This is not a trick question. The answer I’m thinking of is not “at night,” “on a cloudy day,” or “in a window-less room with the lights off.” I’m asking when, if ever, the Sun is directly overhead so that your shadow falls directly below you.
Where I live, near Chicago, the answer is “never.” In Singapore, where I was earlier this year, the answer is “twice a year.” The key difference is that Singapore lies in the tropics while Chicago doesn’t.
World map with the tropics shaded in. By KVDP via Wikimedia Commons.
In my last post, I told some lies. I said the shadow of a stick moves clockwise. This is true north of the tropics. But south of the tropics, it will move counter-clockwise. Within the tropics, it will switch back and forth between the two directions.
Likewise, I told you that the shadow of a stick will always point in the same direction at noon. This is also true outside of the tropics. North of the tropics, the shadow of a stick will always point North at noon. South of the tropics, it will always point South at noon. But in the tropics, it will point North at noon for part of the year and South at noon during the rest of the year.
Notice I haven’t defined the tropics yet. It has to do with the Earth’s tilt which is a big topic for a future post.
For now, what I want you to understand is that if you live outside of the tropics, the Sun will never be directly overhead. That means your shadow will never fall directly below you.
If you live in the tropics, or will be spending some time there, and want to know when you will cast no shadow, you can find out by visiting timeanddate.com/sun. Step outside when the Sun’s altitude is nearly 90 degrees and have someone take a picture of you.
This brings me to another lie I’ve been telling. Whenever I used the word “noon,” I didn’t mean noon according to your clock. “Solar noon” would have been a more accurate term. Shadows are shortest at solar noon, not when your clock says it is noon. If you live at the eastern edge of your time zone, solar noon will occur at a different time than if you live at the western edge. For reasons of convenience and politics, some places are in the “wrong” time zone altogether. In Singapore, solar noon always occurs closer to 1 pm than noon. So the shadow of a stick will always be shorter at 1 pm there than at 12 pm.
Shadows in Singapore at “noon.” The images on the left were taken on January 31, 2016 at 12:00 pm (top) and at 1:18 pm (bottom) when it was solar noon according to timeanddate.com. The image on the right was taken on March 24, 2016 at solar noon (1:11 pm) when the Sun was directly overhead. Image credit: V. Sivaramakrishnan.
Can you handle one more lie being exposed? This one is tough which is why I saved it for last.
Not only does solar noon not occur when your clock says it is noon, it does not occur at the same time every day. It is not exactly 24 hours from one solar noon to the next. The Sun’s speed, as it appears to move across the sky changes over time due to Earth’s axial tilt and the shape of its orbit. Those changes have been averaged out to keep the mean solar day exactly 24 hours long. Otherwise a day would either have more hours in some months than others or hours would be longer in some months than others. Imagine how inconvenient that would be.
In summary, if a few lies don’t bother you, a day is the interval from noon to noon. If you like being precise to the point of sounding ridiculous, a mean solar day is the interval from one mean solar noon to the next.