FIG. 1-1 The scientific method. No hypothesis is ever final because future data may show that it is incorrect or incomplete. Unless it turns out to be wrong, a hypothesis never leaves the loop of experiment, interpretation, testing. Of course, the more times the hypothesis goes around the loop successfully, the more likely it is to be a valid interpretation of nature. Experiment and hypothesis thus evolve together, with experiment having the final word. A hypothesis that has survived testing is called a law or theory.

FIG. 1-2 Constellations near Polaris as they appear in the early evening to an observer who faces north with the figure turned so that the current month is at the bottom. Polaris is located on an imaginary line drawn through the two "pointer" stars at the end of the bowl of the Big Dipper. The brighter stars are shown larger in size.

FIG. 1-3 Orion, the mighty hunter. Betelgeuse is a bright red star, and Bellatrix and Rigel are bright blue stars. Stars that seem near one another in the sky may actually be far apart in space. The three stars in Orion's belt, for instance, are actually at very different distances from us.

FIG. 1-4 Apparent path of a planet in the sky looking south from the northern hemisphere of the earth. The planets seem to move eastward relative to the stars most of the time, but at intervals they reverse their motion and briefly move westward.

FIG. 1-5 The ptolemaic system, showing the assumed arrangement of the members of the solar system within the celestial sphere. Each planet is supposed to travel around the earth in a series of loops, while the orbits of the sun and moon are circular. Only the planets known in Ptolemy's time are shown. The stars are all supposed to be at the same distance from the earth.

FIG. 1-6 The copernican system. The planets, including the earth, are supposed to travel around the sun in circular orbits. The earth rotates daily on its axis, the moon revolves around the earth, and the stars are far away. All planets known today are shown here. The actual orbits are ellipses and are not spaced as shown here, though they do lie in approximately the same plane.

FIG. 1-7 To draw an ellipse, place a loop of string over two tacks a short distance apart. Then move the pencil as shown, keeping the string taut. By varying the length of the string, ellipses of different shapes can be drawn. The points in an ellipse corresponding to the positions of the tacks are called focuses; the orbits of the planets are ellipses with the sun at one focus, which is Kepler's first law.

FIG. 1-8 Kepler's second law. As a planet goes from a to b in its orbit, its radius vector (an imaginary line joining it with the sun) sweeps out the area A. In the same amount of time the planet can go from c to d, with its radius vector sweeping out the area B, or from e to f, with its radius vector sweeping out the area C. The three areas A, B, and C are equal.

FIG. 1-10 As a consequence of the earth's motion around the sun, nearby stars shift in apparent position relative to distant stars.

FIG. 1-13 The equator is a great circle around the earth halfway between the poles.

FIG. 1-14 The prime meridian is a great circle perpendicular to the equator that passes through Greenwich, England.

FIG. 1-15 The longitude of a place on the earth's surface is the angle between the meridian it lies on and the prime meridian. The longitude of New York is 74° W because its meridian is 74° west of the prime meridian. The longitude of the prime meridian is 0° .

FIG. 1-16 New York lies on a parallel of latitude 41° north of the equator.

FIG. 1-17 The latitude and longitude of a point A on the earth's surface.

FIG. 1-18 Latitude and longitude on a Mercator projection of the globe. In this projection, the spacing of parallels of latitude increases from equator to poles in order to avoid distorting the shapes of geographic features. As a result, the scale of the map varies with latitude; Greenland is actually smaller than South America, for instance. Other projections vary less in scale but do not preserve shapes.

FIG. 1-20 The influence of its rotation distorts the earth. The effect is greatly exaggerated in the figure; the equatorial diameter of the earth is actually only 43 km (27 mi) more than its polar diameter.

FIG. 1-21 The origin of the tides. The moon's attraction for the waters of the earth is greatest at A, least at B. As the earth and moon rotate around the center of mass of the earth-moon system, which is located inside the earth, water is heaped up at A and B. The water bulges stay in place as the earth turns on its axis to produce two high and two low tides every day. As the earth turns under the bulges, friction between the oceans and the ocean floors slows down the earth's rotation. The effect of this is to lengthen the day. The rate of increase is a mere 1 s per in every 50,000 years, but it adds up. Measurements of the daily growth markings on fossil corals show that the day was only 22h long 380 million years ago.

FIG. 1-22 Variation of the tides. Spring tides are produced when the moon is at M₁ or M₂, neap tides when the moon is at M₃ or M₄. The range between high and low water is greatest for spring tides.