The Milky Way was once th6,o) mjfxy 8c,9hgzmo ought to be "murky" or "milky" but is now considered to be made uz,m)8 9c,6jx g ofmoyhp of point sources. Explain.

A star is in equilibrium when it radiay:go g; ijd+6etes at its surface all the energy generated at its core. What happens when it begins to generate mog 6e i;g+y:djore energy than it radiates? Less energy? Explain.

Describe a red giant star. Listd i*55q7rsm :ouzer5m some of its properties.

Select a point on the H-R diagram. Mark sever2c zemrq ,z,z w5iv:*rlvk u4*al directions away from this point. Now describe the changes that would take place in a star moving cuqe:,*vz rr4miv,z5zlw2* k in each of these directions.

Does the H-R diagram r4jozg ndcd:t gws09h)c + l+c1eveal anything about the core of a star?

Why do some stars end up as white dwarfs, and others as neutron stars or be db ei4:a- k0,9emdr x94ui-wp3agcg lack ho:g i9-- d 0e93x4rmge4aaepbudkc,i wles?

  Can we tell, by looking wmw /g v:ip 7n0ysa.g)at the population on the H-R diagram, that hotter main-sequence stars have shorter :wsi p0g. wma )yvgn/7lives? Explain.  ----待选择----yesno 

If you were measuring star parallaxes from the Moon instead cpig4lo hq(z /0- gt2bof Earth, what corrections would you g /4ghoqi0bl2tp( -zc have to make? What changes would occur if you were measuring parallaxes from Mars?

Cepheid variable stars change in luminosity with a typical perdt1veyw.b /.-r,w d xf5vmlq7iod of several days. The period has been found to have a definite relationship with the absolute luminosity of the star. How could these stw.1/q erd,7x .l5 -t bdvmwyvfars be used to measure the distance to galaxies?

What is a geodesic? What is its role in General Rsd3m-lr,lt; ; nj65al, uxx oyelativity?

If it were discovered that79 o4 /linxoun8z 7ovt the redshift of spectral lines of galaxies was due to something other than expansion, hton7 oxli8 u/nv7 49zoow might our view of the universe change? Would there be conflicting evidence? Discuss.

  All galaxies appear to be moving away from us. Are we therefo;k7:m4a )r-c m -ce*qcvroglcre at the center of the universe? Explain. qmv;lm roek) -rgc: -c *7cc4a ----待选择----yesno 

If you were located in a galaxy near the b/...v yeun;mvx*xtoon2xm / av3wc0s oundary of our observable universe, would galaxies in the direction of the Milky Way appear to be approaching you or receding ;a/o./vxwtxv x0cm.n*sve2 n yu3mo.from you? Explain.

Compare an explosion on Earth to the Big Bang. Consider such queqfnzcr8o y t19w,.3 bestions as: Would the debris spread at a higher speed for more distant particles, as iwr.yqte 8,1co b9znf3n 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 we,,- jw9pz 6rkvf +x-) cdqxuml tell if one is tpz6l m +xw,dfu r9kc,qjxv-)- here?

  What mass will give a Schwarzschild radius equal to) *u. ir.hnlrtf*bo* yc(t:e t that of the hydrogen atom in its ground sco*..r( teb)ny*rft uhtil *:tate? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion year wa62 ky*b+qwxu*mfh) s. Find that time on (Fig. Below). People have lived on Earth on the order of a million years. Where is that on (Fig. B *aqfw)*yk 6xhwmb 2u+elow)?

Explain what the 2.7-K cosmic microwave background radiation is. Whereod d5c+2st9 mlz ul,i* does it come from? Why is its temperature tlz, di2*o scl5+u 9dmnow so low?

Why were atoms, as opposed to bare nuclei, unable to exist until hundreds of 4 u19juwbe :+/ kukxvkthousands of years after the Bi wu+xkk1 uu/:e4 bvj9kg Bang?

Under what circumstances would thh6vb,/ cq,mbvsajyu d/y 1v)1e universe eventually collapse in on itself?

  Using the definitions of the parsl h9xm60 qh;zeec and the light-year, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a paralae9*gf,:q+qqvz d sj1lax of 0.38 seconds of arc. How far away is it? d =    ly

  The parallax angle of a stn/0t.(lu6) gyf* .7ju50c q(qmvxjhckxd rxxar is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its parallax angr2v7xgx 1o 01f 8gptc q/,nidzle?
State (a) in seconds of arc,$\phi''' \approx $    ($\times 10^{-2}$)''
(b) in degrees. $\approx $(    $\times 10^{-6})^{\circ}$

  What is the parallax angle for8hnzj)f+fh *m3a nhpd ap6 6(xwj6gjj/g8z0h a star that is 55 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 tl8vm z17csegio iq5.+he parallax angle of the farther star be greater or less than vziiq7c eo.g5m +8sl1that of the nearer star? By what factor?

  A star is 35 pc away. Holao. t)2fsn2be he5*y 8 rc(2dbm-qhrelbq 76w long does it take for its light to reach us?    years

  We saw earlier (Chapter 14) that the rate goo3av2dy .vp o4o ,xk7a,a g+energy reaches the Earth from the Sun (the "solar constant")7.4avapxog,o2d k,y+oav go 3 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 from Jupiter as com zw8ch3 a(fggs*d1r/zpared to its brightness from Earth? (Jupiter is 5.2 times farther from the Sun than thgrda/w 3gz18*f( hsz ce Earth.) $\dfrac{l_{\text{Jupiter}}}{l_{\text{Earth}}}$    $ \times 10^{-2}$

  Estimate the angular width that7scdjuc.epdm+ /nhqxd;o ,80 our Galaxy would subtend if observed from the nearest galaxy to us (Table 33-1). Compare to the angular width of the Moon qo/8emxc j ddp+;d7,h0us .cn from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, what will be its averad 3oe kkr58s*kge density if it expands out to the orbit of Eart eo*rs3dk8kk 5h ($1.5 \times 10^{11}\ \text{m}$ from the Sun)? $\rho = $    $ \times 10^{-4}\ \text{kg/m}^3$

  When our Sun becomes a white 4d gu aq2p-1p6kaaj+e5sm* ywdwarf, it is expected to be about the size of the Moon. What anguypjs e wm45p 2au-d*k 1aqa+6glar width will it subtend from the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whose-wxpi x8kh,1/ei4 pdd9l2 sxp mass is equal to the Sun's and whose radius is equal to the Earth's. Hp /lwekhx p 4,dsx1d2ii9-px8ow 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 ql )zp gcdc51yl/j z,9is 1.5 solar masses has a radius of about 11 km. Calculate its average density and compare to ylz5qjl )/g19d,czc pthat 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 E1.w2czwa u7;u dykcf.q. 33-2. (The mass of the vewud fyc acz2k1u.7w.;ry 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 brightnes 1jvg2rz 4y;lvs $l$ 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 certsthfta2/ q8g *0uhu* oain cluster are assumed to be about the same distance from *u t su 28aqhg*ht/fo0us. Two 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 raov sz-( p-*mukcb(iqg(lux, jxuu75 5dius for a star with mass equal to that (a) of our Sun isilx, u5qgums- (p5cz*-(juu (b 7xv ko    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typic 6pge.bwim*0 b-kkg4j al galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a sphere, forc y:gevsgy1f,b,ai25 which the sum of the angles is (a,,v2:gysbc1 eya fgi 5) 359º, and (b) 180°.

  What is the maximum sum-of-the-angles for xn:mqx0.:wb v ;f p)mva triangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the speed of light,nz. ) db;hrqh(ys )xf9nb yn/. roughly how far away is it? hbhyb/( )zydn ;nr.9. xnqsf) v =    Mly

  The redshift of a galaxy indicates a veloc4 1qhy vuzp.icotw)rr 6-lslxgg7,0 4ity 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 observable ot, vz *;exfo1*vnmq0"edge" of the universe, say 12 billion light-ye*v*o,ze t f0qv;xn1moars away. v =    c

  Estimate the observed wavelength for the 656l9uhrt:ykzfo a0o8 3) -nm line in the Balmer series of hydrogen in the spectrum of a galaxy whose dis lorz0of 8 3)uyth:9katance 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 f -c sh8r kq68xc.wxi.9c/ur nsor the hydrogen line at nwh8usx /69-rs kqc..r8 cixc434 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 w -1:72li)d vm.cdzb1dkltzu eith $z = 0.60$? v =    c

  What would be the redshift paksf4a svfz 78qz:ot55 b3wumbt+.5d arameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Doppler shift iue)r m jyly1a, 0;yr.an wavelength is $\Delta\lambda/\lambda \approx v/c$ (Eq. 33-5b) for $v \ll c$. [Hint: use the binomial expansion.]

  Calculate the wavelength at *p ; ptdaffe1j:kr -s5the peak of the blackbody radiation distribution at 2.7 K usinkpf -5:*a;tpd f1 jrseg Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of the universe isr:u hktk*lq p8z1 58i g:rms;u $\rho_c \approx 10^{-26}\ \text{kg/m}^3$. 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 galaxiegliwpx (.ll52js +1 t;nw*dpjs) at any one moment is believed to have been inversely proportional to the absolute temperature. Estimate the size of the universe, compared to today;pdljw t2 gl ix .np+5*swl1(j, 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 the threshk: z) 6yrf0jy3h.but eold temperature f: )b.j hr tf63ukeyz0yor 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 three changes represdo u1p4s+5z+g jk jp2uented by the th1ds jguo4pjzkp 5+2 u+ree 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 to us have an absolute l(suu *,taozz7uminosity about the same as the Sun's. Their apparent brightness, however, is abtuz(uza *o7,s out $10^{-11}$ 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 anguh6v )m3 jqr3x qh67mny7 b-nqzlar 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 equal to that of our Sun (3b hvyzmq7n)-63qj7 x rmn6h q$1.4 \times 10^9\ \text{m}$) 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 4.y1 zvbssx20 ym0 svhthe rotational kinetic energy change when the star in Problem 56 cobyz20m .4vy sxv 10hssllapses 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 1az 27:xf +kfcjl;q z+n.5 times that of the Sun, with diameter 20 km, iaj7 n + kcfz:2xzql;f+s 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 ga zs+7 zpi+fze xe 51n2shzg6y;laxy 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 pfod c/8c 4go-erovide the critical density to close the universe. Assume the neutrino density is- focg4c/od 8e, 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 an+rf,xelw)t+u 5 c /rqymkb9e(d 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 ratke l /(+ceuwxt+ m,q r59)bfyrio of their diameters. [Hint: see Examples 33-4 and 33-5.] $\dfrac{d_{400}}{d_{600}}$ =   

  Suppose we can measure p nc,f.:;(w kohkb94ol( ; pewtaubu,distances with parallax at 100 parsecs. What is our minimum angular resolution (in degrees), based on this bftoc phb;w.a,k ewn(,4 ou;(ul9p k :information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidenc9 3sezcw bf ij;ismx vfabb5*k c+8(1)e, the 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 receding from us? v = f;se+xki)j9c(w1m3 biz s*av8f cb5b    C

  What is the temperature that corresponds to 1.8-TeV collisions at tn9 +sk)85uhls d /g x:wop,rwahe Fermilab collider? To what ergkl: /8)u5ndwhx r9oswp+,as a in cosmological history does this correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation of gas around whatnl7g qgbvx6 3 3u9 syts//6hbh might be a supermassive black hole of abo b63 6hbvgytqlux //7hg9 s3snut 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" wba11vg39i qo hydrogen line at 434 nm emitted from the galaxy is measow3i1va 19gqbured 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 staxq f7glxpho;* i.a- u6 *volu3r (if massive enough) will begin fusing carbon nuclei to formvlaqu o6ug;* hx7l x f-o.3*pi, 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 9z9wt wx4kpindl(5i4 ajp:st;ow/9r
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 tb4q zuctt2 y4w;kp4r/ he critical density of the unizkwqb 2t;tc/r4 4p4yu 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}$