximation, the Moon should move its own width in one hour. The usable intermediate photos were over- or underlain between the hour photos, clearest images on top.
Note that though the Moon's features may appear to rotate as the Moon moves across the sky, they actually do not and all your lunar seas should always line up exactly the same way on the timeline - the seas that seem to form a three-toed footprint should always be on the right (west) side of each drawing. We rotated images and used a horizontal line to make sure all the seas were horizontally lined up.Clearly, we see that the edge of the Earth's shadow has a circular form, but we only see two parts of the circle. Our next job is to make the circle that best fits the visible shadow edge arcs. This required several attempts to get it done well; it IS a BEST FIT after all and it won't be exact or going through all parts of the arc perfectly. In the past we usually found that if you make tangents around the drawn large circular edge at several places, and then use a T-square to get perpendiculars to the tangent lines, you will find they roughly converge near a point. Adjusting your drawing compass in size and center location place, one will eventually find your 'best fit' circle. We initially found a smaller, 72mm circle, but then found an 80mm circle seemed to be a better fit.
The measured Moon image diameter on paper was 34mm. The ratio of umbra and Moon diameters, usually between 2.5 and 3.0, was 2.35. Then the calculated shadow circle diameter in degrees, determined by knowing the Moon being near perigee was not its usual ~0.5-degrees but actually 0.55-degrees, was found by multiplying that by the ratio just determined, i.e 0.55 x 2.35 = 1.29 degrees).
Activity 1 — The Moon’s Distance.
Any object has an angular size in radians equal to its diameter in miles divided by its distance from us in miles. Now, as the distance gets larger, the shadow cone cross section (XSD) will get smaller. It starts at 7926 miles at the bottom of the cone (at Earth), goes to zero at the end, and thus has an proportionally intermediate size between the extremes. At 25% of the 856,000 miles away, you’ll find Earth’s shadow’s cross section is 100-25%, or 75%, the size of Earth, or 5945 miles across. Thus:
Equation 2: XSD = 7926 x (1-f), where f is how far into the shadow cone you are from Earth — above it was 25%.
Conversely if you can measure the size of the cross section in miles, you can determine how far away it is! That’s where the Moon and its eclipse comes in.
We’ve measured the angular size of the umbra. In the box below we take that basic definition of angular size of an object and substitute Equation 2 on top and Equation 1 on the bottom, and generate Equation 3, the f equation at the end of the chain of mathematics. That is what we need.
Let’s put in our observed values.
The shadow cone cross section size we found to be 1.29 degrees. To convert any degree value to radians, divide it by 57.3 degrees per radian; this makes the angular size of the shadow .02256 radians.
Plugging this value for A into Equation 3 gets us f = 1/ [ (0.02256 x 108]+1), getting 29% of the way from Earth to the end of the cone.
Multiply f by the shadow length 856,000 miles makes the Moon about 248,240 miles away. We have found the Moon’s distance!
In reality, the Moon near perigee was at 225,757 miles distant. We are too far by about 10%. Not too bad considering the uncertainties, which were the printed Moon sizes and placements on the timeline, the inch marker placements, the umbral fuzziness, and the center point placement.
Activity 2 — The Moon’s Diameter
This is simpler. Knowing that the Moon (and the umbral cross section) is 29% of the way out, the size of the shadow we see on the Moon is (from Equation 2): 7926 * 1-f, or 7926 x (1-.29), yielding 5627 miles across. As the shadow is 2.35 times the Moon’s size, the Moon must be 5627 / 2.35, or 2394 miles across, about 11% larger than its actual 2160-mile size!
We clearly can determine size and distance of the Moon to within a few percent accuracy! How clever those ancient Greek astronomers were!
How close do you get with your (or your group’s) observations, by drawings or by photographs?
Connections to the Sky
The Sounds of Black Holes…and Other Things
The folks at Chandra X-Ray Observatory have been leaders in sonification of photographs of deep space objects. Sonification is converting images into sound files, a useful device for the visually impaired and blind students. I am particularly keen on sonification, especially in its use for scientific interpretation, such as for data analysis, control of telescopes and devices, etc. Sonification of photographs tend to be more musical than analytical. The site Chandra's Universe of Sound has 17 different objects, from the center of the Milky Way to black holes, M87’s jet to supernova remnants and star clusters, all sonified in either ‘photocopy scan’ modes (across the photo) or circular ‘radar’ mode, where the stars and nebulosity are converted into musical tones that are more reminiscent of musician Jon Serrie’s ambient music than scientific sound files. But it can be entertaining and possibly useful. Give it a listen.
Astronomical Teachniques
From Science to Stanzas, Astronomy Education Poetically Written, Part 2
In the last Classroom Astronomer issue, we started a conversation with UK Professor Sam Illingworth, author of two books on science communication using poetry: he and Stephen Paul Wren wrote A Celestial Crown of Sonnets (Penteract Press, 24pp, 4-Euros), and Illingworth’s own Science Communication Through Poetry (available on Amazon in Kindle, paper and hardcopy, from about $23 to $85).
We ended last time with Illingworth’s first ideas of how to help science teachers use poetry as a way to discuss and investigate astronomy with their students. Let’s fill in the details:
1. Listen to the students and ask them what aspects of astronomy they were interested in.
2. Wrote some list poems to explore these ideas and generate some word banks.
Dr. Illingworth writes, “Here is a list poem that I wrote in 60-secs on the subject of ‘stars’; the idea is just to list everything that falls into your head in this time, and it is a great warmup exercise to generate words and ideas for future poems:
Stars, light, creation, dust, heat, interstellar, distance, brightness, candles, observers, parallax, continuum, infinite, finite, solar systems, binary, collapse, milky way, distance, Hubble, telescope, lens, sight, knowledge, hope.”
3. Maybe invite a speaker in on a certain topic or encourage independent research.
4. Use this research/speaker to form the basis of the topic for a poem.
Perhaps we might want to talk about reaching people with poems on news about black holes. The dryness of science reports may be too much for many without a science background, or of much interest, but an artistic expression could reach some of them otherwise. Some students could find reporting the results of a graph of Kepler’s Third Law to their fellows in rhyme a better way of learning. Would the story of the lives of stars be more comprehensible to some if it was done as a set of quatrains?
Some other ideas for use of poetry—report the results of a lab report; have students take the daily Astronomy Picture of the Day and report the scientific description in a poetic form; give a weekly report of astronomy news as a string of sonnets, rather than in anchorman style. How about showing you really know the current topics by doing a pre-exam review—in poetry?
5. Introduce a poetic form to concentrate on. Maybe a haiku, a nonet, or a sonnet.
There are more poetic forms than there are digital pages to discuss them. No, not all have to rhyme, that’s the first thing budding poets have to learn. Poems can be free verse, with virtually no rules at all. But the one factor that Illingworth says all poetry has is that they all have a rhythm. There is almost a kind of melody to them, if you will, they flow, with or without a repeated sound.
In addition to the three above, he also mentioned to me the kyrielle form.
6. Ask the students to write a poem on that topic using that their form of choice. And encourage them to break poetic rules if they so wish.
7. Invite the students to share their poems and use it to help generate further discussion.
Let’s illustrate and share! Below are some specific examples from Dr. Illingworth, and myself.
A nonet is a nine-line verse in which the poem’s first line has nine syllables and each line thereafter has one less until the ninth line has just one syllable. Here’s yours truly’s take on one….
Kepler was indeed the first person to know how the Solar System was exactly operating. The Third Law sets the scale. Period squared is Distance cubed, if Earth equals scale of 1.
A haiku is known in Western culture as a Japanese form of three lines of 5, 7, and 5 syllables. It is actually more complicated than that, involving juxtaposition of contrasts—there is a seasonal word in it, it is present time, and it’s about nature. But for this demonstration, we will leave off the other details, worrying only about the syllables. Again, if I were a student, here might be my haiku on the lunar eclipse….
My Eclipse Results
Moon eclipse: distance, 2 4 8 thousands. Size? From Hot-lanta to Frisco.
A sonnet has 14 lines made up of three quatrains (each of four lines) and a couplet, where the quatrains internally rhyme (abab—…star, …sky, ….afar, ….die) and the couplet does as well (…Mars, ….cars). Here’s an example of a sonnet from Dr. Illingworth inspired by recent research on meteorite diamonds which found them to have come from a planetary embryo likely formed in the early solar system.
Within the burning heart of molten rocks, Great pressures forced your brilliance to shine; Inclusions marred your body with their pocks, A brownish hue now laced with olivine. Before you ever had a chance to grow, An interstellar pileup set you free; Thrown out into a cold and blank tableau, An empty, unforgiving, blackened sea. Across this bare horizon you now soared, A witness to the newly forming spheres; Your loneliness attracted you toward Our warm embrace with burning, final tears. We gather up your dust amongst the sand, All that remains for what you once had planned.
The final form is the kyrielle. It is a block (stanza) of lines, usually three, but four is also common, and the fourth line is always the same in each stanza, and the third line always ends in a similar sound (e.g. ease, freeze, …). As an example, here is one he wrote about the artwork for Joy Division’s 1979 debut album ‘Unknown Pleasures’. That image is a stacked plot of radio signals from the first observed pulsar – CP1919. [And here is a YouTube of him orating it in a poetry reading.]
Disorder in your massive core, A candidate that we adore; With every pulse that passes by You sweep across the darkest sky. An insight into what might be, Beyond the reach of men like me; A new dawn fades as to my eye You sweep across the darkest sky. It’s shadowplay across the spheres, What reaches us transcends the years; Now frozen in your perfect cry, You sweep across the darkest sky. A scream into the wilderness, The interzone of bitterness; We can no longer ask you why You sweep across the darkest sky. Do I remember nothing right; A New Order has come to light? So even though your star may die, You sweep across the darkest sky.
There are other forms—bring in your English teacher for interdisciplinary learning—but use these for starters.
Some Sources of Science Poetry
In addition to Dr. Illingworth’s books, here are other publications he recommends:
A Quark for Mr. Mark. Riordan, M. and Turney, J. (eds) (2000). Faber and faber Limited, London.
The SciKu Project. Andrew Holmes, AM (2017). Science in 17 Syllables. Science 358 (6365):966. https://thescikuproject.com/
Poetry of Science (Illingworth’s blog). https://thepoetryofscience.scienceblog.com
Litmus (a magazine). Lehand, D., Cleghorn, E. (eds) (2014) Litmus Publishing, London.
Consilience: https://www.consilience-journal.com/
The Galactic Times Inbox Magazine Issue #24 Highlights
TCA’s sister publication. Twice a month, on the 1st and mid-month, with the following columns usually, plus occasional other articles. Here is what was in the most recent issue. Subscribe to it here! It’s Free!·
Cover Photo —The Eclipse via Ipad
Welcome to Issue 24
This Just In —
* Good Water, Maybe. Good Soil, No
* Final Link in the Nova Story
* An Angry Sun?
* A Clouded, Dark Eclipse (Cover Story)Sky Planning Calendar —
* Moon-Gazing - Evenings: Nothing to See; Mornings: A Giant Meet and Greet!
* Observing—Plan-et —
- Mars Points Closely to Two Giant Worlds
- Possible Meteor Outburst on the 30th?* Border Crossings
Astronomy in Everyday Life - A Book of Lessons from Astronomical Mothers
Don’t forget the 20% off Hermograph Sale, including Spectrum Viewers for gas tubes, until the Solstice! See details near the top of the issue!