The Milky Way was once thought to be "murky" nb9hk9 0c g *mol.4zp4t yims.iof,/ zor "milky" but is now considered to be made up o phz44s*ftib.nm/m 9g, i.oy9ck zlo0f point sources. Explain.

A star is in equilibrium when it radiates at its surkm-j 78kbc sfk,p nn2/face all the energy generated at its core./c m,bnf k7-pn 2k8skj What happens when it begins to generate more energy than it radiates? Less energy? Explain.

Describe a red giant star. List some of its h;n01sd1 rnmt tph;h **brz k(properties.

Select a point on the H-R did qjxhazp70 (pj0 ;)vbagram. Mark several directions away from this point. Now describe the changes that would take pz;0(j dvh)px0 pa bjq7lace in a star moving in each of these directions.

Does the H-R diagram reveal anythqwwy9 bx*9o+x ing about the core of a star?

Why do some stars end up as white dwarfs, and other;6s5x vn2et, mww -nucs as neutron stars or black holes56 svem ,2wnt-wcn;ux?

  Can we tell, by looking at the population on the H-R dias+b,sk70 hfae+az nm/ gram, that hotter main-sequence stars ha e /s+b,n kafzsh7+m0ave shorter lives? Explain.  ----待选择----yesno 

If you were measuring star parallaxes *tqh f444xldsvs0-5q )wadc efrom the Moon instead of Earth, what corrections would you have to make? t5sw4 q) -lhv q4a dcx4e*f0sdWhat changes would occur if you were measuring parallaxes from Mars?

Cepheid variable stars change in luminosity flh d z0-6mb+jwith a typical period of several days. The period has been found to have jzh+6mb df0 l-a definite relationship with the 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 in General Relad24bd(l vxtkd0 )cmd*,ul:zativity?

If it were discovered that the redshift of spectral le8v+ug0r qb4uines of galaxies was due to something other than expansi g 4rbvqe+0u8uon, how might our view of the universe change? Would there be conflicting evidence? Discuss.

  All galaxies appear to be movinz cn)ja h2oq4,cu/;ywg away from us. Are we therefore at the center of the universe? Explain. jw ;hu4c oq zc),nay2/ ----待选择----yesno 

If you were located in a galaxy near the bound*x2rwier fz7062g dek zd p*+qary of our observable universe, would galaxies in the directio*6 ddrz+kpx7ewef rz20*gqi2n of the Milky Way appear to be approaching you or receding from you? Explain.

Compare an explosion on Earth to the Big Bang. Consider sb-4cg fm.k cz-nha).k uch questions as: Would the debris spread at a higher speed for)zm4-k fhgn.k -c.ba c more distant particles, as in the Big Bang? Would the debris come to rest? What type of universe would this correspond to, open or closed?

If nothing, not even light, escaz9dm-pgz:i3b 5aczl 5pes from a black hole, then how can we tell if one ab z955 lgm izp:zd3-cis there?

  What mass will give a Schwarzschild radius equal to that of thl7.l tq2g zmky7i7c6f c*j qot.j w+c2e hydrogen atom in its ground state? fc6.yqwi m.z go tj7jq c*7 tl+lk227c M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about3b*ws) d5stcs f k69i:wq/ lez 4 billion years. Find that time on (Fig. Below). People have lived on Earth on the order of a million year 6w9 f)ssqw3s*kle: b/izdt5cs. Where is that on (Fig. Below)?

Explain what the 2.7-K cosm nd;dhocm lqs0/h.5 y 9n4n/daic microwave background radiation is. Where does it come from;d dn amh4 oh/nn5.09qysld/c ? Why is its temperature now so low?

Why were atoms, as opposed to bare nuclei, unable to exist until hundreds of tho 6:osdus /ck;o 9lot3cusands ;ol:uso36ctods ck /9of years after the Big Bang?

Under what circumstances would the universe eventuallybt,2 m1mxu8zeem.fgb 33n(o0 -sbrue collapse in on itself?

  Using the definitions of the parsec and the lv). z1xkjmwj ;ight-year, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.38 seconds of(w7npedgicl1 kl4wh /.:6azp arc. How far away is it? d =    ly

  The parallax angle of a stbh e6/t1zek* vc. g hlghr6)k(ar is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its gut6k mm0 cofr7a s/l2ursr v2l+o6d;8bf4a3 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 angle for a star that is 554cab arm. e5bpkm4l2w:*w ;yc ly away? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as farcqlw be6k mm)7//lztnael( -: away from us as a second star, will the parallax angle of the farther star be greater or less than that of t6:(elela/kwmzlm nqb 7-c )/the nearer star? By what factor?

  A star is 35 pc away. How long does it take for its light to reach fd;q -g y gw610azs0kous?    years

  We saw earlier (Chapter 14) that the rate energy r+fvfrw- 1j3i. sd id u-l91dwmeaches the Earth from the Sun (the "solar constant") is abomdru .ls1d v+9dfi ji-3 1fww-ut $1.3 \times 10^3\ \text{W/m}^2$. 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 as c /v)u)w*akgce ompared to its brightness from Earth? (Jupiter is 5.2 times farther from the Sun than te )wa/)k*vguche Earth.) $\dfrac{l_{\text{Jupiter}}}{l_{\text{Earth}}}$    $ \times 10^{-2}$

  Estimate the angular width that our Galaxy would*6rhokyig: )ax )xxy, subtend if observed from the nearest galaxy to us (Table 33-1). Compareo a)ryhx)ig ,:yk*6xx to the angular width of the Moon from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, what w po hixceb925f2)0fsgill be its average density if it expands eg2i)sf9 cx2fo50 hbpout 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 tlfutjx v jk0(wt 7(*8vo be about the size of the Moon. What angular width will it subtend from the present dista v (jkj*fu xt8tl07wv(nce to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whose mass is equal to the Sun's and w/-ptac-o gf*z hose radius is equal to the Earth's. How many times larger thang-/ta o z*pfc- 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 masses has a radius of about 10d-yg 9gepnu 7xr81cenhhi;41 km. Calculate its average density and comparexne gh yc0niure;4 -g1dh8p97 to that 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 burning a)*8fbmed6i -aazf )i e00fm.(tgndwreactions of Eq. 33-2. (The mass of the very unstable f0fiem aait8.dm)ba)fwe6d n-0g( *z $^8\text{Be}$ 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 byh2d1fu7p +ujk+ 6idorightness $l$ 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 b;g mp(hc *imif52 y7oe 8*gvxhe about the same distance from us. Two such stayvi(hh o*c*pgxm; fi78m5 ge2rs 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 ew n;mb+oo5ppz -9wh0yqual to that (a) of our Sun ;p9w0+ywoz-5h nm po bis    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typical galaxy (like ours)? R t06qw+go )kar =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a sphere, for which the sumvtxvwtv oul8g/0hx6 jy/1 4:q of the angles is (a) 359º, and (b) 180°8htux vtq4 gxlv/ 1 0:w/vjy6o.

  What is the maximum sum-of-the-angles fypm atpq3,2 cey/r+ v+or a triangle on a sphere?    $^\circ$

  If a galaxy is traveling9 b, 0c5pmpoku away from us at 1.0% of the speed of light, roughly how f9ubmk5 0ppc, oar away is it? v =    Mly

  The redshift of a galaxy indicates at br a) 9ur,gdctw bz; *fpn7(s35l)ny velocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (relativq8tvjpz 78j(ie to us) that is near the observable "edge" of the universe, say 12 billion light-years away. j(zp7i8 q8jvtv =    c

  Estimate the observed wavelength for the 656-nm line in the Balm j35nzykchk5 ;er series of hydrogen in the spectrum of a galaxhkk53 j;5 nczyy 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 g4,3+4yyjviqi2l u ffxalaxy, and its distance from us, if the wavelength for the hydrogen line at 434 nm is measured on Earth as bein34q + i 2xjivfuyy,f4lg 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 wi.6 nu8h,k/hgsm1jry8tjnj 7k th $z = 0.60$? v =    c

  What would be the redshift pa did32 po+*vutrameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the2 zjpalgo is8ewwz56 : w/n7o( 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 of the blackbody ra ) febk6lvqir,64t m6adiation distribution at 2.7 K usinkf 6r4 6e6t,qilva b)mg Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closuuj;p57vtxw2 i re 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 between galaxies) at e gy5qvmob b :c.0x/w+any one moment is believed to have been inversely proportional to the absolute tvb/c.: og5 webqyxm+ 0emperature. 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 univers2reysa* z2t :ts5 i;hdfd2rf,e cooled below the threshold temperature for 22rysds ,d*ie f 2:;tfa5 thrzproducing
(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 coiy+,b:agig7yc q , vh 8bof/h6cwu 1x;uld undergo the three changes represented by the three arrows, A, B, and C, in the H-R dibya1 cvf+7:gxw,yoc g;6qbi,hiu h8/ agram of Fig. 33-28. For each case, describe the changes in temperature, luminosity, and size.

  Assume that the nearest stars to *q1hd0v4(qg/r ev y u0sw;bfsus have an absolute luminosity about the same as the Sun's. Their apparent brightness, however, igqv vyefhs0*1r us;w0(/b4 dq s 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 angularf. cit;- ej;my qbpu,0 momentum to estimate the angular velocity of a neutron star which has collapsed to a diameter of 20 km, from a star whose radius was .mi; tc jf,-0by;pequ 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 kinex-mc4knf1l ; jlnt7p 1;hwiq 5 e6x/jttic energy change when the star in Problem x;pjjhq/t1 -tmn1 fk;n4 cil5we 76lx56 collapses to a neutron star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believed to be a neutron star of mass 1.5 times that of the ) yre*jlb5h-iSunrh )5lb j-y*ei, with diameter 20 km, is observed 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 gal7pqaj;si 4 siz7- lzq*axy to our 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 criticallbdu-l 0k;;*b*s:v azpmpdn1 jxd15b density to closl0x* * 1;bszulad- 5dpm1 db k:bjn;vpe the 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 4p0prg2qx8 ;br /1a cfv00 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 Examples 3p gr0/ bcxap; vq1r8f23-4 and 33-5.] $\dfrac{d_{400}}{d_{600}}$ =   

  Suppose we can measure distances with parallax at 1; kwagpbb5v, dj*(k8w00 parsecs. What is our minimum angular resolution (i kwg 8bkaw(vbd;j5,p*n degrees), based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, th,f+97 2- buyqp5 qza zosearfi3 yf0s4e Balmer lines from singly ionized helium in a distant star happen to overlap with the Balmer lines from hydrogen (Fig. 27-22) in the Sun. How fast is the star rece2s izyeaa-o09u, 3 z +7bs5rqfpffqy4ding from us? v =    C

  What is the temperature that correspond9df9meey(0r oore2y lpc7y8 er0n2( es to 1.8-TeV collisions at the Fermilab collider? To what era in cosmological history does this coc(y eer 09 (0ny 7or2epylfr9d mo2ee8rrespond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation of gas around what lh7f.lt(tl;z n2, oramight 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 light-years, what Doppl; hortfn(l,all7z2 t. er 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 line0rpypp/33* kyb)nfszt7zz 3k at 434 nm emitted from the galaxy is measured on Earth to be 65 ysyb*kzt33/)70rppzp n 3 kzf0 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 gxe h3s/f tu)+g na5/rahu9,fevolution, a star (if massive enough) will begin fusing carbon nuclei // +a 3tgsh,uxur)h afg59nef 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 fgqa,po(*tli 9u;k8 g sp6)wj
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 c9k ws2i(vflo *ritical density of the universe, v( l2k ws*i9fo$\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$