The Milky Way was once thought to b1h60cf l;ylrii3 2hfcx .1hpde "murky" or "milky" but is now considered to be made p. y6 lf2h fc1clrh1;xh3iid0up of point sources. Explain.

A star is in equilibriglok1gu *n b2.um when it radiates at its surface all the energy generated at its core. What happenn.*kb2ug1l gos when it begins to generate more energy than it radiates? Less energy? Explain.

Describe a red giant star. Lx /z/u0d tiavguaqgj3tp 7 +))ist some of its properties.

Select a point on the H-R diagqpx*lt b9 ,+ pqoaf9m2ram. Mark several directions away from this point. Now describe the changes that woqlxmb a2op* +p,9q9 ftuld take place in a star moving in each of these directions.

Does the H-R diagram reveal anything about the core of a sta/lkssn 26 se,daq 4k6yr?

Why do some stars end up as white dwarfs, and oth vce4qb;a04 cmh84-smgn rgxm nyts/ok- 4.w1ers as neutron stars or black holes?4mmom ; ny 4/kxcng1e-svr 0 ah4q-b4g .t8wsc

  Can we tell, by looking at tyut7 m/ 7fbsn)sbz )h.he population on the H-R diagram, that hotter main-sequence stars have short 7 zh7nu)byb/mf)sts. er lives? Explain.  ----待选择----yesno 

If you were measuring star parallaxes from the Moon instead of Earth, wha jbf4cuhpzvh*) ,jwo 9bjs9 3sp77 .mdt corrections would you djuvw )fz9b9*h sp, comps347 jj7bh.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 stv8 n/fw vb dmnz4(// xwi;k(feveral days. The period has been found to have axdmkfitvb/8 //wnz;(4(n fvw 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 rolm;i-a ,cyd(be e in General Relativity?

If it were discovered that the redshift of spectral lines of galaxies waszla4e: tj91ky.l3po 91vban x due to something other than expansion, how might our view of the universe change? Would there be cxb joa4z3n1l:9e kt ayl91p. vonflicting evidence? Discuss.

  All galaxies appear to be moving away from us. Are-9e e6nq4udv,h ;xfa 8ohdid: ( bkhg3 we therefore at the center of the unive :(8 hvba4hufdk;-dn 6oexqd93 h,gierse? Explain.  ----待选择----yesno 

If you were located in a galaxy near thezvc* x eqn*k8dm-i dm kl2f0;sbdr 7)- boundary of our observable universe, would galaxies in the direction of the Milky Way *ekfrvk 0zn2)8xb7 -*;lic s d dm-mdqappear to be approaching you or receding from you? Explain.

Compare an explosion on Earth top lxt)lpil/uz(lq ;7- the Big Bang. Consider such questions as: Would the debris spread at a higher speed for more distant particlest/ p)zql-l piull;7( x, 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 tehd3h 0ha/k:ohg8 z: eull if one is t ha /zu oh:deh3gk08h:here?

  What mass will give a Schwarzschild radius equal j)i jce jrn2o-evh3).to that of the hydrogen atom in its ground statjnier3j)v -o ejc.)h2 e? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion years. Find that time on1 lc j9ir57jhi (Fig. Below). People 7l 9i i5jhrcj1have lived on Earth on the order of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K c--s6 r8zp l*(inhqdwmosmic microwave background radiation is. Where does it come*-8zwhpslq-r d (nmi6 from? Why is its temperature now so low?

Why were atoms, as opposed to bare nuclei, unabc0rfq2,8mi2 z7hcng d le to exist until hundreds of thousandsiq7h 2c,cf m0zgr8 nd2 of years after the Big Bang?

Under what circumstances would the universe eventually collajq t 5ka:n7v0ppse in on itself?

  Using the definitions of the parsec and the light-1cwl/ k s38ghxvaw), f4 z8ponyear, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parp 3 l1bov5zu-xayhs+9allax of 0.38 seconds of arc. How far away is it? d =    ly

  The parallax angle of a0k*b :qla(o 9urzkh smj58u3j star is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its parallaolk7 )x 4bw.d;cqa1v jx 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 that is 55 ly away? zpmmcg:/-5v5g9jspp $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away from us as a second star,3 7h(;hbk4 /da xbyzag will the parallax angle of the farther star be greatery7axzh;3gh/ab 4( kbd or less than that of the nearer star? By what factor?

  A star is 35 pc away. How long *mhy7o dyt .; s(g6t,df9tpm8gdi m:idoes it take for its light to reach us?    years

  We saw earlier (Chapter 14) that the rate energy reaches theuqcm/t k av3 .v518gdh Earth from the Sun (the "solar consga5hvc u18 t.k qdmv/3tant") 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 brightnesb/dta)za a +(o+rm*hks of the Sun as seen from Jupiter as compared to its brightness from Earth? (Jupiter is 5.2 times farth(tad hamz+rk/+bao* )er from the Sun than the Earth.) $\dfrac{l_{\text{Jupiter}}}{l_{\text{Earth}}}$    $ \times 10^{-2}$

  Estimate the angular width that our Galaxy would subtk 29 tcw rg-3q8a,uczf5u6wvdm ush9;end if observed from the nearest galaxy to us (Table 33-1). Compare to -vd ftuzkw 9us ;qgcwu5r68amh2 c39,the angular width of the Moon from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, what will ba umu:5vq8xph 7v 8vf5e its average density if it expands out to the orbit of Eartvm a8vf8:5hxuu7 v5 pqh ($1.5 \times 10^{11}\ \text{m}$ 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 tiepzkuz ;yl 8,o qoa)8 1wk94fhe Moon. What angular width will it subtend ff,az 4o;kpeoqzi w89)luk81 y rom the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white d l.qywx4e5n wo43xsz8 warf whose mass is equal to the Sun's and whose radius is equal to the Earth's. How many times l 8w yxs xlne44owz.53qarger 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 whosexg3fn5 g , :tqj*t(cgy mass is 1.5 solar masses has a radius of about 11 km. Calculate its average denfg, 3xgc(: gtqt*5jynsity 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 n qvoyc,v1a77 dh4yllhi-3+yHe burning reactions of Eq. 33-2. (The mass of the venv 3yi771 hqdl+yh,- ycav4 olry 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 b*v m/1h5tl:p.awsm:v)jvoivb ; 25 zr jz6gtrrightness $l$ 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 b 5ftijvp-n;dxejb0.77q l/jbe about the same distance from us. Two s;j/ bfe-bdj0qpx tln. v7ij75uch 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 radius for a star with mass equal to thamg(6f/gyu 9svh,ke mf:(h2ks1 o7 a xkt (a) of our Suamu (h6xo 71fv mgs,y9/(2kefk: k shgn is    km, and (b) of Earth is    mm.

  What is the Schwarzschild;+e; tfk1fwpl radius for a typical galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a sphere, for which the sum of -8(utgzx ,/, vij e8eo-v+6hf / j1wydzcbidkthe anf zw/txz,by6, kdje-icvvei (ho -18uj+ /g8dgles is (a) 359º, and (b) 180°.

  What is the maximum sum-of-the-anglex6+ldz mhja5acp o0 6/s for a triangle on a sphere?    $^\circ$

  If a galaxy is traveling awak( -f9b:(cjghykxt2 :g1x pj ty from us at 1.0% of the speed of light, roughly how far away is it? v(cx bjtjk: 1pk2t-f ygg( h9:x =    Mly

  The redshift of a galaxy g)l*s(3xw t: kfedul* indicates 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 obsez1jksn +;gsl d9t-est; - z;pmrvable "edge" of the universe, say 12 billion light-years away. g9;t 1s;k-jd;z s+eslm-ntpzv =    c

  Estimate the observed wbrjiq87xn2 g,avelength for the 656-nm line in the Balmer series of hydrogen innb 8i7q,2rjxg 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 from us, if the ke i.n;.tw6m(a je,jv wavelength for the w e. v(e,i .6mjjtank;hydrogen 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 ofjfk.ai zaf7y2 3r7*xa97cv am a galaxy with $z = 0.60$? v =    c

  What would be the redshift parameakjl6s.gnj3tls r zj6z3r 8tvj -(1+fter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33- 9peono;ag2j1uwr:9j5nu k/m 3, 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 blackbody radiatsk /a+ /ymq5hcion distribution at 2.7 K using /+ h5qmcys/kaWien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closur l -a9ap9nd(ebdkvt7q( pr(k3 e 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 gab-f mcs gua-))laxies) at any one moment is believed to have been inversely proportional to the absolute temperature. Estimate the size of the universe,-a)mu s-)c fgb 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 cefp7 91-yn i;l8t /mauhwe.zthreshold temperature f8tflcp7z1n myhau9e ie w; /-.or 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 c ;aouf5uz 0cyp9py 4p*hanges represented by the three arrows, A, B, and C, in the H-R diagram of Fig. 33-28. For each case, describe9pc y5u*a0uz yp pof4; the changes in temperature, luminosity, and size.

  Assume that the nearest stars to us havee +gb i04ijmr1 mxq,q4uq 8w:z an absolute luminosity about the same as the Sun's. Their apparent brighq:im8m41u+,4qxwi qbjeg rz0 tness, 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 angula6 ter urd-dzm.x35l* er momentum to estimate the angular velocity of a neutrdeulme- xr 3*.rdt5 z6on star which has collapsed to a diameter of 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 rotational kinetic energy change wc: yy+gr tcju ) c; 6z-y6hzvbi8q7;pbhen the star in Problem 56 i-zcu+ bctp j;by7v6 cz;y:8qhr )gy6collapses to a neutron star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believed to be auq2, ut)ir 7nn neutron star of mass 1.5 times that of the Sun, with diameter 20 km, is n2n)tuqui 7 r,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 a 7pum7yoi- jde8 du1w4bout $2 \times 10^6\ \text{ly}$ 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 v 3 -0sssxvc0l9,lxbw ke(3f3 gjao:vrest mass (in eV) would provide the critical density to close the universe. Assume the neutria0og scl9-:0s lew,x js3f k3(3xb vvvno 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 spe*fozd4ew- d n0c vavr3v8;qwxmw-s *+ctra 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 diagram (Fig. Below) to estimate8x*wrv3w wvd ;o*cfn+zq 0vd 4esa--m the ratio of their diameters. [Hint: see Examples 33-4 and 33-5.] $\dfrac{d_{400}}{d_{600}}$ =   

  Suppose we can measure distances with pt vlrg 1.+6ml ifl mnwpz(m7,6arallax at 100 parsecs. What is our minimum angular resolution (in degrees), based on this information? lzi6,mg(p +n .vlmmltw r76 f1 $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from sinmge 9 .hqk:v x2e5:kh,yjqw ,cgly 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? vw9 ,h5kk:q j ch.meyev: qxg,2 =    C

  What is the temperatuyi5oih+ o 5p8ure that corresponds to 1.8-TeV collisions at the Fermilab collider? To what era in cosmological history does this correspond? [Hint: see (8uih5 y+ 5oopiFig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recentla4xi;o*lns,1 c/ lniv-u- itgy measured 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 li--1n co*gnlia/,isxu 4;tvthe 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" hydrogetfn14 m ug09qwn line at 434 nm emitted from the galaxy is mn1tfu0g9w q4 measured 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 evolutioq,y3l74yqwqqa,uc j )n, a star (if massive enough) will begin fusing ca3 wcqaqq ,,ljqu y4)y7rbon 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 w2z.,k9 9 j uwfkdm dmafv61m+
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 criyxinxv8o 1-d 9tical density of the unixx- i81onv9y dverse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$