The Milky Way was once thought to be "murky" or "milky" but(m)q)aozpv;o w/s 5sst15y3xegp eerz f14z, is now considered to be made u3) vr p1,afw 51 s;4xeqg zo)t pm(ze5yzsos/ep of point sources. Explain.

A star is in equilibrium when it radiates at its ,1*u oy9 *ufzomlhtjs x(4 va1surface all the energy generated at its core. What happens when it begins to generate more energy than it radiat(laz9o jh *u1u fmx,*oy 41tvses? Less energy? Explain.

Describe a red giant star. List sf7eog5;lrl d 6ome of its properties.

Select a point on the H-R diagram. Mark several direr l56wjbutfzm,. 7b:hm vk ih8gk.+d( ctions away from this point. Now describe the changes that would take place in a star moving in eacfm7b..6kz bw(lj+rhh i 8g,kduv :5mth of these directions.

Does the H-R diagram reveal anything about the core of p3q;8yuuj*x .c jy: *zbsbe8qsg+:rma star?

Why do some stars end up as white dwarfs, and others as neutron stars0 +c jdx7y(e0kghyg a/ or black hoj ay0d x+7gh(/c0g yekles?

  Can we tell, by looking at the population on the H-R diagram,v* qcy;,ws*g0 f itc ,zacgj82 that hotter main-sequence si2g,f *j8cc q*,yg;zva0 cwtstars have shorter lives? Explain.  ----待选择----yesno 

If you were measuring sta ory36 yi1.urwr parallaxes from the Moon instead of Earth, what corrections would you hav13u rwyio.r y6e to make? What changes would occur if you were measuring parallaxes from Mars?

Cepheid variable stars change in luminosity withvn 5 wl d94v (mm(ox:0/sfszjg a typical period of several days. The period has been found to have a definite relationship with t 9nzsvlo0g( 4 (jwmf5vm/d:s xhe absolute luminosity of the star. How could these stars be used to measure the distance to galaxies?

What is a geodesic? What is its role .9t. 1tpeaup7 crn7w hin General Relativity?

If it were discovered that the redshift of spectral lines of galaxies was du/ gkthl19c(aim -p m.se to something other than expansion, how might our view of the universe change? Would there be conhsga mmk9tl.1-i/( c pflicting evidence? Discuss.

  All galaxies appear to be moving away from us. Are we therefore at the centergd )3 .kqc+oao of.3ogq a+dcko ) the universe? Explain.  ----待选择----yesno 

If you were located in a galaxy near the boundary of our observable un:6zzfb(9,q +p 9hnn5 -fpo xdhk p:fzwiverse, would galaxies in the direction of the Milky Way appear to be approaching you or receding wf pnh: zpqf b,p-z95xno(9h6zkdf+:from you? Explain.

Compare an explosion on Earth to the Big Bang. Coa: :rd2 yfn6(ct x8yor ls(jk7nsider such questions as: Would the debris spread at a higher speed for more distant particles, as in the Big Bang? Would the debris come to rest? What type of universe would lj (r6f8sco:rnt:2(akyy 7d x this correspond to, open or closed?

If nothing, not even light, escapes from a black ho091: y n( kcx,w6 v fl,o1yizer;pqwfnle, then how can we tell if onw;1:6,cfyye(qri 1ok lfnx, zv9w0 pne is there?

  What mass will give a Schwarzschild radius equ1lj 07zyn dl4lal to that of the hydrogen atom in its ground state? 41l zlnl7j0dy M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given :ff h-wsde8z9lo0js)as about 4 billion years. Find that time on (Fig. Below). People have lived on Earth on the order of a million years. Where is08f:szslofd) e9h- jw that on (Fig. Below)?

Explain what the 2.7-K cosmic microwa 0nc 50sp fsb7ll46+qr sweli.ve background radiation is. Where does it come from? we4sflc qlr0 n.l+i s705bs p6Why is its temperature now so low?

Why were atoms, as opposed to bare :3ppdsz) oe5cnuclei, unable to exist until hundreds of thousands of years after the Big o3c5des pz):p Bang?

Under what circumstances wof72nf*+ w/ kjji:b nwyuld the universe eventually collapse in on itself?

  Using the definitions of the parsec and the ligz .0ybixl9 zb7ht-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 away is it? d =ncqpx4q;g.p/v t 21fy    ly

  The parallax angle of a,ljmr67h su/m ,la7u i star is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its parallax5prz)vn7x a: 48dpkbn angle?
State (a) in seconds of arc,$\phi''' \approx $    ($\times 10^{-2}$)''
(b) in degrees. $\approx $(    $\times 10^{-6})^{\circ}$

  What is the parallax angle for a star that is 55 lubdr ;8j/ kpkja9c p9*y away? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away from us asy0t nw,h/m(ab z/tt8 y a second star, will the parallax angle of the farttyy,8mwa bn//t0(ht z her star be greater or less than that of the nearer star? By what factor?

  A star is 35 pc away. b 7+a-y:bbnm 4s(hez gHow long does it take for its light to reach us?    years

  We saw earlier (Chapte mh61fnft6jr /r 14) that the rate energy reaches the Earth from the Sun (the "solar constant") ifr/h ft6n61mj s 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 be3vpthw l8u4r 1 :vckj w,0df/rightness of the Sun as seen from Jupiter as compared to its brightness from Earth? (Jupiter0 ptw dl18wk:,er4jfcuvh v 3/ is 5.2 times farther from the Sun than the Earth.) $\dfrac{l_{\text{Jupiter}}}{l_{\text{Earth}}}$    $ \times 10^{-2}$

  Estimate the angular width that,lf0kb8bzo ey4vls q .:j9*je;x;di s our Galaxy would subtend if observed from the nearest galaxy to us (Table 33-1). Compare to the angular width of the M4s*j sek 8bqy dfblxz;9le ;:v,0i o.joon from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, what:mt.mnz( dwpxhslfphq t1p57g ::)l5 will be its average density if it expands out7 s)xz 5:.d:w1(pgfp mnlmt hql5:p ht to the orbit of Earth ($1.5 \times 10^{11}\ \text{m}$ from the Sun)? $\rho = $    $ \times 10^{-4}\ \text{kg/m}^3$

  When our Sun becomes a white dwarf, it is expected to be about the size3vgqh/b+:*qajcw usc, z2l,u of the Moon. What angular width will it subtendcaqu:z*cgqwjv,2su3+ /l ,h b from the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white- br) c8y* +l+0wykhjyzvp8 ;i0 xtp3ukpbc, q dwarf whose mass is equal to the Sun's and whose radi;p+0wp ybqy8 j z,h+)y*x03itklp8ukcrbvc -us is equal to the Earth's. How many times larger than Earth's density 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 massuf*,4qjp f0 tdes has a radius of about 11 km. Calculate its average density and compare to that for a white dwarf (Problem 13) and to that of nuclear matterffu4,pt j*q0d.
$\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 burn huwtm 0 oamgg 29i.k8+wme(p8ing reactions of Eq. 33-2. (The mass of the very unstabl.2e mtwi8gp am+(m8huo9 g0k we $^8\text{Be}$ 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 same apparent-s k+asr 1fnvhxm; 81u 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 z5cs-0gkp3 -2w m nlcl:h(yqb be about the same distance fromgs 5lc:hkcmy--wbn3p(q zl0 2 us. Two 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 to thw5)p e(m9i7unj:en v zat (a) of our Sun iz)pw mn :nuie je597(vs    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius ewg/ss5/vi ),dzw :vb for a typical galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, ,4 3rv o1byhpcgzih.: drawn on the surface of a sphere, for which the sum of the angles is (a) 359º, and :hvrc,zgb4pyho1 i.3(b) 180°.

  What is the maximum sum-of-the-angles for -d(fkgdyrekl; fqo3c h ;ton+* 3*,una triangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the speed of light, ro zb,(e66 q;g5sqk -cadkya p2qughly how far away is it? v = a;ekdp qg(62 ska5-q6 zbqc,y    Mly

  The redshift of a galaxy 0o2-nd: gq rih t epl7ap46pk)indicates a velocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (relative to us) that is near the observable1n s 2duj0a+a 9*ah .bxwoeb-g "edge" of the universe, say 12 billion light-years +1j9eu2axn-0h*sd b.ogaw b a away. v =    c

  Estimate the observed wavel8h(s y (tk)glgength for the 656-nm line in the Balmer series of hydrogen in the spectrum of a galaxy whose distance (gt(h8l kysg)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, irb+tq * c)bi(ff the wavelength for the hydrogen line at 434 nm is measured on Earth as being 610 nt i* rbcbqf(+)m.
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 gim/7f m/qmw 2talaxy with $z = 0.60$? v =    c

  What would be the redshift parg6zd0i v2hfd u;*be-h ameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Doppler shif b9.q7sgne mb4t 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 of the blackbody radie k 714znkfps3ation distribution at 2.7 K usn4 kefk317 szping Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for cl589brc cxn3,8ug6.3smeb anm jk.fu iosure 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 distans- nr;7kq 7 c5f0p2lhlrq2h ryce between galaxies) at any one moment is believed to have been inversely proportional to the absolute temperature. Estimate the size of the universe, compared to today, - l fr725h s0qlck7qnr;r 2yhpat
(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 the thres2 mb edshft/2v+*4cyh hold temperature for pros bh+2yv2 mt/4e h*cdfducing
(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-sequen9v8: ;k,ka xdfa bmdm0ce stars could undergo the three changes represented by the three arrows, A, B, and C, in the H-R diagram of Fig. 33-28. dvk k8 a0fdm:a9x;b m,For each case, describe the changes in temperature, luminosity, and size.

  Assume that the nearest stars 4l ir4whl.mp1 kzrmh1/2n;ps bc h:/pto us have an absolute luminosity about the same as the Sun's. Their/.lnpi4 p h4lpkcr;m12m zbh1:s h/wr 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 momentumwjjv4c, 057; ocdiy et to estimate the angular velocity of a neutron star which has collapsed c4ejjvyc; dw7t50o,ito 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 th4/w cuzdu ldh ypz351 atbr39 7-juzl9e star in Problemdczbz194u-l lr yta/ 5dp7hj39uzwu 3 56 collapses to a neutron star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believed yu6 ks zc3w1.gg -b;mcz.ov5fto be a neutron star of mass 1.5 times that of the Sun, with diameter 20 km, is obser ccwgbmv zf guo.;615k.yzs-3 ved to have a rotation speed 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 our Galaxy is s/s-r dl.qv r 7kftc117s)nd dabout $2 \times 10^6\ \text{ly}$ 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 w7 nst vpc)2wr u *3dck-j36 6mdig/xkdensity to close th32 c)k cunwsv*/k pti6ddwg6 mj73r -xe universe. Assume the neutrino density is, 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 peak at 600 nm and 400 nm, respectively, both t/ 8z7nnzwu07aclde7 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 Examples 33-4 and 33-587t770uzzl n den/acw.] $\dfrac{d_{400}}{d_{600}}$ =   

  Suppose we can measure distances with parallax at 100 parsecs. Whatakjwoxhnimt+fl7; -25)slk,) vcj l* is our minimum angular resolution (in degrees), based a j+w* 5fix-)l,k n;ovtlcjl7 k2h )mson this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from siajq0k eub1/mjgx 4v/5eqd 3 r*ngly ionized helium in a distant star happen to overl/ 1ejrvq5d0 kx/ 43qe bagmju*ap with the Balmer lines from hydrogen (Fig. 27-22) in the Sun. How fast is the star receding from us? v =    C

  What is the temperature that corresponds to 1.8h;rct:l a08 qe-TeV collisions at the Fermilab collider? To what era in cotrcq : 8l;0haesmological history does this correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently meas sr uqypjm0+,.9 qnw *in6y4hlured the rotation of gas around 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 gasrjlu0wm 9,y qn q.6hps4y*n i+ clouds is 60 light-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" hydrogen line at 43cl hzrza-;u7 gg6x/,o4 nm emitted from the galaxy iszcgo ,lx7z a-6h rug/; measured on Earth 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 evolutanm6(/jyl 0 dn4-prcn ion, a star (if massive enough) will begin fusing carbon nucl -acy(nln40rd m nj6p/ei to form, for example, 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 reaction jqb o 21ng5wxukk0g19
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 densityb ydn ;*k.xc/j equaled the critical density of the und;cnj kyb.x/* 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}$