What latitude is the sun directly overhead at noon on may 5th August 10th abd October 15th?

Answer 1

Anywhere where the declination of the Sun is equal to your latitude. You can look up the declination of the Sun in the Nautical Almanac.

Declination is the angle of a celestial body north or south of the celestial equator; the celestial equator is the same as the terrestrial one, extended out into space. On June 21, the Sun's declination is about 23.5 degrees north; on the equinoxes, it is zero. On December 21, the Sun's declination is about 23.5 degrees south.

Answer 2

You can look up the declination, which is equivalent to "celestial longitude", in the Nautical Almanac. I've added a link to the Nautical Almanac below.

To determine the declination, you would need to specify the precise time, including the year, and you would need to specify a time zone if you want to use the word "Noon". For this example, we'll use Greenwich Mean Time and this year, 2010.

At 12:00 GMT May 5, 2010, the Sun was directly over latitude 16 degrees, 18.2 minutes North.

At 12:00 GMT August 10, 2010, the Sun was over 15 degrees, 30.5 minutes north.

At 12:00 GMT October 15, 2010, the Sun was over 8 degrees, 34.8 minutes South.