The Milky Way was once thought to be "murky" oufy*-zn w c;f2n tb6n3r "milky" but is now considered to be made up of point sour3- n*bfc zn6t;wu2f ynces. Explain.

A star is in equilibrium when it radiates at its surface all the energ x2l gb(b1gmfo4q9c: 0t.htk gy generated at its cm gbog( lt4fxg1 q:c9khb.t20ore. What happens when it begins to generate more energy than it radiates? Less energy? Explain.

Describe a red giant star. v 1 ln2hcv-6fbssr-i1 0/hbqvc3 ldm3 List some of its properties.

Select a point on the H-R diagram. Mark 1w orlzdp*5hub9 ,8nvruh6s 8+rmb/,w2z zuc several directions away from this point. Now describe the changp z sw,vc1owur,n9u r2bmh du8r5h /68bl+zz *es that would take place in a star moving in each of these directions.

Does the H-R diagram reveal anything about th 0jjvt zp 2jee9gci4e4 6:b2/cddq)rge core of a star?

Why do some stars end up as white dw*x.xbn/g ky4 m(wblq1arfs, and others as neutron stars or black holeyq/* 4l g1xkb bw.m(xns?

  Can we tell, by looking at the populati(g ,4r vxcrt.wv1f* dyon on the H-R diagram, that hotter main-sequence stars have shorter lives? Explar x( d,1.ygcvfrv*4wtin.  ----待选择----yesno 

If you were measuring star parallaxes from the Moon instead of Earth, what corre23yv-44x;0bqjcy w1i w i9ektnqy75 gmiiiz.ctions would you have 1 xg 942-ke5j4y qbynz;cw.iti0q v3ii7mwi yto make? What changes would occur if you were measuring parallaxes from Mars?

Cepheid variable stars change in luminosity with a typical period of sever 9sfbz*oxu5q( 2sj qs8al days. The period has been found to have a definite relationship with the absolute luminosity of the star. How could these stars bebu*s859 qxjqsz2o(f s used to measure the distance to galaxies?

What is a geodesic? What is its role in General Relakqj mfq-9)ne 8tivity?

If it were discovered that the r //p ;iau5ncoaedshift of spectral lines of galaxies was due to something other than expansion, how might our view of the universe change? Would there be conflict/o/;ain aup 5cing evidence? Discuss.

  All galaxies appear to be moving away from us. Are we therefore as6mqeba /pjsrko*jz1 j4 jak*lr71 82t the center of the universe? Explaj/1*l4b1e6jj az m sq82op k7r*as kjrin.  ----待选择----yesno 

If you were located in a n9a1o 1d(wqzqgalaxy near the boundary of our observable universe, would galaxies in the direction of the Milky Way appear to bqa9 ( z1dqw1noe approaching you or receding from you? Explain.

Compare an explosionws)z.*d h0az 4 *zorzf on Earth to the Big 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 woulhw*d rz o z*)4fs.0zzad this correspond to, open or closed?

If nothing, not even light, escapes fzby(oi 13uh2 arom a black hole, then how can we tell if oneuo 1( 2zy3bhia is there?

  What mass will give a Schwarzschild r8 kwpe7c)h+js f: 4rdnmq)7 cyadius equal to that of the hydrogen atom in its ground stat7p8sfc j)n7ymck)wd herq+4: e? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion years. Find that ti l wfr5ss-df9+ qcu57fme on (Fig. Below). People have lf5 wsd9fcq +-sr5u7lfived on Earth on the order of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic microwave backgrotuf 54p vhbc18und radiation is. Where does it come from? Why is its temperatuhbtcfv4 18p5u re now so low?

Why were atoms, as opposed to bareb 4.tnvh9 z4tm nuclei, unable to exist until hundreds of thousmt9b 4 4nh.tzvands of years after the Big Bang?

Under what circumstances would the universe eventually collapse in o/rwl* or, (qjn+eo2mgn itself?

  Using the definitions of the parsec and the light-year, huu2cu2q 4ia(wqvk *sk**v5f show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.38 sztpmx olu,m5n 0l/4*o rff51 +qtr o7feconds of arc. How far away is it? d =    ly

  The parallax angle of a star i nz53ab: z,3w,wktu dbs $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its paraz m/pony( 6(2sgchdf. llax 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?gl qb.xmsi y5 f 8..gn6sa1k)x $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away from us as a second star, wiodo q i 38.c-l, plfo1uepv*a:ll the parallax angle of the farther star be -.cpov3:ooiuqde l, pf* la18greater 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 reach ush+kx; / dz6kw/bahpx -?    years

  We saw earlier (Chapter 14) that theq(4j wkku;s,5ie 6i-jb w9l 2we* ffzy rate energy reaches the Earth from the Sun (the "so9eklz-w4if ;us ,jwjyik(w6*5b2eqflar 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 seen fros2/il2 c 4btv3q:pkqm m Jupiter as compared to its brightness from Earth? (Jupiter is 5.2 times farther from the S22/s qbm vcip t43klq:un than the Earth.) $\dfrac{l_{\text{Jupiter}}}{l_{\text{Earth}}}$    $ \times 10^{-2}$

  Estimate the angular width that our Galavhqz t 9+jg a4+57i9lnfzd-l nxy would subtend if observed from the nearest galaxy to us (Table 33-1). Compare to the angula 9nnlhagz t95j lv7+q4+zf-dir width of the Moon from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, what will be its average density ifyt.v4wzk5 o74a+ ya2t 8 uiepg it expands out to the orbit of Earth (p24vowa7ktayeu5y 4 + 8iztg .$1.5 \times 10^{11}\ \text{m}$ from the Sun)? $\rho = $    $ \times 10^{-4}\ \text{kg/m}^3$

  When our Sun becomes a white dwarf, it is expected0zpk n ;zxelgg/ 1gu4: to be about the size of the Moon. What angular width will it subtend from the presen0zx:; 4epg ugk lg1z/nt distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whose mass is equf3xg wmlas 5q,(8hfxn+v;n. 04jfu gral to the Sun's and whose radius is equal to the Earth's. 8,( 4afnlng ff3x5.;vwug x+shr m 0jqHow 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 masses h.4 h(7hwjkhxxj :rb9mas a radius of about 11 km. Calculate its average jxjb hr4kx h97h.:mw( density and compare 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 reactions of Eq. 33-2. (Tqq+y2-d w41i c*uhtpc s* irs*he mass of the very unstapy*d12hc**q-ws +cqsi t i4 urble $^8\text{Be}$ 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 salyiuur g5o;4s /m,qe-2ugyd-a2ei / o me 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 pqbbey1i)irsc/-a98ss) zrx92yz6f6 , zr dv same distance from us. Tw -)/b6 drf,s2z1qs 6ezs izr)cb8axrip9yv 9yo 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 that (a) of y e+ or ,7w8nze3fygr,gy-f.ecr; e 7xour Sun g fo ezcwr7,.e 7rn;efgy y8-r3ye,+xis    km, and (b) of Earth is    mm.

  What is the Schwarzsc /ip;svg3vx;7 zw xr9ghild radius for a typical galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surkrq*rrg*v0amki 33 s+c r+s)gface of a sphere, for which the sum of the angles is (a)kg)kr +s*mq c0r3ar*+3 rsvgi 359º, and (b) 180°.

  What is the maximum sum-of-the-angles foz-gbqfey;1h5xmtc9pue 3/ m fs 3 l49vr a triangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the speed of light, roughly hx+gep; a: ldcuo/o5;low far away is it? v /+e ;uc:lp olox5ag;d=    Mly

  The redshift of a galaxy inn* .sn:sd-vf 8nx(sq mdicates 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 leg/8 g piqjabs7;r/ st:ut51near the observable "edge" of the universe, say 12 billion light-years awayp; 7e / rti/5g8g :talu1jqssb. v =    c

  Estimate the observed wavelength for the 656-nmpj)dlxvs6r fw +0 2k1m line in the Balmer series of hydrogen in the spectrum of a galaxys)pdwfxr 1lk0vm+26j 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 id7r7wp4wi-my ts distance from us, if the wavelength for the hydrogen line at 434 nm is measured on Earth as being 610 nm. r4w7 d yw7m-pi
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 wv,uul4rxtha.y 0/7b, cejn,tith $z = 0.60$? v =    c

  What would be the redshj-v3l- pqx6-vt q.qjqoy, j v:ift parameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Doppler shift in wavelength 9y3pwabi9o g-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 distributionb* 9*sg b6.ptlj 6ncpc at 2.7 K using Wien’*j6t plsncbc* g.6bp 9s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of ttr n fr; 0afhq o1t298tlbw3v5he 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 anr tzo*jgrc(8 (y one moment is believed to have been inversely proportional to the absolute temperature. Estimate the size of the universe, compared to today, (g 8r zr(otj*cat
(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 hd lh7o i5b+6e94d wnznnyf7e cs g-.n3ad the universe cooled below the threshold temperature foeeglb6 dnnh957 z+ s-fiyndno3w7 .4cr 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 sj)z*(ucze( altars could undergo the three changes represented by the three arrows, A, B, and C, in the H-R diagram of Fige(*zc a ljz)(u. 33-28. For each case, describe the changes in temperature, luminosity, and size.

  Assume that the nearest stars to us have an absolute luminosity about the safks.w-tdpqqmrkk1 o 4u x(1 u2q /:iu.me as the r1u mu-t kqw(q1 idq kx.sufo2/p :.4kSun'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 to estima8am2jk 3kw n9pjupxs4n 3c, *bte the angular velocity of a neutron star which has collapsed to a diameter of 20 km, from a star whose radius was equ9awb 2c*jmns3p4ku,kx 3p 8njal 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 the star inq rgs8a3 k,cf0uzo++ u Problem 56, sgf+o0u a8zrck+uq3 collapses to a neutron star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, belia) -m4wm(gg h. zn;ux w bchbody80.k8eved to be a neutron star of mass 1.5 times that of the Sun, with diamet-4;kxow) m 0 hab.(bmyd .h8gw8cngzu er 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 galaxy rlj2aar b9slu,b-fn *a9o 8 5mvp;.nb 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 y:z+-j oe sly+mass (in eV) would provide the critical density to close the universe. Assume the neutrino density is, likez+ oye ysj-l+: 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,6 nv4 00aih 2+j yyya,85tc sz-nmvj;qlxgae 8 respectively, both lie on the main sequence. Use Wien's law, the Stefan-Boltzmann equation, and the H-R djeymv a,8tsc+v ;a60zny 84q anjhx lg0-2y5iiagram (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 parallax at 100 parsecs. What is our mt;0*-ksujp 4 ow .7tlkmbc hsox,8ho7inimum angular resolution (in degrees), based on thibhkos,us 7l w- 07oto8 ;xmjkp*ch.4 ts information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from c lpblssba1 nm;u4sc/ s60c .:singly ionized helium in a distant star happen to overlap with the Balmer lines from hy : /bs1 clcs0.bsnpa 6s;clu4mdrogen (Fig. 27-22) in the Sun. How fast is the star receding from us? v =    C

  What is the temperature that fsp,1(z s f -;kjh+cmdcorresponds to 1.8-TeV collisions at the Fermilab collider? To what era in cosmological histokssc(-1dphm,;fj f z+ry does this correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured sp qz e+n39bryo;;xl5the rotation of gas around what might be a supermassive black hole of about 2 billion solar masses at the cente+soq5nyrepb 3 z9 lx;;r 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.;pa6yh/b8 .tyt f;nd r h6yn:e The "blue" hydrogen line at 434 nm emitted from the galaxy is measured on Earth tohpy;dnb68t aer nf/ .ty6y :;h 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)480 8w +st xwxds46i9vxnx tut fw 62f0eygec. will begin fusing carbon nuclei to form, for wi cw yx0fgt6w.u0x6e92484n8vsdtx+f etsx 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 reactio)o(mg,lsd1xxes4 5a7 yg,pupe c-mx +n
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 den tk;:d odfwb--:yyjfcr6s/l1t;qi *b sity equaled the critical density of the unibt o:d-l ;rt*j;q bis- /kf1w6ycdf:y verse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$