But we’re getting ahead of our story. In “Astronomy Reborn: 1543–1687,” you’ll find out why we no longer believe that the celestial sphere represents reality; however, the notion of such a fixed structure holding the stars is still a useful model for us moderns. It helps us to communicate with others about the positions of the objects in the sky. We can orient our gaze into the heavens by thinking of the point of sky directly above the earth’s North Pole as the north celestial pole, and the point below the South Pole as the south celestial pole. Just as the earth’s equator lies midway between the North and South Poles, so the celestial equator lies equidistant between the north and south celestial poles.

 Think of it this way: If you were standing at the North Pole, then the north celestial pole would be directly overhead. If you were standing at the equator, the north and south celestial poles would be on opposite horizons. And if you were standing at the South Pole, the south celestial pole would be directly overhead. Astronomers have extended to the celestial sphere the same system of latitude and longitude that describes earthly coordinates. The lines of latitude, you may recall from geography, run parallel with the equator and measure angular distance north or south of the equator. On the celestial sphere, declination (dec) corresponds to latitude and measures the angular distance above or below the celestial equator. While earthbound latitude is expressed in degrees north or south of the equator (Philadelphia, for instance, is 40 degrees north), celestial declination is expressed in degrees + (above) or – (below) the celestial equator.

The star Betelgeuse, for example, is at a declination of +7 degrees, 24 minutes. On a globe, the lines of longitude run vertically from pole to pole. They demarcate angular distance measured east and west of the so-called prime meridian (that is, 0 degrees), which by convention and history has been fixed at Greenwich Observatory, in Greenwich, England. On the celestial sphere, right ascension (R.A.) corresponds to longitude. While declination is measured in degrees, right ascension is measured in hours, minutes, and seconds, increasing from west to east, starting at 0. This zero point is taken to be the position of the sun in the sky at the moment of the vernal equinox (we’ll discuss this in Chapter 3, “The Unexplained Motions of the Heavens’’). Because the earth rotates once approximately every 24 hours, the same objects will return to their positions in the sky approximately 24 hours later.

After 24 hours, the earth has rotated through 360 degrees, so that each hour of R.A. corresponds to 15 degrees on the sky. If the celestial poles, the celestial equator, and declination are projections of earthly coordinates (the poles, the equator, and latitude), why not simply imagine R.A. as projections of lines of longitude? There are good reasons why we don’t. Think of it this way: The stars in the sky above your head in winter time are different than those in summer time. That is, in the winter we see the constellation Orion, for example, but in summer, Orion is gone, hidden in the glare of a much closer star, the sun. Well, although the stars above you are changing daily, your longitude (in Atlanta, for example) is not changing. So the coordinates of the stars cannot be fixed to the coordinates on the surface of the earth. As we’ll see in later chapters, this difference comes from the fact that in addition to spinning on its axis, the earth is also orbiting the sun.

Measuring the Sky

The true value of the celestial coordinate system is that it gives the absolute coordinates of an object, so that two observers, anywhere on Earth, can direct their gaze to the exact same star. When you want to meet a friend in the big city, you don’t tell her that you’ll get together “somewhere downtown.” You give precise coordinates: “Let’s meet at the corner of State and Madison streets.” Similarly, the right ascension and declination astronomers use tell them (and you) precisely where in the sky to look. The celestial coordinate system can be confusing for the beginning sky watcher and is of little practical value to an observer armed with nothing but the naked eye. However, it can help the novice locate the North Star, and to know approximately where to look for planets. There is a simpler way to measure the location of an object in the sky as observed from your location at a particular time. It involves two angles. You can use angles to divide up the horizon by thinking of yourself as standing at the center of a circle.

A circle may be divided into 360 degrees (and a degree may be subdivided into 60 minutes, and a minute sliced into 60 seconds). Once you decide which direction is 0 degrees (the convention is to take due north as 0 degrees), you can measure, in degrees, precisely how far an object is from that point. Now that you have taken care of your horizontal direction, you can fix your vertical point of view by imagining an upright half circle extending from horizon to horizon. Divide this circle into 180 degrees, with the 90-degree point directly overhead. Astronomers call this overhead point the zenith. Altitude and azimuth are the coordinates that, together, make up the altazimuth coordinate system, and, for most people, they are quite a bit easier to use than celestial coordinates. An object’s altitude is its angular distance above the horizon, and its compass direction, called azimuth, is measured in degrees increasing clockwise from due north. Thus east is at 90 degrees, south at 180 degrees, and west at 270 degrees.

Altazimuth coordinates, while perhaps more intuitive than the celestial coordinate system, do have a serious shortcoming. They are valid only for your location on Earth at a particular time of day or night. In contrast, the celestial coordinate system is universal because its coordinate system moves with the stars in the sky.