The Milky Way was once thought to be "murky" or "milky" but is now cons3*vya,;dx;zl grle *eidered to be made up of poxa*,l ry edl3 g*;zev;int sources. Explain.

A star is in equilibrium whe /l1glbfg: p::0/rmihu-ku ( q evpy3ln it radiates at its surface all the energy generated at its core. What happens when it begins to generate more energy than it radiates? Less energyi (qe- pyl 1b:uh0:pvu: //llmgkfrg3? Explain.

Describe a red giant star. r eg9dcfts;( -t-7xt, l, z-uhfuqwt,List some of its properties.

Select a point on the H-R diagram. Mark several di rh jh;msea7+b qy09(erections away from this point. Now describe the changes that would take place in a star moving in each of these dire 0bqe+r7e(9hjms;ah y ctions.

Does the H-R diagram reveal axs ib;g+jw2czme(0 9 :i. lbl8 a5lszinything about the core of a star?

Why do some stars end up as white dwarfs, and others as vvt/95 a,jbeyyva7; f neutron stars or black holesv;975ja,fy/yv betv a?

  Can we tell, by looking at the population on the H-R diagram, that hotter 3nd( hkwriuk:59z7hqk o ./qt main-sequence skowk7ui9t:3zkhr(h n q/5 q. dtars have shorter lives? Explain.  ----待选择----yesno 

If you were measuring star pu )tr4zfddgkd-49n p1arallaxes from the Moon instead of Earth, what correctin u41 )tp k-94dfrgdzdons would you have to make? What changes would occur if you were measuring parallaxes from Mars?

Cepheid variable stars change in luminosity with a ts,uq.. njwvn1 s/ 9boxypical period of several days. The period has been found to have a djnvuosnsb1.x/. w,9 qefinite 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 Relati f2zl6yoxgy;i/g dm 49vity?

If it were discovered that the redshift of spe7 amjs.2(yqo2ni r kl.ctral lines of galaxies was due to si 7nraym.sl 2 k.(qjo2omething other than expansion, how might our view of the universe change? Would there be conflicting evidence? Discuss.

  All galaxies appear to be moving away from us. Are weh;vow) y(xb 7 .x;mwod therefore at the center of the universe? Explain)odm.;y7wo;w(hxbx v .  ----待选择----yesno 

If you were located in a galaxy near the boundary of our observable universe, 2z1 lwd4h0c nxwould galaxies in the direction1 nhlcw2dxz40 of the Milky Way appear to be approaching you or receding from you? Explain.

Compare an explosion on Earth to the Bqa )4yq00i 4 u p,/act*fkjiaoig Bang. Consider such questions as: Would the debris spread at a higher spee0 foi *a4qiacyqjt04)ka ,pu/d 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 closed?

If nothing, not even light, escapes from a black hole, then how can wzochlyn.1)x+6xmz+9; vzb; 1s pqyv se tell if ox ;yo1p ;svzhm9zxq6)ybl+1 c. zs nv+ne is there?

  What mass will give a Schwarzschild radius equal to that of tcv io,m.k)fm )he hydrogen atom in its ground st). ifckv,om) mate? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as abjdd ke t orh54i5+ees2 e0r6)kout 4 billion years. Find that time on (Fig. Below). People have lived on Earth on the order of a million years. Where is thek5 tohede52 rij drs64)0+ keat on (Fig. Below)?

Explain what the 2.7-K cosmic microwave background radiation is. Where does itm** x.f9nv oav coma9*n.vvmxf* o e from? Why is its temperature now so low?

Why were atoms, as opposed to bare nuclei, unau:hhp du9/j v5ble to exist until hundreds of thousands of years after the Big Ba h:/ h9jpdu5uvng?

Under what circumstances would the universe eventually colln*7k r o0:iwwpapse in on itself?

  Using the definitions of the parsec d-9/o2wy p) umau (apwand the 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 igsk-k f zq4a, akfj011y 6+nifar away is it? d =    ly

  The parallax angle of a stac;u,qd5zt4efw h ehh5; 1p1hy:rt 2fvr is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. Woiya:z- . d8zd,xk.2q7k zlk lhat 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 55 ly away?;rpcf)npjd,bf9 :1 k l $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away from us as a second star, will the pon0-3c yy(jd karallax angle of the farther star be greater or less tn0ko d-yj3 yc(han that of the nearer star? By what factor?

  A star is 35 pc away. How lo/9x jsx zkzr*+ng does it take for its light to reach us?    years

  We saw earlier (Chaptercm a6 n+q*ochpv 4m)3m 14) that the rate energy reaches the Earth from the Sun (the "solar constant3mcano4cp )*mh v+6mq") 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 brightnedv4mqrl+0- juk7 i/wfss of the Sun as seen from Jupiter as compared to its brighd 4+/ j-kmiru vq7wfl0tness from 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 thmn(ryb .k ,kj3z fjs4l-;0 hsaat our Galaxy would subtend if observed from the nearest galaxy to us j, 3 b-a0n4m.yk ksj(;lrhsfz(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 an hj4 xs .aqic:07o/dpverage density if it expands out to the o7 cq da/p4nhix:. s0ojrbit 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 tzii o5.8dbn ,9;b:w s6v paf*xw4 ggooo be about the size of the Moon. What angular width wilbd6nvigx w,a5;9wsp4:gfo z.i*b o8 o l it subtend from the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whose mass is equal to thelpzgo7 )l sb,( Sun's and whose radius is equal to the Earth's. How many times larger than Earth's densi7,b slog p)z(lty 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 f(+y7oy e ;wx+ck); v1mvss zrmasses has a radius of about 11 km. Calculate its average density and compare to that for a white dwawxke)1yz;vyfs+oc(vr7s +m ; rf (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 reactions of Eq. 33-2. (The mass of th.2olyb-5 jq ,cy n.8l iphz7uie ve c27.oip q.l,luyb8yi-h5zj nry 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 apparent4 sa44lq xm2xg 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 assuchzcn+- q5 ex6med to be about the same distance from us. Two such sta +xn-6c qcz5ehrs 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 Schwarz lii6gv6py7 9iy70 mm: c8mmmjschild radius for a star with mass equal to that (a) of our Sun: 6cvm9gymly jmm86 7ipi 7i0m is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typical galaxy (like ours)? R ccci;j2ih:12i haen9 =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a sphere, for +rv os6wc .k)qwhich the sum of the angles is (a) 359º, and (b) 18)w+.r 6v scokq0°.

  What is the maximum e3:gl/d m9hadsum-of-the-angles for a triangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% zjbgr q, 51rt:2omuuf(iu 96cof the speed of light, roughly how far awzuuub6 5jrqf, 2c9o 1: m(tirgay is it? v =    Mly

  The redshift of a galaxy indicates a veloe/id y 1bn;9yd.vas /jcity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (reaz:+/ d9 sa41aq04dlbqqpf calative to us) that is near the observable "edge" of the udqaz44: pfl9s+q0a c daba1q/niverse, say 12 billion light-years away. v =    c

  Estimate the observecf3. ts(l+snysdf)fn83zt2 x d wavelength for the 656-nm line in the Balmer series of hydrogen in the sp 2s)c(f .n z+fdl3tssn8f3tyxectrum 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 wg15ow4g gga75.pjmb h avelength for the hydrogen linogg gmhga7wj.154b 5 pe 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 wit*1:6xh r *ts.cmdwhf0y urll 8h $z = 0.60$? v =    c

  What would be the redshift par1 :x2s h- lo9xaxfg5cuameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Doppler ses eelja:l , a-*(v4owhift 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 distributioxhx.o6gzpg8ot hpl c); 8l s;.n at 2.7 K using Ws;;ppz6)oxlt8. 8 o hxg.hgclien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for 6yzvy*g3np,tz4 n -rl 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) attxuvw wl6 lc 7e u:dn/g7*)t:n any one moment is believed to have been inversely proportional to the absolute temperature. Estimate the size of the universe,7w6nu c7:etlnt vx/ ul:*)gw d 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 wha;bt :xef9e(sxt time had the universe cooled below the threshold temperature for producingbxf tse (;x9:e
(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-se+mnuj2n9+ch 6gj zh m yu;zphl6a730cquence stars could undergo the three changes represented by the three arrows, A, B, and C, in the H-R diagram of Fig. 33-28. For each case, describe the changes in tezm3am+6lh9hug 2u;n +h6 cc7 zjyjn0 pmperature, luminosity, and size.

  Assume that the nearest stars to us hk-j)1wl zq1-wng .vww( s iib3ave an absolute luminosity about the same as the Sun's. Their apparent brightnesgbww)i zl( q.1-k 1w vnw-sji3s, 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 angular velocity of a neutraq m5etsz; z67on star which has collapsed to a diameter of 20 km, from a star whose radius was equal to that oft; ea57 q6mzsz 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 Problfhxp cn 9 nj2tecz-k /7o;n*j+em 56 collapspo hne 2nckcj/9zj;-*+x n ft7es 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 oej2u 2ng,xi: jbxh;a.*h6g pi f mass 1.5 times that of the Sun, with diameter 20 km, is observed to have a rotation sp,bp: i;h6n* jjuhx.iea2gx2g eed 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 galaxyd n ri5p4b0lw(w1w; ui 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 neutriuth( ;y jy-yah1js5 5vno rest mass (in eV) would provide the critical density to close the universe. Assume the neutrino density is, lik5 5a ut;yh1y(j- yvhjse 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 ato:9kpus te/m hzcu03sb.x./t 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 of3.spub09 tmhsx.:z /ko tce/u their diameters. [Hint: see Examples 33-4 and 33-5.] $\dfrac{d_{400}}{d_{600}}$ =   

  Suppose we can measure distances with parallax at6/yi n; ;ujj+: eoqif oyt93ns0h rc*x 100 parsecs. What is our minimum ai*/yrqj+y n3;96henou:tx;j fs oc 0ingular resolution (in degrees), based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from -slf.ef 0mssvv6 5h 60iqqcr,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 receding from us? cfi,-0sqherv.6mssq l0v56f v =    C

  What is the temperature that corresponds to 1.8-TeV collise (6/nuw efbs838 gkvhions at the Fermilab collider? Towbefh6g8s ku3 ( ev/8n what era in cosmological history does this correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measu8e c nlak/;a.ckr3; 68wfhhiured the rotation of gas around what might be a supermassive black hole of about 2 billion she 3a n/6uk.icr8waf;c8; khlolar 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 emitted f ee9p 9ml (c21h(rds)urp.nl srom the galaxy is measure9s)pn 9dmlsr(pc2uel( eh1r.d 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) wi vwjn+0j, oxro; gl1*ell begin fusing carbon nuclei to formgj n+*elj ow0vxor ,;1, 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 reactionu y6pt/i-y+8y ujt1 (h4q tjub
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 dfhgnix-x5d9y2 m -5ewensity equaled the critical density of the univgi5fe2w md -xyx9-5h nerse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$