Brightness and Distance Help (page 2)
Brightness and Distance
Have you ever heard that stars are “distant suns”? This is true, but it does not tell the whole story. There are plenty of stars that resemble our Sun, but many are larger or smaller, brighter or dimmer, or hotter or cooler. Some stars radiate more energy at shorter wavelengths than does our Sun; other stars favor the longer wavelengths. Stars are as diverse as snowflakes.
Have you ever been told that interstellar space is a “vacuum”? This is true in a relative sense. We could not breathe in space without special equipment, and the pressure is low enough to be considered a vacuum by most laboratory technicians on Earth. However, interstellar space contains matter. We can see some of it directly, whereas other space matter is visible only because it blocks light from stars behind it.
How Bright? How Distant?
You’ve learned about visual magnitudes of objects in the sky. A difference of one magnitude is the equivalent of a brightness change of 250 percent, that is, 2½ times. As the brightness increases, the magnitude number goes down. However, when you look at a dim star in the sky and then you look at a much brighter one, how do you know which of the two really emits more light? After all, if Star X is 2½ times brighter than Star Y but is only 1/100 as far away, Star Y is more brilliant in an absolute sense.
Absolute Visual Magnitude
The observed magnitude of a star or other celestial object is called its apparent visual magnitude , or simply the apparent magnitude . The actual brightness is called the absolute visual magnitude , or simply the absolute magnitude . Absolute versus apparent: Things are not always as they appear. By definition, the absolute magnitude of a star is the apparent magnitude we would give it if it were 3.09 × 10 14 km (1.92 × 10 14 mi) away. This is the distance that light travels in 32.6 years. By Earthly standards, or even when measured against the scale of the Solar System, this is a huge distance. Compared with the size of the Milky Way, though, it is not far at all. Compared with the size of the known Universe, it is microscopic.
One of the brightest known stars, in absolute terms, is Canopus , which is best observed from the southern hemisphere. People who live north of the thirty-eighth parallel (roughly the latitude of San Francisco) cannot see Canopus. This star has an absolute visual magnitude of –4.4. By comparison, our Sun has an absolute magnitude of +4.8; thus Canopus is approximately 5,000 times as brilliant as our parent star. If the Sun were to increase in brightness suddenly to the same absolute magnitude as Canopus, we would all have to wear dark glasses to get around. However, that wouldn’t be the only problem. Canopus radiates more energy than the Sun at other wavelengths, too. Its ultraviolet rays would sunburn us in seconds; the heat would incinerate Earth and end all life here in a matter of days, if not hours.
Because of its distance, Canopus is not a remarkable object in the sky. People who live north of the latitude of San Francisco aren’t missing much just because they can’t see Canopus. Stars like our Sun, when observed from the same distance as we see Canopus, are so faint that they cannot be seen except by people who live far away from the skyglow caused by city lights and who have keen eyesight.
The standard distance that astronomers use for determining absolute magnitude is a staggering number when you ponder it: 3.09 × 10 14 km is 309 trillion (309,000,000,000,000 kilometers or 309 quadrillion (309,000,000,000,000,000) meters. These sorts of numbers evade direct human comprehension.
Astronomers have invented the light-year , the distance light travels in 1 year, to assist them in defining interstellar distances. You can figure out how far a light-year is by simple calculation. Light travels approximately 300,000 km in 1 second; there are 60 seconds in a minute, 60 minutes in an hour, 24 hours in a day, and about 365.25 days in a year. Thus a light-year is roughly 9.47 × 10 12 km. This turns out to be a little less than 6 trillion miles. There we go with incomprehensible numbers again!
Let’s think on a cosmic scale. The nearest star to our Solar System is a little more than 4 light-years away. The standard distance for measuring absolute magnitude is 32.6 light-years. The Milky Way galaxy is 100,000 light-years across. The Andromeda galaxy is about 2.2 million light-years away. Using powerful telescopes, astronomers can peer out to distances of several billion light-years (where 1 billion is defined as 10 9 or 1,000 million). Well, the light-year helps us to comprehend the distances to stars within our galaxy, but once we get into intergalactic space, even this unit is not enough to make distances easy to imagine.
The actual distances to the stars remained a mystery until the advent of the telescope, with which it became possible to measure extremely small angles. The angular degree represents 1/360 of a full circle. Smaller units are the minute of arc, representing 1/60 of an angular degree, and the second of arc, measuring 1/60 of a minute. These units were introduced in Chapter 1.
To determine the distances to the stars, astronomers had to be clever. Could it be done by triangulation, the way surveyors measure distances on Earth? For this to work, it would be necessary to use the longest possible baseline. What would that be? How about the diameter of the Earth’s orbit around the Sun? This presented a problem for people who believed that Earth was the center of creation and that everything else revolved around it. However, by the time astronomers were ready to seriously attempt to determine distances to the stars, the heliocentric theory had gained general acceptance.
Figure 13-1 shows how distances to the stars can be measured. This scheme works only for “nearby” stars. Most stars are too far away to produce any measurable parallax against a background of much more distant objects, even when they are observed from opposite sides of Earth’s orbit. (In this figure, the size of Earth’s orbit is exaggerated for clarity.) The star appears displaced when viewed from opposite sides of the Sun. This displacement is maximum when the line connecting the star and the Sun is perpendicular to the line connecting the Sun and Earth. A star thus oriented, and at just the right distance from us, will be displaced by 1 second of arc when viewed on two occasions 6 months apart in time. This distance is called a parsec (a contraction of parallax second ). The word parsec is abbreviated pc and is equivalent to approximately 3.26 light-years. Sometimes units of kiloparsecs (kpc) and megaparsecs (Mpc) are used to express great distances in the Universe; in this scheme, 1 kpc = 1,000 pc = 3,260 light-years, and 1 Mpc = 1 million pc = 3.26 million light-years. Now, finally, intergalactic distances become credible.
The nearest visible object outside our Solar System is the Alpha Centauri star system, which is 1.4 pc away. There are numerous stars within 20 to 30 pc of Earth. The standard distance for measuring absolute visual magnitude is 10 pc. The Milky Way is 30 kpc in diameter. The Andromeda galaxy is 670 kpc away. And on it goes, out to the limit of the observable Universe, somewhere around 3 billion pc, or 3,000 Mpc.
Practice problems of this concept can be found at: Stars and Nebulae Practice Problems
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