Constellations help us find our way around the night sky. There are 88 constellations which cover the entire sky. About 80 of them can be seen from Hawaii, but not all are visible during the fall semester. We will study 9 or so constellations which have bright stars and are fairly easy to see.
Reading: Stars & Planets, p. 6 — 12 (Constellations, Star names, and Star brightness). Additional readings for individual constellations are listed below.
For thousands of years, people looking at the sky have grouped stars into constellations. The stars in constellations often seem to trace familiar shapes (Fig. 1). For example, the stars of Orion outline a man with a club, and the stars in Maui's Fish-hook follow the shape of a fishing hook. The stars in a constellation usually have very little to do with each other; some may be relatively close to us, others much further away. Because stars move so slowly through space, the patterns we see today have scarcely changed since the dawn of recorded history.
Fig. 1. The evening sky in early september, with constellations represented by figures from classical western mythology. Image generated using Stellarium.
Fig. 2. The same sky as in Fig. 1. Constellations are represented by lines connecting stars. The boundaries between constellations are also shown.
Modern astronomers still use constellations to divide the sky into different regions (Fig. 2). It may surprise you to learn that professionals don't use constellations to locate targets; instead, they use celestial coordinates (which resemble longitude and latitude used on Earth). To point a computerized observatory telescope at a particular object, you just give its celestial coordinates to the computer, and the machine does the rest. In this class we will use simple telescopes with manual controls, and a knowledge of the constellations will be helpful in finding things to observe.
The pattern of stars in the sky is basically random, much like the pattern made by spattering droplets of ink on a sheet of paper. If you look at a random pattern of dots for a while, your mind will start to group dots together, and some groups might even seem like pictures of things you know. Another person looking at the same pattern might come up with some of the same groups.
Each constellation is shown in a detailed chart in Stars & Planets. The charts show every star you can easily see with your naked eye. Individual stars in each constellation are labeled with Greek letters. These Bayer letters (see Stars & Planets, p. 7 — 10, Star names) are useful as short, unambiguous names for stars; for example, the bright star Antaries in the constellation Scorpius is called α Sco by astronomers. You will need to be familiar with Bayer letters to locate the stars we discuss in this class. Special symbols indicate double stars, variable stars, star clusters, nebulae, and galaxies; these objects may be labeled with Roman letters, the letter "M" followed by a number, or just a 3 or 4-digit number. The charts in Stars & Planets show the brightness of each star, using large dots for bright stars and small dots for faint ones; the system used to measure stellar brightness is described next.
A star's apparent magnitude is a number measuring how bright the star appears in the sky. Bright stars have small apparent magnitudes, and faint stars have large apparent magnitudes; this may seem backward, but it made sense to astronomers thousands of years ago and we've been stuck with it ever since. In modern terms, the difference in the apparent magnitudes of two stars tells you the ratio of their brightnesses. A difference of 2.5 magnitudes implies a brightness ratio of 10:1; to show what this means, suppose we have three stars, called A, B, and C:
|star A has apparent magnitude 0.0||mA = 0.0|
|star B has apparent magnitude 2.5||mB = 2.5|
|star C has apparent magnitude 5.0||mC = 5.0|
Here we are using the symbol m for apparent magnitude; the letter written below the m indicates which star this value refers to. Then,
|star A appears 10 times brighter than star B||mB − mA = 2.5|
|star B appears 10 times brighter than star C||mC − mB = 2.5|
|star A appears 10×10 = 100 times brighter than star C||mC − mA = 5.0|
In other words, you would need 10 copies of star B, or 100 copies of star C, to equal the light of star A.
To give some specific examples, the three bright stars making up the ``Summer Triangle'' are Vega (magnitude 0.03), Altair (magnitude 0.76), and Deneb (magnitude 1.2). The brightest of these — that is, the one with the smallest magnitude — is Vega. The constellation of Lyra, which includes Vega, is defined by several rather dim stars; the faintest is ζ Lyr (magnitude 4.4). With the naked eye, the faintest stars visible from Kapiolani Park have apparent magnitudes of about 4.5 to 5.0, and the faintest stars visible from a really dark location have apparent magnitudes of 6.0 to 6.5.
Knowledge of apparent magnitudes can help in planning observations. For example, you might want to know how much of the constellation of Cygnus will be visible. The five stars outlining the basic shape of this constellation have apparent magnitudes between 1.2 and 3.2; these are all fairly easy to see. However, the chart for Cygnus in Stars & Planets (p. 135) includes several fainter stars with apparent magnitudes between 3.4 and 4.0; these will be harder to see unless you are looking from a reasonably dark location.
The angular separation of two objects is an angle measuring how far apart the objects appear from your point of view. For example, make a ``shaka'' with your arm outstretched, thumb up, and pinkie down; now imagine two lines extending from your eye to the tips of your thumb and pinkie, as shown in Fig. 3. These lines meet at an angle of about 20°, so the angular separation between the tip of your thumb and the tip of your pinkie is about 20° (depending on the length of your arm and the size of your hand, but 20° is average). If two stars have an angular separation of 20°, you should be just about able to cover one with your thumb and the other with your pinkie by holding a shaka up to the sky at arm's length.
|Fig. 3. A ``handy'' measure of angular separation. At arm's length, the angle between your outstretched thumb and pinkie is about 20°.|
You can estimate smaller angles with your hand as well. For example, your fist, held at arm's length, defines an angle of about 10°. A single finger, at arm's length, is about 2° wide.
To measure angular separations more accurately, we will use a device called a cross-staff, which is basically a stick, 57.3 cm long, with a centimeter ruler mounted on one end. The length of the stick was deliberately chosen; if the ruler is 57.3 cm from your eye, 1 cm on the ruler defines an angle of 1°. (If you know trigonometry, note that 57.3 = 1/tan(1°).) To use a cross-staff close one eye and place the end of the stick without the ruler just under the other eye. Sight along the stick towards the two stars you want to measure and adjust the markers on the ruler to line up with these stars. Finally, read off the positions of the markers on the ruler; the difference between them is the angular separation between the two stars.
It's often fairly easy to see a constellation when it's pointed out in the sky, but harder to remember it so you can find it yourself. The best way to really learn the constellations is to draw them; when you do this, your eyes pick out geometrical patterns which will help you remember. Our drawings will be made to scale; this gives you a feeling for the sizes of constellations. (Many people confuse the Pleiades with the Little Dipper; one is about ten times the size of the other!) Here's how to make an accurate drawing:
Because different constellations are visible at different times, we will return to the study of constellations throughout the semester.
|September||Constellation||Description in Stars & Planets|
|Cygnus||p. 136 &mdash 139|
|Sagittarius||p. 222 — 225|
|Scorpius||p. 226 — 229|
These constellations are easy to see; you may already know some of them. Cygnus and Sagittarius lie along the Milky Way; Sagittarius and Scorpius lie along the ecliptic.
|October||Constellation||Description in Stars & Planets|
|Lyra||p. 180 — 182|
|Cassiopeia||p. 108 — 110|
|Cepheus||p. 114 — 115|
Lyra contains Vega, the brightest star in the summer and fall skies, as well as the variable star β Lyr. Cassiopeia continues the sequence of bright constellations along the Milky Way. When observing Cepheus, note the star δ Cep, which is the prototype of an important class of variable stars.
|November||Constellation||Description in Stars & Planets|
|Pegasus||p. 202 — 203|
|Andromeda||p. 74 — 76|
|Perseus||p. 204 — 206|
The ``Great Square'' of Pegasus is good signpost for the Autumn sky. Andromeda, although not very striking, contains the famous Andromeda Galaxy. Perseus lies along the Milky Way; it contains the variable star Algol (β Per).
a) Using the size of the dots as a guide, list the five brightest stars in Cygnus by their Bayer letters.
b) Consider the stars α, γ, and δ Cyg; of these three, which two appear furthest apart?
c) Which of the five brightest stars in Cygnus are double?
Joshua E. Barnes
(barnes at ifa.hawaii.edu)
31 August 2010