Tropical zodiac is based on the Earth's yearly movement around the Sun. The movement of earth around the is the cause of change of seasons. Can you say why? This is because of the tilt of Earth which is 23d 27m from the vertical axis. If the tilt was not there there there would not be any change of season. While the earth moves around the sun, the tilt changes with respect to the ecliptic (the plane of Sun and Earth's orbit). During spring and autumn, when the day and night are the same, the tilt with respect to the ecliptic is zero. While during the Summer, the hemisphere which has summer would tilt towards the face of Sun and the one which has winter would tilt away from the face of Sun. While seen from earth, the Sun would look like as if it is rising from the equator (where it is seen during equinoxes, spring and autumn) to north till tropic of cancer and then would go down towards the tropic of capricorn. So there is a change of declination (tilt as seen from the earth's equitorial plane) of Sun from zero to +23d 27m, then zero and then -27d 27m and then back to zero again. The cycle of Sun starting from the beginning of one of the euinox when Sun's declination is zero to again back to that equinox marks completion of one year, which is known as a tropical year.
However, while on the Spring/ Vernal equinox, is the sun really on the beginning of Aries. The answer is No.. While on Sprint equinox now, the Sun is not in the beginning of Aries but it is somewhere at 7degree Pisces. You can check this in any astronomy program. Why is it so!
There was a time when the equinox was in the beginning of Aries and this was long back. However, this is not now since the tilt of earth is itself changing its direction, tracing a circle on the celestial sphere. With this the alignment of the polestar with the earth's axis is changing. This means that the point in which the equinox falls is itself changing. Astronomers found that the period in which the equinox is tracing the circle on the celestial sphere is some 26000 years (different views exists on this). So each year the equinox is preceeding with a rate of some 49.86 seconds. Over years from the time when equinox actually fell at the beginning of Aries, the equinox has moved backwards to 7degree pisces. This is the basis of the Sidereal zodiac.
While seen on the sky the planets are seen as according to the sidereal zodiac and not in terms of the tropical zodiac since the tropical zodiac is based on the movement of Sun with respect to the equinoxes and not Actual starting of the zodiac. For convinience sake, the astrologers have aligned the equinoxes with the Aries and Libra, which is merely hypothetical and doesnot have a astronomical basis. However for true astrological reasons where the zodiac is more important than the equinoxes, the planets are seen in the zodiacal signs as they are.
Thus unlike the tropical year, the sidereal year is the movement of Sun from beginning from a point in zodiac to again back to that point. This year is slightly longer than the tropical year since, by the time Sun reaches the same declination again (as it was at the start of the year), the equinox has moved little backward due to the precision of equinox and thus Sun has to take little extra time to cover up the distance to the original point of start in the zodiac.
For instance say Sun is in 7d pisces when the declination is zero i.e, at the time of vernal equinox. When after the one year cycle the declination again becomes zero at next vernal equinox, the point of vernal equinox would have moved some 23/24 arc seconds backward with respect to the zodiac i.e., 7 degree Pisces to 6d 59m 36sec. Thus the Sun has to move some 1223 sec (20 min 23 sec approx.) to come to the initial point of 7d pisces and hence the day length is little bit more than a tropical year. Thus the year length of a tropical year is 365. 2422 mean solar days where that of a sidereal year is 365.2564 mean solar days.
Summarising the whole topic, the tropical year is based on the Sun's return to the equator i.e., the point of zero declination or the equinox, whereas the Sidereal year is the Sun's return to the point of start with respect to the Zodiac (static background) and hence is a true measure of a solar year. However, since the sidereal year does not follow the declination of Sun, it would be out of synchronicity with the seasons.
So, we can conclude that for the matter of measuring time for the perpose of seasonal changes, tropical year is the best suited, however for the matter of measuring time for judging the heavenly influence on earthly affairs, sidereal time is more suited.
Since the season (which is defined by Sun's declination) is out of synchrocity of the sidereal year, they come to synchronicity when the precession has completed 360 deg of the zodiac. This can be found in following ways. Get the mean tropical year, which is 365.2422; get the mean difference of the sidereal and tropical zodiac, which is 1223 sec; then number of years the two zodiacs to be synchronous = 365.2422 days / 1233 sec = 25,802 years or approximately 26,000 years. Thus the precession cycle as well as rate of precession (ayanamsa) can be found out by finding the actual measures of mean tropical solar year and the offset between two declinations (and equivalent time period).
More on Ayanamsa to follow...