You might naively always expect a high tide when the Moon is directly overhead and the bulge is the largest. This is usually not the case. Often the highest tide occurs at other times during the lunar cycle and is often related to the timing of the water flows entering an embayment from the ocean.
A flash from lightning arrives almost instantaneously, while sound travels at approximately 340 meters per second to reach the observer. If you start counting at the flash and stop counting when you hear thunder, the distance of the strike is one mile for every five seconds of delay. As a storm approaches, the delay decreases.
Typically, the land cloud will remain stationary, whereas other clouds will move.
The capacity of air to hold moisture depends also on the air temperature: the warmer the air, the more water it holds. As a result summer air is usually humid, while winter air can be quite dry.
The next important property is thermal conductivity, which is the ability to carry heat (or cold) from one place to another. Wet air is very effective at transmitting heat or cold from one place to another. Oftentimes on sultry summer days, people will lament, “It’s not the heat; it’s the humidity.” A strong breeze in cold rain can rapidly drain energy away from the skin of hikers, causing hypothermia.
On the equinox, latitude is the angle of the shadow cast by the stick at its shortest length. The ratio of the shadow length to the stick length gives the tangent of the latitude.
In a large number of early cultures, there are mythological descriptions of a great flood. These include the Gilgamesh epic of Babylon, the Jewish story of Noah, and Chinese and Hindu myths. Early American cultures and Polynesian cultures all had versions of a flood mythology. In many of these legends, a sailor survives the flood and sees land gradually covered by water until it disappears. Eventually, the waters recede, and land is seen, with the highest elevations appearing first.
Many conjectures for the flood mythology have been put forward, but one plausible explanation that has not been advanced is the phenomenon of land disappearing beyond the horizon as the boat departs and on its return the highest elevations appearing first as the ship approaches land. The ubiquity of the deluge myth could possibly be reconciled as the phenomenon of objects disappearing over the horizon for cultures believing in a flat Earth. How else could one account for such a phenomenon if the Earth were flat?
There are many plausible reasons for long-distance voyaging. Fishing and trade are certainly two of the most important, as economic factors can be strong motivators. Long-distance migration over the ocean is less common but is responsible for the Pacific Islands peoples’ hegemony. Growing populations with limited resources can be important factors motivating these voyages.
Imagine a patriarch living with his family circa 7000 BC. He lives in a fertile coastal region but is hemmed in by mountains. He makes his living from fishing and farming and is highly regarded in his society. The priests hold to the concept of a flat Earth, but the patriarch is aware of distant fertile lands beyond the horizon. He visited these on long-distance fishing expeditions trying to chase migrating fish and escape the overfished stocks close to his native land. The population has slowly been rising, and arable farmland is becoming scarce. Fights break out among clans, and blood feuds take their toll. Knowing of the uninhabited fertile land over the horizon, the patriarch sets out to save his family by sailing there.
He supervises his family in the construction of a large, scaled-up version of his fishing vessel, capable of transporting them and the possessions they need to make a new living in the far-off land. When the vessel is complete, it’s only a question of timing when to leave without arousing suspicion. He waits for a storm, then moves his livestock, plants, water, food, and family onto his vessel and sets off. While the scene is familiar to him, his passengers witness an amazing sight as they depart from land. First the low-lying farmlands disappear under water, followed by the upland forests, and finally, the mountaintops vanish.
For those raised with the notion of a flat Earth, there is only one inescapable conclusion: the Earth has flooded. Everywhere they look they are surrounded by water. Knowing that there’s no possibility of return to the precarious situation in their homeland, the patriarch allows this idea to take hold as if to emphasize the impossibility of turning back. After sailing for several weeks, the patriarch knows that he should be close to land and releases the pigeons he has brought along. Although many now believe that pigeons navigate by “seeing” the Earth’s magnetic field, ancient sailors knew of their utility as shore-finding birds. Finally, one departs in a direction indicating land.
He alters course, and as he approaches, what do his passengers see? At first, only the tops of mountains are visible, then the lowlands. The floodwaters are receding! They’re saved. They make landfall. The patriarch goes to his grave with his secret, and his story becomes one of divine intervention.
The mythology of the great flood is quite common, yet there is no geological evidence for a global flood in any historical time. It’s plausible to imagine that the scenario described above happened a number of times in different settings as population pressures forced a long ocean migration, and the witnesses who believed in a flat Earth carried with them the story of a great flood.
In the late seventeenth and eighteenth centuries, the phenomenon of refraction close to the horizon was called looming by sailors. In addition to the simple hot-road mirage and distorted horizons, layers of hot air over cold water could cause unusual distortions. On a kayak trip I took off the coast of Downeast Maine, the water temperature was in the 50s, but the air temperature was in the 90s. During the course of the trip, there were many strange sightings: oddly elongated structures, magnification of distant trees, container ships apparently floating in midair, and lighthouses appearing where there were no signs of any on maps until the coast of Nova Scotia, some eighty miles away.
The usual corrections used by navigators work well under most conditions, but strange things can happen near the horizon with distant images. The discussion above assumes that the air temperature and pressure drop slowly the higher you go in the atmosphere. Weather conditions can completely change this, however. In the summer, when the hot Sun beats down on a road, mysterious “puddles” seem to appear on the surface of the road. This is sometimes called the hot-road mirage and is illustrated in Figure 94.
Cool air is denser than hot air and has a higher index of refraction. In the summer Sun the surfaces of roads heat up rapidly, creating a layer of hot air trapped just above the surface, with cooler air overlaying it. Light rays approaching the surface will get bent upward from the hot surface. The observer will see both the direct rays—the “real” image—and also rays that look as though they’ve been reflected, creating a second image. This second image is inverted, meaning that top and bottom are reversed in the refracted image. The effect that looks like puddles is created by the reflection of light from the sky and objects above. Another feature of images seen in the distance on a hot day is the shimmering quality of distant images. Hot air rises in waves and will focus and defocus the light rays reaching our eyes.
One strange consequence of refraction is the timing of sunrise and sunset. When you see the Sun’s image touch the horizon, it has already set. How can this be? The Sun has a diameter of thirty-two arc minutes, and the average refraction at the horizon is about thirty-four arc minutes. It is somewhat remarkable, but it is an accident that they are nearly the same. Since the Earth rotates through 1 degree every four minutes, this means that it takes a little over two minutes for the Earth to rotate by an amount equal to the diameter of the Sun. At the moment you see the lower limb of the Sun touch the horizon, it is already physically below the horizon. At sea level, the true moment of the sunset is roughly one minute before you see the lower part of the solar disk just touch the horizon.
Earth’s orbit around the Sun is an ellipse. It moves faster at the point of closest approach (perihelion) than at the farthest distance (aphelion).
Many people have an intuitive sense of the time of day based on the character of sunlight: its intensity and color. The blue color of the sky comes from scattering of sunlight from air molecules. Blue light scatters off air molecules more easily than red light.
On the other hand, when the Sun is low in the sky, its light has a red coloration. Seen at low altitudes, sunlight takes a long path through the atmosphere, and most of the blue gets scattered out, leaving mainly red. Photographers often take portraits around sunrise and sunset, as the rosy coloration produces flattering results. This is the case when light scatters once off an air molecule before reaching your eyes. On the other hand, when light scatters many times, as through a cloud, all the color information gets scrambled, and the cloud appears white.
The scattering that creates the blue sky also produces another effect: polarization. Light can vibrate in different directions, but if it vibrates in only one direction, it is said to be polarized. When light reflects from a surface, such as from a puddle of water or the roof of a car, only the horizontal vibration survives: the direction parallel to the reflecting surface. This is how polarizing sunglasses work: they have a filter that will block horizontally vibrating light to the eyes, reducing glare from horizontal surfaces. Light reflecting from vertical surfaces, such as windows, however, will pass through the sunglasses. If you want to see this yourself, take a pair of polarizing sunglasses and rotate them against the glare of light reflecting off a surface and you will see the change in intensity with the rotation angle.
The builders of Stonehenge placed emphasis on the summer solstice with an opening in a large embankment to the northeast. When one stands at the center of the complex, a heel stone in the middle of the opening points toward the rising Sun on the summer solstice. A number of other megalithic complexes show orientations toward the rising or setting Sun at the solstices.
The tropical temperatures are relatively constant around 26° Celsius (79°F). The effect of changing insolation with latitude is clear in the figure. As you move away from the equator in the temperate zone, the mean temperature drops about 1°C for every one hundred kilometers of travel toward the poles (1°F for every thirty-five miles). It levels out at −25°C (–13°F) in the polar regions.
During the spring the Sun rises higher in the sky, and the quality of light changes rapidly with each passing day. In the summer when the Sun is at its highest and the days are longest, light produces strong contrasts and bright colors. In the autumn days rapidly become shorter, and the Sun drops in the sky. In the winter the Sun is low in the sky, and the character of lighting is dim and in short supply.
The amount of solar warming is called insolation. The effect of insolation produces the change in temperature as one moves away from the equator toward the poles. The zone of latitudes where the Sun reaches the zenith at some time during the year is called the tropics, bounded by the Tropic of Cancer at 23 degrees N and the Tropic of Capricorn at 23 degrees S. These are named for the zodiacal signs where the Sun appears at its extremes in declination. The northern temperate zone stretches north from the Tropic of Cancer to the Arctic Circle, where the Sun becomes circumpolar. Likewise, the southern temperate zone extends from the Tropic of Capricorn to the Antarctic Circle.
You might think that most people know “why it’s cold in the winter and warm in the summer,” but you’d be surprised. In 1987 filmmakers interviewed a group of twenty-three graduating Harvard seniors and faculty members. Twenty-one of the twenty-three gave the wrong answer. Most offered up the explanation that the Earth is closer to the Sun in the summer (it is a little closer in January).
When the Sun is shining down from the zenith, directly overhead, it blasts a thousand watts of power per square meter onto the Earth.
On any date, if the solar declination is known, there is an equation that gives the maximum altitude of the Sun at the time of its meridian passage:
Alt = 90° − | Lat − decl |
The Earth’s orbit around the Sun and the tilt of its axis create an apparent motion of the Sun against the fixed background of stars. This path is called the ecliptic and moves from a high declination of 23 degrees N at the summer solstice to a low declination of 23 degrees S at the winter solstice. It crosses the celestial equator twice, once at the spring equinox and once at the autumnal equinox.
The convention of dividing the world into an Eastern and Western Hemisphere comes from Ptolemy’s description of an occupied half of the world stretching to the east from a prime meridian or zero of longitude. Ptolemy’s choice for a zero of longitude was the westernmost point of land known in his time, which he named the Fortunate Islands and were likely the present-day Canary Islands.
In northern latitudes the Big Dipper and Cassiopeia are both circumpolar, meaning that they orbit the North Pole and never set below the horizon. The circumpolar nature of the Big Dipper and its distinctive shape figure in sailing directions, as it can be seen at night any time of the year above latitudes of 35 degrees.
One of the most impressive mapping feats was the Great Trigonometric Survey of India conducted by the British in the nineteenth century. This survey had control networks thousands of miles long extending the length and width of the subcontinent, with countless numbers of control stations creating a vast interlocking network that was used to establish locations that were precise to better than a centimeter. It was during this survey that the highest mountain peaks had their altitudes measured through sightings in the distance. Mt. Everest, which bears the name of the leader of the survey, was simply a distant peak that was cataloged in the field as part of the effort. Only after the data were analyzed in London was it realized that it was the highest mountain on Earth.
After the time of Ptolemy, Western Europe plunged into the anarchy of the Dark Ages. Where order existed, it was enforced by the Catholic Church, which established rigid canons of belief. Muslim cultures in the Middle East, Persia, and North Africa, however, flourished with great importance accorded to the legacy of Greek inquiry. Much of Ptolemy’s work was translated into Arabic, along with the works of other scholars, such as Euclid. Pioneering work in astronomy, geography, and mathematics was furthered by such scientists as the Persian polymath al-Bīrūnī. Tables of the latitude and longitude of major cities were generated for the purposes of astrology and figuring out how to face Mecca.
You can estimate the distance to objects if you know their physical size and can estimate their angular size. This is a matter of trigonometry (steps omitted), which gives a rough conversion that can be used to associate the angular size of a known object to its range. At a distance of one mile, an object one hundred feet tall will span about 1 degree of angle. This gives a conversion formula:
Range (miles) = size (feet) ÷ (100 [feet] × angular size [degrees])
The word “mile” comes from the Latin phrase mille pacem, which means “a thousand paces.” Roman legionnaires kept track of the distance traveled by counting paces. A pace is the distance you cover when the same foot (left or right) hits the ground. Two steps—left, then right—equal one pace.
There can be other factors in the downhill bias: men and women frequently recall folkloric advice that they can walk to civilization by following water flowing downhill.
The habit of dogs urinating on trees is a distant evolutionary habit of trail marking. They can find their back-trail from the periodic scent mark they leave. This comes at the price of attracting predators, so canines clean their feet by rubbing them on the ground to remove the scent from their paws. Frequently, dog owners confuse this behavior with “burying” the droppings.