91Ó°ÊÓ

About how far apart are the stars in an open cluster? In a globular cluster? (Hints: What share of the cluster's volume belongs to a single star? The volume of a sphere is \(\frac{4}{3} \pi r^{3} .\))

Suppose a planetary nebula is \(1 \mathrm{pc}\) in radius. If the Doppler shifts in its spectrum show it is expanding at \(30 \mathrm{km} / \mathrm{s}\), how old is it? (Note that 1 pc equals \(3.1 \times 10^{13} \mathrm{km},\) and 1 year equals \(3.2 \times 10^{7}\) seconds. to 2 significant figures.)

If a star the size of the sun expands to form a giant 20 times larger in radius, by what factor will its average density decrease? (Hint: The volume of a sphere is \(\frac{4}{3} \pi r^{3} .\) )

The Crab Nebula is now 1.35 pc in radius and is expanding at \(1400 \mathrm{km} / \mathrm{s} .\) About when did the supernova occur? (Note that \(1 \mathrm{pc}\) equals \(3.1 \times 10^{13} \mathrm{km} .\)

If the Cygnus Loop is 25 pc in diameter and is 10,000 years old, with what average velocity has it been expanding? (Note that 1 pc equals \(3.1 \times 10^{13} \mathrm{km},\) and 1 year equals \(3.2 \times 10^{7}\) seconds, to 2 significant figures.)

Observations show that the gas ejected from SN 1987 A is moving at about \(10,000 \mathrm{km} / \mathrm{s}\). How long will it take to travel one astronomical unit? One parsec? (Note that 1 AU equals \(1.5 \times 10^{8} \mathrm{km}\), and \(1 \mathrm{pc}\) equals \(3.1 \times 10^{13} \mathrm{km} .\))