The tropical and sidereal years
 

It was stated that the year used in civil life is based on the tropical year, defined as the interval in time between successive passages of the Sun through the vernal equinox. We now see that because of precession, the vernal equinox moves along the ecliptic at an average rate of 50''·2 per annum in the direction opposite to that in which the Sun moves. The tropical year (of length 365·2422 mean solar days) is, therefore, shorter than the sidereal year, defined to be the time it takes the Sun to make one complete circuit of the ecliptic. Its length is found from the relation that
 

giving the length of the sidereal year as 365·2564 mean solar days.