What is the difference between the sidereal year and the tropical year? Why are these two kinds of year slightly different in length? Why are calendars based on the tropical year?

The precession of the equinoxes is a complex motion of Earth's axis that influences the length of a year. Imagine Earth not just as spinning top but also as a wobbling one. This 'wobble' is due to gravitational forces from the sun and the moon on Earth's equatorial bulge, and it causes our planet's axis to trace out a cone shape over a period of approximately 26,000 years. As a result, the celestial pole (the point directly above the North and South poles) slowly shifts against the background of stars, affecting the position where the Sun crosses the celestial equator.

This process changes the coordinates of the vernal equinox, which is one of two points in the year when day and night are of roughly equal length. Over time, this shift causes the vernal equinox to occur slightly earlier each year in relation to the fixed stars, by about 50 arcseconds. This is the reason why the sidereal year, which measures time in relation to the fixed stars, is about 20 minutes longer than the tropical year, which aligns with the seasons and cycle of the equinoxes.

Picture the Earth, encased in an imaginary bubble that extends into space: this is the celestial sphere. The celestial equator is the projection of our planet's equator onto this sphere. It's an abstract line that holds significance for astronomers and navigators alike, as it helps in specifying the apparent positions of celestial objects.

The celestial equator is crucial for understanding the changing positions of the stars and planets as Earth moves. It's at the celestial equator where the equinoxes occur: when the Sun crosses this line, it heralds the start of spring and fall, marking equal lengths of day and night across the Earth. As the seasons transform, the celestial equator remains a steady reference line, dividing the sky into northern and southern hemispheres and assisting us in tracking the Sun’s yearly journey and its shifts due to the precession of the equinoxes.

Our four seasons—spring, summer, autumn, and winter—make up the seasonal cycle, a fundamental concept linked to Earth's tilt and orbit around the Sun. The tilt of approximately 23.5 degrees means different parts of Earth receive varying amounts of sunlight throughout the year, giving us our seasons. The tropical year times this seasonal cycle, starting and ending with the vernal equinox.

For instance, during the summer solstice, the Northern Hemisphere is tilted towards the Sun and experiences the longest day of the year, while during the winter solstice, it's tilted away, and we have the shortest day. Understanding this cycle not only helps us anticipate the weather but also regulates agricultural patterns, and it is crucial for calendars since it affects the timing of holidays and traditional events.

Calendars are systems for organizing time to align with astronomical events, ensuring a consistent seasonal pattern year after year. They are fundamental for planning agricultural, religious, social, and administrative activities. Most modern calendar systems, such as the Gregorian calendar, are based on the tropical year because it closely follows the seasonal cycle significant for these human endeavors.

Different civilizations have created various calendars, with some like the Islamic calendar based on lunar cycles and others, such as the Jewish calendar, combining lunar and solar cycles. The Gregorian calendar, the most widely used today, was designed to bring the date of Easter closer to the time it was celebrated by the early Church and to fix the date drift problem of its predecessor, the Julian calendar. Adjustments, such as leap years, are added to keep the calendar in sync with Earth's revolutions around the Sun, balancing the practical need to match the average length of a tropical year.