Using Constellations in Observations

The Constellations and Coordinate Systems

• Introduction
• Constellations
• Practice with Concepts
• Discussion Questions
• Optional Website Reading

Introduction

Humans try to organize information. We look for patterns in both space and in time. Some of this quest for pattern is apparently hardwired: newborn babies will turn their heads to focus on cartoon drawings of a face that have two circles for eyes, a triangle for a nose, and a curved half-circle mouth, in preference to other abstractions. We classify things and group them together so that we can think about them in lumps, and by associating some object with a group that has certain characteristics, we endow the object with those characteristics.

Ancient civilizations certainly looked for order in the patterns of stars in the sky, and the movements of the sun, moon, and planets across them. Many of the star groupings or constellations visible from the northern hemisphere were described in early myths and legends, as visual aids to the stories (or perhaps the stories arose to explain the patterns). If we look at the winter sky, Taurus the Bull chases the seven sisters or Pleiades, and is itself pursued by Orion the Hunter with his dog Sirius (Canis Major) and his friends Castor and Pollux and their dog (Canis Minor). Around Polaris are grouped the constellations of the Dragon (Draco), attacking the princess Andromeda, while the hero Perseus bearing the Medusa's head with its fluctuating star (Algol) on his shield attempts to defend her, and her parents Cassiopeia and Cephus look on. Using these stories will help you remember the constellations, and knowing the constellations will help you identify some of the moving objects (like planets) or explain your observations to others.

Constellations

One of the most basic experiences of all humans is the diurnal pattern of daylight and nighttime. The earliest civilizations we know left records of their calculations and observations of these patterns.

Even in the ancient world, it became obvious that the sun, moon, planets, and stars did not move entirely randomly through the sky. Because the earth rotates on its axis, some motions repeated themselves daily, like the rising and setting of the sun and stars. Because the earth revolves around the sun, some motions repeat themselves annually, such as the reappearance of stars from behind the sun on a given day of the year, or the position of the sun north or south of the east horizon at dawn. Some motions and events, such as the positions and phases of the moon, or the motions and positions of Venus and Mercury, have a different period, but still follow a predictable repetitive pattern. Observers in the ancient world had to come up with a way to record and compare positions, so that they could create calendars that would let them predict important dates like the beginning of the spring planting season.

We also have to realize that we make observations of the heavens from a moving platform: one that moves through space and spins on its axis at the same time. In order to visualize what is going on, you will need to identify which observations depend on the earth's rotation, which depend on its revolution around the sun, and which are actually a result of the object's own motion through space. At the same time, the objects we are looking at are also moving, and are at different distances from Earth. Once we figure that out, we need ways to unambiguously identify which object we were looking at.

Constellations were originally used to identify bright stars visible to the naked eye. As telescopes made more stars visible, the boundaries of the constellations were formalized, so that objects could be definitively catalogued by association with the constellation.

Just using constellations, observers in the ancient world were able to realize that the "wandering stars" or planets, along with the sun and moon, were always found or close to a particular group of constellations. Because some of the constellations were named after animals, the whole group became known as the Zodiac. We know now that the planets all move around the sun in orbits that lie in or near the same plane, so from our point of view on earth, they move against the background of these twelve constellations. When you start studying the sky, you should learn to recognize the signs of the zodiac, so that you can quickly determine whether there is an "odd" or extra star in one of them that might be a planet.

For example, when Mars rises during the month of September, 2005, it will be the extra odd bright star-like object just above the horizon, on the edge of Aries near Taurus and the cluster of stars called the Pleiades. We say that Mars is "in Aries".

Coordinate Systems

The altitude-azimuth (altazimuth) system is an observer-centered system. The point directly above the observer is the zenith (B); the point directly below the observer's feet (out the opposite side of the earth) is the nadir. The horizon forms a circle around the the observer on which we measure the azimuth (C). We start counting around this circle from the north point (0 degrees, where D intersects C) eastward to the east point (90 degrees) to the south point (180 degrees) to the west point (270 degrees) and finally back to north. The altitude of a star (A) above the horizon is counted in degrees from the ground up through the star toward the observer's zenith. The altazimuth system is useful for communication if you are talking to someone standing right next to you, or using a telescope with a Dobsonian mount.

The celestial coordinate system is an "exploded" version of the earth's own latitude/longitude system. The celestial equator is the series of points directly over the earth's own equator. The celestial north pole is directly above the earth's north pole. If you stand at the north pole, the celestial equator is on or just below your horizon. If you stand at the equator, the north and south celestial poles will be on your horizon. Since the equator and the poles are unambiguously defined, we count from 0 at the equator to 90 degrees at the poles.

The tough part comes, as it did on the earth's system, with determining where to start counting along the equator. On the earth, the convention is to count from the longitude line of London, simply because the English made the best maps at the time the systems were being developed, and they counted from their capital. In the sky, the point is identified by the intersection of the celestial equator with the apparent path of the sun against the background stars. The sun's path crosses the equator at two points; we start counting along the equator where the sun crosses it moving northward (called the Aries point). In the diagram below, the earth's north pole points up to the celestial north pole (A), while its equatorial plane extends out to intersect with our imaginary celestial sphere (D). The sun (B) moves around its ecliptic path, crossing the celestial equator going from south to north at the vernal equinox (E) and reaching maximum declination north of the celestial equator at the summer solstice (C).

To complicate things even further, the earth "wobbles" on its axis, which causes the celestial equator to move with respect to the background sky. The vernal equinox point on the celestial equator was in the constellation Aries when the Greeks first started recording information about it. In the intervening years, it has moved along the celestial equator, and during the 1970s, it moved into the constellation Aquarius (hence the song in the musical Hair "This is the Dawning of the Age of Aquarius").

Using the celestial coordinate system, though, we can get an unambiguous location for a star in the sky using reference points that anyone, anywhere on the surface of the earth, can use. We measure eastward (in the direction of solar motion against the background sky), but along the celestial equator, from the vernal equinox (pink line). This measure is in hours of Right Ascension, which run from 0 to 24. We then measure up or down from the celestial equator in degrees of declination, from 0 at the celestial equator to 90 degrees at the poles.

Let's take a look at how using the Celestial Coordinate system applies to the current night sky of mid-September, as seen from my front lawn near Seattle, WA. If we look at the evening sky for 10 September, 2005, we see the moon hanging just above the south horizon (notice the SE and S compass coordinates):

From the horizon, we can see that the moon is not very high -- perhaps just a bit more than 1/10 of the way between the horizon and the zenith, or point directly over head. Let's estimate the moon's altitude at about 14°. From the directions, we can see that it is almost exactly due south. In azimuth terms, south is one-half way around the 360° circle from the north point, so the moon is about 186° in azimuth. This completely describes the moon's position for someone standing right next to us at the same time, but it doesn't help the person in New York City (for whom the moon has set), or the person in Hawaii (for whom the moon is still much higher above the horizon).

If we change the picture and use the celestial coordinate system, we can get set of location coordinates that will work for any observer, anywhere in the world.

Now we can see that the moon is just above 30 south °, and a bit less than 17h right ascension. A check of the lunar calendar for the time of the observation (7:00pm Local Seattle time) shows the moon at 16h 45m RA and -27° 49' declination.

We can put the two systems together. In the diagram below, our star will be positioned at a right ascension of 8 hours and a declination of about 60 degrees north no matter where we view it from. For a sky enthusiast on earth at about latitude 30 (roughly that of Orlando FL), both the celestial equator and the ecliptic appear "tilted". If we pick a moment several hours after the sun has set in the west in late winter, our star appears above the eastern horizon. We calculate right ascension along the celestial equator from the vernal equinox (blue line) and declination through the star toward the celestial north pole from the equator (red line). We calculate azimuth along the horizon from the north point, and altitude above the horizon through the star to the zenith. As the night progresses, the star's altitude and azimuth will change, but its right ascension and declination will not.

Practice with the Concepts

What are the celestial coordinate of B (approximately) in the celestial map below? When is the best time of year to view it?

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Discussion Questions

• How are the celestial and altazimuth systems related?
• How can annual motions of the sun be used to predict which constellations appear overhead at a given date and time?

Optional Readings

• The Introduction to the Constellations at the University of Michigan.
• Sky and Telescope has an online site .

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