Activity 5. Angles in the sky
What is the angle between the horizon and the zenith? [90 degrees] You can measure other angles in the sky using the following rules of thumb: At arm's length, the width of your little finger is 1 degree; the width of your three middle fingers is 5 degrees; the width of your fist is 10 degrees; the width of your outstretched thumb and little finger is 25 degrees. Using your hand as a ruler, what is the length and width of the bowl of the Big Dipper? What is the total length of the Big Dipper?
Because clusters are all about the same actual size, we can determine their distances from their apparent sizes. This gives us another handle on how distant the stars are.
Activity 6. Apparent size as a measure of distance
The Ursa Major, Hyades, and Pleiades clusters are at different distances. By measuring the angles, as in activity 5, rank these three star clusters in apparent size. How do they rank in distance? If the Big Dipper cluster is about 65 light- years away, how far away is the Hyades? [140 light-years] The Pleiades? [400 light-years] How do you know?
Stars differ not only in distance, but also in apparent brightness. In activity 2.4, you looked for the star in the Big Dipper which had a significantly different brightness from the others. It was the star that joins the handle to the bowl.
Activity 7. Ranking stars by brightness
Locate the constellation Cassiopeia. You can find it by facing north. Hold the star map so that NORTH is down. Find the Big Dipper and then Polaris. Cassiopeia is on the other side of Polaris from the Big Dipper. It's almost overhead in mid-evening at this time of year. It looks like either a `W' or a giant McDonald's sign, depending on your point of view (see figure 4).
Cassiopeia. On the left is what you actually see in the sky. On the right is a diagram of the official constellation. The splotches labeled M52 and M103 are distant star clusters. Photo and diagram courtesy of O. Richard Norton, Science Graphics, Bend, Ore.
The apparent brightness of a star depends on its distance and its power, the amount of energy it generates each second. The Sun's power is 400,000,000,000,000,000,000,000,000 watts -- a quadrillion times more energy than is produced by every electric power plant in the United States. Most of the brighter stars in the sky are much more powerful than the Sun. The brightness of the star decreases as the square of the distance. If the distance is twice as great, the brightness is four times less. If the distance is 10 times as great, the brightness is 100 times less. This inverse-square law of brightness is one of the most important tools of the astronomer (see figure 5). It provides a third means to estimate distance. If we measure the brightness, and know the power, we can determine the distance. Conversely, if we measure the brightness, and know the distance from parallax, we can determine the power.
The inverse-square law of brightness. Because light travels in straight lines, the amount of light crossing each unit of area decreases as the square of the distance. Figure by John Percy.
Activity 8. Estimating the distance of brighter stars
At what distance would a 100-watt light bulb have the same brightness as the brighter stars? There are two ways in which you can answer this.
Brightness and color are the two most important identifying characteristics of a star. The color of a star depends on its temperature. The Sun is a yellowish star. Its "surface'' temperature is about 5,800 kelvin (10,000 degrees Fahrenheit). The Sun and stars do not actually have surfaces; they are gases throughout. What we call the surface is the layer where the gases become so thick that we cannot see further in. Hotter stars appear blue-white; their surface temperatures may be over 20,000 kelvin (35,500 degrees Fahrenheit). Cooler stars appear reddish-white; their surface temperatures may be lower than 3,000 kelvin (4,900 degrees Fahrenheit).
The best example is a light with a dimmer switch. Increase the current through the bulb using the dimmer switch. Watch the color change as the temperature of the filament increases. This works best if you take off the lamp shade and use a clear bulb, rather than a frosted one.
Stars also come in different sizes. There are giant stars, ten or a hundred times bigger than the Sun. Arcturus and Aldebaran are examples. The supergiant stars are, as you might guess, even larger. One example of a supergiant is Polaris. Polaris is also a variable star (see below). Its brightness changes because it is expanding and contracting.
Watching a variable star gradually change brightness is an excellent observing project for high-school lab classes and junior-high science fairs (see below). Many students have even sent their observations to the American Association of Variable Star Observers, which collects and analyzes variable-star measurements from amateur astronomers all over the world. Not only can your students learn about star science, they can do star science.
JOHN R. PERCY is an astronomer at the University of Toronto in Mississauga, Ontario, Canada. He is president of IAU Commission 46 and vice- president of the ASP Board of Directors. His email address is firstname.lastname@example.org.
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