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Figure 1.18 The Earth's rotation axis as the Earth orbits the Sun. This is an oblique view of the orbit, which is nearly circular.

to the Sun at the vernal (March) equinox is used as the reference direction T in the ecliptic plane that you met in Section 1.4.2.

We now turn to the period of rotation. Figure 1.19 shows the Earth moving around a segment of its orbit. As it does so it also rotates, and the arrow extending from a fixed point on the Earth's surface enables us to monitor this rotation. Between positions 1 and 2 the Earth has rotated just once with respect to a distant star. This is the sidereal rotation period. The distant stars, to sufficient accuracy, provide a non-rotating frame of reference (just as for the sidereal orbital period in Section 1.4.1). For the Earth, the sidereal rotation period is actually called the mean rotation period - astronomical terminology can be perverse. However, the Earth has not yet rotated once with respect to the Sun. The Earth has to rotate further to complete this rotation, and in the extra time taken it moves further around its orbit, to position 3. The period of rotation of the Earth with respect to the Sun is called the solar day. It is clearly longer than the mean rotation period, though only by a few minutes.

□ State in what way the motions in Figure 1.19 are not shown to scale. In Figure 1.19 the Earth's motion around its orbit between positions 1, 2, and 3 has been exaggerated for clarity. As there are just over 365 days in a year, the Earth should only proceed about 1° around its orbit in the time it takes the Earth to rotate once.

Earth rotatio

Earth

Earth rotatio

Earth

Earth orbital motion

Figure 1.19 The rotation of the Earth with respect to the Sun and with respect to the distant stars (not to scale).

Earth orbital motion

Figure 1.19 The rotation of the Earth with respect to the Sun and with respect to the distant stars (not to scale).

The mean rotation period does not vary significantly through the year, but the solar day does. This is a consequence of the eccentricity of the Earth's orbit and the inclination of its rotation axis (we shall not go into details). By contrast, the mean solar day is defined to be fixed in duration, and has the mean length of the solar days averaged over a year. If solar time and mean solar time coincide at some instant, they will coincide again a year later, but in between, differences develop, sometimes solar time being ahead of mean solar time and sometimes behind. The maximum differences are about 15 minutes ahead or behind. The day that we use in our everyday lives, as marked by our clocks, is the mean solar day. Even this varies in length, very slightly, and so for scientific purposes a standard day is defined, very nearly the same as the current length of the mean solar day. It is this standard day that appears in Tables 1.1-1.4 and elsewhere. It is exactly 24 x 60 x 60 seconds in length, and thus consists of exactly 24 hours of 60 minutes, with each minute consisting of 60 seconds.

The mean rotation period is 23 h 56 min 4 s, i.e. 3 min 56 s shorter than the mean solar day. Over one sidereal year, this difference must add up to one extra rotation of the Earth with respect to the distant stars. You can convince yourself of this by considering a planet that is rotating as in Figure 1.20. In this case there are three rotations per orbit with respect to the Sun and four with respect to the stars. For the Earth, during the sidereal year there are 365.26 mean solar days and 366.26 mean rotation periods.

Table 1.1 gives the axial inclination and sidereal rotation period of each planet and also of the Sun. The inclination of each planet is with respect to the plane of its orbit, whereas in the case of the Sun it is with respect to the ecliptic plane. Note that, with three exceptions, the inclinations are fairly small. This means that the prograde swirl of motion of the orbits, almost in one plane, is shared by planetary and solar rotation. The exceptions are Venus, Uranus, and Pluto. The inclination of Venus is not far short of 180°. □ What is the difference between an axial inclination of 180° and 0°? The difference is that 0° is prograde rotation whereas 180° is retrograde rotation, in each case with the rotation axis perpendicular to the orbital plane. Any inclination greater than 90° is retrograde, and so Pluto and Uranus are also in retrograde rotation, though Uranus's inclination

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