The Milky Way was once thought to be "murky" or 7newrr.do ;iqc *h5bd5k74nn "milky" but is now considered to be made up ofnh577i;n. n rb k4owecdqdr *5 point sources. Explain.

A star is in equilibrium when it radiates at its surface jd sl4s*v,r9fgdy(5ezul4 - j,g acv 1all the energy generatee5dydr9zj1, *4vjlv fc,as gs4g ul- (d at its core. What happens when it begins to generate more energy than it radiates? Less energy? Explain.

Describe a red giant std*5tq( ncu-flfc9e :x ar. List some of its properties.

Select a point on the H-R diagram. Mark several directions away frj 1;8 os,zf* jniyk5nrom this point. Now describe the changes that would take place in in* j s8n1,fk5yjzro; a star moving in each of these directions.

Does the H-R diagram ,kutah :el2+nnp xy+7reveal anything about the core of a star?

Why do some stars end up as white dwarfs, and others as neutron stars4 5 m-sgfo5y ansq e+dx -j9ed3al4n(f or black hol m(jsa+ed9 -g fnesy4qd3-lax nof54 5es?

  Can we tell, by looking at the population on theo rap7zs-w*ipsar 43dr g8*d),te)cd H-R diagram, that hotter main-sequence )d3ride)ca wdp 4s*azr-s 78gt ,p*orstars have shorter lives? Explain.  ----待选择----yesno 

If you were measuring star parallaxes from the M3bcl-jcma ;i zzt+v*,oon instead of Earth, what corrections wouldac lzzvbm; - t*+cj,3i you have to make? What changes would occur if you were measuring parallaxes from Mars?

Cepheid variable stars change in luminosity with a typj+jw7nlr4fb *q8(v kj ical period of several days. The period has been found to have a definite relationship with the absolute luminosity of k 84qn+*l jbr7vjjf w(the star. How could these stars be used to measure the distance to galaxies?

What is a geodesic? What is its role in General Relativity?glzf+ 04ffp/ c,vejh 4

If it were discovered thcctcx4x7 5,vp -or,caat 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 conflic7,4pcx-crtc,oacx 5 vting evidence? Discuss.

  All galaxies appear to be moving away from us. Are we therefor icqbllrdaz930+ a-8ce at the center of the univ8 bl-a ai+09 qczldr3cerse? Explain.  ----待选择----yesno 

If you were located in a galaxy near th5b 6n1b j(4dd-uyxxj xs (q8kve boundary of our observable universe, would galaxies in the direction of the Milky Way appear to be approaching you orb j-dxxu(xnyk6 (q 845ds1b jv receding from you? Explain.

Compare an explosion on Eara1lxxwes6980r 1 zt1q lr9eot+5ca zcth to the Big Bang. Consider such questions as: Would the debris spread at a higher speed for more distant particles1z9s+9l15 l 0wezx1orqre txca t86ac, 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 fr(9pvgygem 38do /tpg (om a black hole, then how can we tell if one is t9tyd/3pg (ggvem8( pohere?

  What mass will give a Schwarzschild radius equalqbfmzs5f k-2 2x eyh:t9/rg6 m to that of the hydrogen atom in its ground state? M = s:h2kmtzm2rbfey 6 9x g5/ fq-   $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion years. Finh*7 vlm*i t3t fcw9fqrpp:97j d that time on (Fig. Below). People have lived on Earth on the o* rfi vp7*9cj:lp 37f9mq htwtrder of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic microwave background radiat: 2c0jw kja,9iuaqz m.ion is. Where does it come from? Why ikj,.2 :0 aijwzc9 mauqs its temperature now so low?

Why were atoms, as opposed to bare nuclei, unable to exist until hew0moh f*vkyn:ok1 b:0s 8r.aundreds of thousands of years after the Big Ba*0o r.nyf:whkakvob8 e: sm0 1ng?

Under what circumstances would thju0b(ti w;mzbd5 y/ tss+ 69gde universe eventually collapse in on itself?

  Using the definitions of the parsec and the light-yy 5a p3i(mq)lv6jen8 yy5h +dgear, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.38 seconds of arc. How far away is upmy+frc:j.0av )6 mtit? d =    ly

  The parallax angle of a star is9xp wxi 6 +dh3 26jq5yrrml1vy $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its parallax a f b fgxwsis,u.76bdh91y o73ungle?
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 staaspot,-4 dme4 sf4o*ur 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 the parallaxy5,s5c5;oyce :gna dn7 jis9d angle of the farther star be greater or less than that of the nearer star? By what factadi 75sy5 djn s,9 ncyco;g5:eor?

  A star is 35 pc away. How long does it take for its light to rioo;bla;+ uw8i*+kod each us?    years

  We saw earlier (Chapter 14) that the rate energy reaches the Earth from them7s.w uor22 jq Sun (the "solar constant") is q2wjr72o m .suabout $1.3 \times 10^3\ \text{W/m}^2$. 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 sz0qce95w8g+yffo+s n :z;7eue *uc xas seen from Jupiter as compared to its brightness from Earth? (Jupiter is 5.2 times farther froge sfe +zfuc+7xyq8;s : c0z*n5ou9wem the Sun than the Earth.) $\dfrac{l_{\text{Jupiter}}}{l_{\text{Earth}}}$    $ \times 10^{-2}$

  Estimate the angular width that our Galaxy would subtend if observed f+awqqw si)b;8 rom the nearest galaxy to us (Table 33-1). Compare to the angular width of the Moon;8wqqsiw)a b+ from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a xwa vh;o4z,w2red giant, what will be its average density if it expands out to the orbit ofw2; 4h,vowaxz 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 k/f kg6y/dq8w is expected to be about the size of the Moon. What angular width will/ q8/dgkywk 6f it subtend from the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of aw45xbd5s(h .9c mbg xmp,pgk6 white dwarf whose mass is equal to the Sun's and whose radius is equal to th4 gk(c5pdbm. bs59x6wgpmxh, e Earth's. How 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 has a radius of about 11 kwkd64vp)*zf9j4jnl.uf g4d w m. Calculate its avfjg .dnjp zfvu64w kd)w 4l9*4erage 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. (The mas+:fmf m *k* e*s1rvhqls of the mrv :1h se**+*lqmkffvery 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 the6ty+ tq(jm )fc same 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 k/4w*k ujxk b5be about the same distance from us. Two such 5b/ k*jwkx u4kstars 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,tmep 0h j,*5og 9rh/ +axiakf) of our S, hfam*k0tgh+/j 95ia px,e roun is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typick 6z;8y) k b8gslm6obuy wq0.tal galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a g)t+s.4eqrds sphere, for which the sum of the angles is (at)+4qd.e rsgs ) 359º, and (b) 180°.

  What is the maximum sum-of-the-angles for a triangy69g4f wus2rb le on a sphere?    $^\circ$

  If a galaxy is traveling away from us athf 9n g.*miy(q9qadb:i5cf4 k 1.0% of the speed of light, roughly how far awnag f99iyi(hqmb5.:* kqf4cday is it? v =    Mly

  The redshift of a galaxy indicates-td -/s,zcke z2 i2awh 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 the observable "gd/4/4m5 uj a2w g0n sgtyvn*zedge" of the u/ *zgd 0ygwtn54 sgm/42jnvau niverse, say 12 billion light-years away. v =    c

  Estimate the observed wavs;f psdd*6g d;elength for the 656-nm line in the Balmer series of hydrogen g sdds;fd*; 6pin the spectrum 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 ce 3lpa3xm 5 oxtu.30afrom us, if the wavelength for the hy30xupamco l.a5te33 xdrogen line 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 w mq;ko/o9qy m,ith $z = 0.60$? v =    c

  What would be the redshift parameter3kfm7s,:au7e zw,a o l $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3,3yx( 0 j . gwb2pkyxmv2sc+nt7 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 blx0mo )vc23 bfoc gqh+/ackbody radiation distribution at 2.7 K usi/c+ vcq0o xobg f32h)mng Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closurerasdyv(;:8q.d d )*lw.vuj wv 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 qd)sl+8fbs qkc . )bt:distance between galaxies) at any one moment is believed to have been inversely proportiodtb s)+:q.lsb ) f8kqcnal 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 universe cooled below the thresholg(l /or:6j1fmv/dc,p ti-l x-(ty ghed temperature fo-ft ,6t1xg/jl:lopcg ri /vy h(d(e-m r 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 f9mmre;a*z: m 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, describemem z*r9f:;a m the changes in temperature, luminosity, and size.

  Assume that the nearest stars to us hg h*v :scwcs4kx7um5n 5f) ,eaave an absolute luminosity about the same as the Sun's. Thgea:7kh4 s cwc)m*fvu5ns5x ,eir 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 estimate the angular velocity of d;)mr lt*35dnp zy/iaa neutron star which has collapsed to a diameter of 20 km, from a star amy) rp /dd5zi;*t3ln 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 the star in Probl hyum,-e+2n) ,pwgt zxem 56 col2 eynwpgz), +-xt,u mhlapses to a neutron star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believed to be a neutron stawbs::8q t1rnm1ahd. qr of mass 1.5 times that of the Sun, with diameter 20 km, is observed to have a rowa:18 1d.r: b tqhqmnstation 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 Gyl4b csurqg8l6bu/*/(0 p hl: rw:qpx alaxy 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 (x0ml .v9wvx)ojvy(g ,z 6dr7yin eV) would provide the critical density to clos,y g7 dxr9(zv. ylm0)6jvvwoxe the universe. 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 pe(r.29cr i jc0qba5g paak at 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 (Fb9j i(a .0qc2rrap5gcig. 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 pare1g7w 2-)gxk hikp ;5(nca nlzsecs. What is our minimum (17al5pegn nx2 ki zhw; gck-)angular resolution (in degrees), based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from singly ionized he q43-;v yjzxbalium 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 = zx4 bvj3a;-yq   C

  What is the temperature that corresponds to 1.8-TeV collisions at th4 3,bvxg9psbf si62x ue Fermilab collider? To what era in cosmological histo4v3spxu6b bxs9i,2g f ry does this correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently meagm.wn ; ice n9elhy te)e;8v;b:f6 ;rusured the rotation of gas around what might be a supermassive black hole of about 2 billion solar masses at the cenhue:n6reif).;c y8 bl; tgvewen9m;; ter 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 Eartmuxq) p-p (eda.jm6gp jz9 g0 wib28m8h. The "blue" hydrogen line at 434 nm emitted from the galaxy is measured on Earth t mx60 apm (j 8wjg -8gp2qud9)ezm.pbio 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 p cwe9017wsw4* +yamfftgx;i ) will begin fusing carbon nuclei to9+ w ag x7tc1wfy4wi*emf0; ps 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 reaction5 mna2hoje.0 a
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 cr ,zt chs94fg2gitical density of the universg 42zghs,9t fce, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$