What causes the variation in length of days and nights?

The variation in length of days and nights is caused by the tilt of the Earth's axis and its orbit around the Sun.

The Earth's axis is tilted at an angle of approximately 23.5 degrees relative to its orbit around the Sun. This tilt, combined with the Earth's elliptical orbit, results in varying amounts of sunlight reaching different parts of the Earth at different times of the year. This is what causes the variation in the length of days and nights.

During the Earth's orbit around the Sun, there are times when the North Pole is tilted towards the Sun, and times when it is tilted away. When the North Pole is tilted towards the Sun, it is summer in the Northern Hemisphere and winter in the Southern Hemisphere. During this time, the Northern Hemisphere experiences longer days and shorter nights because it is receiving more direct sunlight. Conversely, when the North Pole is tilted away from the Sun, it is winter in the Northern Hemisphere and summer in the Southern Hemisphere. The Northern Hemisphere experiences shorter days and longer nights during this time because it is receiving less direct sunlight.

The tilt of the Earth's axis also results in the Sun appearing to move across the sky at different heights at different times of the year. During summer, the Sun appears high in the sky and there are more daylight hours. During winter, the Sun appears lower in the sky and there are fewer daylight hours.

The equinoxes, which occur twice a year around 21st March and 23rd September, are the only times when the Earth is not tilted towards or away from the Sun. On these days, all parts of the Earth experience roughly equal amounts of day and night. This is because the Sun is directly over the equator, resulting in equal amounts of sunlight reaching both the Northern and Southern Hemispheres.