USAAAO 2022, I кръг — Задача 30

• D

The hour angle of the Sun during sunrise and sunset is given by the following formula:

The negative solution corresponds to the hour angle at sunrise and the positive solution corresponds to the hour angle at sunset.

In the Northern Hemisphere, the longest day of the year occurs when the Sun is at its maximum declination. In that case:

Since the hour angle of the Sun has a variation of 24 hours in a day, the amount of daylight hours will be the difference between the hour angles:

In the shortest day of the year corresponds to the minimum declination of the Sun:

The amount of daylight hours in that case will be the following:

The difference in the amount of daylight hours:

Answer: D