温伯格《解释世界》第六章 天文学的应用

即使在史前时代天穹一定已经常常被当作指南针，时钟和日历应用。人们不难注意到每天早晨太阳基本从同一方向升起，从白天太阳在天空的高度人们可以判断离天黑还有多长时间，人们也意识到当白天最长时，天气将转暖。 我们知道在早期历史上人们也这样利用天上恒星。早在公元前3000年左右埃及人就知道与农业生产息息相关的尼罗河6月河水泛滥正好与天狼星的偕日升一致。（即在这一天天狼星首度在拂晓时可见。在这之前它在夜间不可见。在这之后，拂晓前已经可见。）公元前700年之前荷马在他的作品中把阿基里斯比作夏末高挂在夜空中的天狼星：“那颗秋季出现的星星在夜空中熠熠发光，光芒超越所有星星，人们称其为猎户之犬，夜空中最为闪亮，然而征兆着邪恶，给不幸的人间带来灾难。”之后不久，诗人赫西俄德在《劳作与时日》中告诉农夫葡萄最好在大角偕日升时采摘，应该在昴星团偕日落时播种。（在这一天昴星团在日出之前刚好从西方落下，早于这天昴星团不会在日出之前西落，而在此之后它们在拂晓之前已经西落。）赫西俄德之后那些生活在城邦，没有其他通用识别日期方法的希腊人开始广泛使用帕里米格米塔（paramegmata）日历，该日历记载了每天夜空亮星的升落。 许多早期文明社会的人们在观察夜空时（那时夜空还没有被城市灯光污染）都会注意到除个别星星例外（后面会详细介绍这些星星），天上的星星相对位置保持不变。所以每个星座在不同时间观察形状不会发生变化。但是整个天穹每个晚上都会围绕北方一个点从东向西旋转，这个点被称为北天极。用现代术语表述的话是指地球自转轴向北延伸与天球的假想交点。 海员很早就可以利用星星在夜间寻找方向。荷马描写了奥德修斯在回家乡伊萨卡的路上如何被女神卡吕普索困于西地中海的岛上，直到宙斯下令要求卡吕普索把奥德修斯释放。她告诉奥德修斯在海上航行时一直保持“大熊，也有人叫北斗七星 …… 在你的左手方向。”大熊当然是指大熊星座，这个星座也被称为北斗七星。现代也称其为斗。大熊星座靠近北天极。这样在地中海纬度附近大熊星座永远不会落山（就像荷马说的：“永远不会在海水中沐浴或浸泡），而且总是在偏北方。保持大熊在他的左边，奥德修斯就可以一直向东航行，回到伊萨卡。 有些希腊人学会利用其它星座来更好地辨别方向。据阿里安撰写的亚历山大大帝传记记载，虽然多数海员那时用大熊星座来辨别北方，古代杰出的航海能手腓尼基人却用小熊星座。虽然不如大熊星座那么显眼，但小熊星座更靠近北天极。如戴奥真尼斯·拉尔修所引述，诗人卡利马科斯声称使用小熊星座辨别方向可以上溯到泰勒斯， 太阳白天看起来也在以北天极为中心由东向西旋转。当然我们在白天一般看不到星星，赫拉克利特或许更早一些人早已意识到其实星星一直在天上，只不过白天它们的光芒被太阳遮蔽。天上的一些星星刚好在日出之前可以看到，有些星星刚好在日落可以看到，由此可以确定太阳的位置，很明显太阳相对于星星的位置不是固定不变的。而就像巴比伦人和印度人早已知晓的，太阳除了每天与其他星星一样由东向西旋转，太阳也每年自西向东沿黄道十二宫运行，依次为白羊座，金牛座，双子座，巨蟹座，狮子座，室女座，天秤座，天蝎座，人马座，摩羯座，水瓶座和双鱼座。我们后面会看到，月亮和行星也沿黄道十二宫运行，不过路径不完全一致。太阳运行的这个路径被称为“黄道”。 明白了黄道十二宫，太阳在天空背景星星的位置就很容易确定。只要观察午夜时分十二宫中哪个星座位置最高，太阳一定位于此星座正相对的那个十二宫星座。据说是泰勒斯指出太阳完成环绕黄道十二宫一周需要365天。 人们可以把星空设想为环绕地球运转的天球，天北极位于地球北极正上方。但是黄道十二宫不在天赤道，而是（据说是阿那克西曼德所发现的）相对于天赤道倾斜231/2度。巨蟹座和双子座离北天极最近，摩羯座和人马座最远。用现代术语表述的化，这个倾斜（地球之所以有季节变化的原因）是由于地球自转轴并不垂直于其公转面（太阳系内所有物体几乎都在该平面运行），而是与垂向成231/2度交角。在北半球夏季或冬季太阳会朝向或背离地球北极倾斜方向。 随着圭表的应用，天文学开始演变为一门精确科学，人们可以用圭表准确测量太阳的视运行。公元四世纪主教凯撒里亚的尤西比厄斯认为是阿那克西曼德发明了圭表，而希罗多德则将之归功于巴比伦人。圭表不过是直立于太阳光可照射到的平地上的一根标杆。使用圭表很容易识别午时。在午时太阳升到最高，圭表的影子最短。北回归线以北的地方午时太阳位于正南，此时圭表的影子指向正北，这样人们可以在地上标记方位。圭表也可以作为日历使用。春夏季太阳从东偏北升起，秋冬季太阳从东偏南升起。若拂晓时分圭表的影子指向正西，那太阳是从正东升起，这天肯定或是春分--冬去春来，或是秋分--夏终秋始。夏至或冬至时圭表的影子在午时最短或最长。（日晷与圭表不同，它的指针平行于地球自转轴，而不是垂直。这样影子每天同一时刻都指向同一方向。因此上日晷是很好的计时工具，但无法用于计日）。 圭表是科学和技术相结合一个极好的例子。一种为实用目的而发明出来的技术可能为科学发现打开一道大门。由于圭表的发明，人们可以准确记录每个季节的天数。比如从一个二分点到夏至或从夏至到下一个二分点的间隔天数。与苏格拉底同代的雅典人攸克特蒙采用这种方法发现每个季节的长短不同。如果太阳以地球为中心环绕地球（或地球以太阳为中心环绕太阳）均速运行，那每个季节都应该一样长。天文学家历经几个世纪试图解开季节长短不同之谜。但这个谜团一直到十七世纪才被解开，约翰尼斯·开普勒开始意识到地球环绕太阳运行轨道不是正圆，而是椭圆。太阳不在轨道中心，而是偏向一边，位于椭圆的一个焦点上。地球在接近或远离太阳时其运行速度会加快或减慢。 月亮每个晚上看起来与星星一样环绕北天极由东向西运行，而且也像太阳一样自西向东在黄道十二宫穿行，不过不像太阳需要一年时间在背景星星中完成一周运行，月亮只需要27天多一点。因为太阳与月亮看起来是以同一方向穿行十二宫（只不过慢很多），这样一来月亮重新回到相对太阳的同一位置需要29天半（精确的说是29天，12小时，44分，3秒）。因为月相取决于月亮与太阳的相对位置，所以这个29天半的周期被称为一个月，即从一个新月到下一个新月的时间间隔。（注：准确地说这通常被称为朔望月。月亮每27天回到相对背景恒星同一位置的间隔被称为恒星月。）人们早就注意到每隔18年在满月时会发生一次月蚀，这时月亮相对背景星星的行径路线穿过太阳行径路线。（注：月蚀不会每个月都发生。因为月亮环绕地球运行的轨道平面相对于地球环绕太阳的运行平面有稍许倾斜。每个恒星月月亮穿过地球绕太阳轨道平面两次，但是发生在满月，而且地球正好位于日月之间，那18年只有一次。） 依据月亮运行规律来制定日历在某些方面比依据太阳运行规律制定日历要方便。通过观察月相变化人们很容易识别距离上一次新月已经过了多少天—比通过观察太阳来识别日期要容易很多。所以古代阴历极为常用。即使现代还有地方沿用阴历，比如伊斯兰出于宗教目的依然应用阴历。当然如果是为了农耕，航海或战争的需要，人们必须知道季节的变化，这取决于太阳的运行。令人遗憾的是一年中的月份不是整数，一年大约比12个月长11天。这样基于月相制定日历的话二至点和二分点的日期都不能固定。 另一个熟知的难点是每年的天数也并不是整数。凯撒大帝时期设定了每四年一个闰年。但这并不能完全解决问题，因为一年不是整3651/4天，而是少了11分钟。 人类历史上历经了无数次努力试图解决制定日历所面临的繁杂问题，这里无法一一赘述。公元前432年雅典的默冬（可能与攸克特蒙一起）做出了一个突出贡献。默冬可能借助了古巴比伦人的记载，他注意到19年正好是235个朔望月，两者相差只有2个小时。这样人们可以制定一个覆盖19年而非1年的日历，采用这种日历的话每天的日期和月相都可以准确识别。这种日历每19年重复一次。但是虽然19年几乎正好是235个朔望月，但是要比6940天少1/3天。默冬不得不在几个19年循环以后从日历中减去一天。 从对复活节的定义可以看出天文学家基于日月运行制定日历所付出的努力。公元325年尼西亚内阁会上规定复活节必须在每年春分后的第一个满月后的第一个星期天庆祝。狄奥多西一世统治期间宣布在错误日期庆祝复活节是死罪。不幸的是地球上不同地方观察到的春分日期并不相同。（注：二分点指太阳在相对背景恒星运行时穿过天赤道的时刻。（用现代术语表述的话是指地球和太阳的连线垂直于地轴的时刻。）地球上不同经度地区二分点的时间不同，不同地区观测者可能得出相差一天的日期。月相也一样。）为了避免复活节在不同地方庆祝时间不同，有必要规定春分的确定日期以及其后的第一次满月日期。为此罗马教会在晚古时期采用了默冬周期，但是爱尔兰修道会采用更古老的犹太84年周期日历。公元7世纪罗马传教士与爱尔兰僧侣之间控制英国教会的争斗主要是针对复活节日期的冲突。 自古以来天文学家一项主要职能就是制定日历。公元1582年在教皇格里高利十三世支持下启用了我们的现代日历。为了方便计算复活节日期，春分日期被固定在每年的3月21号。但是西方采用格里高利历的3月21号，而东正教采用儒略历。这样世界不同地方庆祝复活节的日期依然不同。 虽然天文学在希腊化时代投入了实用，但柏拉图并不以为然。这从《理想国》中苏格拉底和格劳康的一段对话中可以看出来。苏格拉底认为哲学家国王的教育应该包括天文学，格劳康表示欣然赞同：“我是说不仅农夫和海员需要对季节，月份和年份敏感，在军事上也一样重要。”苏格拉底觉得这种说法过于幼稚。对他来说，天文学的作用是“通过研究这门学科来澄清以及重新激发一个特定的心智器官，这个器官比肉眼珍贵1000倍，因为这是唯一识别真相的器官。”这种恃才傲物在亚历山大不像在雅典那么普遍，但是在公元一世纪哲学家亚历山大里亚的斐罗文章中有所体现。他评述说：“学者的认知永远优于外部观察”。幸好也许是迫于实用的压力，天文学家知道不能只靠学者。

Even before the start of history, the sky must have been commonly used as a compass, a clock, and a calendar. It could not have been difficult to notice that the Sun rises every morning in more or less the same direction, that during the day one can tell how much time there is before night from the height of the Sun in the sky, and that hot weather will follow the time of year when the day lasts longest. We know that the stars were used for similar purposes very early in history. Around 3000 BC the Egyptians knew that the crucial event in their agriculture, the flooding of the Nile in June, coincided with the heliacal rising of the star Sirius. (This is the day in the year when Sirius first becomes visible just before dawn; earlier in the year it is not visible at night, and later it is visible well before dawn.) Homer, writing before 700 BC, compares Achilles to Sirius, which is high in the sky at the end of summer: “that star, which comes on in the autumn and whose conspicuous brightness far outshines the stars that are numbered in the night’s darkening, the star they give the name of Orion’s Dog, which is brightest among the stars, and yet is wrought as a sign of evil and brings on the great fever for unfortunate mortals.”2 A little later, the poet Hesiod in Works and Days told farmers that grapes are best cut at the heliacal rising of Arcturus, and that plowing should be done at the cosmical setting of the Pleiades constellation. (This is the day in the year when these stars first are seen to set just before sunrise; earlier in the year they do not set at all before the Sun comes up, and later they set well before dawn.) Following Hesiod, calendars known as paramegmata, which gave the risings and settings of conspicuous stars for each day, became widely used by Greeks whose city-states had no other shared way of identifying dates. By watching the stars at night, not obscured by the light of modern cities, observers in many early civilizations could see clearly that, with a few exceptions (about which more later), the stars always remain in the same places relative to one another. This is why constellations do not change from night to night or from year to year. But the whole firmament of these “fixed” stars seems to revolve each night from east to west around a point in the sky that is always due north, and hence is known as the north celestial pole. In modern terms, this is the point toward which the axis of the Earth extends if it is continued from the Earth’s north pole out into the sky. This observation made it possible for stars to be used very early by mariners for finding directions at night. Homer tells how Odysseus on his way home to Ithaca is trapped by the nymph Calypso on her island in the western Mediterranean, until Zeus orders Calypso to send Odysseus on his way. She tells Odysseus to keep the “Great Bear, that some have called the Wain . . . on his left hand as he crossed the main.”3 The Bear, of course, is Ursa Major, the constellation also known as the Wagon (or Wain), and in modern times as the Big Dipper. Ursa Major is near the north celestial pole. Thus in the latitude of the Mediterranean Ursa Major never sets (“would never bathe in or dip in the Ocean stream,” as Homer puts it) and is always more or less in the north. With the Bear on his left, Odysseus would keep sailing east, toward Ithaca. Some Greeks learned to do better with other constellations. According to the biography of Alexander the Great by Arrian, although most sailors in his time used Ursa Major to tell north, the Phoenicians, the ace sailors of the ancient world, used Ursa Minor, a constellation that is not as conspicuous as Ursa Major but is closer to the north celestial pole. The poet Callimachus, as quoted by Diogenes Laertius,4 claimed that the use of Ursa Minor goes back to Thales. The Sun also seems during the day to revolve from east to west around the north celestial pole. Of course, we cannot usually see stars during the day, but Heraclitus5 and perhaps others before him seem to have realized that the stars are always there, though with their light blotted out during the day by the light of the Sun. Some stars can be seen just before dawn or just after sunset, when the position of the Sun in the sky is known, and from this it became clear that the Sun does not keep a fixed position relative to the stars. Rather, as was well known very early in Babylon and India, in addition to seeming to revolve from east to west every day along with the stars, the Sun also moves each year around the sky from west to east through a path known as the zodiac, marked in order by the traditional constellations Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius, and Pisces. As we will see, the Moon and planets also travel through the zodiac, though not on precisely the same paths. The particular path through these constellations followed by the Sun is known as the “ecliptic.” Once the zodiac was understood, it was easy to locate the Sun in the background of stars. Just notice what constellation of the zodiac is highest in the sky at midnight; the Sun is in the constellation of the zodiac that is directly opposite. Thales is supposed to have given 365 days as the time it takes for the Sun to make one complete circuit of the zodiac. One can think of the firmament of stars as a revolving sphere surrounding the Earth, with the north celestial pole above the Earth’s north pole. But the zodiac is not the equator of this sphere. Rather, as Anaximander is supposed to have discovered, the zodiac is tilted by 23½° with respect to the celestial equator, with Cancer and Gemini closest to the north celestial pole, and Capricorn and Sagittarius farthest from it. In modern terms, this tilt, which is responsible for the seasons, is due to the fact that the axis of the Earth’s rotation is not perpendicular to the plane of its orbit, which is pretty close to the plane in which almost all objects in the solar system move, but is tilted from the perpendicular by an angle of 23½°; in the northern summer or winter the Sun is respectively in the direction toward which or away from which the Earth’s north pole is tilted. Astronomy began to be a precise science with the introduction of a device known as a gnomon, which allowed accurate measurements of the Sun’s apparent motions. The gnomon, credited by the fourth-century bishop Eusebius of Caesarea to Anaximander but by Herodotus to the Babylonians, is simply a vertical pole, placed in a level patch of ground open to the Sun’s rays. With the gnomon, one can accurately tell when it is noon; it is the moment in the day when Sun is highest, so that the shadow of the gnomon is shortest. At noon anywhere north of the tropics the Sun is due south, and the shadow of the gnomon therefore points due north, so one can permanently mark out on the ground the points of the compass. The gnomon also provides a calendar. During the spring and summer the Sun rises somewhat north of east, whereas during the autumn and winter it comes up south of east. When the shadow of the gnomon at dawn points due west, the Sun is rising due east, and the date must be either the vernal equinox, when winter gives way to spring; or the autumnal equinox, when summer ends and autumn begins. The summer and winter solstices are the days in the year when the shadow of the gnomon at noon is respectively shortest or longest. (A sundial is different from a gnomon; its pole is parallel to the Earth’s axis rather than to the vertical direction, so that its shadow at a given hour is in the same direction every day. This makes a sundial more useful as a clock, but useless as a calendar.) The gnomon provides a nice example of an important link between science and technology: an item of technology invented for practical purposes can open the way to scientific discoveries. With the gnomon, it was possible to make a precise count of the days in each season, such as the period from one equinox to the next solstice, or from then to the following equinox. In this way, Euctemon, an Athenian contemporary of Socrates, discovered that the lengths of the seasons are not precisely equal. This was not what one would expect if the Sun goes around the Earth (or the Earth around the Sun) in a circle at constant speed, with the Earth (or the Sun) at the center, in which case the seasons would be of equal length. Astronomers tried for centuries to understand the inequality of the seasons, but the correct explanation of this and other anomalies was not found until the seventeenth century, when Johannes Kepler realized that the Earth moves around the Sun on an orbit that is elliptical rather than circular, with the Sun not at the center of the orbit but off to one side at a point called a focus, and moves at a speed that increases and decreases as the Earth approaches closer to and recedes farther from the Sun. The Moon also seems to revolve like the stars each night from east to west around the north celestial pole; and over longer times it moves, like the Sun, through the zodiac from west to east, but taking a little more than 27 days instead of a year to make a full circle against the background of stars. Because the Sun appears to move through the zodiac in the same direction, though more slowly, the Moon takes about 29½ days to return to the same position relative to the Sun. (Actually 29 days, 12 hours, 44 minutes, and 3 seconds.) Since the phases of the Moon depend on the relative position of it and the Sun, this interval of about 29½ days is the lunar month,* the time from one new moon to the next. It was noticed early that eclipses of the Moon occur at full moon about every 18 years, when the Moon’s path against the background of stars crosses that of the Sun.* In some respects the Moon provides a more convenient calendar than the Sun. Observing the phase of the Moon on any given night, one can easily tell approximately how many days have passed since the last new moon—much more easily than one can judge the time of year just by looking at the Sun. So lunar calendars were common in the ancient world, and still survive, for example for religious purposes in Islam. But of course, for purposes of agriculture or sailing or war, one needs to anticipate the changes of seasons, and these are governed by the Sun. Unfortunately, there is not a whole number of lunar months in the year—the year is approximately 11 days longer than 12 lunar months—so the date of any solstice or equinox would not remain fixed in a calendar based on the phases of the Moon. Another familiar complication is that the year itself is not a whole number of days. This led to the introduction, in the time of Julius Caesar, of a leap year every fourth year. But this created further problems, because the year is not precisely 365¼ days, but 11 minutes longer. Countless efforts, far too many to go into here, have been made throughout history to construct calendars that take account of these complications. A fundamental contribution was made around 432 BC by Meton of Athens, possibly a partner of Euctemon. Perhaps by the use of Babylonian records, Meton noticed that 19 years is almost precisely 235 lunar months. They differ by only 2 hours. So one can make a calendar covering 19 years rather than one year, in which both the time of year and the phase of the Moon are correctly identified for each day. The calendar then repeats itself for every successive 19-year period. But though 19 years is nearly exactly 235 lunar months, it is about a third of a day less than 6,940 days, so Meton had to prescribe that after every few 19-year cycles a day would be dropped from the calendar. The effort of astronomers to reconcile calendars based on the Sun and Moon is illustrated by the definition of Easter. The Council of Nicaea in AD 325 decreed that Easter should be celebrated on the first Sunday following the first full moon following the vernal equinox. In the reign of Theodosius I it was declared a capital crime to celebrate Easter on the wrong day. Unfortunately the precise date when the vernal equinox is actually observed varies from place to place on the surface of the Earth.* To avoid the horror of Easter being celebrated on different days in different places, it was necessary to prescribe a definite date for the vernal equinox, and also for the first full moon following it. The Roman church in late antiquity adopted the Metonic cycle for this purpose, but the monastic communities of Ireland adopted an older Jewish 84-year cycle. The struggle in the seventh century between Roman missionaries and Irish monks for control over the English church was largely a conflict over the date of Easter. Until modern times the construction of calendars has been a major occupation of astronomers, leading up to the adoption of our modern calendar in 1582 under the auspices of Pope Gregory XIII. For purposes of calculating the date of Easter, the date of the vernal equinox is now fixed to be March 21, but it is March 21 as given by the Gregorian calendar in the West and by the Julian calendar in the Orthodox churches of the East. So Easter is still celebrated on different days in different parts of the world. Though scientific astronomy found useful applications in the Hellenic era, this did not impress Plato. There is a revealing exchange in the Republic between Socrates and his foil Glaucon.6 Socrates suggests that astronomy should be included in the education of philosopher kings, and Glaucon readily agrees: “I mean, it’s not only farmers and sailors who need to be sensitive to the seasons, months, and phases of the year; it’s just as important for military purposes as well.” Socrates calls this naive. For him, the point of astronomy is that “studying this kind of subject cleans and re-ignites a particular mental organ . . . and this organ is a thousand times more worth preserving than any eye, since it is the only organ which can see truth.” This intellectual snobbery was less common in Alexandria than in Athens, but it appears for instance in the first century AD, in the writing of the philosopher Philo of Alexandria, who remarks that “that which is appreciable by the intellect is at all times superior to that which is visible to the outward senses.”7 Fortunately, perhaps under the pressure of practical needs, astronomers learned not to rely on intellect alone.