CHAPTER 2 Knowing the Heavens

The Earth’s rotation makes stars appear to trace out circles in the sky. (Gemini Observatory)

What you will learn… The importance of astronomy in ancient civilizations around the world That regions of the sky are divided around groups of stars called constellations How the sky changes from night to night How astronomers locate objects in the sky What causes the seasons The effect of changes in the direction of Earth’s axis of rotation The role of astronomy in measuring time How the modern calendar developed

Figure 2-1 The Sun Dagger at Chaco Canyon On the first day of winter, rays of sunlight passing between stone slabs bracket a spiral stone carving, or petroglyph, at Chaco Canyon in New Mexico. A single band of light strikes the center of the spiral on the first day of summer. This and other astronomically aligned petroglyphs were carved by the ancestral Puebloan culture between 850 and 1250 A.D. (Courtesy Karl Kernberger)

Figure 2-2 Three Views of Orion The constellation Orion is easily seen on nights from December through March. (a) This photograph of Orion shows many more stars than can be seen with the naked eye. (b) A portion of a modern star atlas shows the distances in light-years (ly) to some of the stars in Orion. The yellow lines show the borders between Orion and its neighboring constellations (labeled in capitals). (c) This fanciful drawing from a star atlas published in 1835 shows Orion the Hunter as well as other celestial creatures. (a: Luke Dodd/Science Photo Library/Photo Researchers; c: Courtesy of Janus Publications)

Figure 2-3 Day and Night on the Earth At any moment, half of the Earth is illuminated by the Sun. As the Earth rotates from west to east, your location moves from the dark (night) hemisphere into the illuminated (day) hemisphere and back again. This image was recorded in 1992 by the Galileo spacecraft as it was en route to Jupiter. (JPL/NASA)

Figure 2-4 Why Diurnal Motion Happens The diurnal (daily) motion of the stars, the Sun, and the Moon is a consequence of the Earth’s rotation. (a) This drawing shows the Earth from a vantage point above the north pole. In this drawing, for a person in California the local time is 8:00 P.M. and the constellation Cygnus is directly overhead.

Figure 2-4 Why Diurnal Motion Happens (b) Four hours later, the Earth has made one-sixth of a complete rotation to the east. As seen from Earth, the entire sky appears to have rotated to the west by one-sixth of a complete rotation. It is now midnight in California, and the constellation directly over California is Andromeda.

Figure 2-5 Why the Night Sky Changes During the Year As the Earth orbits around the Sun, the nighttime side of the Earth gradually turns toward different parts of the sky. Hence, the particular stars that you see in the night sky are different at different times of the year. This figure shows which constellation is overhead at midnight local time—when the Sun is on the opposite side of the Earth from your location—during different months for observers at midnorthern latitudes (including the United States). If you want to view the constellation Andromeda, the best time of the year to do it is in late September, when Andromeda is nearly overhead at midnight.

Figure 2-6 The Big Dipper as a Guide The North Star can be seen from anywhere in the northern hemisphere on any night of the year. This star chart shows how the Big Dipper can be used to point out the North Star as well as the brightest stars in two other constellations. The chart shows the sky at around 11 P.M. (daylight savings time) on August 1. Due to the Earth’s orbital motion around the Sun, you will see this same view at 1 A.M. on July 1 and at 9 P.M. on September 1. The angular distance from Polaris to Spica is 102°.

Figure 2-7 The “Winter Triangle” This star chart shows the view toward the southwest on a winter evening in the northern hemisphere (around midnight on January 1, 10 P.M. on February 1, or 8 P.M. on March 1). Three of the brightest stars in the sky make up the “winter triangle,” which is about 26° on a side. In addition to the constellations involved in the triangle, the chart shows the prominent constellations Gemini (the Twins), Auriga (the Charioteer), and Taurus (the Bull).

Figure 2-8 The “Summer Triangle” This star chart shows the eastern sky as it appears in the evening during spring and summer in the northern hemisphere (around 1 A.M. daylight savings time on June 1, around 11 P.M. on July 1, and around 9 P.M. on August 1). The angular distance from Deneb to Altair is about 38°. The constellations Sagitta (the Arrow) and Delphinus (the Dolphin) are much fainter than the three constellations that make up the triangle.

Figure 2-9 The Celestial Sphere The celestial sphere is the apparent sphere of the sky. The view in this figure is from the outside of this (wholly imaginary) sphere. The Earth is at the center of the celestial sphere, so our view is always of the inside of the sphere. The celestial equator and poles are the projections of the Earth’s equator and axis of rotation out into space. The celestial poles are therefore located directly over the Earth’s poles.

Figure 2-10 The View from 35° North Latitude To an observer at 35° north latitude (roughly the latitude of Los Angeles, Atlanta, Tel Aviv, and Tokyo), the north celestial pole is always 35° above the horizon. Stars within 35° of the north celestial pole are circumpolar; they trace out circles around the north celestial pole during the course of the night, and are always above the horizon on any night of the year. Stars within 35° of the south celestial pole are always below the horizon and can never be seen from this latitude. Stars that lie between these two extremes rise in the east and set in the west.

Figure 2-11 The Apparent Motion of Stars at Different Latitudes As the Earth rotates, stars appear to rotate around us along paths that are parallel to the celestial equator. (a) As shown in this long time exposure, at most locations on Earth the rising and setting motions are at an angle to the horizon that depends on the latitude. (David Miller/DMI)

Figure 2-11 The Apparent Motion of Stars at Different Latitudes (b) At the north pole (latitude 90° north) the stars appear to move parallel to the horizon.

Figure 2-11 The Apparent Motion of Stars at Different Latitudes (c) At the equator (latitude 0°) the stars rise and set along vertical paths.

Figure 2-12 The Seasons The Earth’s axis of rotation is inclined 23.5° away from the perpendicular to the plane of the Earth’s orbit. The north pole is aimed at the north celestial pole, near the star Polaris. The Earth maintains this orientation as it orbits the Sun. Consequently, the amount of solar illumination and the number of daylight hours at any location on Earth vary in a regular pattern throughout the year. This is the origin of the seasons.

Figure 2-13 Solar Energy in Summer and Winter At different times of the year, sunlight strikes the ground at different angles. (a) In summer, sunlight is concentrated and the days are also longer, which further increases the heating. (b) In winter the sunlight is less concentrated, the days are short, and little heating of the ground takes place. This accounts for the low temperatures in winter.

Box 2-1 Celestial Coordinates Your latitude and longitude describe where on the Earth’s surface you are located. The latitude of your location denotes how far north or south of the equator you are, and the longitude of your location denotes how far west or east you are of an imaginary circle that runs from the north pole to the south pole through the Royal Observatory in Greenwich, England. In an analogous way, astronomers use coordinates called declination and right ascension to describe the position of a planet, star, or galaxy on the celestial sphere. Declination is analogous to latitude. As the illustration shows, the declination of an object is its angular distance north or south of the celestial equator, measured along a circle passing through both celestial poles. Like latitude, it is measured in degrees, arcminutes, and arcseconds (see Section 1-5). Right ascension is analogous to longitude. It is measured from a line that runs between the north and south celestial poles and passes through a point on the celestial equator called the vernal equinox (shown as a blue dot in the illustration). This point is one of two locations where the Sun crosses the celestial equator during its apparent annual motion, as we discuss in Section 2-5. In the Earth’s northern hemisphere, spring officially begins when the Sun reaches the vernal equinox in late March. The right ascension of an object is the angular distance from the vernal equinox eastward along the celestial equator to the circle used in measuring its declination (see illustration). Astronomers measure right ascension in time units (hours, minutes, and seconds), corresponding to the time required for the celestial sphere to rotate through this angle.

Figure 2-14 The Ecliptic Plane and the Ecliptic (a) The ecliptic plane is the plane in which the Earth moves around the Sun. (b) As seen from Earth, the Sun appears to move around the celestial sphere along a circular path called the ecliptic. The Earth takes a year to complete one orbit around the Sun, so as seen by us the Sun takes a year to make a complete trip around the ecliptic.

Figure 2-14 The Ecliptic Plane and the Ecliptic (a) The ecliptic plane is the plane in which the Earth moves around the Sun.

Figure 2-14 The Ecliptic Plane and the Ecliptic (b) As seen from Earth, the Sun appears to move around the celestial sphere along a circular path called the ecliptic. The Earth takes a year to complete one orbit around the Sun, so as seen by us the Sun takes a year to make a complete trip around the ecliptic.

Figure 2-15 The Ecliptic, Equinoxes, and Solstices This illustration of the celestial sphere is similar to Figure 2-14b, but is drawn with the north celestial pole at the top and the celestial equator running through the middle. The ecliptic is inclined to the celestial equator by 231⁄2° because of the tilt of the Earth’s axis of rotation. It intersects the celestial equator at two points, called equinoxes. The northernmost point on the ecliptic is the summer solstice, and the southernmost point is the winter solstice. The Sun is shown in its approximate position for August 1.

Figure 2-16 The Sun’s Daily Path Across the Sky This drawing shows the apparent path of the Sun during the course of a day on four different dates. Like Figure 2-10, this drawing is for an observer at 35° north latitude.

Figure 2-17 Tropics and Circles Four important latitudes on Earth are the Arctic Circle (661⁄2° north latitude), Tropic of Cancer (231⁄2° north latitude), Tropic of Capricorn (231⁄2° south latitude), and Antarctic Circle (661⁄2° south latitude). These drawings show the significance of these latitudes when the Sun is (a) at the winter solstice and (b) at the summer solstice.

Figure 2-17 Tropics and Circles Four important latitudes on Earth are the Arctic Circle (661⁄2° north latitude), Tropic of Cancer (231⁄2° north latitude), Tropic of Capricorn (231⁄2° south latitude), and Antarctic Circle (661⁄2° south latitude). These drawings show the significance of these latitudes when the Sun is (a) at the winter solstice and (b) at the summer solstice.

Figure 2-18 The Midnight Sun This time-lapse photograph was taken on July 19, 1985, at 69° north latitude in northeast Alaska. At this latitude, the Sun is above the horizon continuously (that is, it is circumpolar) from mid-May to the end of July. (Doug Plummer/Science Photo Library)

Figure 2-19 Precession Because the Earth’s rotation axis is tilted, the gravitational pull of the Moon and the Sun on the Earth’s equatorial bulge together cause the Earth to precess. As the Earth precesses, its axis of rotation slowly traces out a circle in the sky, like the shifting axis of a spinning top.

Figure 2-19 Precession Because the Earth’s rotation axis is tilted, the gravitational pull of the Moon and the Sun on the Earth’s equatorial bulge together cause the Earth to precess.

Figure 2-19 Precession As the Earth precesses, its axis of rotation slowly traces out a circle in the sky, like the shifting axis of a spinning top.

Figure 2-20 Precession and the Path of the North Celestial Pole As the Earth precesses, the north celestial pole slowly traces out a circle among the northern constellations. At present, the north celestial pole is near the moderately bright star Polaris, which serves as the North Star. Twelve thousand years from now the bright star Vega will be the North Star.

Figure 2-21 The Meridian The meridian is a circle on the celestial sphere that passes through the observer’s zenith (the point directly overhead) and the north and south points on the observer’s horizon. The passing of celestial objects across the meridian can be used to measure time. The upper meridian is the part above the horizon, and the lower meridian (not shown) is the part below the horizon.

Figure 2-22 Why the Sun Is a Poor Timekeeper There are two main reasons that the Sun is a poor timekeeper. (a) The Earth’s speed along its orbit varies during the year. It moves fastest when closest to the Sun in January and slowest when farthest from the Sun in July. Hence, the apparent speed of the Sun along the ecliptic is not constant. (b) Because of the tilt of the Earth’s rotation axis, the ecliptic is inclined with respect to the celestial equator. Therefore, the projection of the Sun’s daily progress along the ecliptic onto the celestial equator (shown in blue) varies during the year. This causes further variations in the length of the apparent solar day.

Figure 2-22 Why the Sun Is a Poor Timekeeper (a) The Earth’s speed along its orbit varies during the year. It moves fastest when closest to the Sun in January and slowest when farthest from the Sun in July. Hence, the apparent speed of the Sun along the ecliptic is not constant.

Figure 2-22 Why the Sun Is a Poor Timekeeper (b) Because of the tilt of the Earth’s rotation axis, the ecliptic is inclined with respect to the celestial equator. Therefore, the projection of the Sun’s daily progress along the ecliptic onto the celestial equator (shown in blue) varies during the year. This causes further variations in the length of the apparent solar day.

Figure 2-23 Time Zones in North America For convenience, the Earth is divided into 24 time zones, generally centered on 15° intervals of longitude around the globe. There are four time zones across the continental United States, making for a 3-hour time difference between New York and California.

Box 2-2 Sidereal Time (a) A month’s motion of the Earth along its orbit If you want to observe a particular object in the heavens, the ideal time to do so is when the object is high in the sky, on or close to the upper meridian. This minimizes the distorting effects of the Earth’s atmosphere, which increase as you view closer to the horizon. For astronomers who study the Sun, this means making observations at local noon, which is not too different from noon as determined using mean solar time. For astronomers who observe planets, stars, or galaxies, however, the optimum time to observe depends on the particular object to be studied. The problem is this: Given the location of a given object on the celestial sphere, when will that object be on the upper meridian? To answer this question, astronomers use sidereal time rather than solar time. It is different from the time on your wristwatch. In fact, a sidereal clock and an ordinary clock even tick at different rates, because they are based on different astronomical objects. Ordinary clocks are related to the position of the Sun, while sidereal clocks are based on the position of the vernal equinox, the location from which right ascension is measured. (See Box 2-1 for a discussion of right ascension.) Regardless of where the Sun is, midnight sidereal time at your location is defined to be when the vernal equinox crosses your upper meridian. (Like solar time, sidereal time depends on where you are on Earth.) A sidereal day is the time between two successive upper meridian passages of the vernal equinox. By contrast, an apparent solar day is the time between two successive upper meridian crossings of the Sun. The illustration shows why these two kinds of day are not equal. Because the Earth orbits the Sun, the Earth must make one complete rotation plus about 1° to get from one local solar noon to the next. This extra 1° of rotation corresponds to 4 minutes of time, which is the amount by which a solar day exceeds a sidereal day. To be precise: 1 sidereal day 23h 56m 4.091s where the hours, minutes, and seconds are in mean solar time.

Box 2-2 Sidereal Time (a) A month’s motion of the Earth along its orbit

Key Ideas Constellations and the Celestial Sphere: It is convenient to imagine the stars fixed to the celestial sphere with the Earth at its center. The surface of the celestial sphere is divided into 88 regions called constellations. Diurnal (Daily) Motion of the Celestial Sphere: The celestial sphere appears to rotate around the Earth once in each 24-hour period. In fact, it is actually the Earth that is rotating. The poles and equator of the celestial sphere are determined by extending the axis of rotation and the equatorial plane of the Earth out to the celestial sphere. The positions of objects on the celestial sphere are described by specifying their right ascension (in time units) and declination (in angular measure).

Key Ideas Seasons and the Tilt of the Earth’s Axis: The Earth’s axis of rotation is tilted at an angle of about 23.5° from the perpendicular to the plane of the Earth’s orbit. The seasons are caused by the tilt of the Earth’s axis. Over the course of a year, the Sun appears to move around the celestial sphere along a path called the ecliptic. The ecliptic is inclined to the celestial equator by about 23.5°. The ecliptic crosses the celestial equator at two points in the sky, the vernal (March 21) and autumnal (September 21) equinoxes. The northernmost point that the Sun reaches on the celestial sphere is the summer solstice (June 21), and the southernmost point is the winter solstice (December 21).

Key Ideas Precession: The orientation of the Earth’s axis of rotation changes slowly, a phenomenon called precession. Precession is caused by the gravitational pull of the Sun and Moon on the Earth’s equatorial bulge. Precession of the Earth’s axis causes the positions of the equinoxes and celestial poles to shift slowly as seen against the background of more distant stars. Because the system of right ascension and declination is tied to the position of the vernal equinox, the date of observation must be specified when giving the position of an object in the sky.

Key Ideas Timekeeping: Astronomers use several different means of keeping time. Apparent solar time is based on the apparent motion of the Sun across the celestial sphere, which varies over the course of the year. Mean solar time is based on the motion of an imaginary mean sun along the celestial equator, which produces a uniform mean solar day of 24 hours. Ordinary watches and clocks measure mean solar time. Sidereal time is based on the apparent motion of the celestial sphere. The Calendar: The tropical year is the period between two passages of the Sun across the vernal equinox. Leap year corrections are needed because the tropical year is not exactly 365 days. The sidereal year is the actual orbital period of the Earth.