The table below shows the solar years of both systems in comparison with the actual mean tropical year.

This approximation has an error of about one day per 3,300 years with respect to the mean tropical year.

Both equations estimate that the tropical year gets roughly a half second shorter each century.

Before 1984, both the Julian year and the mean tropical year were used by astronomers.

The difference between the sidereal and tropical years is due to precession.

This may not seem much, but it means that the Julian year gains a full day on the tropical year in 128 years.

The five or six extra days needed to approximate the tropical year were placed after the months at the end of each year.

Rather, the tropical year would be likely to be used because it gives the best match to the progression of the seasons.

This month was supposed to be inserted every two or three years to align the 355-day common year with the tropical year.

It approximates both the sidereal year and the tropical year to about 0.008 days.

Since this discovery a distinction has been made between the tropical year and the sidereal year.

There are two solstices and two equinoxes in a tropical year.

The Northward equinox is one point in time commonly used to determine the length of the tropical year.

Very probably it was made to approximate the tropical year, which was known at least since Hipparchus.

Modern astronomers define the tropical year as time for the Sun's mean longitude to increase by 360 .

The history of the tropical year.

The tropical year is about 365 days, while the synodic month is also slightly longer than 29 days on average.

The tropical year is the period of time for the ecliptic longitude of the Sun to increase by 360 degrees.

In either case, his calendar was more accurate to the mean tropical year than the Gregorian calendar of 500 years later.

If managed correctly this system allowed the Roman year, on average, to stay roughly aligned to a tropical year.

This slightly shorter period is known as 'tropical' month; cf. the analogous tropical year of the Sun.

As already mentioned, there is some choice in the length of the tropical year depending on the point of reference that one selects.

This is the "tropical year," because it also measures the time required for the Sun to move from tropic to tropic and back again.

The almanac also names all the full moons, including blue moons, at the beginning of each tropical year calendar.

Note however that in none of the arithmetic calendars is the average year length exactly equal to a true tropical year.