At local noon on March 21, when the Sun is at the vernal equinox, a sidereal clock will say that it is midnight. Explain why.

The vernal equinox is an astronomical event that occurs once a year when the Sun crosses the celestial equator, moving northward. This crossing usually happens around March 20th or 21st and signifies the onset of spring in the Northern Hemisphere. During the vernal equinox, day and night are approximately equal in length across the planet, as the Earth's tilt on its axis is in such a position that both hemispheres receive nearly equal amounts of sunlight.

Understanding the vernal equinox is crucial for studying the seasonal changes on Earth, as well as for creating various calendars. It also serves as a reference point in astronomy for the celestial coordinate system. When celestial navigators or astronomers talk about the 'First Point of Aries', they are referencing the vernal equinox, which historically was in the constellation of Aries, but due to precession of the equinoxes, it now occurs in Pisces.

Solar time is based on the position of the Sun in the sky, widely used to structure our days in society. There are two common types of solar time: apparent solar time, which directly tracks the motion of the Sun, and mean solar time, which averages out the variations in the apparent solar time. The difference between the two is known as the 'equation of time'.

Apparent solar time can be observed with sundials; however, due to the elliptical shape of Earth's orbit and its axial tilt, the solar day, which is the period from one solar noon to the next, varies throughout the year. Mean solar time is similar to the time kept by clocks — allowing for a more regular timekeeping system. While solar time is instrumental in our daily lives, it is slightly different from sidereal time, which is used by astronomers for tracking celestial objects.

The celestial coordinate system is akin to a map for the sky. It allows astronomers to pinpoint the location of stars, planets, and other celestial objects. This system is fixed relative to the background stars, unlike Earth-based latitude and longitude, which are fixed relative to the planet's surface. The celestial coordinate system is essential for accurately tracking the movement of celestial bodies through the sky.

The two main components of the celestial coordinate system are right ascension and declination, analogous to longitude and latitude on Earth, respectively. Right ascension is measured in hours, minutes, and seconds from the First Point of Aries, which is the reference point located at the vernal equinox. Declination is measured in degrees north or south of the celestial equator. Using this system, any location in the sky can be consistently described regardless of the observer's location on Earth.