Where on Earth do you have to be in order to see the Sun at the zenith? As seen from such a location, will the Sun be at the zenith every day? Explain.

The Earth's axial tilt, also known as its obliquity, is the angle between the planet's rotational axis and its orbital plane around the Sun. This tilt is about 23.5 degrees and is responsible for the changing seasons and the varying length of day and night throughout the year.

Significantly, it also determines the migration of the solar zenith—the point at which the Sun is at its highest point in the sky as viewed from the Earth, directly overhead at noon—between the Tropics of Cancer and Capricorn. This axial tilt helps to understand why certain locations experience the Sun's zenith position at different times of the year.

The Tropic of Cancer is an imaginary line of latitude located at approximately 23.5 degrees North of the equator. It is the northernmost point at which the Sun can be directly overhead at noon. This happens during the June solstice, when the Northern Hemisphere is tilted towards the Sun.

The presence of the Tropic of Cancer indicates the limit of Earth's tropical zone in the north. Areas located between the Equator and the Tropic of Cancer are known for their typically warm climates because they receive a high concentration of sunlight throughout the year.

In symmetry with the Tropic of Cancer, the Tropic of Capricorn exists at approximately 23.5 degrees South of the equator and represents the southernmost latitude where the Sun can appear directly overhead at noon. This celestial event occurs during the December solstice, when the Southern Hemisphere is maximally inclined towards the Sun.

The Tropic of Capricorn delineates the southern boundary of the Earth's tropical zone. Similar to its northern counterpart, regions between the Equator and the Tropic of Capricorn enjoy a warm climate with ample sunlight year-round.

The solar zenith angle is a measure of how far the Sun is from being directly overhead at a particular location and time. Mathematically, it is the angle between the direction of gravity (downward vertical line) at that point and the direction of the Sun. When the solar zenith angle is zero, the Sun is exactly overhead, and this only occurs within the band limited by the Tropics of Cancer and Capricorn.

This angle is a crucial concept for understanding solar radiation and its intensity on Earth's surface. As the Earth rotates and travels around the Sun, the solar zenith angle at any given location changes, influencing the amount of solar energy that location receives.

Solstices occur twice a year when the Sun reaches its most extreme position north or south of the equator, which corresponds to the highest or lowest apparent position in the sky at noon. The December solstice, often around December 21, results in the shortest day in the Northern Hemisphere and the longest day in the Southern Hemisphere. The June solstice, around June 21, is the opposite, marking the longest day north of the equator and the shortest day to the south.

During solstices, the solar zenith is situated at one of the Tropics, Cancer or Capricorn, which explains why locations on these latitudes experience one day each year when the Sun is directly overhead. The solstices are key to understand the variations in daylight and the shift of seasons around the globe.