• Erik Petigura

On the Shoulders of Eratosthenes — An Silver Lining to Remote Instruction

Fall quarter begins this week, and I've been getting ready to teach another course over Zoom. It's one that I'm particularly excited about called "Evolution of Cosmos and Life." It's a yearlong course at UCLA geared toward freshmen students outside the physical sciences where we cover the origin of the universe, the Earth, life, and our species. It's co-taught by me, Dave Jewitt (Earth, Planetary, & Space Sciences), Tony Friscia (Integrative Biology & Physiology), and Caitlin Brown (Ecology & Evolutionary Biology).

One of the biggest challenges of remote instruction is adapting lab work. We can't ship expensive equipment to 200+ students, and online emulators just feel second rate. I was complaining about this during a particularly hot summer day when my wife, my baby, and I were having a (socially distant) visit with a couple of friends on our deck. As we slowly melted under the oppressive sun, we wondered if we could come up with some instructive lab that made use of the sun.

Our idea was to have students recreate one of the most influential experiments all time.

Back around 240 BCE, Eratosthenes of Cyrene (c. 276 BCE – c. 195 BC), then the chief librarian at the Library of Alexandria Egypt noticed that, on the longest day of the year, vertical columns in Syene, Eygpt some 800 km to the south cast no shadows (i.e. the sun was directly overhead) while those in Alexandria clearly still cast noticeable shadows. Eratosthenes reasoned correctly that the Earth was a sphere and measured its circumference based on the difference in angles.

For this lab, students form pairs separated by at least 300 km North-South latitude. They design an experiment from ordinary household items to measure the elevation of the sun (i.e. its angle above the horizon) at solar noon. If done carefully, the maximum solar elevation should differ based on their difference in latitude. From this difference in angles (and a little trig) the students calculate their difference in latitude and the size of the Earth.

I few weekends ago, I workshopped this lab with my parents and brother in Palo Alto and San Francisco. I used a bedside lamp with a sturdy base and some paper to mark the progress of the shadow. It was fun to compare what was going on in realtime over Zoom. Not only could we confirm the difference in sun elevation, but we could tell the time delay between solar noon in Los Angeles and in Palo Alto / San Francisco. LA is slightly to the east and solar noon occurs about 10min earlier. In the end, we got the answer right to 10%, and we had a lively discussion about the leading sources of error were and how we could improve the experiment if we were to repeat it.

I've attached a link to lab in case others are interested in trying it. It touches on a surprising number of cool concepts: the curvature/rotation of the Earth, latitude/longitude, solar vs. civil time, statistical vs. systematic errors, and the enigmatic analemma. Also, I think it's awesome that this is a lab where students need to be dispersed around the country/globe. Here remote learning is a feature, not a bug. It's great for any intro astronomy class, or for anyone who's looking for something fun to do over Zoom.

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