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SearchReSearch

Answer (1): Time and date from a shadow?

Dan Russell • October 8, 2021
 SearchReSearch
Republished with permission from SearchReSearch
Answer (1): Time and date from a shadow? Dan Russell

Can you actually get the time and date from just a shadow?


This isn't the post I thought I was going to make. As you'll see, this has turned out to be much more complicated than I thought it would be. So I'm going to do this as a multi-part post--I'll show you my working-out process. I'll show you what worked, what didn't, and what I learned along the way. Hope you'll stick with me through the next couple of posts until we get this Challenge solved. Hope you'll find this as fascinating as I do!


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In our last Challenge we met the SkyTree in Tokyo, Japan. (That is, 東京スカイツリー, Tōkyō Sukaitsurī) It's a very tall tower in Tokyo that's known around the world as a landmark.

And we saw its mighty shadow, extending from the base of the tower to just beyond the bridge over the Sumida river.


Our Challenge was simple:

1. What day and time-of-day was this photograph taken?

As always, I'm going to start with a simple, fairly open-ended query:

[ how to find time and date from shadow ]

which leads to a bunch of fascinating web pages, each of which tells us how to do exactly this. (Along with lots of details about the geometry and astronomy involved.)

A really useful summary of this calculation can be found on the Instructables site at "Time and Date of Satellite Maps." On this page there's a summary of how and why you can make this calculation.

When I wrote this Challenge, I knew about this "Time and Date of Satellite Maps" page and the computations involved. I figured that I'd just do the math, compute the answer, and call it a day. It turned out to be more complicated than that. But here's what I did first....

TL;DR - over the course of the year, the sun moves throughout the sky on a figure 8 path called an analemma. If there was a tall tower standing, you'd see the tip of the tower trace the analemma on the ground. Like this:





Or, if you track the sun across the sky, you'll see that every day is just a bit different. The sun rises in a slightly different place each day, takes a gentle curve across the sky, and sets in a slightly different place.

P/C Petapixel showing the sun's path across the sky each day. Filmed in Scotland using very clever pinhole cameras (the article is worth reading).