The Milky Way was once thought to s o9dl1346k wefu2 mcpbe "murky" or "milky" but is now considered to be made up 6sm19 lpefw2d3ok4cu of point sources. Explain.

A star is in equilibrium when it raexcdw.u/ ,lpe ): i*fwx zbd17mg)kb:8kl s(qdiates at its surface all the energy generated at its core. What happens when it begins to generate more energy than it radia*bx) m pl7w .debi)k8 :fgdq se:u, 1lcwx(zk/tes? Less energy? Explain.

Describe a red giant star. List some of its properti+y+ge8q* qe t++ex6n skq/bg des.

Select a point on the H-R diagram. Mark several directions away fd3 l+ee w/v t6:cc8mdvfmbik 5mamx+5;m+ tb0 rom this point. Now describe the changes that would take place in a stv+:fmm5iattcm bek w mb6 em8d+53v;xdc /l0+ar moving in each of these directions.

Does the H-R diagram reveal anything about the core of a sx,tx tk+a7/iiyg7u :utar?

Why do some stars end up as.j(3;h hy8f hwavhrh ; white dwarfs, and others as neutron stars or black hor y3;w h8vh.; j(ahfhhles?

  Can we tell, by looking at the population on the H-R diagram, that hotter ma-bkfig(y8 r,win-sequence stars have shorter lives? gk(w ,i y8frb-Explain.  ----待选择----yesno 

If you were measuring stahh755g caiqw8qq dwh*w) ;k6x r parallaxes from the Moon instead of Earth, what corrections would you have to make? What changes would occur if you were meaida;g hh5w x7 )8q*65 hkqwwqcsuring parallaxes from Mars?

Cepheid variable stars change in luminosity with a typia9 (w,e,refm ical period of several days. The period has been found to have a definite relationship with the absolute luminosity of the star. How could these stars be used to measu,ae,w(erif 9mre the distance to galaxies?

What is a geodesic? What is its role in General Relativit4; *+gxo ovqnr0 w:aptv4r.wry?

If it were discovered that the redshift of spectral lines of galavk,t it* d:b o8uy7r2gxies was due to something other than expansion, how might our view of the universe c t bi,*y8t7o:grvdu2khange? Would there be conflicting evidence? Discuss.

  All galaxies appear to be moving away from us. Are we therefore at the c9e;v4 g -ytrx4q- yczdenter of the universe? Expr 4-9qd-zvc4gt;yy xelain.  ----待选择----yesno 

If you were located in a galaxy near the boundary of our observable universe, wo2mb-xa+n ef yc1v) p*9 *b xv7j.rgfqculd galaxies in the direction of t *xf.+cp v bn)- 9x12bv7*rqajcm gfeyhe Milky Way appear to be approaching you or receding from you? Explain.

Compare an explosion on gr.nq9ud/ b(2 a8lp xdEarth 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 would thxd9qlp. (adr8/gnb2uis correspond to, open or closed?

If nothing, not even light, escapes from a black hole, then how cqp h(9m 8cwb;xan we tell if one isbm; hp9xw(qc8 there?

  What mass will give a Schwarzschild rm:h/y ;q2mw5 k.r8r geg7nfaiadius equal to that of the hydrogen atom in gnrkf.wai7mqh 5m:;r2 / e 8gyits ground state? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion years. Find that time on (F*f;n,ud n;e hqig. Below).;dq*fnnuh; e, People have lived on Earth on the order of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic microwave background radiation is. Wherigc*n65b 5pj-nrtd 6 de does it come5 rg5n6itp*jn c-6db d from? Why is its temperature now so low?

Why were atoms, as opposed to bare nuclei, unable to ex(to: p bw*i2hqd j),zoist until hundreds of thousands of years after the Bibi*qp (jd2 ow,o hzt:)g Bang?

Under what circumstanc *v az 2ohl7+ef c0shpqlxmfn52w8r 0/es would the universe eventually collapse in on itself?

  Using the definitions of thu obo: fbm(,z1e parsec and the light-year, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.38 secg*ao8 hbbs0+londs of arc. How far away is it? d =    ly

  The parallax angle of qn4*:eu,ggrm jny;)za star is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its paraled*2e m*/fvb eh3q/+4zdaz.efz 3u vc .agdj4lax 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 thatmslwhe j,qj)ckdpz :3,m- s5 , is 55 ly away? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away fc.bt1j -dizattg 7f4r16 5lrvrom us as a second star, will the parallax angle of the ad i6g1zr bf17l5tv.ctrt -4jfarther star be greater or less than that of the nearer star? By what factor?

  A star is 35 pc away. How long doesi8 wacrg,ko*0 it take for its light to reach us?    years

  We saw earlier (Chapter 14) that the xqh92 ck+if/.8h dqwe rate energy reaches the Earth from the Sun (the "solar constant") is abo+wq8e. k h/ch9qfdxi2 ut $1.3 \times 10^3\ \text{W/m}^2$. 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 comparb) 5qg t/,dwxied to its brightness from Earth? (Jupiter q) gxt5,dbiw/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 Galauvc; 5a ouo51mxy would subtend if observed from the nearest galaxy to us (Table 33-1). Comparm 1uc5ovo;a5 ue 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, yehkk05(qpt:;q w bj average density if it expands out to the orbit ofh5kwt ,(p k0:qy ejqb; 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 ,dn1c .g.ah:-vyqhpp about the size of the Moon. What angular width wnp:yp, .qg.1avh-dh cill it subtend from the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whose mass is e6 51m carqyf-dqual to the Sun's and whose radius is equal to t5r qf-yd6c1m ahe 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 a880xz rd4*rmxxtysi , radius of about 11 km. Calculate its average d48m 8x0xxd rrts, y*izensity 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 t - kf.em5 yexj7y t.5*ig,lf pm;v5jenhe He burning reactions of Eq. 33-2. (The mass of the very unjm lp.ejg y5x7-ffe 55eykvt.im;, *n stable $^8\text{Be}$ 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)l poek 8-6 : ; 9asovl4adxu lw9ndov+fku+0a 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 assumtyo7hg32 u;l 7t 5rkqqed to be about the same distance from us. Two such stars have spectra that peak at ktr52uyl oq3h;7 7gqt $\lambda_1 = 500\ \text{nm}$ 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 wit-7;m/ l 0ji. ztvviarzh mass equal to that (a) of our Sun is-zvl/ja i;tz7m 0 r.vi    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typical galaxy (like ours)? Rkpj2me vh ax( yv -c:p,d.7i,w =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a sphc fc79iwe.e5f)r ruc 1 )l:xpjere, for which the sum of the angles is (a) 35crrwc7lucp 5 fj.fix:9)ee1 )9º, and (b) 180°.

  What is the maximum sum-of-the-angles for a tri2:ny lf hck0o+angle on a sphere?    $^\circ$

  If a galaxy is traveling away,fojr8es* q a3,hdz*/ratay j-65eys from us at 1.0% of the speed of light, roughly how fa3s yyz*t ead as,8*,h jrf-a5 qo/j6err away is it? v =    Mly

  The redshift of a gala5lc )cksev,1 ixy indicates a velocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (relative to 7v e-igrw(s (+mp3tp+ udfi*l us) that is near the observable "edge" of the universe, say t*(d++ igsm7 (e pwi-3flvpru12 billion light-years away. v =    c

  Estimate the observed wavelength for the 656-nm lineb5t1s ; on3cqvb:8q fb in the Balmer series of hydrogen in the spectrum of a galaxy whose distance ftnbsvf;q q:b b8c15 3orom 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 distan e9zf i1j0edjdpusr5u oj28 (+ce from us, if the wavelength for the hydrogen line at 434 nm is measured on Earth as being 6102f9uj 8zd1d 05sei j rjuop+(e 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 galaxf +y:m;1uy knyy with $z = 0.60$? v =    c

  What would be the redshift parameter apfo;r7 0z s,p$z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Doppler shift in wavelengty uyxs)y3q) dkfd fh/-*k ih91h 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 thzp0xrc ;jiv80b4 - +7eulcq she blackbody radiation distribution at r8c s -b;i0e+7h0l quzxjpc4v2.7 K using Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density folmn 4n;n(*2pec0 1fpmrcpw ek 3o;jf+r 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+ wk3l1yk bd0ei a8cl u:/awi,) at any one moment is believed to have been inversely proportional to the absolute temperature. E/ky:ce8 +wdi ,l 13ilkbu0aaw stimate 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 univeijdf)k:nnw i(o7s2;7 a( tqbhjz 69 awrse cooled below the threshold temperature for produz( wbk7h o2(n:79fdw)iij 6an;jqs atcing
(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 repre; ( ag33dftl oh.jqppg/e,7 yusented by the three arroge(,ja 7tu3 p.ly/3;phq gofdws, 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 nearjgsu.i6ni r q;n:p*u8vr u2/q est stars to us have an absolute luminosity about the same as the Sun's. Their apparent brightneuv *8 sn6jiur;q2up .r:qign/ss, 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 fwolg/qx j9*n ulg 45:-h+a4jg+nkxs a neutron star which has collapsed to a diameter of 20 km, from a star whose radius was equal to tha gxh:*+9sjln5/fagu l4j-4k xw +q gont 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 iqg-bapl3v: 0bm ;c) mcn Problem 56 collapses to a neutrlv)q :m;c-c0pbb ag3mon star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, beli 1z se;( mh;szvc7c6sexfj +5ueved to be a neutron star of mass 1.5 times that of the Sun, with diameter 20 + z5f1ees;s hcc(z6j;7v xmu skm, 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 to our Galaxy is about fvy i s3oz 17q-1poca3arckx:m+)u k +$2 \times 10^6\ \text{ly}$ 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 massrof3z)v v)a .dsfi)u;s z)lx9 (in eV) would provide the critical density to close the univer )3vs ;fr)) saiodv) lfxz9zu.se. 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 spe4w64rj89qnr* iq y /kal uh3vlctra peak 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 diagramlwn/v* q9hrrluj 34aqy 8 i64k (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 paralla4y+o, sf0s(c9bg ljiry8 of8dx at 100 parsecs. What is our minimum angular resolution (in degrees), based on this information?yy dsf0cfrjl o8i94,(og8sb+ $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, thqc4qnx 4t7 uu s:plu1z:2 el8xe Balmer lines from singly ionized helium in a distant star happeu 7tlupuq nc zx2x4l:e4s1q:8n to overlap with the Balmer lines from hydrogen (Fig. 27-22) in the Sun. How fast is the star receding from us? v =    C

  What is the temperature that corresponds to 1.8-TeV collisions at the Fermi4w,nl ,nn-z6w l6 sfcwkv, *ellab collider? To what era in cosmological history does this correspond? [Hintk,-vf6,w ll4nclw n,ns 6ew z*: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently me(vpz3/ rdz(g aasured the rotation of gas around what might be a supermassive black hole of about 2 billion solar masses at the center of a galaxy. If the dr( z/ z(p3vagradius 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 "bml3 a7cx0w-jzc) / f g2;fdtzhlue" hydrogen line at 434 nm emitted from the galaxy is measured g/ lxh zcd3 m)jafw; 27tz0f-con 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 ste5k-awuiengv; -iu6 5 nllar evolution, a star (if massive enough) will begin fusing carbon nuclei to form, for example, k 5 g56wv;--ui ieuannmagnesium:
$^12\text{C} + ^12\text{C} \to ^{24}\text{Mg} + \gamma$.
(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 n8:ibm4 v:gb9jn v7k b
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 : 4n c- dm)ugh9ly tpo5-n5vigits density equaled the critical density of the univ gp59 hcovi:yg 5n-u4mn)l-dterse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$