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Leap seconds are added almost every year and in the future, leap seconds will be added more often. Officially a day is still 86 400 seconds, and when a leap-second is added, the "leap-day" is 86 401 seconds. But you could use either number for number of days in a year, average day (currently 86 400.002) or SI day* (86 400). As I understand it ...
It precesses in a circle. This means that the moment of the vernal equinox isn't at the same point in the orbit each year. In fact we reach the vernal equinox in slightly less time than it takes to orbit the sun. The time between successive equinoxes is 365.24219 days. One mean tropical year is 365.24219 days. One sidereal year is 365.256363 days.
5. We do have one planet in our solar system with a neat orbital resonance: Mercury, with an orbital period of 87.9691 Earth days, and a sidereal rotation period of 58.646 days, which works out to almost exactly 1.5 sideral days, or 0.5 solar day, in its year.
A tropical year is defined "as the period of time for the mean ecliptic longitude of the Sun to increase by 360 degrees," and is 365.24219 days in length. One way to think of the tropical year is the length of time it takes for the sun to complete its north-south journey through our sky.
We take N1 and subtract in by the value of (N2 * N3), which will be 2 on a non-leap year if February has passed, 1 on a leap year, or 0 if we haven't passed February. We add in the days in the current month, and we subtract 30 to get the offset in N1 values. This should consistently give you the day of the year.
To account for the remaining $\sim60$ days, Mensis Ianuarius (January) was added to the beginning of the year and Mensis Februarius (February) to the end of the year during Numa's reign around 700 B.C. with a leap year every 4 years. Leap years were decreed by proclamation the pontifex maximus, in such years an extra month was added to the ...
1. The 7 days of the week certainly fit somewhat as a quarter of a month. But there was another argument for the ancients to use the number seven, because they knew about seven "planets", seven objects which wander across the sky relative to the thousands of fixed stars. The Sun, the Moon, Mercury, Venus, Mars, Jupiter, Saturn.
The Earth is about 4.543 billion years old. However, the length of a year can be changed by anything from an impact to a natural cycle of orbit changes to a slow drift toward or away from the sun to the tug of a nearby body. So while the Earth is about 4.543 billion modern years old, it may have revolved around the sun a significantly different ...
This leads to a third astronomical definition of a year, which is the time from one vernal equinox to the next. This is the tropical year, 365.24219 days long. This is shorter than the sidereal year, primarily due to the precession of the Earth's rotation axis. Some want the year to be highly predictable for planning purposes.
There are not an integer number of days in a year. People perceive a need to keep the seasons where they are on the calendar. Given the above, there is no way to avoid leap years, or something similar. Defining the calendar year as being a fixed number of days (e.g., 365 days) would result in the seasons shifting by one day per four years.