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At true solar noon, the subsolar point should be directly north or south of you, and therefore a vertical stick's shadow should point directly north or south, right?

The Wikipedia page for Sun Path is confusing me. It claims that at the equinoxes, a vertical stick's shadow will point 23.5° off of true north or south. It says that you only get straight north/south shadows at solar noon at the solstices.

On the equator, the sun will be straight overhead and a vertical stick will cast no shadow at solar noon on the equinoxes. On the vernal equinox, north of the subsolar point (on the equator) the vertical stick's shadow will point a little westwards of true north (NNW) reading 336.5° from true north and little eastwards of true south (SSE) reading 156.5° from true north. On the autumnal equinox, north of the subsolar point (on the equator), the shadow will point a little eastwards of true north (NNE) reading 23.5° from true north (and south of the subsolar, the shadow will point a little westward of true south (SSW) reading 203.5° from true north).

--https://en.wikipedia.org/wiki/Sun_path#Shadow_of_a_vertical_stick_at_solar_noon

Why would this be true? My understanding is that true solar noon is defined by when the Sun is directly north or south, and the subsolar point is on your longitude. Mean solar noon is a different story, thanks to the equation of time.

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    $\begingroup$ I agree, Josh. At solar noon, the shadow of a vertical stick (or a plumb line) on a horizontal surface should run north-south. That's a standard way that sundial makers use to find the meridian. $\endgroup$ – PM 2Ring Oct 5 at 13:22
  • $\begingroup$ That whole section of the linked Wikipedia page seems both incorrect, unclear and unimportant. $\endgroup$ – antlersoft Oct 5 at 17:26
  • $\begingroup$ It's also unsourced, which makes it even more dubious. Maybe I should try to delete that section. $\endgroup$ – Josh Haberman Oct 5 at 19:20
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Your understanding is correct, the shadow of a vertical stick on a level plane always points north or south at solar noon, except in the Tropics where sometimes it will not have any shadow due to the Sun being at the zenith, and at the Poles, where solar noon is undefined. The sun can also be below the horizon at solar noon: places inside a polar circle can experience polar night, when the Sun does not rise for at least an entire day. On those days, even at solar noon, the Sun remains below the horizon.

This erroneous passage seems to originate from edits on 13 April 2012. The original text made more sense:

On the Equator, the sun will be straight overhead and a vertical stick will cast no shadow at noon (solar time) on March 21 and September 23, the equinox. 23.5 degrees north of the equator on the Tropic of Cancer, a vertical stick will cast no shadow on June 21, the summer solstice for the northern hemisphere. The rest of the year, the noon shadow will point to the North pole. 23.5 degrees south of the equator on the Tropic of Capricorn, a vertical stick will cast no shadow on December 21, the summer solstice for the southern hemisphere, and the rest of the year its noon shadow will point to the South pole. North of the Tropic of Cancer, the noon shadow will always point north, and conversely, south of the Tropic of Capricorn, the noon shadow will always point south.

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