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then, it continued to move silently into deep space and sent the last signal Figure 14.2. Perhaps intelligent life will find the plaque and decipher
on January 22, 2003, when it was 12.2 billion km (7.6 billion mi) from the image to learn about us. What information is in the image? Try to
Earth. It will now continue to drift for the next 2 million years toward do your own deciphering to reveal the information. When you have
the star Aldebaran in the constellation Taurus. exhausted your efforts, see grin.hq.nasa.gov/ABSTRACTS/GPN-2000-
As the first human-made object to go out of the solar system, 001623.html. For more on the Pioneer 10 mission, see nssdc.gsfc.nasa.
Pioneer 10 carries a gold-plated plaque with the image shown in Box gov/nwc/tmp/1972-012A.html.

BOX FIGURE 14.2 Pioneer plaque symbology.

PARALLEL EXERCISES

The exercises in groups A and B cover the same concepts. Solutions to group A exercises are located in appendix E.

Group A Group B
14
1. The star Vega is 2.4 × 10 km away from Earth. What is this 1. Sirius A is 8.6 light-years (ly) away from Earth. What is this
distance in light-years (ly)? distance in kilometers?
2. A first-magnitude star is 100 times brighter than a sixth- 2. A first-magnitude star is 100 times brighter than a sixth-
magnitude star, which means each difference in magnitude magnitude star, which means each difference in magnitude
represents a brightness change of 2.51 times. Compare the represents a brightness change of 2.51 times. Compare the
brightness of a star with an apparent magnitude (m) of −1.6, to a brightness of Polaris which has an apparent magnitude (m) of
star with an apparent magnitude of +3.4. +2.1 to Vega, which has an apparent magnitude of +0.1.
3. Compare the brightness of Venus which has an apparent 3. Compare the brightness of Spica which has an apparent
magnitude (m) of −4.6 to a full Moon, which has an apparent magnitude (m) of +1.2 to Vega, which has an apparent
magnitude of −12.7. magnitude of +0.1.
4. The ratio of brightness of two stars can be determined by a 4. The ratio of brightness of two stars can be determined by a
constant of 2.512 raised to the power of the magnitude constant of 2.512 raised to the power of the magnitude
1 where b 1 and b 2
1 where b 1 and b 2
difference. The formula is b 1 /b 2 = 2.512 (m 2 – m ) difference. The formula is b 1 /b 2 = 2.512 (m 2 – m )
represent the brightness and m 1 and m 2 refer to the magnitudes represent the brightness and m 1 and m 2 refer to the magnitudes
of the stars being compared. The star Arcturus has a magnitude of the stars being compared. One star has a magnitude (m 1 ) of
of 0.2, and the star Alberio has a magnitude of 3.2. What is the −1.6, and another star has a magnitude (m 2 ) of +0.4. What is
ratio of brightness of these two stars? the ratio of brightness of these two stars?
5. The star Sirius A has a magnitude of −1.6, and the star Castor 5. The star Betelgeuse has a magnitude of 0.6, and the star
has a magnitude of 1.6. What is the ratio of brightness of these Alderamin has a magnitude of 2.6. What is the ratio of
two stars? brightness of these two stars?

374 CHAPTER 14 The Universe 14-24