# The Tropical and the Anomalistic Year

### Why the Average Length of the Tropical Year is Different for Different Starting Points in the Tropical Year.

A tropical year is the time it takes the Sun to appear to travel around the sky from a given point of the tropical zodiac back to that same point in the tropical zodiac. This is, in the mean, a little less time than the period it takes the Earth to complete one dynamical circuit of its elliptical* orbit around the Sun.

The average time it takes to complete one ellipse is called the anomalistic year (currently about 365.26 days or 365 days, 6 hours and some 14 minutes). The elliptical shape of the Earth's orbit characterizes the varying speed with which the Earth travels. It travels faster while it is closer to the Sun (near the perihelion of of its ellipse) and slower while it is farther from the Sun (near the aphelion of its ellipse).

Because the ellipse or anomaly governs the dynamics of the Earth's motion around the Sun, the mean anomalistic year will necessarily be the same wherever in the ellipse or anomalistic period we begin timing this kind of year. Wherever we begin an anomalistic year the Earth will go through the complete cycle of its varying speeds while completing an ellipse back to the starting position. It will cover the same angles (from the Sun) in the same intervals of time as it would if the measurement were begun from some other point in the orbit; only the order of the varying angles in the varying intervals will be different.

A tropical year, however, is completed before the Earth recovers its same position and velocity in the ellipse. This is because the Earth's axis is not perfectly upright or perpendicular with respect to its path around the Sun. The Earth thus wobbles** like a top, its axis of rotation slowly and steadily changing at a rate that (if held at its current value) would take some 21,000 years to complete a circuit (around a perpendicular through its orbital plane) with respect to the perihelion-to-aphelion axis.

A tropical year is fulfilled when the Earth's axis completes a full cycle of angles with respect to the line joining the center of the Earth to the Sun. Because of the wobble*** this cycle is completed before an ellipse is completed.

The small angle that the Earth's axis has wobbled in one tropical year (about 0.0003 radians), and which the Earth must travel through (with respect to the Sun and the perihelion-aphelion axis) in order to complete an ellipse, will require a travel-time which is dependent upon the Earth's position in the ellipse. This must be so because the Earth's position in the ellipse determines its angular speed. A mean tropical year can thus be thought of as a constant mean anomalistic year, less a small variable period of time (between 24 and 26 minutes of an hour), which depends for its exact duration upon the position in the ellipse from which we choose to begin our mean tropical year.