Short answers, pulled from the story.
A tropical year takes 365 days, 5 hours, 48 minutes, and 45 seconds to return to the same position relative to the stars. This precise measurement creates a fundamental problem for human civilization because calendars are built on whole days while the planet's orbit is a fraction of a day longer.
Pope Gregory XIII introduced the Gregorian calendar in 1582 to realign the equinox and establish a new rule for leap years. This system skipped ten days to correct the drift and established that years divisible by 100 would not be leap years unless they were also divisible by 400.
The Islamic calendar uses a lunar year of roughly 354 days which causes the month of Ramadan to shift backward through the seasons by about 11 days each year. This ensures that the fasting month eventually occurs in every season of the solar cycle.
The length of the year changes over millennia due to the gravitational tugs of other planets and the slowing rotation of the Earth. Tidal drag between the Earth and the Moon transfers angular momentum causing the day to lengthen by about 1.7 milliseconds per century.
The solar system orbits the center of the Milky Way galaxy completing one revolution in roughly 230 million Earth years. This duration is known as the Galactic year and represents a vast timescale that challenges human comprehension.