Author Archives: Charles Henebry

Solar Noon – old

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Determine the clock time corresponding to solar noon. This is trickier than you might think, and may require several tries before you get it right. I’m happy to give a week’s extension on this experiment, but do make a first stab at it the first week, so you have a sense of the challenges.

Full details in Fabian, Ex 2.1, “Gnomons and Shadow-Casting,” pp 33-34. You need to find a spot where the sun shines at noon and where the ground is level. An outdoor patio or bench is probably ideal: sidewalks and parking lots are often built on a grade, and the sun’s light may bend as it passes through glass to reach an indoor location.

Start by guesstimating the time of solar noon by looking up the time of sunrise and sunset in your location. Set up your apparatus 10 minutes before this time, and record the position of the gnomon’s tip at 1-minute intervals.

Apparatus:

  • Solar Noon radial graph paper, ruled in cm. Download and print.
  • A gnomon with a sharp tip—a sharpened pencil or the like. If possible, bring a range of possible gnomons, choosing one that casts neither too long nor too short a shadow—no longer than 9 and no shorter than 5 on the sheet.
  • Clay, gum, or scotch tape to anchor the gnomon at the center of the worksheet.
  • Scotch tape to anchor the worksheet.
  • A smartphone with a compass app.
  • If possible: a carpenter’s level. Otherwise, something rectangular to serve as a right angle tool.
  • A pencil to record your measurements.

Instructions:

  1. Find a surface with good sun exposure. If available, use the level to check that the surface is level. Otherwise, do your best to check it by eye. Flat concrete benches are likely level; sidewalks generally are not.
  2. Use the compass on your phone to align the paper so that the arrow at the top points due West. Anchor the worksheet to the surface with scotch tape.
  3. Anchor the gnomon at the center of the sheet, using the level or right angle tool to ensure it is vertical.
  4. Take a photograph of your experimental apparatus in action.
  5. Record measurements at 1-minute intervals, starting about 10 minutes before your guesstimate of solar noon, and finishing 10 minutes after. For each, mark an X on the worksheet at the tip of the gnomon’s shadow along with the clock time of the measurement.
  6. If you’ve done everything right, the gnomon’s shadow should get shorter, reach a minimum, then grow longer. The mark you made at the minimum represents Solar Noon.

Calculations:

  • Reading from the mark when the gnomon’s shadow was shortest, what clock time corresponded with Solar Noon? How many minutes is Clock Noon off from Solar Noon, positive or negative, in the city where you did the experiment (specify your city in your answer)? Would you need to travel East or West in your Time Zone to be in a place where Solar Noon coincides with Clock Noon?
  • Use a ruler to draw a line from the center of the worksheet to the mark corresponding to Solar Noon. That line is True North, by contrast to the 0° mark which corresponds to Compass North. Using a protractor, or estimating from the angle measures provided on the sheet, how many degrees does Compass North deviate from True North, positive or negative, in the city where you did the experiment?
  • Calculate the ratio between the length of the shadow at Solar Noon and the length of the physical gnomon you used. From this you can calculate the latitude of the city where you live. Tangent (Latitude) = Shadow / Gnomon. You’ll need a calculator with the inverse tangent function—make sure you get an answer in degrees (DEG), not radians (RAD).

Upload your results in a comment below, attaching your a photo or scan of the completed worksheet and (in a reply to your first comment), the photo you took of your experimental apparatus.

End-of-Semester Results

As shown in the graph below, the sun’s shadow at noon definitely got longer as we moved from the Autumnal Equinox on Sep 23 toward the Winter Solstice:

I was surprised to learn from your data that the time of solar noon shifted subtly over the course of the semester, moving from 12:35 to about 10 minutes earlier in the day by mid-November. At first I assumed that this was an error, but it turns out to be correct (link):

Compass measurements for the direction of the sun’s shadow were all over the map. They should be clustered around 14˚, but ours were as much as 90˚ off, essentially at a right angle to the correct answer. Given this range of error, I didn’t bother drawing a trend line:

Galileo’s Moons

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The Harvard-Smithsonian Center for Astrophysics offers the public access to a network of small robotically-controlled telescopes. The following fieldwork assignment invites you to work with images collected from that telescope to replicate Galileo’s discovery that the planet Jupiter has a number of moons orbiting it.

Here’s what Jupiter looks like through one of the Harvard-Smithsonian telescopes, with a setting that shows the planet against a field of stars. Some of those stars are actually moons—but which ones?

Jupiter and its moons, 7:30am on 9/25/22

Jupiter’s moons differ from stars in two respects. First, they aren’t bright pointlike sources of light. When the telescope is adjusted to exclude pointlike sources of light, this is the result:

Jupiter and its moons, 7:34am on 9/25/22, filter set to highlight the moons

This telescope adjustment will help us a lot in our study, but what really sets Jupiter’s moons apart from background stars is that they MOVE. That’s the property that got Galileo excited, and it’s the one which we will focus on in this fieldwork. To detect the moons’ movement, we need to compare images taken over a sequence of hours or days. I’ve assembled a bunch of images for you (download here), but I’m leaving it up to you to decide which subset of these images to focus on.

Due week 7: preliminary
From the collection of 15 images linked above, select 3-4 that tell a story of the moons’ motion relative to Jupiter. Consider whether you get better results comparing hour-by-hour or day-by-day photos. Consider also how you might present this data, visually, to maximum effect? Post your reflection in the comments below.
Due week 9: final version
Report: drawing exclusively on the image set linked above, what can you conclude about the moons revolving around Jupiter? How many distinct moons do you see? Taking into account the timestamp of each image, are some of the moons orbiting faster than others? To be clear, your goal is NOT to get the “right” answer to any of these questions, but rather to get the best answer(s) you can based on the evidence available to you.

Your report should draw from at least three of the images, and should present them visually so as to highlight the moons’ motion. Image processing: to better isolate this motion, you will likely need to manipulate the images so that Jupiter is stationary. Note that all these images all have the same magnification and angle, so all you need to do here is shift the images up, down, right or left to bring Jupiter into the same position from one image to the next. Clear visual presentation of this data will be one factor considered in the grade for this assignment.

Options for your write-up:

  1. You can assume the persona of Galileo, one of his assistants, or a contemporary rival, writing in the early 1600s as one of the first people to see Jupiter’s moons.
  2. Alternatively, you can write from a modern perspective, evaluating your results by comparison to modern data (Wikipedia).

Either way, match your language to the occasion. Your writeup should detail the procedure you followed in processing the data, and should conclude by meditating on how your results might be improved upon.

Turn your report in by emailing it as a .pdf to Prof Henebry.

Show/Hide due Week 7
Show/Hide due Week 9

Solar Noon

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Determine the clock time corresponding to solar noon. This is trickier than you might think, and may require several tries before you get it right. I’m happy to give a week’s extension on this experiment, but do make a first stab at it during the second week of classes, so you have a sense of the challenges and can complete the project in time.

Full details in Fabian, Ex 2.1, “Gnomons and Shadow-Casting,” pp 33-34. You need to find a spot where the sun shines at noon and where the ground is level. An outdoor patio or bench is probably ideal: sidewalks and parking lots are often built on a grade, and the sun’s light may bend as it passes through glass to reach an indoor location.

Start by guesstimating the time of solar noon by looking up the time of sunrise and sunset in your location. Set up your apparatus 10 minutes before this time, and record the position of the gnomon’s tip at 1-minute intervals.

Apparatus:

  • Solar Noon radial graph paper, ruled in cm. Download and print.
  • A gnomon with a sharp tip—a sharpened pencil or the like. If possible, bring a range of possible gnomons, choosing one that casts neither too long nor too short a shadow—no longer than the ring marked 9 and no shorter than the ring marked 5 on the sheet.
  • Clay, gum, or scotch tape to anchor the gnomon at the center of the worksheet.
  • Scotch tape to anchor the worksheet.
  • A smartphone with a compass app.
  • If possible: a carpenter’s level. Otherwise, something rectangular to serve as a right angle tool.
  • A pencil to record your measurements.

Instructions:

  1. Find a surface with good sun exposure. If available, use the level to check that the surface is level. Otherwise, do your best to check it by eye. Flat concrete benches are likely level; sidewalks generally are not.
  2. Use the compass on your phone to align the paper so that the arrow at the top points due West. Anchor the worksheet to the surface with scotch tape.
  3. Anchor the gnomon at the center of the sheet, using the level or right angle tool to ensure it is vertical.
  4. Take a photograph of your experimental apparatus in action.
  5. Record measurements at 1-minute intervals, starting about 10 minutes before your guesstimate of solar noon, and finishing 10 minutes after. For each, mark an X on the worksheet at the tip of the gnomon’s shadow along with the clock time of the measurement.
  6. If you’ve done everything right, the gnomon’s shadow should get shorter, reach a minimum, then grow longer. The mark you made at the minimum represents Solar Noon.

Calculations:

  • Reading from the mark when the gnomon’s shadow was shortest, what clock time corresponded with Solar Noon? How many minutes is Clock Noon off from Solar Noon, positive or negative, in the city where you did the experiment (specify your city in your answer)? Would you need to travel East or West in your Time Zone to be in a place where Solar Noon coincides with Clock Noon?
  • Use a ruler to draw a line from the center of the worksheet to the mark corresponding to Solar Noon. That line is True North, by contrast to the 0° mark which corresponds to Compass North. Using a protractor, or estimating from the angle measures provided on the sheet, how many degrees does Compass North deviate from True North, positive or negative, in the city where you did the experiment?
  • Calculate the ratio between the length of the shadow at Solar Noon and the length of the physical gnomon you used. From this you can calculate the latitude of the city where you live. Tangent (Latitude) = Shadow / Gnomon. You’ll need a calculator with the inverse tangent function—make sure you get an answer in degrees (DEG), not radians (RAD).

Upload your results in a comment below, attaching your a photo or scan of the completed worksheet and (in a reply to your first comment), the photo you took of your experimental apparatus.

Autumnal Equinox

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Challenge: Use the position of the sun as it dips below the horizon on the Autumnal Equinox (Sep 22, 2025) to define true West.

Due week 2: data collection trial run
On a day with relatively clear skies, look up the expected time of sunset, then use your cellphone camera to document the sun setting. Take multiple photographs from the same position starting roughly ten minutes before sunset.

Under the appropriate heading in the comments below, post your best image along with a 1-¶ reflection: Did the sun appear to set before or after the official time of sunset? Why do you suppose that is? How might you improve data collection in preparation for documenting the Autumnal Equinox next week?

Due week 3: data processing trial run
Using a photograph of the setting sun as reference, mark on a local map your position as well as the direction of the sun as it set.

Under the appropriate heading in the comments below, post a 1-¶ reflection: how confident are you in these findings? How might you use landmarks in the photographs to improve the accuracy of your findings?

Due week 4: data collection
Use your cameraphone to document the sun as it dips below the horizon on the Autumnal Equinox (Sep 22, 2025), standing on or near a landmark in your area where you have a good view of the western horizon. (In case of cloudy weather, perform this experiment on an evening shortly after the equinox.) Be sure to record your own position as well as capturing the sun’s position as it sets.

Under the appropriate heading in the comments below, post your best image along with a 1-¶ reflection: Did the sun appear to set due West? How can you tell?

Due week 5: final version
Under the appropriate heading in the comments below, post your finalized Autumnal Equinox fieldwork as a .pdf, including annotated photographic data and a map showing the direction of the sun as it set. Your writeup should detail both the experimental procedure you followed in week 4 and the data processing you used to create the map. It should conclude by meditating on the accuracy of your results—and how they might be improved upon if you were to repeat the experiment next year.

Show/Hide due Week 2
Show/Hide due Week 3
Show/Hide due Week 4
Show/Hide due Week 5

Marking Sunset-old

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In a series of measurements over the course of the semester, determine (a) the clock time and (b) the magnetic compass bearing of sunset. Full details in Fabian, Ex 2.2, “Marking Sunrise and Sunset,” pp 34-35.

Post your fieldwork measurements via this Google Formvia this Google Form (link is now offline). Each entry should include a photograph of the sun against the horizon, the date of measurement, your physical latitude and longitude, and the two data points listed above.

Final Report

Use the Marking Sunset data (linked below) to reach an empirically driven conclusion about the timing and location of sunset in the fall of 2021. If you’re not sure what to focus on, think back to our earliest classes: “how did the time of sunset change?” is a good default research question, but it’s far from being the only one you might answer. It’s generally best to focus on how two variables relate to one another: date and time, date and compass bearing, time and latitude, etc., but you can give a more complex analysis if you’re feeling ambitious.

Note that this is a messy data set: in addition to possible measurement errors and typos during data entry, students took measurements in different locations (both latitude and longitude), and some had “true north” turned on while others had it off and still others “weren’t sure.” This means you’ll likely need to exclude some data or normalize the data set in the process of your analysis.

Your writeup should contain the following sections (aim for brevity, clarity, and specificity):

  • Goal: what phenomenon did you explore through analysis of this data set? What findings did you expect?
  • Procedure: what methods did you use in analyzing the data? If you excluded some data or normalized the data set, on what basis did you do so?
  • Results: your findings, including at least one visual representation of the data (i.e. a graph)
  • Conclusion: how did your findings differ from expectations? What does this suggest?

The Marking Sunset data is posted here. This link should give you view-only access. Please don’t ask me for edit access. Instead, go to the File menu visible within Google Sheets and either (1) make a copy so you can work with the data directly in Google Docs or (2) download to your laptop as an Excel file.

Email your results as a .pdf to Prof Henebry.

Course Description

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How has stargazing shaped our understanding of the world and our place within it? How have changes in our conception of the universe altered our understanding of human nature—and vice versa? While we tend to conceptualize art and science as separate spheres, astronomy has always been interwoven with culture, and artists and astronomers continue to draw inspiration from one another even today. This team-taught course traces the shared, often symbiotic, history of these two ways of knowing and exploring the cosmos. Combining scientific instruction with discussion and analysis of literature, the visual arts, music, and theater, the course culminates in creative artistic projects that draw on astronomy and the history of human stargazing.

We will examine three distinct phases in scientific understanding: the earth-centered systems of the Ancient Mediterranean and Central America, the sun-centered system developed in sixteenth- and seventeenth-century Europe, and the radically uncentered, infinitely expanding universe of twentieth-century science. Students will observe the apparent motion of heavenly bodies across the sky, and will learn how that motion was explained in antiquity—as well as how it was harnessed for the creation of calendrical time. Students will make telescopic observations of the moons of Jupiter, and grapple with the paradigm shift of Copernicus, Galileo, and Newton. Finally, students will learn about Hubble’s use of spectroscopy and red shift observations in the development of the Big Bang Theory.

In connection with these distinct phases, or epistemes, we will examine ancient astronomical artifacts, calendrical systems, the Music of the Spheres, the Great Chain of Being, early and more recent science fiction, Romantic-era stargazing, and twentieth-century avant-garde music and art.

HUB Coverage

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This course will address the following Hub areas:

Scientific Inquiry I

  • Students will observe the diurnal and long-term apparent motions of the sun, moon, stars, and planets—both directly and through a visit to a local planetarium. Students will employ the astronomic models of three distinct eras (Antiquity, the seventeenth century, and the twentieth century) to explain the apparent motion of heavenly bodies. They will engage in naked eye astronomical observations, and they will learn about the use of telescopes, as well as the wide array of more advanced equipment used by astronomers today. Through close study of the Copernican Revolution, students will grapple with the processes through which scientists entertain new theories and (sometimes) reject old ones—resulting in significant changes to our understanding of the universe and of our place within it.

Writing Intensive

  • In both formal and informal writing assignments, students will discuss the influence of astronomy on the art and culture of the past and the present. They will write about astronomy-inspired literature and art. They will formulate a grant proposal for an educational project (museum exhibit, curriculum, etc.) on topic related to Astronomy. And they will craft an artist’s statement in conjunction with a work of art (visual, musical, spoken-word, or multimedia) that responds to astronomical lore of the past or present.
  • Students will write in response to a variety of prompts, for a total of 16 pages of graded work: two experimental fieldwork reports (2p each); two critical essays on cultural artifacts (3p each); a grant proposal (4p); and an artist’s statement (2p). The two essays draw inspiration and language from low-stakes HW assignments; the grant proposal and artist’s statement are submitted in draft form and then revised. Total graded work: 2 fieldwork reports (4p total), 2 essays (6p total), 4p project proposal and 2p artist statement = 16p. This will provide experience in different modes, from the report to the essay to the proposal. Students will receive feedback on all submitted work.

Pedagogy

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This team-taught course brings together faculty from the Natural Science and the Rhetoric Divisions of the College of General Studies. Both professors will be on-site for the entirety of each class. Classes will run in the evening, once weekly for three hours, with each session devoted to a variety of educational strategies:

  • Lecture-style presentation of key concepts from science and philosophy, broken up by active learning as described below.
  • Active learning promoted through short in-class writing assignments followed by peer-to-peer discussion—leading in turn to whole-class discussion as described below.
  • Whole-class discussion of scientific discoveries and their impact on the arts—as well as the influence of art, culture, and society in shaping scientific inquiry and discovery.

Outside of the classroom we will draw on a variety of experiential learning strategies:

  • rooftop stargazing during class sessions
  • fieldwork assignments requiring astronomical measurements
  • possible planetarium visit