# Zero Shadow Day

This online calculator calculates the dates of zero shadow days at a given latitude. The latitude of the observation site must be south of the Tropic of Cancer and north of the Tropic of Capricorn.

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What is a zero shadow day? It is when the Sun at noon rises exactly to the zenith, that is, the point on the celestial sphere above the observer's head. That is, the Sun is exactly "overhead", orthogonal to the horizontal plane at the point of the observer's position. The observer's shadow at such a point is exactly below him, hence the day of zero shadow. The possibility of the Sun being at the zenith is related to the Sun's declination. During the year, the declination of the Sun varies from -23°26′16″ to 23°26′16″ (approximate value of the tilt of the Earth's axis), and it is possible to observe the Sun at the zenith at the moment when the declination of the Sun is equal to or very close to the latitude of the place of observation.

It follows that the day of zero shadow can only be observed between 23°26′16″ south latitude and 23°26′16″ north latitude, or between the Southern Tropic or Tropic of Capricorn and the Northern Tropic or Tropic of Cancer. Between the tropics, the Sun is at its zenith twice a year; on the tropics themselves, it is at its zenith once, on the summer and winter solstices respectively. The day of zero shadow over the equator occurs on the spring and fall equinoxes.

The calculator below uses the Declination and maximum altitude of the Sun above the horizon on a given date calculator to calculate the Sun's declination for each day of the year. The days when the declination is closest to a given latitude are tabulated as zero shadow days.

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