# (4) The Moon: the Distant View

 The Moon's the North Wind's cookie He bites it, day by day Until there's but a rim of scraps That crumble all away. The South Wind is the baker He kneads clouds in his den, And bakes a crisp new moon that ... greedy.... North.... Wind ....eats....again! "What the Little Girl Said" Vachel (Nicholas) Lindsay, 1879-1931.

The moon's path across the sky was found to be close to the ecliptic, inclined to it by about 5 degrees. Eclipses of the Sun always occurred when moon and Sun were due to occupy the same spot in the sky, suggesting that the moon was nearer to us and obscured the Sun. Eclipses of the moon, similarly, always occurred at full moon, with the two on opposite sides of the Earth, and could be explained by the shadow of the Earth falling on the moon.

Lunar eclipses allowed the Greek astronomer Aristarchus, around 220 BC, to estimate the distance to the moon (see section #8c). If the moon and the Sun followed exactly the same path across the sky, eclipses of both kinds would happen each month. Actually they are relatively rare, because the 5-degree angle between the paths only allows eclipses when Sun and moon are near one of the points where the paths intersect.

.     The cycle from each new moon to next one takes 29.5 days, but the actual orbital period of the moon is only 27.3217 days. That is the time it takes the moon to return to (approximately) the same position among the stars.

Why the difference? Suppose we start counting from the moment when the moon in its motion across the sky is just overtaking the Sun; we will call this the "new moon," even though the thin crescent of the moon will only be visible some time later, and only shortly after sunset. Wait 27.3217 days: the moon has returned to approximately the same place in the sky, but the Sun has meanwhile moved away, on its annual journey around the heavens. It takes the moon about 2 more days to catch up with the Sun, to the position of the next "new moon," which is why times of the new moon are separated by 29.5 days.

## The Face of the Moon

The visible face of the moon has light and dark patches, which people interpreted in different ways, depending on their culture. Europeans see a face and talk of "the man in the moon" while children in China and Thailand recognize "the rabbit in the moon." All agree, however, that the moon does not change, that it always presents the same face to Earth.

Does that mean the moon doesn't rotate? No, it does rotate--one rotation for each revolution around Earth! The drawings on the left, covering half an orbit, should make this clear. In them we look at the moon's orbit from high above the north pole, and imagine a clock dial around the moon, and a feature on it, marked by an arrow, which initially (bottom position in each drawing) points at 12 oclock.

In the top drawing the marked feature continues to point at Earth, and as the moon goes around the Earth, it points to the hours 10, 8 and 6 on the clock dial. As the moon goes through half a revolution, it also undergoes half a rotation     If the moon did not rotate, the situation would be as in the bottom drawing. The arrow would continue to point in the 12-oclock direction, and after half an orbit, people on Earth would be able to see the other side of the moon. This does not happen.

We need to go aboard a spaceship and fly halfway around the Moon before we get a view of its other side--as did the Apollo astronauts who took the picture below.

This strange rotation of the moon is maintained because the moon is slightly elongated along the axis which points towards earth. To understand the effect we look at the motion of a body with a much more pronounced elongation--an artificial satellite with the shape of a symmetric dumbbell (drawing).

It can be shown that if the forces on the dumbbell (or indeed on a satellite of any shape) are unbalanced, it rotates around its center of gravity. That point will be defined later, but in a symmetric dumbbell with two equal masses marked A and B, the center of gravity is right in the middle between them.

Next Regular Stop: #4a The Moon: A Closer Look

Optional excursion: #4b Librations of the Moon

Author and Curator:   Dr. David P. Stern
Mail to Dr.Stern:   stargaze("at" symbol)phy6.org .

Last updated: 9-17-2004