A calendar year has to be a whole number of days, but a solar year is not a whole number of days, nor are there a whole number of lunar months in a solar year.
The Egyptians had a calendar of twelve months of thirty days, with five days of feasts to celebrate the festivals of their gods. They had measured the length of the solar year accurately enough to understand the importance of leap years by before 3000 BCE; in fact by 2500BCE their measurements were accurate enough to have given them the Gregorian calendar! (Reference 7)
The Egyptian Calendar is discussed, simply but more detail, in a section on Egypt intended for younger readers - to see it click here
It was a Greek called Sosigenes who lived in Alexandria at the time of Julius Caesar who introduced him to the Egyptian calendar, and in 46 BCE Caesar began to enforce a calendar based upon the Egyptian calendar throughout the Roman world. We call this the Julian Calendar, after Julius Caesar, with 365 days for three years and then a leap year, with 366 days, for the fourth year, and the months of the calendar not corresponding exactly to lunar months. July is named after Julius Caesar and August after Augustus Caesar his nephew who became the first Roman Emperor. The Julian Calendar was designed to ensure that the longest day always fell on the same day in the calendar so that the calendar and the seasons kept in step. Although the Egyptians were aware that a solar year was not exactly 365¼ days Julius Caesar chose a calendar with a leap year every four years, probably because he doubted whether the Roman world was ready for anything more complicated. See also Note.
There were also other early calendars designed to overcome the same problems in other parts of the world but the Julian Calendar is important because it forms the basis of our modern, internationally recognised, calendar. In our modern calendar the days the Equinoxes and Solstices occur on are considered to be
Remember however that the equinoxes and solstices are moments in time not days of the year.
Note also that we always refer to the March equinox as the vernal equinox even though for people in the Southern Hemisphere it falls in the autumn!
Astronomers, and also other people, often use what they call a Julian date. This is the number of days on an extrapolated Julian Calendar since noon on the Julian date 1st January 4713 BCE. This date was chosen for a particular astronomical reason, and has the advantage that all historically attested astronomical events have occurred since then, so all Julian dates are positive. So the start of the year 2000, at 0000 on 1st January 2000, was Julian date 2451544.5 (Reference 9). The Julian date starts at midday (at Greenwich) so that all astronomical observations made during one night can be recorded as being on the same Julian date. (Only in Europe of course, but when the Julian date was first introduced the people who introduced it were very definitely Eurocentric.)
