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While researching an answer to this question I stumbled across the term "חצות האמצעי".
What does it mean? Does it refer to halachic midday, i.e. halfway between netz hachama and shkias hachama, or something else? How does it differ from "חצות האמיתי"?

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It refers to "mean noon," as opposed to "solar noon." True solar noon is when the sun crosses the imaginary meridian in the sky between east and west, i.e., when the sun is exactly in the south. The time this occurs varies slightly every day due to a number of factors; the variation is known as the "equation of time." (See here for an excellent explanation of this phenomenon.) The average time at which noon occurs is called the mean noon, and by definition it is at the same time every day. (Theoretically 12:00, but due to uniform time zones, it is usually off by a few minutes. In NYC, for example, it is at 11:56.)

For more information, see here and here in Wikipedia.

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    Great answer! Is there a halachic source for this?
    – HodofHod
    Nov 20, 2011 at 17:53
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    There are many sources who say that the computation of 'mystical' times (for lack of a better term), such as tikkun chatzos and "kiddush-avoidance hour," are based on average hours rather than actual solar hours. Also, R' Moshe Feinstein famously held that all zemanim are to be computed based on the average noon. An exhaustive analysis of the topic (with many sources) can be found in this essay: docs.google.com/…
    – Dave
    Nov 20, 2011 at 18:50
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    @Alex - solar noon is certainly not at the same time every day. It varies according to the equation of time mentioned above. That's why sundials need to be used in conjunction with a graph or table of numbers, to adjust for the difference. It's also why the position of the sun in the sky at any given time follows a figure-8 pattern (called the "analemma") over the course of the year.
    – Dave
    Nov 20, 2011 at 22:53
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    So "חצות האמיתי" is solar noon?
    – HodofHod
    Nov 21, 2011 at 3:33
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    HodofHod - Correct.
    – Dave
    Nov 21, 2011 at 5:40

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