The tropics and the subsolar point

In Honolulu, at 21.3° N, the noon Sun is straight overhead twice a year: around 26 May and 15 July.

The point under the Sun

At any moment there is exactly one place on Earth where the Sun is straight overhead at 90°. Geographers call it the subsolar point. Its latitude is the Sun's declination, the number shown in the readout as "Sun overhead at". Because Earth spins, the subsolar point races west around the planet once a day. Because Earth orbits with a tilted axis, it also drifts north and south through the year, never going farther than 23.44° from the equator.

The calendar of the subsolar point is the calendar of the seasons. On the March equinox it crosses the equator heading north. On the June solstice it reaches its northernmost latitude, 23.44° N, the Tropic of Cancer, and turns back. On the September equinox it crosses the equator again heading south, and on the December solstice it reaches 23.44° S, the Tropic of Capricorn. The word solstice comes from Latin for "sun stands still", because the Sun seems to pause there before turning around.

Noon Sun height anywhere

Once you know the subsolar latitude δ, the height of the noon Sun at any latitude φ is simple: 90° minus the difference in latitude, written 90° − |φ − δ|. If you stand on the subsolar point, the difference is zero and the Sun is at 90°. For every degree of latitude you move away, the noon Sun sinks one degree. At the equator on an equinox it is 90°. In Sydney (33.9° S) on the December solstice it is 90° − |−33.9° + 23.44°| ≈ 79.5°, and on the June solstice only about 32.7°.

Life in the tropics

The band between the two tropics is the only part of Earth where the Sun can ever stand straight overhead, and every place inside it gets that twice a year as the subsolar point passes going north and again coming back. Honolulu at 21.3° N is close to the Tropic of Cancer, so its two dates, about 26 May and 15 July, are only seven weeks apart. Near the equator the two dates are about six months apart, close to the equinoxes.

Because the noon Sun is always high in the tropics, the energy arriving each day changes much less through the year than at higher latitudes. Day length barely changes either. That is why many tropical places have little difference between "summer" and "winter" temperatures. Their seasons are set by rain instead. Australia's Bureau of Meteorology, for example, divides the year in its northern tropics into a wet season (October to April) and a dry season (May to September) rather than four temperature seasons.

You can use the rule backwards, the way sailors once did. Measure the height of the noon Sun, look up the declination for that date in an almanac, and your latitude follows: φ = δ ± (90° − noon height). If the subsolar point is on the equator and the noon Sun stands 60° above the southern horizon, you are 30° north of the equator. Navigators did this with a sextant for centuries before satellite positioning.