The Milky Way was once thought to be "murky" or "milky" but is now considered gbcgi,c jave/ is (79. bn5x(hto be made up of point,/x (9ab.j gci5ns ei(cvbgh 7 sources. Explain.

A star is in equilibrium when it radiates at its surface :ce*3 yj.ga-t5j m5yea y(dlaall the energy generated at its core. What happens when it begins to generate more energy than itj5yelm.3a*d (cy:a -agyet5 j radiates? Less energy? Explain.

Describe a red giant star. List some of its propertlxpj+ i5g- v,jies.

Select a point on the H-R diagram rd7fnfozuv wfnj7x 4vp/ ,i9 .d;zo*;. Mark several directions away from this point. Now describe the changes that would take place in a star moving in each of these direc do4. ,niv/;oxzzd rnv f7f;w7up9*fj tions.

Does the H-R diagram vtn 1b* -siai 2ap02bb m.5ohyreveal anything about the core of a star?

Why do some stars end up as whit cj*sdknm/-kn(d hfvbv)o+5/ e dwarfs, and others as neutron stars or black holedk-(/5 s vh) ovdknnc/*+mjbfs?

  Can we tell, by looking at cy:8a .omyp p0(zj1rb the population on the H-R diagram, that hotter main-sequence stars have shorter lives? Explain.z8.( b1cyp:ao r0jymp  ----待选择----yesno 

If you were measuring star parallaxes from the Moon instead of Ear +x*nc2(( g :aly,qk:knzv mmwth, what corrections would you have to make? What changes would occur if you2:lyqg wxa(m(k m*,nc+ v:knz were measuring parallaxes from Mars?

Cepheid variable stars change in luminosity with a typical period of sev 847sn4oltj/kytki q*9h u -beeral days. The period has been found to have a definite relationship with the absolute luminosity of the star. How could these stars be useln/tibo 7q4 k-8 ye49*sukh tjd to measure the distance to galaxies?

What is a geodesic? What is its role in General e1bzry-7 zu (g(f).kaap7anuyuu *ung. 6 e5qRelativity?

If it were discovered that the redshift of spectral lin6 bk cm*oks53extwufe */ba:4es of galaxies was due to something other than expansion, how might our view of the univers* f4owmas 6b:ce5e 3ukx*t /kbe change? Would there be conflicting evidence? Discuss.

  All galaxies appear to be movio yvv; ccmw13:bjl- ha/rr:xk.,ti 5o ng away from us. Are we therefore at the center of the universe? Exp/ yb1 -jma c::r;vocr h,k5lvx3i.otw lain.  ----待选择----yesno 

If you were located in3gz7g: ;i0rxs/4m tqy2m4fojs s*ogc a galaxy near the boundary of our observable universe, would g;fox3mgs/y2jm*g7i:sc0z r 4t4q o sgalaxies in the direction of the Milky Way appear to be approaching you or receding from you? Explain.

Compare an explosion on Earth to the Big x,at*lwouw2 rz1p w 5+Bang. Consider 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 this correspond to, open or closed5w*2wzw u tx+rpa,l 1o?

If nothing, not even light, escapes from a black holx01xjxg -yi )r ey0bh (,/jgvae, then how can we tell if one is there,yrxb exj(-x)0 yj 1hag0vi/ g?

  What mass will give a Schwarzschild radius equal to that of the hydrogen atom i+gkmt8qs68bf jeg (d 1oww 54mn its geoq 8djk61ww5gg tmfbsm +8(4 round state? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion ye )n 8a1ezq9jlnars. Find that time on (Fig. Below). People have lived on Earth on the order of a million years. Where is t)anl 8ejn9 qz1hat on (Fig. Below)?

Explain what the 2.7-Kz c96s :69-hsgfued mgc4lio, cosmic microwave background radiation is. Where does it come from? Why is its temperature now s fglzi-4dcu gh6sm99 oc6:,eso low?

Why were atoms, as opposed to bare nuclei, unable toczrt8r 9bav q+hboe32(u7up( exist until hundreds of thousands of years after the9uu27+8v(cr rebto (p3 azbhq Big Bang?

Under what circumstances would the unijmr3pzve k;-/ dtp. r(verse eventually collapse in on itself?

  Using the definitions of the parsec and tbu 94)pprasot ihw4 v8l+k 5l(c5n5u mhe light-year, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parall3*; l cdzsa:syax of 0.38 seconds of arc. How far away is it? d =    ly

  The parallax angle of a star is k+dw8a57 p;ozscmh m /1 pc5gvey-ak 4$0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. ;) abda1+)gltral8p uWhat is 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 angle for a star that is 5av fa2g p/kvb+5gqxn-e (y/q05 ly away? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away from us as a second star, will the parqgri 3oo b.wa0 3v080ue d6tujov6w ,pallax angle of the farther star be g .uw uoov 6tw,g3jobpaq0rvi 3d680e0reater or less than that of the nearer star? By what factor?

  A star is 35 pc away. How long does it take for its light8t1,.p(pkp b6cdn wbf to reach us?    years

  We saw earlier (Chapt:6z6/0f6gkx p5 q:nt trktzfter 14) that the rate energy reaches the Earth from the Sun (fk 5 t/6t6 pn kz6gzrttx0qf::the "solar constant") 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 seenwa/ypesz,+ n: from Jupiter as compared to its brightness from Earth? (a/s+:z y,nwepJupiter 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 our Gall1*vqt 8imuzo7s id jv2 :7v.maxy would subtend if observed from the nearest ga2dj7 87: m.ilvsm*zv1uv toiqlaxy to us (Table 33-1). Compare to the angular width of the Moon from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, what will be its average density if it expa6) v;9 yq dqgmgyz0nr:v)jx o;nds out to the orbit of Earth y nq:j)90)o;6r qv gdmvz;gxy($1.5 \times 10^{11}\ \text{m}$ from the Sun)? $\rho = $    $ \times 10^{-4}\ \text{kg/m}^3$

  When our Sun becomes a white dwarf, ch xvvav3w;k *2s 1 0tx5fe(qwkocd4 3it is expected to be about the size of the Moon. What angular width will it subtend from the present distance 1hefw2x;vtkw*54 3v c0c(kd3voxqas to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whose mass ist g udar1 59t*fy,ly7c equal to the Sun's and whose radius is equal to the Eartg57tf9c1ru y*y a td,lh'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 1.5iu4)1a:z;o /raqu4pw n/0 tt rkkcq3u solar masses has a radius of about 11 km. Calculate its average density and compare to that for4azqr :3 cr n/4k ;qw1p)uktua0itu/o 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 the3+ +o/o9ql(vz a jqttu He burning reactions of Eq. 33-2. (The mass of thet(t zo/ajqq+3+9ulv o very unstable $^8\text{Be}$ 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 samtn3itbe3l j-1wn* :kle 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 sa2623 og9 5u qrln1gt) hansfykme distance from us. Two suny f1a)gtgqlso nu2hk5r296 3ch 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 8 yv5iz5. sfb0k/c tgwradius for a star with mass equal to that (a) of our Su. igs btfwv55y08ck z/n is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typical galaxy (like oura-oda- 2g0xc+g(it rth; f)a2lflen.s)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surfacoe d1kq:t, 2uw1pc:pze of a sphere, for which the sum of the angles is (at1 2 eqdpou::wp,c1z k) 359º, and (b) 180°.

  What is the maximum sum-of-the-angles8msu v+4mdt7 l for a triangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the speed of liu4(lfp;r oj: ldn2:qq ght, roughly how far away is it? v2d:np4j urqll(q f:; o =    Mly

  The redshift of a galaxy indicatedy7nk*sacf+d aoxv28x l3 e8 ;s 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 observab05 7u p;b z2p8rwdmxomle "edge" of the universe, say 12 billion light-years awayw 5bdo 2x0mzup8 p7mr;. v =    c

  Estimate the observed wavelength for the 656-nm line in the Balmerbe;k,nj g12i y series of hydrogen in the spectrum of a galaxy whose distance from us is nb,kj2i;e g 1y
(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, 9/k-0 ehnn ruagdgm 68if the wavelength for the hydroge0gnk 6-g 8/r9em nuadhn line 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 gala9xx)(m8d,* z), bu ppb hmppfzxy with $z = 0.60$? v =    c

  What would be the redshift paramete2vei9ngg,nwpx h5 r7q0, j* 8r ibh/tck gw*z4r $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show t 9ibi*90o ppajsiz)(ehat the 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 radiation distributiorc uq;q.p 9o-ln at 2.7 K using q. rqp-lc;9o uWien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density f1mq jxi)j gi,-or closure 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 any oneikwr yx7c19n n+ *pu2e momn2*9x +yik u 1prnwc7eent is believed 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 th8syek9zsm.: ge threshold temperature for producing z: sk9y.gs8 me
(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 three change5g)derh4e*b xs represented by the three arrows, A, B, and b rd4h)*egxe5C, in the 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 luminosity 79/ :u8va zhkhllmn7gabout the same as the Sun's. Their apparent brightness, howevakh8:7lh zmg7l/ nuv 9er, 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 momepq f.;.sq s-pdi (lze0ntum to estimate the angular velocity of a neutron star which has collapsed lpqs. pe;.i-ds(qz f0to 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 rotational9og4loqs7p (, b cg(nn kinetic energy change when the star in Problem 56 collapses t (c lgb4,o7n(q p9ogsno 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.z69skoh+3gdn 7(ylq2 khidg , 5 times that of the Sun, with diameter 20 km, is obser3+6,hsd2d lhy9kni (7ggzqok 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 Galakobe g)4b die o0ih4o85,9glfxy 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 prcpg2h4 ;kvvfq/gl ,r- ovide the critical density to close the universe. Agv; /-cvf plg4 2qkhr,ssume 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 lie g+1kpuk,:am0)5 o pfk2aqrgcon the main sequence. Use Wien's law, the Stefan-Boltzmann equation, and tm qap+okp1kau),g r 52kcg0f: he H-R diagram (Fig. Below) to estimate the ratio of their diameters. [Hint: see Examples 33-4 and 33-5.] $\dfrac{d_{400}}{d_{600}}$ =   

  Suppose we can measure distances with parallax1vm m w 0g5 v(o4;d6dbt+ oh5ochpwr+e at 100 parsecs. What is our minimum angula+5v mbo+d(5gocr014 e o; wmhv6dwph tr resolution (in degrees), based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines d iz*jeru3 ,:pug;nuoe a207x from singly ionized helium in a distant star happen to overlap with the Balmer lines from hydrogen (Fiu ee3r7g:0uja;pz,i od x2*n ug. 27-22) in the Sun. How fast is the star receding from us? v =    C

  What is the temperature ttykb:-v pr3 /dhat corresponds to 1.8-TeV collisions at the Fermilab collider? To what era in cosmological history does this correspond? [Hint: see (Fig. Bel3pktv: r y/d-bow).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have rece, g4: pluc-fafntly measured the rotation of gas around what might be a supermassive black hole p-cfl4:,ga fu 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 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 434 nm e,zd.2 ugug3nb mitted from the galaxygbn.3gu z ud,2 is 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 evolution, a star (if massive enough) will 6l s qh9z3vr9zbegin fusing carbon nuclei to form, for example, magz9vr 3qhz6 ls9nesium:
$^12\text{C} + ^12\text{C} \to ^{24}\text{Mg} + \gamma$.
(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 gi* d0: gwylgt,txt0 i8-6l/w l3ccis
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 density o z)czbpl2* -xuf the univers2zpl*-xubz c)e, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$