The Moon Help

Libration

As the Moon makes its way around Earth, it keeps the same face toward us, more or less. This is so because the Moon’s mass is not uniformly distributed within the globe, and Earth’s gravity has managed, over millions of centuries, to tug the Moon’s rotation rate into near-perfect lockstep with its revolution. But the Moon still wobbles back and forth a little; it has not completely “settled down.” We can see 59 percent of the Moon’s surface from Earth if we make enough observations. The wobbling of the Moon’s face relative to Earth is called libration (not to be confused with libation).

Libration can give rise to interesting phenomena. For example, when amateur radio operators bounce their signals off the Moon to communicate with their fellows on the opposite side of the world, libration produces multiple signal paths whose lengths vary constantly, making the radio waves add and cancel in a manner so complicated that precise analysis would challenge any computer. The resulting received signals sound like someone babbling or hooting underwater. The wavelengths of light are too short for this effect to be observed visually. If we could see at radio wavelengths, the Moon would seem to sparkle and scintillate as if fireworks were constantly being set off all over its surface.

Phase

The appearance of the Moon is drastically affected by its orientation relative to the Sun. When the Earth, the Moon, and the Sun are in line or nearly in line, the Moon is said to be new , and its existence is not visually apparent unless there happens to be a solar eclipse. As the Moon orbits Earth, a journey that takes place in a counterclockwise direction as viewed from high above Earth’s north pole (Fig. 4-3), it presents more and more and then less and less of its lit-up face to us. Three or four days after the new Moon, it is a waxing crescent . About a week after the new Moon, we see half its globe illuminated by the Sun; this is first quarter . Three or four days after that, most of the Moon is illuminated as we see it; this is waxing gibbous . Two weeks and 18 hours after the new Moon, it is entirely illuminated for us unless a lunar eclipse happens to be taking place. This is the full Moon . Phases proceed in timely fashion after the full Moon through waning gibbous, last quarter, waning crescent , and finally, back to new again.

Figure 4-3. The Moon’s phases result from the relative orientation of the Moon and the Sun, as seen from Earth.

Almost nobody lives in this world without getting to know the lunar phases before they get into kindergarten. The waxing crescent is visible just after sunset; the first-quarter Moon can be seen until midnight. The waxing gibbous Moon stays in the sky into the wee hours of the morning, and the full Moon is above the horizon all night, setting as the Sun rises. After the full phase, the waning gibbous Moon rises a couple of hours after sunset; the last-quarter Moon rises around midnight; the waning crescent Moon waits until the predawn hours to rise. Moonset in the waning phases takes place in the daytime, and some people say that there is “no moonset” during this half of the lunar cycle.

Of North And South

Most people envision the Moon’s phase-to-phase progress and appearance as seen from the northern hemisphere. This is natural because there are more people living north of the equator than south of it. As far as Earth itself is concerned, however, this is only half the story.

Figure 4-4 shows the way the Moon looks at various stages in its orbit around Earth as seen from a midlatitude northern location such as Kansas City, Missouri, or Rome, Italy. (There is some variance in the tilt, depending on the season of the year; moonrise and moonset occur somewhat north or south of due east or west.) The waxing crescent appears in the southwestern or western sky just after sunset and sets 2 to 4 hours after the Sun. The Moon at first quarter is in the southern sky at sunset, moves generally westward, and sets around midnight. The waxing gibbous Moon is in the southeast at sunset, moves generally westward, and sets in the predawn hours. The full Moon is opposite the Sun, rising at sunset and setting at or near sunrise. The waning gibbous Moon rises some time after sunset and sets after sunrise the next day. The last-quarter Moon rises around midnight and sets around noon. The waning crescent waits until the predawn hours to rise and sets in the afternoon.

Figure 4-4. Lunar phases as seen from middle latitudes in the northern hemisphere. The Moon’s tilt varies somewhat, depending on the season and the time of night.

Figure 4-5 illustrates the appearance of lunar phases as seen from a midlatitude southern location such as Perth, Australia, or Napier, New Zealand. (As with the northern-hemispheric situation, there is some variance in the Moon’s tilt. Depending on the season of the year, moonrise and moonset occur somewhat north or south of due east or west.) The waxing crescent is in the northwestern or western sky just after sunset and sets 2 to 4 hours after the Sun. The Moon at first quarter is in the northern sky at sunset, moves generally westward, and sets around midnight. The waxing gibbous Moon is in the northeast at sunset, moves to the west, and sets a couple of hours before dawn. The full Moon rises around sunset and sets around sunrise, tracking across the northern half of the sky during the night. The waning gibbous Moon rises shortly after sunset and sets after sunrise the next day. The last-quarter Moon rises at about midnight and sets around noon. The waning crescent rises a couple of hours before dawn and sets in the afternoon.

Figure 4-5. Lunar phases as seen from middle latitudes in the southern hemisphere. The Moon’s tilt varies somewhat, depending on the season and the time of night.

The Face Of The Moon

When you look at the Moon without the binoculars or a telescope, it’s impossible to know much about the true nature of the surface. Before Galileo Galilei and other astronomers began looking at the heavens through “spy glasses” a few hundred years ago, no one could be certain that the terrain was dry, scarred, and lifeless. In fact, the true austerity of the Moon would surprise even the most pessimistic dreamers of old.

The naked-eye Moon, especially the full Moon, has light and dark features. In absolute terms, the whole Moon is a rather dark object; it reflects only a few percent of the solar light that strikes it. If the Moon were as white as snow or powdered sugar, it would shine several times more brightly. Even without the help of telescopes, people long ago surmised that the Moon’s light areas represent irregular terrain and the dark regions are flat by comparison. Some people thought the light regions were clouds and the dark zones were areas of clear weather, but after observing the Moon for many nights and seeing that the “clouds” never moved, most people rejected that theory. However, these general ideas were as far as pretelescopic people got. Many people considered the dark areas to be liquid oceans made up of water. They were called maria (pronounced “MAH-ree-uh”), a word that means “seas.” To this day, flat plains or plateaus on the Moon have names such as the Sea of Tranquillity and the Sea of Crises . The light areas were assumed to be land masses, but few people supposed they were strewn with mountain ranges and crater fields.

When Galileo and others began looking at the sky with telescopes in the seventeenth century, humanity’s ideas did not change overnight, as they might have if our race had been driven more by hunger for knowledge and less by ego, fear, and superstition. People’s imaginations were more active in Galileo’s day than they had been a few centuries earlier, but they were not quite as daring as we are now. When Galileo announced that the Moon had craters and mountains, his fellow scientists became interested right away, but those who held power over people’s lives had other notions. To them, Galileo was a troublemaker, and he was treated as one. He ended up spending his last years under house arrest. It was not a tyrannical government dictator that subjected him to this, but the Pope. Imagine the reaction the Pope would get today if he demanded that some scientist spend the rest of his life under confinement!

The Tides

The Earth-Moon system stays together because of gravitation. Earth pulls on the Moon, keeping it from flying off into interplanetary space. The Moon also pulls on Earth, although we are not aware of it unless we make certain observations. The Moon’s gravitational effects vary depending on where in the sky (or beneath the horizon) it happens to be at any given time.

The lunar day is about an hour longer than the synodic day—roughly 25 hours—but the Moon, like the Sun, appears to revolve around any stationary earthbound observer. The effects of gravity propagate through space at the speed of light, some 299,792 kilometers (186,282 miles) per second. This covers the Earth-Moon distance in only a little more than 1 second, so there is essentially no lag between the Moon’s position and the direction in which its “tugging” takes place. The Moon’s pull is extremely weak compared with the gravitation of Earth at the surface; it is nowhere near enough to affect the reading you get when you stand on a scale and weigh yourself, for example. But this does not mean that the gravitational effect of the Moon can be disregarded, as any ocean beach dweller will attest.

The Moon’s gravitation, and to a lesser extent the Sun’s gravitation too, cause Earth’s oceans to be slightly distorted relative to the solid globe of the planet. When considered to scale, the oceans form a thin, viscous coating on Earth. Even the deepest undersea trenches reach less than 0.2 percent from Earth’s surface down to the center, and most of the oceans are far shallower than this. Even so, the depth of the oceans is affected by the combined external gravitational effects of the Sun and the Moon. The effect is greatest when the Sun, the Moon, and Earth are all in line, that is, at the times of new and full Moon. When the Moon is at first or last quarter, its gravitational field acts at right angles with respect to that of the Sun, and the two almost cancel each other out, although the Moon’s effect is a little greater than the Sun’s.

As Earth rotates under its slightly distorted “coating” of ocean, the level of the sea rises and falls at specific geographic locations. In certain places, the rise and fall is dramatic, and people who live on the shore must take its effects seriously. In other places, these tides are much less extreme. There are two high tides and two low tides during the course of every lunar day; the reason for this can be envisioned by looking at Fig. 4-6. However, these drawings represent an oversimplification. The actual tides are delayed by the fact that on a planetary scale water behaves more like molasses than the freely running liquid with which we are familiar. Also, the contours of the ocean floor and the continental shelves have an effect. This is not all: Land masses break the planetary ocean up, so wave effects cannot propagate unimpeded around the world. The tides are waves, although they are very long, having two crests and two troughs with the passage of every lunar day. Actually, the tides consist of two waves of different frequencies. Superimposed on the lunar tidal waves , which have a period of about 25 hours, are solar tidal waves (truly tidal in nature, unlike tsunamis , which are caused by undersea earthquakes, not by tides) with a period of 24 hours, but whose crests and troughs have smaller magnitude.

Figure 4-6. Simplified diagrams showing why lunar tides occur. These views are from high above Earth’s north geographic pole.

The Moon and Sun are not the only natural entities that affect sea level. Weather systems, especially ocean-going storms, have an effect, and in some places a storm surge can cause the sea to rise 10 times as much as the astronomical tide. A tsunami comes in and pounds away at the shoreline in a manner similar to that of a storm surge, except that the tsunami is caused by a jarring of the sea floor (or, occasionally, by a volcanic eruption) rather than by high winds piling the water up onto shore. Neither of these phenomena are true tides.

Tides don’t occur to a significant extent in land-locked seas and lakes. This is so because in order for water to rise in one location, it must fall somewhere else where the lunar-solar gravitational composite is different. This can’t happen in a small body of water, on which, relative to every point, the Moon and Sun are in the same positions at any given time.

There has been some debate about the effects of the solar and lunar gravitational fields on the behavior of living cells. No one has yet come out with a respected scientific study that quantifies and defines exactly how such effects, if any, are manifest. For example, so-called Moon madness (lunacy) has not been explained on the basis of increased intracellular tidal effects during the full Moon. Because a similar loss of reasoning power does not seem to grip its perennial victims during the new Moon, it is almost certain that Moon madness (if it really exists) is not caused by gravitation.

How The Moon Was Formed

Earth-Moon pair is unique in the Solar System; no other major planet has a satellite so large in proportion to itself. (Pluto and its moon Charon are sometimes called a double-planet system, but both of them are hardly larger than asteroids and might better be classified as such.) If the Moon were only a few hundred miles across, say the size of the asteroid Ceres, there would be little doubt that it was captured from solar orbit by Earth’s gravitation. However, because the Moon practically qualifies as a planet, being almost as large as Mercury, there are competing theories about its origin.

One theory holds that the Moon was once a planet in its own right, orbiting the Sun rather than Earth, but something, such as a collision with a large asteroid, deflected it from its solar orbit and caused it to pass so close to Earth that Earth captured it permanently. Few astronomers believe this. If it were true, then the Moon’s orbit likely would be an elongated ellipse sharply inclined to the plane of the ecliptic.

Another theory suggests that Earth originally had no Moon but that a Mars-sized object struck Earth a glancing blow and sent vast quantities of material into orbit. This would have produced rings around Earth, something like those around Saturn. These rings eventually would have congealed into the Moon. One problem with this theory is that an impact severe enough to blast that much matter off Earth might have shattered our planet. However, an increasing number of astronomers accept this theory, and it is lent support by the fact that the Moon lacks a metallic core; most or all of the blown-off material would have come from Earth’s mantle and crust. It also might explain why Earth’s equator is tilted significantly with respect to the plane of the ecliptic. A major impact could have jarred Earth and caused its axis to shift by 23.5 angular degrees.

Still another theory contends that Earth and the Moon formed as a double planetary system over the same period of time as the other planets, condensed from the disk of gas and dust orbiting the newborn Sun. This is a popular theory and is fairly consistent with what we observe about the Moon. It explains why the Moon orbits Earth in a nearly circular path and why the Moon’s orbit is tilted only a little (about 5 angular degrees) with respect to Earth’s orbit around the Sun.

Practice problems of this concept can be found at: The Moon and the Sun Practice Problems