on which day the sun overhead to the equator in the noon?
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The sun is directly overhead at noon on the equator on the first day of spring (vernal equinox) and on the first day of fall (autumnal equinox). The sun is directly overhead at noon on the first day of summer at a point 23.5 degrees north of the equator (called the Tropic of Cancer)
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The Sun is directly overhead at "high-noon" on the equator twice per year, at the two equinoxes. Spring (or Vernal) Equinox is usually March 20, and Fall (or Autumnal) equinox is usually September 22. Except at the equator, the equinoxes are the only dates with equal daylight and dark.
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