Appearance of the Heavens

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If a time exposure photograph of the night sky is taken over a period of a few hours, the result will be as shown in Fig. 2.3. During the time that the camera shutter is open, the positions of the various stars in the sky change, the paths of their apparent motions being traced by arc-like streaks, just as photographs of a city street at night show streaks of light from the headlights of passing automobiles. If the camera shutter is left open for 24 hours (and if somehow the Sun could be "turned off"), many of the streaks, in particular those near the pole star, would become complete circles. Because the Sun cannot be turned off, the picture can only be taken during the hours of darkness, and thus only a fraction of the complete circles can be obtained, equal to the fraction of 24 hours during which the camera shutter is open. If the photograph is taken night after night, it will be almost the same, with a few exceptions to be discussed below.

It appears that the Earth is surrounded by a giant spherical canopy or dome, called the stellar sphere or the celestial sphere, and the stars are little pinpoints of light mounted on this dome (Fig 2.4a). The dome rotates about us once in 24 hours in a direction from east to west (rising to setting). The Sun, Moon, and planets are also mounted on this sphere. Of course, when the Sun is in view we cannot see the stars because the bright light of the Sun, as scattered by the Earth's

Kinetic Energy Imagas

Figure 2.4. Celestial sphere, (a) Schematic of sphere showing Earth at center and the ecliptic, (b) Greatly enlarged view of part of the path of a planet along the ecliptic, showing retrograde motion.

Figure 2.4. Celestial sphere, (a) Schematic of sphere showing Earth at center and the ecliptic, (b) Greatly enlarged view of part of the path of a planet along the ecliptic, showing retrograde motion.

atmosphere, makes it impossible to see the relatively weak starlight. (When there is an eclipse of the Sun, it is possible to see the stars quite well.)

By patient observation and measurement, the ancient astronomers and astrologers, who did not have photographic equipment, were able to observe and keep track of this daily rotation, called the diurnal rotation or diurnal motion of the celestial sphere. They were able to determine that all the heavenly objects, with a few exceptions, are fixed in position on the rotating celestial sphere. In the course of time it was recognized that the Earth itself is also spherical and appears to be located at the center of the celestial sphere. The part of the celestial sphere that can be seen depends on the location of the observation point on the Earth. Standing at the North Pole of the Earth, the centers of the circles will be directly overhead. At a latitude of 45° the celestial pole (the centers of the circles) will be 45° up from the north horizon (in the northern hemisphere), whereas at the equator, the celestial pole will be down at the north horizon.

Fairly early it was recognized that certain objects on the celestial sphere are not fixed; that is, these objects appear to move as compared with the general background stars. The position of the Sun on the sphere, for example, changes over the course of a year. It follows a path, called the ecliptic, shown in Fig. 2.4a as a dashed circle tilted at an angle of 23^° from the celestial equator. The direction of motion of the Sun is from west to east (opposite in direction to the daily rotation.)3 The position of the Moon also changes, and it travels from west to east along the ecliptic making a complete circuit in 27^ days, on the average. Similarly, the planets that are visible to the unaided eye—Mercury, Venus, Mars, Jupiter, and Saturn—travel roughly along the ecliptic, from west to east also, taking 90 days to 30 years to make the complete circuit.

The motion of the Sun is called annual motion and is fairly, but not completely, smooth and even. The motion of the Moon is also somewhat smooth, but less so than the Sun's motion. The motion of the planets, on the other hand, is variable in speed, and sometimes in direction as well. Indeed, this is the origin of the word planet, which means wanderer. The planets also normally move from west to east, relative to the fixed stars. When a planet occasionally varies its direction of motion, it moves from east to west relative to the fixed stars, rather than follow its overall west to east path. This motion, called retrograde motion, is illustrated in Fig 2.4b, which shows the planet not only changing direction, but wandering slightly off the ecliptic as well. Accompanying the retrograde motions are variations in the apparent brightness of the planet.

At times a planet is just ahead of the Sun on the ecliptic, and at other times it is just behind the Sun. This is called alternate motion. If the planet is just west of the Sun, the daily rotation will bring it into view as the morning star; if it is just east of the Sun, it will be seen as the evening star just after sunset.4 Because of their varying speeds, there will be times when the two planets appear very close to each other. Such an event is sometimes called a conjunction. Ancient astrologers and soothsayers who searched for "signs" in the heavens attached great significance to conjunctions as portending or reflecting momentous events for humans. Even more rare (and portentous) are double conjunctions, when three planets appear very close to each other. (In current astronomical usage, conjunction has a different meaning, the discussion of which is beyond the scope of this book.)

As already mentioned, over the centuries the various great civilizations attached much importance to the appearance of the heavens. These appearances were used to establish the calendars necessary for the governance of extensive empires and recording important events in human affairs. They were also important for travel to distant places, because navigators could determine where they

3This does not contradict the common observation that the daily motion of the Sun is from east to west. It means rather that if one could observe the position of the Sun against the background of ' 'fixed'' stars (such as during an eclipse), one would see that the Sun slowly moves from west to east on the celestial sphere.

4The Moon and Sun were also considered to be planets, but they do not exhibit retrograde motion or the same degree of variation of speed as the other planets. In this book, the word planet does not include the Moon and Sun.

were by the appearance of the heavens in their particular location. In fact, the calculation and use of accurate navigation tables played a very important part in the exploration of the world by various seafaring nations, and in their ability to carry out commercial and military expeditions. Until the last few centuries, astrological predictions, based on the appearance of the heavens in general, or some unusual event such as a conjunction, or a comet, or a nova, have had widespread influence on political decision making. Even today horoscopes are surprisingly popular.

The Babylonians developed one of the great Mesopotamian civilizations. Their astronomers carried out rather accurate measurements and calculations of the heavenly appearances. They were more concerned with the accuracy and reliability of their astronomical measurements and predictions than with the development of a general understanding of the whys and wherefores of the workings of the universe.

The Greeks, on the other hand, although interested in accurate and reliable knowledge of the heavens, did not improve the Babylonian measurements significantly. The Greek contribution to astronomy came more from their concern with understanding on a philosophical level, as already indicated. They regarded the heavens as being the regions where perfection could be found, because the true nature of the heavens was perfection. The appearances of the heavens, they felt, had to be interpreted in terms of their inherent perfection and constancy. The Sun and Moon seem to have the "perfect" shape—namely, circular. The fact that the diurnal motion of the stars resulted in circular motion was appropriate because a circle represented the perfect figure, as discussed in Section A2 above.

Although the detailed motion of the planets seemed to depart from smooth and circular motion, on the average the motion was circular. Therefore it was asserted that the essential nature of their motion was circular, and the departures from circular motion that were observed represented but the shadows of the true reality, as understood from Plato's Allegory of the Cave. The Greek philosophers took seriously Plato's command to "save the appearances," that is, to explain all motions of heavenly bodies in terms of circular motions. In modern terms, they undertook to develop a model of the universe that would explain how it ' 'really works."

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