A “New Year” is a very subjective notion. It constitutes a chronological marker defined only by an anthropocentric standard. The duration of a year is merely constructed as per corresponding astronomical phenomena that have been deemed significant by humans. Even though we have largely been preconditioned to assume that there is a naturally ordained fixed duration of time that is defined as a year, the definition of a year is flexible and only depends on how one chooses to define it.
The mean tropical solar year, or the period of time required for the Earth to complete one full revolution around the Sun, as measured by successive arrivals of the sun to the vernal (spring) equinox is equal to 365 days, 5 hours, 48 minutes, 48 seconds. The “tropical solar year” is the basis of the modern civil calendar.But, the concept of a year can also be defined depending on when the Sun arrives to some fixed background star, from where it last set out. This is known as a sidereal year and is 365 days, 6 hours, 9 minutes, 11 seconds. The sidereal year is 20 minutes, 26 seconds longer than the tropical year. The difference arises due to the precession of the Earth’s equinoxes, which results in the Sun returning to the same equinoctial point not being in the same position with respect to the fixed stars in the subsequent year. The Sun ultimately moves eastwards along the ecliptic whereas the equinoxes move westwards to meet the Sun. And, indeed, since one complete precessional cycle takes about 26,000 years, the equinoxes shift about 1/26000 (20 minutes) every year. This makes the use of a calendar based on a sidereal year rather problematic. For each successive year, the seasons would start arriving 20 minutes earlier and the calendar would eventually begin to err rather conspicuously. The original dates specified by the calendar would be dis-harmonized and sooner than later, winter would correspond to August and summer would correspond to December. By contrast, a calendar based on the tropical year would, obviously, not have this problem.
The subjectivity around calendars also extends to New Year’s Day itself. There is indeed no obvious reason why a year should start on January 1st rather than on any other seasonal event such as, for instance, the time of the vernal equinox (March 20th). Indeed, the early Roman calendar which included 10 months, saw the New Year begin on March 1st, a time seen auspicious enough for military campaigns to resume. In 46 BC, however, with help from the Egyptian astronomer Sosigenes, the Roman Emperor Julius Caesar revised the Roman calendar and decreed the beginning of the New Year as January 1st, seeing as it represented the time new Roman Consuls were chosen, a revision which did not click with much of later Western Christian Europe, which, instead, for the next 1000 years and further on, would celebrate the New Year’s Day as corresponding to events of more theological significance such as Christmas, Easter, or the Feast of the Annunciation. Caesar, further, added two extra days to each of the five 29 day months in the Roman calendar, except for February, which retained its 28 day designation. The Julian calendar, now functioning on the notion of a year comprising 365 days (up from the 355 days of the Roman calendar), also included an extra leap day every four years, added to February 23rd, in order to remove any drifts that a 365.25 day cycle of a year, as concurrently thought to have exactly been, would cause (i.e. 1/4 of a day each year compensated in the fourth year by virtue of the leap year). However, by the time Caesar’s reforms were instituted, the calendar had still been venturing 80 days off course. As such, the year 46 BC was revised to contain 446 days, leading to its being known as Anuus Confusionis (Latin for year of confusion). But, the Julian calendar, averaging out on 365.25 days, still erred by being 0.00781th of a day (i.e. 11 minutes and 15 seconds) in excess over the actual tropical year, an amount which added up with time. This presented a notable problem by the year 1582, where the vernal equinox occurred 10 days earlier than it should on March 11th, rather than on March 21st. Since that meant religious holidays moving earlier into the season, Pope Gregory XIII decreed for a new calendar to be established, the Gregorian calendar. He removed 10 days from that year (October 4th was followed by October 15th) and corrected the Julian calendar by omitting leap years divisible by 100 but not leap years divisible by 400. Pope Gregory XIII also restored January 1st as New Year’s Day.
But, even the Gregorian calendar is not perfect! Its 0.0003 day discrepancy from the actual tropical year will accumulate to a day in 3300 years.