The Milky Way was once thought to be "mumrgabn-fg 4p /24uo,h(f t0 ulrky" or "milky" but is now considered to be mn h(pgou/, 4b2f lt -uframg40ade up of point sources. Explain.

A star is in equilibrium when it radiates at its surfaef ik.06xbwl-ce all the energy generated at wifl-kb 6e0.xits core. What happens when it begins to generate more energy than it radiates? Less energy? Explain.

Describe a red giantl8gy k):(vxv r; drc1q star. List some of its properties.

Select a point on the H-R diagram. Mark several dirdgr, lq4 z:)ltections away from this point. Now describe the changes that would take place in a ,d zl:rqlgt)4star moving in each of these directions.

Does the H-R diagram reveal anything about the core 30(s bzouo s.nal om(6x /7tlxof a star?

Why do some stars end up as white dwarfs, and others as 38;cflee :dc y9b h92obxpvc 6neutron stars or black hol8vbc:b hce o 9e; yd62lcx39fpes?

  Can we tell, by lookinv.taflq a d.w.+o17/hvf5h mng at the population on the H-R diagram, that hotter main-sequence stvd.a .tho hv/qf5nw.l 7am+1 fars have shorter lives? Explain.  ----待选择----yesno 

If you were measuring am ,(r-g zh8ahstar parallaxes from the Moon instead of Earth, what corrections would you have to make? What changes would occur if yo g8r(h z-aham,u were measuring parallaxes from Mars?

Cepheid variable stars ccj jdnuq9+ e0e(8 oh:xhange in luminosity with a typical period of several days. The period has been found to have a definite relationship with the absolute luminosity of the star. How could these star0d (hecj+xq:oj98u en s be used to measure the distance to galaxies?

What is a geodesic? What is its role in General Rel2lv5qfn ks1 pgz3:( yakbst97kp 7o e5ativity?

If it were discovered that the redshift of spectra (o irbgsiz5);xz4f ;gl lines of galaxies was due to something other than expansion, how might our view of the universe change? Would there be conflicting b5;(ox;4szi )fgzrgi evidence? Discuss.

  All galaxies appear to be moving away from us. Are we therefowypk bo(*tu1p+- n d9qre at the center of the univer- kby9tu1pwo qn+d*p (se? Explain.  ----待选择----yesno 

If you were located inqsz8s sm7 pgpxwgp;g:v1t3l ; ** o*nc a galaxy near the boundary of our observable universe, would galaxies in the direction of the Milky Way appear to be approaching you or receding from ggstlqp ovwpp3*;z;*ns: xc81s7 g m* you? Explain.

Compare an explosion on Earth to the B7 fx .;o(jvwuv4x(t7-uf nstpig Bang. Consider such questions as: Would the debris spread at a higher speed for more distant particles, as in the Big Bang? Woup-vtff 7w uj4 t7xuos((nv.; xld the debris come to rest? What type of universe would this correspond to, open or closed?

If nothing, not even light, escapes from a black hole, then how can we telx/y;dx:to rv,vplh 7 2l if one is there?72/;h p,ryxxod :lv tv

  What mass will give a Schwarzschild radius equal to that of tb2z q: e-6pyythe hydrogen atom in its gret qyyz 6b:-2pound state? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is of zuee+bmgw.l pd8hoe770 ig78ten given as about 4 billion years. Find that time on (Fig. Below). People have lived on Earth on pelob +wu0z788 egeghm d7i7.the order of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic microwave background radiation is. Where dodnz(+o0ub, y.mknrb (gi,nt/es it come from? Why is its tr/(0ngd,kutb(n.o bn m+,zyi emperature now so low?

Why were atoms, as opposed to bare nuclei, unable to ex6rpng5 wjj-;w a/e0j zh a::enist until hundreds of thousands of years after the Big Ban0/je wjrwepn;hg zj6a: a:-5ng?

Under what circumstances would the universe evenihtqgij -+a1 4tually collapse in on itself?

  Using the definitions of the parsec and thc*8 47bwktb dhe light-year, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.38 seconds of arc. How far aie b9y*,-wltw way is it? d =    ly

  The parallax angle of a star idfxs l;uim .e,)rv o0**kfy*ws $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What i:w 8tyu; vh/qzs its parallax angle?
State (a) in seconds of arc,$\phi''' \approx $    ($\times 10^{-2}$)''
(b) in degrees. $\approx $(    $\times 10^{-6})^{\circ}$

  What is the parallax anglead02s)e unken g.2g8n for a star that is 55 ly away? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away fromv 3tmpnku*q+cyr- ) n1zw,j+ y us as a second star, will the parallax angle o*,+k-) p m1 +zq twu3ynvcrnyjf the farther star be greater or less than that of the nearer star? By what factor?

  A star is 35 pc away. How long does it ta:4rap tkxg1 9 rucd3arl1*f t(ke for its light to reach us?    years

  We saw earlier (Chapter 14) that the rate energy reaches the Earth from th70 zw3xjgyh k. 8ife(le Sun (the "solar constant"70fegwzh jyi(x. 3kl8 ) is about $1.3 \times 10^3\ \text{W/m}^2$. What is
(a) the apparent brightness $l$ of the Sun,    $\times 10^3\ \text{W/m}^2$
(b) the absolute luminosity $L$ of the Sun?    $\times 10^{26}\ \text{W}$

  What is the relative brightness of the Sun as seen from Jupiter aszfo (rw(b:+p w ke:sct; o*rlwl zz//2 compared to its brightness from Earth? (Jupiter is 5.2 times ;r sz:wcr+eot*k/( /:bzz2 pol ww(fl farther from the Sun than the Earth.) $\dfrac{l_{\text{Jupiter}}}{l_{\text{Earth}}}$    $ \times 10^{-2}$

  Estimate the angular width that our Galaxy would subtend if observed fropntldrw 2q+1. bnt f+6m the nearest galaxy to us (Table 33-1). Comp2n6 +tdfpr.1wnq +lb tare to the angular width of the Moon from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red gianwr +m 25quv.fl5f(bfjdh9z0tt, what will be its average density if it expands out to the orbit of E0+f5 hzu2(b tjv wrfdmqlf59.arth ($1.5 \times 10^{11}\ \text{m}$ from the Sun)? $\rho = $    $ \times 10^{-4}\ \text{kg/m}^3$

  When our Sun becomes a white dwarf, it is expected to be about t+vp.if bhv)i9zk 9vb7 he size of the Moon. Whavv ). k7pfihb9b+vz9 it angular width will it subtend from the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whok3.lgoib6* sck ze-.ux p4.zua5umg -se mass is equal to the Sun's and whose radius is equal to the Earth's. How many times larger than Earth's densit3..i5lzmk6s-xgkbo*z - ugeaup c.u4 y is this?
$\rho = $    $ \times 10^{9}\ \text{kg/m}^3$
$\dfrac{\rho}{\rho_{\text{Earth}}} = $    $\times 10^5\ \text{times larger}$

  A neutron star whose mass is 1.5 solar masses has a radius of ab 4spp7roa)kz 9out 11 km. Calculate its average density and compare to to 94r7pkszpa)hat for a white dwarf (Problem 13) and to that of nuclear matter.
$\rho_{\text{neutron star}} \approx $    $\times 10^{17}\ \text{kg/m}^3$
$\dfrac{\rho_{\text{neutron star}}}{\rho_{\text{white dwarf}}} =$    $\times 10^8$
$\dfrac{\rho_{\text{neutron star}}}{\rho_{\text{nuclear matter}}}$ =   

  Calculate the Q-values for the He burpa (8p2hzxyf08 usc5aning reactions of Eq. 33-2. (The mass of the very unstah(zucxp5 2f8sy p 80aable $^8\text{Be}$ is $8.005305\ \text{u}$.)

$^{4}_{2}\text{He} + ^{4}_{2}\text{He} \rightarrow ^{8}_{4}\text{Be}$Q =    MeV

$^{4}_{2}\text{He} + ^{8}_{4}\text{Be} \rightarrow ^{12}_{6}\text{C}$Q =    MeV

Suppose two stars of the f;q-cr z a6 +k*ze ,+3eumwtcysame apparent brightness $l$ are also believed to be the same size. The spectrum of one star peaks at 800 nm whereas that of the other peaks at 400 nm. Use Wien's law (Section 27-2) and the Stefan-Boltzmann equation (Eq. 14-5) to estimate their relative distances from us.

  Stars located in a certain cluster are assumed to be about the same distance, 3agdlkqeuqq*(,l1( iyd 6 yr from us. Tw,,geyi*l ay1(l uqqdk(drq 63 o such stars have spectra that peak at $\lambda_1 = 500\ \text{nm}$ and $\lambda_2 = 700\ \text{nm}$, and the ratio of their apparent brightness is $l_1/l_2 = 0.091$. Estimate their relative sizes (give ratio of their diameters). [Hint: use the Stefan-Boltzmann equation, Eq. 14–5.]   

  Calculate the Schwarzschild radius for a star with mass equal t.tk)ba 0 ;q;mqpn-p-tl+fwsuo that (a) of our Sun ist)l;fmtkp-wbpa. s;qq -n 0u+    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typical galaxy (likez)di;ahodk- fzgu/ 86 ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a sphere, for which tkbvuy. jru-, m89g+lcj w a1v,he sum of the angles is (a) 359º, and (b cr,l+.v,aj1yumu8- wkgvb j9 ) 180°.

  What is the maximum sum-of-the-an.r)z:izzr-ts 7i- utkgles for a triangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the speed of light, roe6(8xs-d zw(06kjnz yjig,p.)qg bv4r +v ld mughly how far away is it? v v8gd zm4() 6lz ,pigyknjw q .0de(b-rjs6v+x =    Mly

  The redshift of a galaxy indicatei*haynp+mgk3wy2*x8 3y jx +0bk bm1es a velocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a gala65uni9; jzd nd(iyxe-xy (relative to us) that is near the observable "edge" of theyn(;dx ez695din-jui universe, say 12 billion light-years away. v =    c

  Estimate the observed wavelength for the 656-nm line in the Balmer series of w u-xo vkdmn9oxv v,d*lq79 d7dx0:y.hydrogen in the spectrum of- ldd *vk.wu7 v0m9d79ydo xqoxn:,vx a galaxy whose distance from us is
(a) $1.0 \times 10^6\ \text{ly}$, $\approx$    nm
(b) $1.0 \times 10^8\ \text{ly}$, $\approx$    nm
(c) $1.0 \times 10^{10}\ \text{ly}$. $\approx$    nm

  Estimate the speed of a galaxy, and its distance from us, if the wavelengt(n7ka*t4-ba ilu lr 8hh for the hydrogen lin (h8kl7nut*rl4-ab ai e at 434 nm is measured on Earth as being 610 nm.
Eqs.33-4 and 33-5a v $\approx$    c
Eq.33-6 v $\approx $    $ \times 10^9\ \text{y}$

  What is the speed of a galaxy win3z prluen -3(th $z = 0.60$? v =    c

  What would be the redshift param9 b9oflxcp.3s eter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that tht aiv6a:,t 73+vd)kavndhl i9 e Doppler shift in wavelength is $\Delta\lambda/\lambda \approx v/c$ (Eq. 33-5b) for $v \ll c$. [Hint: use the binomial expansion.]

  Calculate the wavelength at the peak ofhhm3-q , 3tn+p 4u tkka4a9gnk the blackbody radiation distribution at 2.7 K ukt4 mn+ a k kn3hpag93t4-q,husing Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for clos/lk b-csi/il- ure of the universe is $\rho_c \approx 10^{-26}\ \text{kg/m}^3$. State $\rho_c$ in terms of the average number of nucleons per cubic meter.    $\ \text{nucleons/m}^3$

  The scale of the universe (the average distance bhp(9fjvp53a wqskueq66/8 zu etween galaxies) at any one moment is believ /8uq9hs6z pkwu5ev q(a6jp3fed to have been inversely proportional to the absolute temperature. Estimate the size of the universe, compared to today, at
(a) $t = 10^6\ \text{yr}$, $\approx$    $\times 10^7\ \text{ly}$
(b) $t = 1\ \text{s}$,    ly
(c) $t = 10^{-6}\ \text{s}$, $\approx$    $ \times 10^{-3}\ \text{ly}$
(d) $t = 10^{-35}\ \text{s}$. $\approx$    $ \times 10^{-17}\ \text{ly}$

  At approximately what time had the universe cooled below tytzimv)(zr76 he threshold temperature for producing vit67) (yzmrz
(a) kaons ($m c^2 \approx 493\ \text{MeV}$), $\sim 10^{a}\ \text{s}$ a =   
(b) $\Xi$ baryons ($m c^2 \approx 1321\ \text{MeV}$), $\sim 10^{a}\ \text{s}$ a =   
(c) muons ($m c^2 \approx 106\ \text{MeV}$)? $\sim 10^{a}\ \text{s}$ a =   

Suppose that three main-sequence stars could undergo the thrvos ,tso4 -*cu m;eom,ee changes represented by the three arrows, A, B, and C, in t4 outsmoc*,mse v-;o ,he H-R diagram of Fig. 33-28. For each case, describe the changes in temperature, luminosity, and size.

  Assume that the nearest stars to us have an absolute luminosmmb0c7:d.qm yw7m r( ttq)y3s- qpmk .ity about the same as th. mc-t 7ym3t smbdr)q 0.ykm(7pq: mwqe Sun's. Their apparent brightness, however, is about $10^{-11}$ times fainter than the Sun. From this, estimate the distance to the nearest stars. (Newton did this calculation, although he made a numerical error of a factor of 100.)    ly

  Use conservation of angular momentum to estimate the angulcv7f y8xm9t/2sx37bij * -oz iqxx-sfar velocity of a neutron star whif*-7y3xzb7tx2 ifi xsj sm9-/ ocx 8qvch has collapsed to a diameter of 20 km, from a star whose radius was equal to that of our Sun ($1.4 \times 10^9\ \text{m}$) of mass 1.5 times that of the Sun, and which rotated (like our Sun) about once a month. $\omega_{\text{final}} = $    $\ \text{rev/s}$

  By what factor does the rotational kinetic energy change when the star in Pr.vx;3wp ,hmqn oblem 56 xvnw3;,. qhmpcollapses to a neutron star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believed wz*j1nnlx / b30m1ykfto be a neutron star of mass 1.5 times that of the Sun, with diameter 20 km, is observed to have a rotation spenwj/n z*k 1fby 03xlm1ed of $1.0\ \text{rev/s}$. If it loses rotational kinetic energy at the rate of 1 part in $10^9$ per day, which is all transformed into radiation, what is the power output of the star? P$=$    $ \times 10^{25}\ \text{W}$

  The nearest large galaxy to o+.6pgg wu8xv cur Galaxy is about $2 \times 10^6\ \text{ly}$ away. If both galaxies have a mass of $10^{42}\ \text{kg}$, with what gravitational force does each galaxy attract the other? F$\approx $    $\times 10^{28}\ \text{N}$

  Estimate what neutrino rest mass (in eV) would provide the critical cdpczb-.4w+p2a )byn density to close the universe. Assume the neutrino density is,z.4+ bbc2wnaydc p)p- like photons, about $10^9$ times that of nucleons, and that nucleons make up only
(a) 2% of the mass needed,    $\ \text{eV}/c^2$
(b) 5% of the mass needed.    $\ \text{eV}/c^2$

  Two stars, whose spectra -btroh 4m /qc+e*yq .xpeak at 600 nm and 400 nm, respectively, both lie on the main sequence. Use Wien's law, the Stefan-Boltzmann equation, and the H-R diagram (Fig. Below) to estimate the ratio of their diameters. [Hint: see Exat- h/cmo xe*qb .ry+4qmples 33-4 and 33-5.] $\dfrac{d_{400}}{d_{600}}$ =   

  Suppose we can measure distances withtwoj;r7j+,+p e-rm*ukp * zs5tzw/lb parallax at 100 parsecs. What is our minimum angular resolution5j +w+7w o*tz/,j-b p* ru;kmrels ptz (in degrees), based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from singly ionigq6a1t: ))ipithl+w0fzob 9-l cgv 8 ized helium in a distant star happen to overlap with the Balmer lines from hydrogen (Fig. 27-22) in the Sun. How fast gt8h 9 )pcol6iw 0g- bti1f+l) qvz:aiis the star receding from us? v =    C

  What is the temperature that corresponds to 1.8-TeV collisisgsjn p; nmb2:8h9 2itons at the Fermilab collider? To what era in cosmological history does this correspond? [Hint: see (Fig. Belopm:n82;g 2 snbh9si jtw).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation of gas aro -e(mj85 zuyu);pelyhk: kaef; y(7vqi7pf3 cund what might be a supermassive black hole of about 2 billion solar masses at the center of a galaxy. If the radius from the galactic center to the gas clouds is 60 lf-khpuiy zk ;v8q c(; a: jm )ef7py7ee5u3(lyight-years, what Doppler shift $\Delta\lambda/\lambda_0$ do you estimate they saw? z$\approx $    $ \times 10^{-3}$

  A galaxy is moving away from Earth. The "blue" hydrogenbg5 m -2h0wsq)sf mbz0 line at 434 nm emitted from the galaxy is measured on Earthzqm 02b0mh bw-gs)s5f to be 650 nm.
(a) How fast is the galaxy moving? v $\approx$    c
(b) How far is it from Earth? d $\approx $    $ \times 10^9\ \text{y}$

  In the later stages of stellar evolution, a star (if massive o * 8 s)mxvvjb2dzdy-)enough) will begin fusing carbon nuclei to form, for eo* )dyz2d)- s8jx vbmvxample, magnesium:
$^12\text{C} + ^12\text{C} \to ^{24}\text{Mg} + \gamma$.
(a) How much energy is released in this reaction (see Appendix B). Q =    MeV
(b) How much kinetic energy must each carbon nucleus have (assume equal) in a head-on collision if they are just to touch (use Eq. 30-1) so that the strong force can come into play? $\text{KE}_{\text{nucleus}}$ =    MeV
(c) What temperature does this kinetic energy correspond to? T$= $    $ \times 10^{10}\ \text{K}$

  Consider the reactioncg.gas. 7xc5( fg (tck
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
and answer the same questions as in Problem 67.
(a)Q =    MeV
(b) $\text{KE}_{\text{nucleus}}$ =    MeV
(c) T $= $    $ \times 10^{10}\ \text{K}$

  How large would the Sun be if its density equaled the critical d qi43ld m+6ubnr 7h5hwensity of the un rhhu7mq4wbd3 56nl+i iverse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? Express your answer in light-years and compare with the Earth-Sun distance and the size of our Galaxy.
$r_{sun}$ $\approx$    ly
$\dfrac{r_{\text{Sun}}}{d_{\text{Earth-Sun}}} \approx $    $ \times 10^{-3}$