The Milky Way was once thought to be "murky" or "milky" but is nm8pjpt ce:*,2 ksszd. ow considered to be ma8m pk2 dzsc:e *,p.sjtde up of point sources. Explain.

A star is in equilibrium when it radiates at its surface ali*gf)bc k272i ifeh5h l the energy generated at its core. Whahkch5i7f*g 2 )eiibf2t happens when it begins to generate more energy than it radiates? Less energy? Explain.

Describe a red giant sdc bzv f(5rgd2)1efl)tar. List some of its properties.

Select a point on the H-R diagram. Marxe6q xwvdv gkrg;iy.ojh07 0ni: 3lw u g.3--yk several directions away from this point. Now describe the changes that would take place in a star moving in ..h ynko3irxlwi-67 ;0uq g w-0d j:vyggxe3veach of these directions.

Does the H-R diagram reveal anything about the co,uh06efdsk :fre of a star?

Why do some stars end up as white dwarfs, and others as neutron star, ru p:/,q3 w2nrwrnlrs or black holeslrqn:2rw r 3pwn/u,,r?

  Can we tell, by looking at the population on the H-R diagram, that hotter mag4 ercw, e- ys60ls8jyin-sequence stars have shorter lives? Explal ,w-6rj 8s4e gces0yyin.  ----待选择----yesno 

If you were measuring star para7tahbp86 ed qbuhm *1mdz 90z.llaxes from the Moon instead of Earth, what corrections would yoz *bmaubh0 q71z98d.phde6 mt u have to make? What changes would occur if you were measuring parallaxes from Mars?

Cepheid variable stars change in luminosity with a typical period o i+d )5;q kyehtzj)os2f several days. The period has been found t)tjz 2; khq+5oesdiy)o have 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? Whua+anrw1+;l2l: thak at is its role in General Relativity?

If it were discoverefln a0 eu ) )tfz;3beqmf7qcb9.q u85od that the redshift of spectral lines of galaxies was due to something other than expansion, how might our view of the universe change? Would there be conflicting evidence? Discuss.7.mc)fe89e5fo n ua f3tqlb ;u)qq0 zb

  All galaxies appear to be moving away from us.kzmdsjoexbk y;7, 7/ . Are we therefore at the center of ko;j,z/sb m.x7k7d eythe universe? Explain.  ----待选择----yesno 

If you were located in a galaxy near the boundary of our observable universeoe 8)6arb +vtb3wqu-nttmk lkl2d l)w1 8:r1b, would galaxies in the direction of the Milky Way appear to be approaching you or receding from youowutwl)re1q2)nklad br3 b8k-6 8+t 1v bm: tl? Explain.

Compare an explosion on Earth to the Big Bang. Consider such question/ j*wam61 5el,a3l5wnpq:*rvip e i gks 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 close5q5 wai*g*rp n3ima1 vll,ep:6w/jekd?

If nothing, not even light, escapes from a black hole yg/a+y*gi8aq xq r,*i, then how can we tell if one is thegr8 q+yy* *i,x/aiqgare?

  What mass will give a Schwarzschild radius equal to that of ty;lgefidws(/q ++ )enhe hydrogen atom in its ground state? Mge q d(f+l/;n iy)sw+e =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as a, lfk -*m;nv2e* rgpeobout 4 billion years. Find that time on (Fig. Below). People hr-* n vg2l;ompkfe ,e*ave lived on Earth on the order of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmice58a;vtq r 1rx microwave background radiation is. Where does it come from? Why is its temperature atve;8rr5q 1xnow so low?

Why were atoms, as opp8aacg uea-hp01.cltr e+a69hosed to bare nuclei, unable to exist until hundreds of thousands of ythcl aue0a cae.p gh8+19ar6-ears after the Big Bang?

Under what circumstances would the universe eventual bl((nu y4pi fqbd8kv328fmub/t6st /ly collapse in on itself?

  Using the definitions of the parsec and the light-year, show thatyu or k:8xv-(v $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.38 seconds of arc. Hotn3 si sn;r;p6w far away is it? d =    ly

  The parallax angle of a star i(-ipqqr7 p m*ig.1iip s $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What izairlh 6(d.g8s 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 d ,bixgc9 (nxu lalli33ol,1 n+/y;ze*o6pkbfor a star that is 55 ly away? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away from usx8avc*1,fbx j as a second star, will the parallax angle of the farther star be v, f*xx1jbac8greater or less than that of the nearer star? By what factor?

  A star is 35 pc away. How long does it take for its light to rw(2( x7suctwb wao*;d :qh /zoeach us?    years

  We saw earlier (Chapter 14) that the rate energy reaches the Earth from a1anlny1m*q ) the Sun (th)nlqn1 aa y1m*e "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 Su5rv /ri nnpo o,s y)m5toge) -(i2l8 ay-nyax)n as seen from Jupiter as compared to its brightness xoge(y, t)p yvna-ny rr oai)2m5 8)nsl-5o/ifrom Earth? (Jupiter 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 Galaxy s) c5y e(bwwl: se h+t+t)g)htwould subtend if observed from the nearest e s hc (+w)hb)yegts:5ttw+) lgalaxy 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 densi bo0g,5bi7jbii)p yq4 ty if it expands out to tbi0g7b5) i ,oqjyb4i phe 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 whited4h:/dba a h)9hxgam2w jo bsfpw-(lx40 )af3 dwarf, it is expected to be about the size of the Moon. What angulf(pls0-dwbh4:a jgh)aax3fhb 2)9 4 oa mxd/ war width will it subtend from the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whose ma4(quw2hby5fifv 7q6a ss is equal to the Sun's and whose radius is equal to the Earth's. How ma57 uqf y2q ih4wab6fv(ny 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 masses ha, fnv* pzojvtc-/ +w+zs a radius of about 11 km. Calculate its average density and compare to that for a white dwarf (j w+oz+ptn *v,fc/-zvProblem 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 burq c2jz-5g( pbjning reactions of Eq. 33-2. (The mass of thejpg(5 2zjbc -q 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 same apparent brih.ad tib77 g /ga(u+(ueg i 7sua0hfz+ghtness $l$ 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 abouty ( (.v( 6asitubfs8fs the same distance from us. Two such stars have spectra that peak asf(sb t86v.s(yu f(a it $\lambda_1 = 500\ \text{nm}$ 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 Schwarzschl z6w4y *cb edg3;v4aiild radius for a star with mass equal to that (a) of our Sun gb 6 eavc4z4iy* wld;3is    km, and (b) of Earth is    mm.

  What is the Schwarzschz fcmq 798o-gwild radius for a typical galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a sphere, for 56 q+ 1nvwzdaunms01 kwhich the sum of the angles i0qn 5kwmsn +16zv1udas (a) 359º, and (b) 180°.

  What is the maximum sum-of-the-anglabab;g ifnnk:*f,76+j3feuk 2g/ gives for a triangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1zm) z)p1zkvku3 :d lb9.0% of the speed of light, roughly how far away is it?k:zdp)z3bzlv1u m )k 9 v =    Mly

  The redshift of a galaxy in;r2v pjd6- m8gp +yf/xqnlji* 8vsh/fdicates 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 therra d; *kpb82y observable "edge" of the universe, say 12 billion lightp2;8 ybrdrk* a-years away. v =    c

  Estimate the observed wavelength for the 656-nm line x:j :)dkp oqu4xg3bz 3in the Balmer series of hydrogen in the s4dbqx:j: x 3uok)pg3zpectrum of 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 wavelength foi. u9 e6f*ygb+y wp;mpr the hydrogen line at 434 nm i fbmug+6w yep9 .yp;i*s 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 k 0ovp4+ k1xtagalaxy with $z = 0.60$? v =    c

  What would be the redshift psli(p-4nv x 1 ljel5 vr:l2/ibarameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3,w2gnty4: yf (s6fbd(o show that 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 distribution b2jpk tbh6 4q;at 2.7 K using Wien’s 6jbt2k hqb; p4law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for cloc1ryd8(s.jo 3 jtz.on7m.5o l rhe9zfsure 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 n 8/h.bexwkf n7s 87z-fanoi0(the average distance between galaxies) at any one moment is believed to have zn0.o 7/8wa ne7nhf-8if sb kxbeen 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 hadd kife1zay*up5 c93 8b the universe cooled below the threshold temperatur kfd 15ab8*zu 39iycpee for producing
(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: t 5v;:l/slyes lqe4q three changes represented by tqtv:ssl ye :e4l;l/5qhe three arrows, A, B, and C, 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 toj 7f91 30 qb 2mx,8b y/vbjmmszwil)le us have an absolute luminosity about the same as thfj 7 x1sm0w,) bilbvq/3l2 8jmb9mzeye 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 to6gs;jfshzl - /udftd,: +3 unj estimate the angular velocity of a neutron sta:+ d sfj zg/;thusjd3n,- fu6lr which 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 ) ytho1dx-jq1 the star in Problem 56 collapse-o) 11 htqdjxys to a neutron star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, be, +pd1 fpcw2yalieved to be a neutron star of mass 1.5 times that of the Sun, with diameter 20 km, is obserpfdp+2, ay1w cved 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 2 ;olhc+r3tl sto 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 critical dens )np1f4f u eq6ldt25nh.oa0zyity to close the universe. dl)u5n 0nz2p of6qty ea4h1f.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 anu7x 2.xm-l kogd 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 Examples 33xgku-. 2mxo 7l-4 and 33-5.] $\dfrac{d_{400}}{d_{600}}$ =   

  Suppose we can measure distanceshvrwz5(8z( r y with parallax at 100 parsecs. What is our minimum angular resolution (in degrees), based on this iy z5v8r(zrwh( nformation? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from singly ionizediy 4n8 e/ 4fi69vfx*e ox82w4 mcwktyu helium in a distant star happen to overlap with the Balmer lines from hydwyn/e9vo8y4 x4eu f x2i4m8c* t6 ifkwrogen (Fig. 27-22) in the Sun. How fast is the star receding from us? v =    C

  What is the temperature that correspo*.ivnkv+ ++o63kxjejc8 zc jrnds to 1.8-TeV collisions at the Fermilab collider? To what era in cosmological history does this correspond? x+c8+kc re6nv.jjv o*3j+ik z[Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation3lg5au1iy:.zpl3e uv s9 h/gn 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 cent3uz 13nulgh 9e /5psv:.lyag ier 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" hpx k;o0a c/wn0ydrogen line at 434 nm emitted from the gak0/w ;0xcnoaplaxy 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, as4spik.fn hl abm44pz c,75 +m star (if massive enough) will begin fusin7m pp4sh4,+ bn4.lfsia 5ck zmg carbon nuclei 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 brq9+0yq w -el
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 q*(8 ;b , qxmmyz r:ves:9ptkidensity of the universe, xz8p *kv:;mey:r9b s mt(iqq,$\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$