The Milky Way was once thought to be "murky" or "milky" but is now considered t(s +l g8ogq 44 ts;pay8dx;ewt8utxs,o be madea ds,sue;8tt sltxpgg(x;88wqo44 y + up of point sources. Explain.

A star is in equilibrium when it radiates at its surface all the envl fuz (budb:9)t8x6gg8a*n nergy generated at its core. What happens when it begins to generate more energy than it radiates? Less ene ld*nb 98t8na6zugugfb)x(v:rgy? Explain.

Describe a red giant star. List some of its p;amx 2x4jchdob /l36cmsrv* 9roperties.

Select a point on the H-R diagr, bs0xn+zmg yk543)b*-y;hod .7jml gp edzonam. Mark several directions away from this point. Now describe the changes that would take place in a star movjg+d p.3mzh*nn 7z)mobxb-d e o 04y;s,ygl5 king in each of these directions.

Does the H-R diagram reveal anything about the core of aqpin2l a.d87bhg c3+o star?

Why do some stars end up as white dwarfs, and others as neutron stars or blackmq ds/9t;v fh* holesv; */ts9d hfmq?

  Can we tell, by looking at the population on the H-R d -;sk a 4h7u9dgluuvd+ko4p j(iagram, that hotter main-sequence stars have short pg44s;l -dvuhoj d+ka 7u9(uker lives? Explain.  ----待选择----yesno 

If you were measuring star parallaxes from the Moon instead of Earth, what cojw,x+ox)em+ fm us3 3prrections would you have to make? What changes would occur if you were measuring parallaxe 3, ou xxfmejpw+)3+mss from Mars?

Cepheid variable stars change in lumchna, ,, 8i2 tadwhivv7j/8zh inosity with a typical period of several days. The pei, i2azwd78vt,,hjanhch v /8riod 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 is its role in General Relat(8 bgbcuc.c.9fc od 9pivity?

If it were discovered thatw*ysdmrj pn -y+27kw 4 the redshift of spectral lines of galaxies was due to something other than 2 rsp myw*4y +dwk7jn-expansion, how might our view of the universe change? Would there be conflicting evidence? Discuss.

  All galaxies appear to be moving away from us. Are we therefore a)omb+ tly2w5 xt the center of the univyt2wm5 )lxob+erse? Explain.  ----待选择----yesno 

If you were located in a galaxy near the s, rnc2d82 qt g edm:52x-a(dbs+vvxx boundary of our observable universe, would galaxies in the direction of the Milky Way appb2 ma(gdxx5v qc8tns2,dx svde+-2 r:ear to be approaching you or receding from you? Explain.

Compare an explosion on Earth to the Big Bang.+:vl/bnn 0by) j6d qhgq kc/dwic9.l* Consider such questions as: Would the debris spread at a higher speed for more distant g+0c n9 /dq. ln hb k*d/6yc)bvjw:iqlparticles, 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 from a black hole, then how can we tellm(narq: v6s*t if one is thereasn(m:rqv 6t*?

  What mass will give a Schwarzschild radius equal to that ot66mhbuz;g2+ ;yf,gk-mzjbpc.v li6 f the hydrogen atom in its gr 6fk, ;z6j6p .i+u2lgy;t bc gvm-hmbzound state? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as a. gw :o7dt6szmbout 4 billion years. Find that time on (Fig. Below). People have lived on Earth on the order of a million years. Where is that on (so gd6t z7m.:wFig. Below)?

Explain what the 2.7-K cosmic micr :6 wou.j8cwf-w2a3trr 7qi*b:mw rbyowave background radiation is. Where does it come from? Whyt:2rfboc bwurw6w.qi37:y r*a-wm j8 is its temperature now so low?

Why were atoms, as opposed to bare nuclei, unable to exist until hundre honhx9,j8+ cq n;:au fo;i1z9u(k ybeds of thousands yqnjo+i9u;f1ec hh zu noa8x (,k; b:9of years after the Big Bang?

Under what circumstances wo7c)c:pe zrervxpc, (8uld the universe eventually collapse in on itself?

  Using the definitions of the parsec and the light-year, )udcvfb)t v7t6a3t) ashow that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.38 seuf( 5rqet)mj+ conds of arc. How far away is it? d =    ly

  The parallax angle of a s3k:k h io7:fcaxmegl3p2;e; 9d kd-xqtar is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its pgg1a)a l 4f2l2mi5jd6ky )fpfarallax angle?
State (a) in seconds of arc,$\phi''' \approx $    ($\times 10^{-2}$)''
(b) in degrees. $\approx $(    $\times 10^{-6})^{\circ}$

  What is the parallax bqcdh,p1(oed9ln2 cy - s3j0oangle for 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 the parallw 45t wcqo*yn1b;1oub ax angle bt;5u4ow bw1n*o1ycq of the farther star be greater 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 us? st2 2)jsyo d.r*y02)tql s msl gcw00p   years

  We saw earlier (Chapter 14) that the rate energy reach.qtcd+w x,(s v5e:z ;aook5pyes the Earth from the Sun (the w kp(t q :x,d+va5s5;ecoyz.o"solar 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 6l53d8z-p*-zpcrlaok kb rfuci z 413seen from Jupiter as compared to its brightness from Earth? (Jupiter is 5.2 time l zpzril1zf3ac3ub- d pk5or-8ck 64*s farther from the Sun than the Earth.) $\dfrac{l_{\text{Jupiter}}}{l_{\text{Earth}}}$    $ \times 10^{-2}$

  Estimate the angular wifn3j)x .o7khskk v8hpe ;rh6 4dth that our Galaxy would subtend if observed from the nearest galaxy to us (Table 33-1). Compare to the angular width of thnr fe8k7v4 .jxkk36 h)sph;ohe Moon from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, what will be its average ubds i 55qndbxj t 4*pxbe9i7:++bk3fdensity if it expands out to the 95 +d*3b7ie 5 bj fx:pb+xb dqsitkn4uorbit 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 m3 zjb+1;cbs jthe size of the Moon. What angular width will it subtend from the present distance b1; zb +3sjmcjto Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whose mass is equal to thhwe.w*jfr t s99h .ma:e Sun's and whose radius is equal to the Earth's. How many times larger than Earth's density is thi.:atr 9m w.ews9hjf* hs?
$\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 op7;mw-fjt qy 2f about 11 km. Calculate its average density and compare to that for a whitjtf7 2pq -ywm;e 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 Eqjl/ ve1v9n )r2t0xqs5ugald;gy( j7 w. 33-2. (The mass of the v1xq7js/ju a9yle lg 0;nvrt5w2) dv(gery 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 sam6q*; k2a5xz hjldj)bce 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 same diur kd m1b+.niov(e5.t stance from us. Two such n .i+kmt(.u verob 5d1stars 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 :f/qri 8wz.i)8linzgto that (a) of our Sugfz:qilr/niz i 8.8 )wn is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radqo-r3 wcxq8pyu8p(8: xigc- t /hx9 tgius for a typical galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawnak( zve;2 +4-(pwtowb jci zo+ on the surface of a sphere, for which the sum of the anglesjotew-+w aov2i( bzc+kz4; p ( is (a) 359º, and (b) 180°.

  What is the maximum sum-of-the-angles for a triangle on a sphere.,nqye3rb lyt4 m 7,sx?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the speed of light, f:.gzc6 e;b tjroughly how far away is ic 6ft.:je; bgzt? v =    Mly

  The redshift of a galaxy indicates1ukghr3p 3*t45sj iof 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 observabjz j:d 4k2:zblle "edge" of the universe, sa b2z:j d4:lkzjy 12 billion light-years away. v =    c

  Estimate the observed wz ezosvh :x y-5-3xm2wavelength for the 656-nm line in the Balmer series of hydrogen in the spectrum of a galaxy whose distaezo-m2x s:-3xz hw 5yvnce 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 for i*hsl n d( 8syi*oo3r7cf(6t uthe hydrogen line at 434 nm is measured on Earth as being 610 nm*unsc hdyfli t*6 io8(s3or(7.
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,uw u ;0cde jbbk5 eg4*it;gs6ith $z = 0.60$? v =    c

  What would be the redshift parampwdi:68a9 ovov-2*k c bx sm8geter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Doppler shift v3j 6ur/f8wt h2 4 -boofp7vlnin wavelength is $\Delta\lambda/\lambda \approx v/c$ (Eq. 33-5b) for $v \ll c$. [Hint: use the binomial expansion.]

  Calculate the wavelength at+4 tivn56zvgd4p u9rj the peak of the blackbody radiation distribution at 2.7 K using Wien’s l 6j p9vu4g+tri45z ndvaw. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure o3wv-*.v xgq .ivc)gpaf 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) at any one momp(upz8lidef8: (kzj :owg5 f +ent is believed to have been inversely proportional to the absolute temperature. Estimate 5dw :eop(g+(kf uj:8fzzilp8the 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 thc wu4499o2odumvet6)j b 1zn ue threshold temperatureud 6w4jv 1tco2obe) uzm49 u9n 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-sequence stars could undergo the thrdzsucu)1 16uz ee changes represented by the three arrows, A, B, and C, in the H-R diagram of Fig. 33-28. For each case, describe the changes in temperature usuuzd61 )1cz, luminosity, and size.

  Assume that the nearest stars to us have an absolute luminosity about the q6ay )s*.j4rer,bbxhsame as the Sun's. Their a *raq.bxj4 r6,eb)hsypparent 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 axfq c5cf o081cpfu-1,1 bcjldngular momentum to estimate the angular velocity of a neutron star which has collapsed to a diameter of dcffc01q1fp5,jc club1- o8x 20 km, from a star 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 rot lx8b(y/t )/ irjj.whrational kinetic energy change when the star in Problem 56 collapses to a neutrowr.xi )/jr/j( 8hly tbn star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believed to be a neutron star of mass 1.exh u vn4k;h;y. ux3kl;(fn+l5 times that of the Sun, with diameter 20 km, is observed to have a rotationxnueu l; (;x.;nkh+ hk3yvl f4 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 oew: zue76,gpzlc 6g(y ur 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) wouuk*( 2hykwgv1ld provide the critical density to close (*wvguy k12hkthe 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 peak atgxvr5auzhv-lp n-4 ;5oa 2/on 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 (Fig. Below) to estimate the ratio of their diameters. [Hint: see Examples 33-4 an24o5/r5oh-g u xnvpaz-lvna; d 33-5.] $\dfrac{d_{400}}{d_{600}}$ =   

  Suppose we can measure dis1us:j +p1kocej3*1 gb yjd o, 5oxofh-tances with parallax at 100 parsecs. What is our minimum angular resolution (in degrees), based on this inform1s3pdooj j5*1 kofcgby,h-+xu :o 1jeation? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer line.q/bu o7yraxd ,l9 yn;s 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 f/ ra;q,y dx7buy9o.nlrom us? v =    C

  What is the temperature that corresponds to 1.8w .7;yuw6g *5mo):zic oghwxh -TeV collisions at the Fermilab collider? To what era in cosmological history does thi7 gwi.owgz*6 hm)yuhcw:5 ;xos correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotatio; d1 ) - neqjwinh1yi)rg(p5sqn of gas around what might be a supermassive black hole of about 2 billion solar masses at the center of a galaxy. If the radius from the galactic center to the gas clouds i hq1nsnp(d)i;)rgwi-e5j 1 y qs 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 ln ay6 5l5mn4(tctio .kine at 434 nm emitted from the galaxy is measured on Earth to be taiyn(.o55lt 4mk6cn 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 sjy:h5j zsbi6/dlj3-/j 2z btf tellar evolution, a star (if massive enough) will begin fusing carbon nuclei to form, for example, majybj /ib s l:j5jzfd23/-z6htgnesium:
$^12\text{C} + ^12\text{C} \to ^{24}\text{Mg} + \gamma$.
(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 reactionduke;xo-6ymdwxp9 y ;/x0+cl
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 itsza4b;)9a hjlu density equaled the critical density of the universj u;h9)zb4laa e, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$