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Figure 1.21 Seasonal changes in the solar radiation at the Earth's surface.

Figure 1.22 Precession of the Earth's rotation axis.

motion called the precession of the rotation axis. It is a result of the torques exerted by other bodies in the Solar System on the slightly non-spherical form of the Earth. The Moon and the Sun account for almost the whole effect. All planets are slightly non-spherical, so all of them are subject to precession. For the Earth, one complete coning takes 25 800 years, an interval called the precession period of the Earth.

One consequence of precession is that the positions of the equinoxes and solstices move around the orbit, giving rise to the term precession of the equinoxes. In the case of the Earth this motion is in a retrograde direction (taking 25 800 years to move around once). Figure 1.23 compares the present configuration (dashed lines) with the configuration 12 900 years from now (solid lines) - each equinox and solstice has moved half way around the orbit. Recall that the reference direction in the ecliptic plane is the line from the Earth to the Sun when the Earth is at the vernal equinox. Therefore, with respect to the distant stars, this reference direction has moved through 180° in Figure 1.23. At present, when the Earth is at the vernal equinox, the direction is to a point in the constellation Pisces, but about 2000 years ago, when precession became widely recognised, it was in the constellation Aries, when its location was called the first point of Aries. The name sticks, even though the point long ago moved into the constellation Pisces, and is now not far from the boundary with the constellation Aquarius.

The slow retrograde motion of the vernal equinox around the Earth's orbit means that the time taken for the Earth to traverse its orbit from one vernal equinox to the next is very slightly less than the sidereal year. The time interval between vernal equinoxes is called the tropical year, and it is the year on which our calendars are based. Its duration is 365.242 190 days, whereas the sidereal year is 365.256 363 days. From now on, the term year will mean the tropical year. It is this year that is the unit of time measurement in Tables 1.1, 1.3, and 1.4, and elsewhere. It is denoted by the symbol 'a', from the Latin word for year, annus.

Vernal equinox now

Midwinter northern hemisphere

Figure 1.23 The effect of the precession of the Earth's rotation axis on the position of the equinoxes and solstices. The dashed line is the Earth's rotation axis now, and the solid line the axis 12900 years from now.

Vernal equinox now

Midwinter northern hemisphere 12 900 years from now

Midwinter northern hemisphere now

Earth orbit

(oblique view) Vernal equinox

12 900 years from now

Figure 1.23 The effect of the precession of the Earth's rotation axis on the position of the equinoxes and solstices. The dashed line is the Earth's rotation axis now, and the solid line the axis 12900 years from now.

Question 1.10

What would be the problem with basing our calendar on the sidereal year?

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