The Milky Way was once thought to be "murky" or "milky" bui95i 8lnehs*xm6lnu +t is now considered to be made up of point sources. Explai+m 5s hllne*i6 98iuxnn.

A star is in equilibrium when it radiates at its surface at2gu81)vi)/hf r :rxckx s4s all the energy generated at its core. What happens when it begins to generate more energy than /aruk s1r)hstcg4x : v8fx2)iit radiates? Less energy? Explain.

Describe a red giant star. List some oj+ 0 csyy5-9itf/wngt6 q;keb f its properties.

Select a point on the H-R diagram. Mark several directionvi (c-ct :n wk ;,avli7+j/jht9mp r,p. 3czjqs away from this point. Now describe the changes that would take place in a star moving in each of these directionti9 w,mcn :j3cvvjrp,7(zjat lk+-p .hi/cq ;s.

Does the H-R diagram reveal anything about the core of a star?a16 l. pm2+7pelfgk pr6p e/:zchm1b g

Why do some stars end up as white dwarfs, and others as neutrnqp)2 i7hug:jon stars or black hol ugq 7pin:j)h2es?

  Can we tell, by lookinj;l eb+eue7s-lxg)tl8h n0f7 ; )astcg at the population on the H-R diagram, that hotter main-se c+fljgxna)hubt lses 8);e77-;0ltequence stars have shorter lives? Explain.  ----待选择----yesno 

If you were measuring star parallaxes from the Moon instead of Earth, what co7cpxzv7 zx8-o:y dyk ojt:21l2j wh r+rrections would : od x217x7k-j r8 wc+2hyv:lz ptozyjyou have to make? What changes would occur if you were measuring parallaxes from Mars?

Cepheid variable stars change in luminosity with a typical period of several sy2 ie6 n4yuz0days. The nyi4su 6zy2 e0period has been found to 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? What vkh: cir49/dp5k6l nris its role in General Relativity?

If it were discovered that the redshift of spectrnjzqy8:;f7 l j f;x+yeal lines of galaxies was due to something other than expansion, how might our view of the universe change? Would there be conflicting e ;e:+yjfjq y78lnx;zfvidence? Discuss.

  All galaxies appear to be moving away from us. Are we tdaf-cvl0t8t;68g ggbk-wu.pherefore at the center of the univert- f8d. bgwt6v ;kc8l0g-p ugase? Explain.  ----待选择----yesno 

If you were located in a galaxy near the boundary of our observable univgil*2jog-a6z9q/;j )ir omo q erse, would galaxies in the di6goi )j;/ooz gq-a9*mrlj2 qirection of the Milky Way appear to be approaching you or receding from you? Explain.

Compare an explosion on Earth to the ( pqas3-)ppbpBig Bang. Consider such questions as: Would the debris spread at ap)a-sb(pq3p p 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 closed?

If nothing, not even light, escapebucquh8o::+1w2 t yar s from a black hole, then how can we tell if one iyuu :twq2 bro1h :+8cas there?

  What mass will give a Schwarzschild radius equal to that of t+6sn+ bixayj8mc iu w 67tk6:ohe hydrogen atom in its gri6ao:j xniu7bc 6yw 8+6stmk+ound state? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion years. Find o *7igkdd05uuxyov o0;9e4 fi that time on (Fig. Below). People have l4 douki uy;x9g00d eifo *5vo7ived on Earth on the order of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic microwave backg ym2jod8fh h 6b2q4l,oround radiation is. Where does it come from?dj248h,yo b flh2om 6q Why is its temperature now so low?

Why were atoms, as opposed to bare nuclei, unable to exist until hundreds of th8:t/ac* b 2kwyd9xorkousands ok:9 2 bytr8w a*c/xkdof years after the Big Bang?

Under what circumstances would the universe eventu2 s;gjpjme mc .)lq+5cally collapse in on itself?

  Using the definitions of the (b1 *pkwc:bzxuintl zi80kfr17q u9)parsec and the light-year, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parall ywfkjtg6 cu.h: .gl4:nlo2)sax of 0.38 seconds of arc. How far away is it? d =    ly

  The parallax angle of a starv1h*lkm bh a*6 f.6 d*owxh4ta is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is itkj8 n9onpx;d/s 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 t-qe c,8kwm9y fhat 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 the paraj0.7zw(,)cnjbh s(dbt5xehm -dr,r0v l -ztfllax angle of the farther star be greater or less than that of the nea,rrefv c b0 sj) -j7zld-zth. m(nbt,x( h05dwrer star? By what factor?

  A star is 35 pc away. How long does it take for its light a:8 3q:gmnwte- v ;w;dov:x ypnvpy4+to reach us?    years

  We saw earlier (Chapter 14) that the rate energy reaches the Earth wda;+.yrrv 1qzk+ od /from the Sun (the "solar constant") is abourkz+r;o/qddv 1y. w+ at $1.3 \times 10^3\ \text{W/m}^2$. 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 of8 *5+/gx6 zbtloiqs we the Sun as seen from Jupiter as compared to its brightness fr 6seglo* x/5zqbwi8t+om 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 would subtend if9(n9qbcrrq rjr6k-b- xvgf,xl8 31ri observed from the nearest galaxy to us (Table 33-1). Compare to the angular width of the Moon from Earthbr( 9-983v1rr,jgxfc-6 lqiq r xbrnk. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, what will be i.: osrr*zhh,d+3r +z:u5kvrxx 6ajmix0iai 6 ts average density if it expandsu5:*6 hj3saozri ak r.+m6r0xdir vxz :h, x+i out to the 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 white dwarf, it is expected to be about the size of thegvqj 6 ra7/vgnbbe((h7gaq4 9 Moon. What angular width will it subtend from the g agj7(6e4q qgrban h(97vb/vpresent distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a na.ml8 (rhc. ii +opz-u-lnh1white dwarf whose mass is equal to the Sun's and whose radius is equal to the Earth's. How many times larlao .1h hn(-lz+8. mn -icipurger 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 mas8pmv p6ir,7 p gxey*)bs is 1.5 solar masses has a radius of about 11 km. Calculate its average density and comi x6vy7e mpg)*b ,r8pppare 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. (Th;h- 0 *yj.kmqo:mtzus*: mnaje mass of the vy.a: t*so um n*mkmhq;z0:jj-ery 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 appa 2ouuif*b -z(3g6nsayrent 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 same -.jy bq 78ycmu( ietgb2sg8m9 distance from us. Two sjtgbu e8cim29y g-8bm. (7yqsuch 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 ris -th+0/ptu wylh0. madius for a star with mass equal to that (a) of ourw-h0+t/tsyl hp . m0ui Sun is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius foe0(8/vxdndbtqs4 m2u r a typical galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the /io;fvoph akt3m gx71z2/3u3 wocj y7surface of a sphere, for which the sum of the angles is (a) zkf x7u7/1/o y3 hcta 2gjv3o oimw;p3359º, and (b) 180°.

  What is the maximum 0m-rpgt j3fvod7w9+soo2,l xsum-of-the-angles for a triangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0%d yoeqo5ju l7hc wztb *+6.3m- of the speed of light, roughly how far away is it? vmhq.-d3o5u l7wezb ty+6cjo* =    Mly

  The redshift of a galaxy indicates a veloc q8x ip)d 465pdifz1izity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (relative t3 c ycky-k*(j-h b,nrto us) that is near the observable "edge" of the universe, say 12 billion l b(h3tyc*ckk-jr ,-n yight-years away. v =    c

  Estimate the observed wavelength q,)no: q6cxprfor the 656-nm line in the Balmer series of hydrogen in the spectrum of a galaxy whose distance from us inro6)x q :qp,cs
(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 itslm t2+0ikot2p0g wyo ) distance from us, if the wavelength for the hydrogen li0+m 2o0g )i ytwtpkol2ne 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 galaxyyo 33bwaub8s * with $z = 0.60$? v =    c

  What would be the redshift ).hvzfgl8 uirlwj.e :+)0d fvparameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Doppler shift in wavey9 p8jqcp (nib ug/x5g1 dy7k8length is $\Delta\lambda/\lambda \approx v/c$ (Eq. 33-5b) for $v \ll c$. [Hint: use the binomial expansion.]

  Calculate the wavelength at tf3k, x:b- pzswhe peak of the blackbody radiation distribution at 2. xk3 w,-:pzfbs7 K using Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for6k3hewd/v * dat(s a6.7cafxcir(:fp pd+uy* 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 be micpdz cse: (bwmcm()*2 ks-1tween galaxies) at any one moment is believed to have been inversely p1e pwssz cm: cb(i- d(*)ck2mmroportional 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 unisj.* pj5:yw akverse cooled below the threshold temperatu5yjs.wp* kj a:re 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-sequy6 3mrnah29j cence stars could undergo the three changes represented by the three arrows, A, B, and C, in the H-R diagr9caj3y6mh nr2 am 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 about the o,s p ml-ux*fc.3o1b dqpk6o:*ee h l9same as the Sun's. Their apparent brightness, however, is aboe csf .kxod*1 p,o*l :36p9o u-lqbehmut $10^{-11}$ 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 velocitd wve/ (3zs /v5kvbaba+4w4tv y of a neutron star which has collapsed to a diameter of 20 km, from a star whose rsz b bv/wv4vw5av+dkea43 ( /tadius 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 the star in Proble-cbicbu34 u )dm 56 collapu)u- bd4bi cc3ses 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 massrn4va/;rqu i tg3*ez2y 6 brt+ 1.5 times that of the Sun, with diameter 20 km, is observed to have a z/b;+r2gvt ter* 36u4i qra nyrotation 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 Galax+)bqrf.c;e 2;fk :c2z idmvuwy 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 qu2mx ; 4v)gorrest mass (in eV) would provide the critical density to close the universe. Assume the neutrino 24)g;ruox vmq 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 plbh 6r3lh 6h,0b:j5q -o gpesand 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 bs:r5hl0 g6phlj3eb-po,hq6 their diameters. [Hint: see Examples 33-4 and 33-5.] $\dfrac{d_{400}}{d_{600}}$ =   

  Suppose we can measure distances with parallax at 100 parset;/ 5m.z5/h lrq/tnnc3b : p;utqdmuycs. What is our minimum angular resolution (in degrees), based on this inf;:/c hz5nm 5d .qnpy; mrbqt/tutu3/lormation? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidenb(8tdv r4a 0ence, 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 froa 4tnd(b r80vem us? v =    C

  What is the temperature that correspond; d7u2.c nkwaos to 1.8-TeV collisions at the Fermilab collider? To what era in cosmological history does this corrk a. odwun;72cespond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the s:lc7h6k/ )bb8nu qhtrotation of gas around what might be a supermassive black hole of about 2 bu 7b8hcn/)hs6q:tklbillion 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 43g05*d(phsy uv* e/cy. lgy n;x4 nm emitted from the galaxy is measured on Earth to be 650* 5(y v y;0gx. gds*lh/yupnce 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 bri6u7fwrle oa2v( 2jd6 z8+jx3ihj,stellar evolution, a star (if massive enough) will begin fusi6 jdf+aur2 6 8owhiv,j 3(e2 7xlbrzijng 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 dt*+fs.flh9ta db z(8+xh d9j
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 n(32l jxd cb9hits density equaled the critical density of the universeldc9 3xjh2b (n, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$