## Lunar puzzles

The fact that we observe the Moon from the surface of another world that is itself in motion makes the Moon behave in ways that can seem puzzling. Here are two such puzzles.

The first of these is the way in which the Moon appears to rotate as it moves across the sky. An observer at mid latitudes sees the full Moon rise in the east with its north-south axis inclined to the horizon. As it moves across the sky, the Moon appears to rotate in a clockwise direction so that it crosses the southern sky with this axis approximately perpendicular to the horizon. Finally, when it is on the point of setting on the western horizon, the north-south axis is once again inclined to the horizon. The effect is particularly noticeable at quarter Moon because the asymmetry of its semicircular outline makes it easy to notice the apparent change in orientation. Of course, the Moon cannot actually swing about in this way.

Looking west at moonset

Looking south

### Looking east at moonrise

Figure 9.18 Moon paradox 1. Because of the Earth's rotation, the Moon appears to rotate as shown in these diagrams. At A an observer will see the Moon rise above the eastern horizon. Its N-S axis is then more or less parallel to the horizon. some six hours later, the observer is at B and the Moon's N-S axis is more or less perpendicular to the horizon. Finally, as the Moon is about to set, its N-S axis is once again parallel to the horizon, but pointing in the opposite direction relative to the observer.

Looking west at moonset

Looking south

Looking east at moonrise

Like the Earth's axis, the Moon's axis always points in the same direction in space.

The illusion is brought about by the gradual change in the orientation of the observer's horizon with respect to the Moon's axis. This change is due to the fact that we are standing on a spinning, spherical Earth. Because of its rotation, we are carried past the Moon in a great arc. The effect this has upon how we see the Moon is shown in figure 9.18. The degree to which the Moon's axis nods back and forth varies with the time of year and with latitude. Someone in the southern hemisphere sees the Moon the other way around, i.e. the Moon's northern pole is closest to the horizon. The effect is further proof that the Earth is a sphere.

A second puzzle concerns the direction from which the Moon appears to be illuminated. This coincides with the Sun only at the beginning or at the end of the lunar cycle, i.e. when the Moon is a slim crescent. Throughout

Figure 9.19 Moon paradox 2. Although the Moon's crescent appears to point away from the Sun, you will realise that this is an illusion by stretching a length of string so that it joins the centre of the Moon to the centre of the Sun. The string will be lined up with the ecliptic.

Moon's crescent appears to

Moon's crescent appears to

Figure 9.19 Moon paradox 2. Although the Moon's crescent appears to point away from the Sun, you will realise that this is an illusion by stretching a length of string so that it joins the centre of the Moon to the centre of the Sun. The string will be lined up with the ecliptic.

the rest of the cycle the illuminated portion does not appear to point at the Sun. The effect is very pronounced when one can see either a quarter or gibbous Moon in the sky at the same time as the Sun.

This illusion, for it is an illusion, involves an error of parallax and can be explained as follows. The distance between the Earth and the Sun is approximately 400 times greater than that between the Earth and the Moon. Consequently the direction from which the Moon is illuminated is almost parallel (to within a few minutes of arc) to that from which the Earth is illuminated. This means that the line-of-sight of an Earth-bound observer looking towards the Sun can be taken to be parallel to the direction from which the Moon is illuminated. From the vantage point of someone on the Earth's surface, the two directions do not, indeed cannot, appear to converge and so the illuminated portion of the Moon appears to point away from the Sun. The reason why the effect is less pronounced when the Moon is a crescent is that it is then seen close to the Sun and so the direction from which it is illuminated almost coincides with the Earth observer's line-of-sight to the Sun.

Nevertheless, the fact that the Moon is illuminated by the same body as we are can be confirmed if a long, narrow, straight stick held at arms length is used to join the centre of the visible portion of the Moon to the Sun. The stick will trace out the great circle that joins the two bodies on the celestial sphere. This great circle is the ecliptic. Since each of us is at the centre of the celestial sphere, the projection of any section of a great circle appears as a straight line.

Earth's orbit about the Sun

Moon's orbit about the Sun

Moon's orbit about the Earth

Figure 9.20 (a) The Earth and Moon orbit the Sun together. The relative position of the Earth, Moon and Sun determine the Moon's phase.

(b) This shows the Earth-Moon system to scale (scale 1 mm = 400000 km.) On this scale, Earth would be a mere dot less than 0.03 mm across (i.e. about half the thickness of a human hair). The Sun would have a diameter of 3.5 cm and is 40 cm from Earth.

Earth's orbit about the Sun

Moon's orbit about the Sun

Moon's orbit about the Earth

First quarter

Figure 9.20 (a) The Earth and Moon orbit the Sun together. The relative position of the Earth, Moon and Sun determine the Moon's phase.

(b) This shows the Earth-Moon system to scale (scale 1 mm = 400000 km.) On this scale, Earth would be a mere dot less than 0.03 mm across (i.e. about half the thickness of a human hair). The Sun would have a diameter of 3.5 cm and is 40 cm from Earth.

' Last quarter

' Full Moon

+1 0