Eclipse from Mt Strawberry and Some Calculations

Mt. Strawberry, OR (alt. 2700 m | 9000 ft).

Just moments from the total solar eclipse I saw the shadow of the moon coming from the horizon. It crept slowly but then at one point it sprinted so fast I didn’t realize when the shadow hit me. It was a surreal moment. The darkness took hold and frigid wind just sends chills to my bones. Then I saw total solar eclipse for the first time in my life, a ring of light with an organic life-like corona dancing slowly about the dark sphere that used to be the sun. All life stood still at that moment. Time stops. And of course, everyone boomed in excitement. I was too mesmerized by the scenery to care. It was worth going up the mountains. I loved every moment of it.

I could swear there was a temperature drop of 10 C/20 F since I had to actually wear my double layer and everyone else started wearing jackets, or maybe it was the wind?

Back Of the Envelope Calculations

Since I am back home, tired, and did not wish to deal with real life yet. I made some rough calculations regarding the event I have seen.

At the top of the mountain (2700 m | 9000 ft) I was able to see about 195 km | 120 mi away (Bohren and Fraser, 1986). Since the speed of the shadow provided by Rao averaged around 3600 km/h | 2240 mi/h which is about 1 km/s | 0.62 mi/s this would mean it took roughly 3 minute for the shadow to travel from the horizon to my place (Rao, 2017). Of course the speed of the moon shadow itself actually varies because it was projected on an oblate spheroid surface of Earth. Becoming progressively slower with distance. But we can safely assume the speed to be constant because of the short distances involved relative to the total distance the moon shadow travels. Therefore I should see a constant speed moon shadow no?

Well no, since human perception, and in extension human vision does not operate linearly but is logarithmic, this is called Weber-Fechner’s Law which relates the relationship between actual change and perceived change (Weber, 1996). Similar to how a person looking at oncoming train as slow from afar, but it is actually progressing quicker than what it seems to be. This will only be apparent to the poor lad who tried to pass the train way too close and it’s already too late. So far it all makes sense, but I’m not sure it will still make sense when I wake up tomorrow.

I wrote this for a sort of journaling and fun writing practice. But if anyone happen to read this and have any corrections/questions/clarifications please email me at agustinuslaw@gmail.com.

References

Bohren, C. F., & Fraser, A. B. (1986). At what altitude does the horizon cease to be visible?. American Journal of Physics, 54(3), 222-227.
d ~ 3.57*sqrt(h). Where d is distance of sight in km, h is the altitude in m.
This approximates how far we can see from a given altitude disregarding the effect of refraction. Though that was also discussed in the paper. 

Rao, J. 2017. “How Long Will the 2017 Solar Eclipse Last? Depends Where You Are”. https://www.space.com/36388-total-solar-eclipse-2017-duration.html. This gave the average speed of moon’s shadow. In Oregon that will be about 3600 km/h ~1 km/s and 2240 mi/h ~ 0.62 mi/s. 

Weber, E. H. (1996). EH Weber on the tactile senses. Psychology Press.
This elaborates on the Weber-Fechner’s Law on logarithmic human perception which I used qualitatively here.

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