The Firmament

The heavens declare the glory of God,
And the firmament showeth His handiwork;
Day unto day uttereth speech,
And night unto night revealeth knowledge;
There is no speech, there are no words,
Neither is their voice heard.
Their line is gone out through all the earth,
And their words to the end of the world.
In them He has set a tent for the sun,
Which is like a bridegroom coming out of his chamber;
And rejoiceth as a strong man to run his course.
His going forth is from the end of the heaven,
And his circuit unto the ends of it;
And there is nothing hid from the heat thereof.

They noticed that the stars in that celestial canopy, the "firmament," maintained fixed patterns--constellations--night after night. Each culture gave them different names; the ones we use came from the Greeks and Romans--Big Bear, Big Dog, Scorpion, the Twins (a constellation with two evenly matched stars), and names from legends such as Orion, Cassiopeia, Perseus and Andromeda.

The Celestial Sphere

(If you mount a camera on a dark night in a way that the pole is in the middle of its field of view, open the shutter and take a time exposure, the image of each star will be smeared into part of a circle, and all the circles will be centered on the pole. Click here to see such a picture.)

The globe of the Earth has an equator around its middle, halfway between the poles. In a similar way, the sphere of the sky is circled by the celestial equator, halfway between the celestial poles. As the sky rotates, stars on the equator trace a longer circle than any others.

Of course, we know well (as the priests in Babylon didn't) that the stars are not attached inside a huge hollow sphere. Rather, it is the Earth which rotates around its axis, while the stars are so distant that they seem to stand still. The final effect, however, is the same in both cases. Therefore, whenever that is convenient, we can still use the celestial sphere to mark the positions of stars in the sky.

If on a clear night you find yourself lost in the wilderness or at sea, the pole star can tell you where north is, and from that you easily deduce east, west and south. Any other star is unreliable for determining direction--it will move across the sky, and may even set--but not this one. For instructions on finding the pole star at night, click here.

The closer you are to the equator, the closer is the pole star to the horizon, and at the equator (point C) it is on the horizon, and probably not easy to see. Further south, at points such as D, it is no longer visible, but now you can see the southern pole of the sky. Unfortunately, no bright star comparable to Polaris marks that position. The existence of a bright star near the north celestial pole is just a lucky accident, and as will be seen, it wasn't always so, and will not be a few thousand years from now.

The Mounting of a Telescope

As the drawing above makes clear, during the night we view the pole star from different positions (such as A and B). This however makes no noticeable difference in its place in the sky, because it is so distant from us. If the Earth rotated not around its axis but along a parallel line through A or B, the sky would not appear any different.

The equtorial mounting of a telescope. To track a star it is only necessary to rotate  !the telescope around its polar axis.

To the eye the rotation of the sky is very, very slow (it is most noticeable when the Sun or Moon are rising or setting). A telescope however greatly magnifies the rotation rate, and any star observed with it quickly drifts to the edge of the field of view and then disappear, unless the direction of the telescope is constantly adjusted. That is usually done automatically, by turning the telescope around an axis parallel to the Earth's rotation, for as explained above, a parallel shift does not change the apparent rotation of the stars.

A surveyor's telescope ("theodolite"; see below) usually has two axes--one allows it to scan all horizontal directions over 360 degrees, while the other adjusts its elevation and allows it to set its sights on reference marks higher than the viewer, such as mountaintops. A telescope for viewing stars (above) also has two perpendicular axes, but the main one (the "equatorial axis") is slanted to point at the pole star and is therefore parallel to the Earth's axis. As the celestial sphere rotates, a clockwork (or in cheap telescopes, the hand of the observer on a suitable knob) turns the telescope at a matching rate, maintaining the same stars in the field of view.

An old surveyor's tele-   scope (theodolite).

Planets and the Zodiac

The Big Dipper

When the territory of Alaska in 1926 decided to create a flag of its own, it asked citizens to submit proposed designs for the new flag. The winning design was that of Benny Benson, age 13, and is reproduced on the right. It shows the 7 stars of the Big Dipper and Polaris, the north star. When Alaska became a state, this became the state flag, and Alaska's Flag, a song about it by Marie Drake, was chosen as the state song. For more details, click here.

The flag also shows how the north star can be found. Imagine a line connecting the two stars at the front of the "dipper", continue it on the side where the dipper is "open" to a distance 5 times that between the two stars (the flag shortens this a bit!), and you will arrive at (or very close to) the pole star. Because of their role in locating Polaris, these two stars are often called "the guides." And by the way--the last-but-one star in the handle of the "dipper", named Mizar by Arab astronomers, is a double star, whose components are readily separated by binoculars--or, some say, by very sharp eyes during good viewing conditions.

Cassiopeia

The name of Cassiopeia's husband, King Cepheus, goes with a nearby constellation, above the other "V" (the brighter one), but Cepheus is nowhere as striking as Cassiopeia. Her daughter Andromeda has another constellation, framed by a big undistinguished rectangle of four stars. An unremarkable constellation to the eye--but it contains a large galaxy, our nearest neighbor in space (not counting two dwarf galaxies in the southern sky), one which seems to resemble ours in size and shape.

Ursa Minor, the "Small Bear" or "Little Dipper" is a constellation somewhat resembling the Big Dipper, and Polaris is the last star in its tail. The "dipper" itself faces the tail of the Big Dipper, so that the two "tails" (or "handles") point in opposite directions. The two front stars of the "little dipper" (quite smaller and more square than the big one) are fairly bright, but other stars are rather dim and require good eyes and a dark sky.

Astrologers, who believe that stars mysteriously direct our lives, claim it makes a great difference "under what sign" a person was born. Be aware, however, that the "sign" assigned to each month in horoscopes is not the constellation where the Sun is in that month, but where it would have been in ancient times. The difference is discussed in the section on the precession of the equinoxes

The Ecliptic

The path of the Sun across the celestial sphere is very close to that of the planets and the moon. After clocks became available, it was a relatively straightforward job for astronomers to relate the path of the Sun in the daytime to the one of stars at night, and to draw it on their star charts. Because of its relation to eclipses, that path is known as the ecliptic.

The orbit of the Earth around the Sun. This is a perspective view, the shape of the actual orbit is very close to a circle.

The significance of the ecliptic is evident if we examine the Earth's orbit around the Sun. That orbit lies in a plane, flat like a tabletop, called the plane of the ecliptic (or sometimes just "the ecliptic"). In one year, as the Earth completes a full circuit around the Sun (drawing above), the Earth-Sun line and its continuation past Earth sweep the entire plane. The far end of that line then traces the ecliptic on the celestial sphere; if you have a star chart handy (it is often included in an atlas), you will find the ecliptic traced there, too.

The Planets and the Moon

Planets seen in the sky are always near the ecliptic, which means that their orbits are never too far from the plane of the ecliptic. In other words, the solar system is rather flat, with all its major parts moving in nearly the same plane.

What about the connection between "ecliptic" and eclipses?

The moon's orbit cuts the ecliptic at a shallow angle, around 5 degrees, which means that on the celestial sphere the Moon, too, follows a path through the zodiac. Half the time the Moon is north of the ecliptic, half the time south of it. If the shadow of the moon hits the Earth, the Sun is eclipsed in the shadow area; if on the other hand the shadow of the Earth covers the moon, the moon goes dark and we have an eclipse of the moon.

Either of these can only happen when the Sun, Earth and Moon are on the same straight line. Since the Sun and Earth are in the plane of the ecliptic, the line is automatically in that plane too; if the moon is also on the same line, it must be in the plane of the ecliptic as well.

It takes close to a month for the Moon to go around the Earth ("month" comes from "Moon") and during that time its orbit crosses the ecliptic twice, as it goes from one side to the other. At the time of crossing, the Sun may be anywhere along the ecliptic; usually it is not on the Earth-Moon line, and therefore an eclipse usually does not take place. Occasionally, however, it is on that line or close to it. If it then happens to occupy exactly the same spot on the celestial sphere, we get an eclipse of the Sun, because the moon is then between us and the Sun. On the other hand, if it occupies the spot exactly opposite from that of the Moon, the Earth's shadow falls on the Moon and we have an eclipse of the Moon.

Exploring Further

"Some people can tell what time it is by looking at the sun. But I have never been able to make out the numbers."
        (Attributed to an essay by a student
         in elementary school.)

As the Sun rises, passes the highest point in its path (at noon and to the south, in the northern hemisphere) and sets, the shadow rotates around the stick in a clockwise direction, and its position can be used to mark time. Indeed, it has been claimed that the "clockwise" direction in which the hands on a clock rotate was chosen for this reason.

A sundial with a vertical pointer ("gnomon") will indicate noon correctly when its shadow points north. However, the direction of the shadow at some other time of the day may depend on the season--its value in summer, when the Sun's path is high, may differ from what it is in winter, with Sun low above the horizon.

A Paper Sundial

Note: In this printed version of many files together, the sundial plan must be on a page of its own, printed separately

Instructions:

1. Cut the paper along the marked line: one half will serve as base, the other will be used to construct the gnomon.

2. In the gnomon part, cut away the two marked corners.

3. Fold the sheet in its middle, in a way that the two secondary printed lines (leading to the cut-off corners) remain visible. The line of the fold is the gnomon.
   
   Note: In stiff paper, straight folds are helped by first scoring the paper, by drawing a line along them with a black ballpoint, guided by a ruler and pressed down hard.

4. With the page folded in its middle, cut out along the curved line, cutting a double thickness of paper in one cut. The cut begins near the top of the gnomon-fold and ends on the secondary line. Do not cut along the secondary line. No pieces come off.

5. Score the other two secondary lines, then fold the gnomon sheet along them. The fold is opposite to that of the fold in the middle. These two folds should form 90-degree angles, so that the two pieces with the corners not cut in step 2 can be placed flat on the table, and the triangular gnomon rises above them.

6. In cut (4), the fin of the gnomon was separated from two pieces with curved outlines. Fold those pieces so that they, too, are flat with the table. One goes above the other, and the slots they form near the secondary lines create a place for the fin to fit into.

7. You are almost done. Take the base sheet, and note the apex where the hour-lines all meet (that is where the bottom corner of the fin will go). Carefully cut the sheet from this point along its middle line, up to the small cross-line marked on it. Do not cut any further!

8. Slide the fin into the cut you made, so that all horizontal parts of the first sheet are below the base sheet; only the fin sticks out. Its bottom corner should be at the apex.
   
   The sundial is now ready, but you might use tape on the bottom of the base-sheet to hold the two pieces together firmly. For further stability, and to prevent the sundial from being blown away, you may attach its base with thumbtacks to a section of a wooden board or a piece of plywood.

9. Finally, orient the fin to point north. You may use a magnetic compass; before pocket watches were available, folding pocket sundials were used in Europe, with small magnetic compasses embedded in their bases. If clear sunlight is available, the shadow of the tip of the fin now tells the time.

If you want to make a sundial of more durable materials, draw the pre-noon hour lines at the angles to the fin (given in degrees) given below. These lines are meant for a latitude of 38 degrees; if your latitude is markedly different, see note at the end.

Accuracy

   In addition, "clock time" (or "standard time") will differ from sundial time, because it is usually kept uniform across "time zones"; each time zone differs from its neighbors by one full hour (more in China and Alaska). In each such zone, sundial time matches clock time at only one geographical longitude: elsewhere a correction must be added, proportional to the difference in longitude from the locations where sundial time is exact.

(Up to the second half of the 19th century, local time and sundial time were generally the same, and each city kept its own local time, as is still the case in Saudi Arabia. In the US standard time was introduced by the railroads, to help set up uniform timetables across the nation.)

Note on Latitude

Here 15N (=15 times N) is an angle in degrees, ranging from 0 to 90, and of course, the afternoon angles are mirror reflections of the morning ones. If your calculator has a button (sin^-1), if you enter (sin A) and press it, you will get the angle A. For an explanation of sines and cosines, look up the math refresher. And don't forget to adjust the angle of your fin to L, too!

1. Let AB in the drawing represent the pointer of a sundial, aimed at the celestial pole, parallel to the Earth's axis.

2. Usually the stars and Sun are visualized as attached to a rotating "celestial sphere." For explaining the sundial, however, it is more convenient to visualize them as attached to a rotating cylinder, with AB on its axis.

3. The cylinder can be viewed as marked with many straight lines parallel to AB. Each time of the day has such a line, marking where the Sun is at that time of the day. Let SW be that line for some particular time.

4. Consider two dates in the year, one in summer, one in winter. At the summer date, at the chosen time, the Sun is high in the sky. at point S, while at the winter date, it is low in the sky, at point W.

5. The shadow of the gnomon is always in the plane containing the Sun and the points A and B.
     If AB is a thin line, the shadow will also be a thin line, the intersection of this plane with the base of the sundial.

6. In summer, therefore, the shadow is in the plane SAB, and in the winter, in the plane WAB.

7. However, because AB points along the axis of the cylinder, the lines SW and AB are parallel, like opposite sides of a page. All 4 points are therefore in the same plane, and the two planes (S,A,B) and (W,A,B) are one and the same.
    Summer or winter, the shadow is therefore along the same line, the intersection of the above plane and the base of the sundial.

8. Suppose the pointer had a different direction, out of the plane of the paper. Then the planes SAB and WAB would be different, and their intersections with the base--which are the shadows cast by the pointer, at that time but on two different dates--are also different.

  Actually, the axis of rotation makes an angle of about 23. 5 degrees with the direction perpendicular to the ecliptic. That makes life a lot more interesting.

Equinox and Solstice

  Twice a year, the angle is as big as it can get, at the summer and winter solstices, when it reaches 23.5 degrees. In the summer solstice (around June 21) the north pole is inclined towards the Sun, in the winter solstice (around December 21) it faces away from it.

Let us look at the summer solstice first, with the Sun on the left.

Summer and Winter

  But because of the tilted axis, as each point on Earth is carried on its daily trip around the rotating Earth, the part of the trip spent in daylight (unshaded part of the drawing) and in the shadow (shaded) are usually not equal. North of the equator, day is longer than night, and when we get close enough to the north pole, there is no night at all. The Sun is then always above the horizon and it just makes a 360-degree circuit around it. That part of Earth enjoys summer.

  A mirror-image situation exists south of the equator. Nights are longer than days, and the further one gets from the equator, the larger is the imbalance--until one gets so close to the pole that the sun never rises. That is the famous arctic night, with 24 hours of darkness each day. In that half of the Earth, it is winter time.

  Half a year later, the Earth is on the other side of the Sun, that is, the Sun's position in the above drawing should be on the right, and the shaded part of the Earth should now be on the left (light and dark portions in the drawing switch places). The Earth's axis however has not moved, it is still pointed to the same patch of sky, near the star Polaris. Now the south pole is bathed in constant sunshine and the north one is dark. Summer and winter have switched hemispheres.

  A big difference between summer and winter is thus the length of the days: note that on the equator that length does not change, and hence Spring, Summer, Fall, and Winter do not exist there (depending on weather patterns, however, there may exist a "wet season" and a "dry season"). In addition (as the drawing makes clear), the Sun's rays hit the summer hemisphere more vertically than the winter one. That, too, helps heat the ground, as explained further in section #4, "The Angle of the Sun's Rays."

  At equinox, the situation is as in the first drawing, and night and day are equal (that is where the word "equinox" comes from)

Some interesting facts

  If June 21 is the day when we receive the most sunshine, why is it regarded as the beginning of summer and not its peak? And similarly, why is December 21, the day of least sunshine, the beginning of winter and not mid-winter day?

  Blame the oceans, which heat up and cool down only slowly. By June 21 they are still cool from the winter time, and that delays the peak heat by about a month and a half. Similarly, in December the water still holds warmth from the summer, and the coldest days are still (on the average--not always! ) a month and a half ahead.

  And what about our distance from the Sun? It, too, varies, because the Earth's orbit around the Sun isn't an exact circle. We are closest to the Sun--would you believe it? --in the cold wintertime, around January 3-5. This may have an interesting implication for the origin of ice ages, as will be explained later. It also ties to an interesting story of the unusually bright Moon of December 22, 1999.

In the US and in other mid-latitude countries north of the equator (e.g those of Europe), the sun's daily trip (as it appears to us) is an arc across the southern sky. (Of course, it's really the Earth that does the moving.) The sun's greatest height above the horizon occurs at noon, and how high the sun then gets depends on the season of the year--it is highest in mid-summer, lowest in mid-winter.

Boy scouts used to be taught (perhaps still are) that someone lost in the woods can often tell the north direction by checking on which side of tree-trunks moss grew best. Moss avoids direct sunlight, and with the sun's path curving across the southern sky, the north side of a tree-trunk is the one most shaded.

The Month

The civil year, January to December, no longer ties its months to the moon, but some traditions still do and their terms for "month" reflect the connection--in Arabic, "shahr", in biblical Hebrew "yerach" and also "chodesh" from "new," since it was reckoned from one new moon to the next. Jericho (pronounced Yericho), one of the oldest cities on Earth, took its name from "yerach," and of course, legends tell of many moon-gods and goddesses, e.g. Artemis and Diana.

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 occured 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 occured 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.

The Face of the Moon

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.

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.

The Gravity Gradient

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.

Both masses A and B are attracted to the Earth, and if the attracting forces were equal, their tendencies to rotate the satellite ("rotation moments" or "torques") are equal and cancel each other, so that no rotation occurs. Actually, the force on A is just a little stronger, because A is slightly closer to the center of the Earth. Therefore the satellite will rotate until A is as close to Earth as it can be, which is a possible position of equilibrium.

Of course, if it started from an off-equilibrium position, it can overshoot the mark and then swing back and forth around equilibrium, like a pendulum. The elongated moon acts like a dumbbell too, and does in fact swing a little from side to side, like a pendulum of like balanced scales; this has allowed astronomers even before the space age to see a little more than half the moon. Such motion is known as "libration," from " libra", balance-beam scales--also the name of a constellation of the zodiac and of an ancient unit of weight, from which our abbreviation lb is derived.

The rotating force which lines up the moon or an orbiting dumbbell therefore depends not on how strongly gravity pulls it, but on how rapidly the pull of gravity changes with distance--on the "gravity gradient." Near Earth that is a gentle force, though it is strong enough to line up elongated satellites. Among those was Triad, shaped like a long dumbbell with an additional payload in the middle, the first satellite to map the electrical currents associated with the polar aurora. It did swing back and forth with a 6-minute period, complicating the analysis of its data.

Near a black hole or pulsar, on the other hand, the gravity-gradient force is fierce enough to rip a spacecraft apart.

When Galileo became the first human to view the Moon through a telescope, our understanding of the Moon changed forever. No longer a mysterious object in the sky, but a sister-world full of ring-shaped mountains and other formations!

Giovanni Riccioli in 1651 named the more prominent features after famous astronomers, while the large dark and smooth areas he called "seas" or "maria" (singular "mare," mah-reh). Some of the names he used for the Moon's crater are of persons discussed in "Stargazers"--Tycho (distinguished by bright streaks that radiate from it), Ptolemy ("Ptolemaeus"), Copernicus, Kepler, Aristarchus, Hipparchus, Erathosthenes; Meton and Pythagoras are on the edge, near the northern pole.

Late-comers who lived after the 17th century had to make do with left-overs: the craters Newton and Cavendish are at the southern edge of the visible disk, Goddard and Lagrange too are near the edge. Also, "Galilaei" is a small undistinguished crater (because of Galileo's banishment?). However, since the Russians were the first to observe the rear side of the Moon, a prominent crater there bears the name of Tsiolkovsky, who at the end of the 19th century promoted the idea of spaceflight.

Note: Strictly for moon junkies--all you ever wanted to know, perhaps even more. From Cambridge University Press (1999), Mapping and naming the moon: A history of lunar cartography and nomenclature by Ewen A. Whitaker, xix+242 pp., $59.95.

The Craters

What had created those strange round "craters"? ("Krater" is Greek for a bowl or wide-mouthed goblet.) They reminded some observers of volcanic craters on Earth, or better, of the large "calderas" (cauldrons) formed by the internal collapse of volcanos, e.g. Crater Lake in Oregon. Others suggested that they were formed by the impact of large meteorites, but this was countered by the argument that most meteorites probably arrived at a slanting angle, and were expected to leave not a round ring but an elongated gouge.

Part of the evidence has come from the nicely rounded impact remnants found on Earth, e.g. Meteor Crater (Canyon Diablo) in Arizona and Manicougan lake in Canada, in northern Quebec (picture on left), which is about 100 km (60 miles) wide and 214 million years old. Note that rather than having a pit in its center, the Manicougan lake has a round island. After the impact, the land rose again to the level of its surroundings, pushed by fluid pressure of the material below it, which acts like a viscous fluid and tries to establish equilibrium between the different loads which it supports. (For another picture of Lake Manicougan, and more about it, click here.)

Other solid bodies of the solar system also diplay round craters. On the large ice-covered moons of Jupiter, the return to equilibrium is much more pronounced, because ice sags and flows much more readily than rock. Those moons display "palimpsest" craters which are merely surface markings, because as time passed, the walls which originally existed sagged back onto the flat surface.

The Airless Moon

Why? By the laws of motion, the Moon orbits not the center of the Earth, but the center of gravity of the Earth and Moon (this will be discussed in section #11a, and the center of gravity is defined in section #25). The location of that point allows astronomers to deduce the mass of the Moon, and from that, the pull of the Moon's gravity. At the surface of the Moon, it turned out, gravity is only 1/6 as strong as at the surface of the Earth.

Gravity is important for the retention of an atmosphere. It holds an atmosphere down, while heat is what can make it escape.

Heat is atomic or molecular motion. In a hot solid or liquid, it can be viewed as a shaking motion of atoms or molecules around their average position, like the rustling of leaves in a wind. The higher the temperature, the more vigorous the motion, until the material boils or evaporates, at which point its particles shake loose altogether. In a gas atoms and molecules fly around randomly, colliding constantly (if the gas is as dense as it is in the atmosphere), and their collisions lead to a very good explanation ("the kinetic theory of gases") of the observed properties of a gas.

The average velocity of a gas molecule depends on the temperature of the gas, and at room temperature it is comparable to that of the speeding bullet, quite below the "escape velocity" needed for escaping Earth's gravity. However, that is just an average: actual velocities are expected to be distributed around that average, following the "Maxwellian distribution" first derived by James Clerk Maxwell, whom we meet again in the discovery of the three color theory of light (section #S-4) and the prediction of electromagnetic waves (section #S-5). According to that distribution, a few molecules always move fast enough to escape, and if they happen to be near the top of the atmosphere, moving upwards and and avoiding any further collisions, such molecules would be lost.

For Earth, their number is too small to matter, but with the Moon, having only 1/6 of the surface gravity, it can be shown that any atmosphere would be lost within geological time. The planet Mercury, only slightly larger, also lacks any atmosphere, while Mars, with 1/3 the Earth's surface gravity, only retains a very thin atmosphere.

Water evaporates easily and once in gas form, is quickly lost by the same process. That suggested the "maria" could not possibly be oceans, though their name remained. They actually turned out to be basaltic flows, hardened lava which long ago flowed out of fissures on the Moon; no present-day volcanism on the Moon has been reliably identified. The vast majority of craters probably date back to the early days of the solar system, because the lava of the maria has very few craters on it, suggesting it flooded and obliterated older ones.

The picture of a dry Moon was reinforced by Moon rocks brought back by US astronauts. Earth rocks may contain water bound chemically ("water of hydration"), but not these. Water, of course, would be essential to any human outpost on the Moon. Yet small amounts of water may still exist, brought by comets which occasionally hit the Moon. All this water is sure to evaporate in the heat of the collision, but some of it may re-condense in deep craters near the Moon's pole, which are permanently in the shade and therefore extremely cold. Observations by the "Clementine" spacecraft suggest that one such crater may indeed contain a layer of ice.

In the Space Age

In 1970 a Soviet spacecraft landed and returned a rock sample, and later that year a remotely controlled "Lunokhod" vehicle was landed, exploring its surroundings for nearly a year. Other sample returns and Lunokhods followed, the series ending in 1976. However, failures marked tests of a large rocket developed for human Moon flights, ending any plans of manned lunar exploration by the Soviet Union.

Early attempts by the US to send unmanned spacecraft to the Moon (1958-64) either failed or returned scanty data. In July 1964, however, Ranger 7 returned clear TV pictures of its impact on the Moon, as did Rangers 8 and 9. Of the 7 "soft landers" in the "Surveyor" series (1966-8), 5 performed well and sent back data and pictures. In November 1969, after Apollo 12 landed 500 feet (160 meters) from the "Surveyor 3" lander, astronauts retrieved its camera and brought if back to Earth. In addition to the Surveyor project, 5 lunar orbiters photographed the Moon and helped produce accurate maps of its surface.

On May 25, 1961, about one month after Russia's Yuri Gagarin became the first human to orbit the globe, US president John F. Kennedy proposed to the US Congress "that this nation should commit itself to achieving the goal, before this decade is out, of landing a man on the Moon and returning him safely to Earth. "

The Apollo missions followed, with Apollo 8 rounding the Moon in 1968 and Apollo 11 finally landing there, on July 20, 1969. Five other lunar landings followed, the last of them in December 1972. Only Apollo 13 failed to land, its crew members narrowly escaping with their lives after an explosion aboard their craft on the way to the Moon.

• Bringing back to Earth extensive samples of lunar rock and soil. The rocks turned out to be ancient, suggesting no significant change since the surface of the Moon formed, about 4.5 billion years ago. The "soil" (regolith) had probably been pulverized by impacts, but as the "Surveyor" missions showed, it was firm enough to provide support.

• Crews of Apollo 15, 16 and 17 explored the Moon aboard an electrically driven "moon buggy. " (picture on the right).

• Extensive video pictures from the Moon were beamed to Earth--even one (by a remotely controlled camera) of the take-off from the Moon by the Apollo 17 crew. Also, the Earth and its "geocorona" of glowing hydrogen were photographed by a special camera using ultraviolet light.

• A seismometer was placed on the Moon, showing that the Moon was seismically much quieter than Earth.

• Metal foils were hung out (like a flag) to receive the solar wind. They were then returned to Earth where the composition of the ions caught in them was analyzed.

• Corner reflectors were placed on the Moon, so that laser beams reflected from them could accurately measure the distance.

    The Moon was found to have no global magnetic field like the Earth, but its surface was weakly magnetized in some patches. Molten rock can become permanently magnetized if it solidifies in the presence of an external magnetic field, suggesting that in some ancient era the Moon, like Earth now, had a molten metallic core in which electric currents generated a magnetic field. Somewhat similar observations were made near Mars in 1998-2000.

    Some excitement was caused by indications from the Lunar Prospector spacecraft, which suggested that ice may exist on the moon, inside a deep crater near the Moon's south pole. A possible explanation was that some time in the past (perhaps long ago) a comet had crashed into the Moon, and comets contain considerable amounts of water ice. The energy of the impact, turned into heat, would of course evaporate the ice. However, some of the water vapor would form a temporary atmosphere around the Moon, and might condense again to ice in very cold locations, like craters near the pole, which are permanently shaded from sunlight.

    At the end of its mission, on July 31, 1999, Lunar Prospector was therefore steered to deliberately crash inside the crater. It was hoped the impact might create (briefly) a cloud of water vapor, which could be observed from Earth, but none was detected.

    There is little doubt that the future will see further lunar exploration, though a "lunar base" is probably far off. Astronomical and other observations can readily be made from Earth orbit, and providing life support on the Moon is not easy. Such a base will probably become attractive only after ways are developed for utilizing local lunar materials for construction and for fuel.

Exploring Further

• Apollo--Expeditions to the Moon, Edited by Edgar M. Cortright.
  
• "Contact Light"by Kipp Teague.
  
• Where no Man has gone before by the NASA History Office

A site about impact craters on Earth.

Since moonshine is really reflected sunlight, the full Moon is on the average slightly brighter in mid-winter, when Earth is closest to the Sun. In addition, the distance of the full Moon also varies, due to the ellipticity ("eccentricity") of the Moon's orbit. On 22 December, 1999, the two effects combined to produce the brightest full Moon of the century. On the preceding day, NASA released the following "Educational Update":

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This year will be the first full moon to occur on the winter solstice, Dec. 22nd, commonly called the first day of winter. Since a full moon on the winter solstice occurs in conjunction with a lunar perigee (point in the moon's orbit that is closest to Earth), the moon will appear about 14% larger than it does at apogee (the point in it's elliptical orbit that is farthest from the Earth). Since the Earth is also several million miles closer to the sun at this time of the year than in the summer, sunlight striking the moon is about 7% stronger making it brighter. Also, this will be the closest perigee of the Moon of the year since the moon's orbit is constantly deforming. If the weather is clear and there is a snow cover where you live, it is believed that even car headlights will be superfluous.

On December 21st. 1866 the Lakota Sioux took advantage of this combination of occurrences and staged a devastating retaliatory ambush on soldiers in the Wyoming Territory.

In laymen's terms it will be a super bright full moon, much more than the usual AND it hasn't happened this way for 133 years! Our ancestors 133 years ago saw this. Our descendants 100 or so years from now will see this again.

Remember this will happen December 22, 1999.

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(Superfluous or not, we hope drivers that night kept their headlights shining!)

Additional Exploring

On 12.22.1999 it showed the difference in the apparent size of the Moon,
      between its closest and most distant positions.
On 1.13.2000 it showed a striking picture of the "brightest moon."

Actually, these are two angles, measured in degrees, "minutes of arc" and "seconds of arc." These are denoted by the symbols (°,',") e.g. 35° 43' 9" means an angle of 35 degrees, 43 minutes and 9 seconds (do not confuse this with the notation (', ") for feet and inches!). A degree contains 60 minutes of arc and a minute contains 60 seconds of arc--and you may omit the words "of arc" where the context makes it absolutely clear that these are not units of time.

Calculations often represent angles by small letters of the Greek alphabet, and that way latitude will be represented by l (lambda, Greek L), and longitude by f (phi, Greek F). Here is how they are defined.

Latitude

To specify the latitude of some point P on the surface, draw the radius OP to that point. Then the elevation angle of that point above the equator is its latitude l--northern latitude if north of the equator, southern (or negative) latitude if south of it.

[How can one define the angle between a line and a plane, you may well ask? After all, angles are usually measured between two lines!
  Good question. We must use the angle which completes it to 90 degrees, the one between the given line and one perpendicular to the plane. Here that would be the angle (90°-l) between OP and the Earth's axis, known as the co-latitude of P.]

Longitude

  A lines of longitude is also called a meridian, derived from the Latin, from meri, a variation of "medius" which denotes "middle", and diem, meaning "day." The word once meant "noon", and times of the day before noon were known as "ante meridian", while times after it were "post meridian." Today's abbreviations a.m. and p.m. come from these terms, and the Sun at noon was said to be "passing meridian". All points on the same line of longitude experienced noon (and any other hour) at the same time and were therefore said to be on the same "meridian line", which became "meridian" for short.

In the sky, the equator is also divided into 360 degrees, but the count begins at one of the two points where the equator cuts the ecliptic--the one which the Sun reaches around March 21. It is called the vernal equinox ("vernal" means related to spring) or sometimes the first point in Aries, because in ancient times, when first observed by the Greeks, it was in the zodiac constellation of Aries, the lamb. It has since then moved, as is discussed in the later section on precession.

The celestial globe, however, uses terms and notations which differ somewhat from those of the globe of the Earth. Meridians are marked by the angle a (alpha, Greek A), called right ascension, not longitude. It is measured from the vernal equinox, but only eastward, and instead of going from 0 to 360 degrees, it is specified in hours and other divisions of time, each hour equal to 15 degrees.

Similarly, where on Earth latitude goes from 90° north to 90° south (or -90°), astronomers prefer the co-latitude, the angle from the polar axis,equal to 0° at the north pole, 90° on the equator, and 180° at the south pole. It is called declination and is denoted by the letter d (delta, Greek small D). The two angles (a,d), used in specifying (for instance) the position of a star are jointly called its celestial coordinates.

The next section tells how the stars, the Sun and accurate clocks allowed sailors to find their latitude and longitude.

Before the space age, however, it was not as easy. One had to use the Sun and the stars.

Finding latitude with the Pole Star

The angle between the direction of the pole and the zenith is then (90°-h) degrees. If you continue the line from zenith downwards (see drawing) it reaches the center of the Earth, and the angle beween it and the Earth's axis is also (90°-h).

Therefore (as the drawing shows) h is also your latitude.

Finding latitude with the noontime Sun

Noon is when the Sun reaches the highest point in its journey across the sky. It then crosses the north-south direction--in the northern hemisphere, usually south of the observer. Because the axis of the Earth is inclined by an angle e = 23.5° to a line perpendicular to the ecliptic, the height of that point above the horizon depends on the season. Suppose you are at point P. We examine 3 possibilities:

Look at the drawing and imagine you could rotate
  the equator and the north pole N
until they reached the
   ecliptic and the pole of the ecliptic N'.
Then all three angles marked e fold up together, showing that they are equal. You get

For any other date, navigation tables exist that give the proper angle (smaller than 23.5 degrees) which must be added or subtracted. They also provide formulas for deriving the height of the noontime Sun from observations made at other times.

As with the pole star, rather than measuring the angle a from the zenith--which is not marked in the sky!--it is simpler to measure the angle (90°-a) from the horizon, which at sea is usually sharply defined. Such observations, known as "shooting the Sun," are done with an instrument known as the sextant. It has a sliding scale covering 1/6 of a circle (hence the name) and an attached pivoted mirror, providing a split view: by moving the scale, the sea-officer brings Sun and horizon simultaneously into view and then reads off the angle between them.

Longitude

Longitude was a much harder nut to crack. In principle, all one needs is an accurate clock, set to Greenwich time. When the Sun "passes the meridian" at noon, we only need to check the clock: if Greenwich time is 3 p.m., we know that 3 hours ago it was noon at Greenwich and we are therefore at longitude 15° x 3 = 45 degrees west.

However, accurate clocks require a fairly sophisticated technology. Pendulum clocks can keep time quite accurately on firm land, but the pitching and rolling of a ship makes them quite unsuitable for sea duty.

Non-pendulum clocks--e.g. wristwatches, before they became electronic--use a balance wheel, a small flywheel rotating back and forth through a small angle. A flat spiral spring is wrapped around its axis and it always brings the wheel back to its original position. The period of each back-and-forth oscillation is then only determined by the strength of the spring and the mass of the wheel, and it can replace the swing of the pendulum in controlling the motion of the clock's hands.

Gravity plays no role here, and motions of the ship also have very little effect; as discussed in a later section, a vaguely similar method was used in 1973 for "weighing" astronauts in the weightless environment of a space station. For navigation, however, such a clock must be very accurate, which is not easy to achieve: friction must be minimal, and so must changes in the dimensions of the balance wheel and properties of the spring due to changing temperature and other factors.

In the 17th and 18th century, when the navies of Britain, Spain, France and Holland all tried to dominate the seas, the "problem of longitude" assumed great strategic importance and occupied some of the best scientific minds. In 1714 Britain announced a prize of 20,000 pounds--a huge sum in those days--for a reliable solution, and John Harrison, a British clockmaker, spent decades trying to achieve it. His first two "chronometers," of 1735 and 1739, though accurate, were bulky and delicate pieces of machinery; they have been restored and are ticking away on public display, at the Royal Astronomical Observatory in Greenwich. Only his 4th instrument, tested in 1761, proved satisfactory, and it took some additional years before he received his prize.

An extensive and delightful web site on the story of the "longitude problem," by Jonathan Medwin, can be reached here. Another recommended source is the book Longitude by Dava Sobel.

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Nansen