The Milky Way was once thought to be "murkyx c 0km+p;jmwpxmr3+9 " or "milky" but is now considered to be made up of point sources. Expla+;m 0cw9rxkmpx+3j mpin.

A star is in equilibrium when it radiates at its surf;i.8:n gwvth 3i tvke)ace all the energy generated at its core. Whe h ntviwtk:.;v)8g 3iat happens when it begins to generate more energy than it radiates? Less energy? Explain.

Describe a red giant star. List some of i* -mfcnmhtf md-9z+1mts properties.

Select a point on the H-R diagrz b709 sf5kkrp,v i9ycam. Mark several directions away from this point.k7z0rkpvc5 b ,iysf99 Now describe the changes that would take place in a star moving in each of these directions.

Does the H-R diagram reveal anything about the corwx4l /p0qo7nj ey wc7 qpsw;89e of a star?

Why do some stars end up as white dwarfs, and others as neutron stars o d4i;hobp j;x+r black holes+;4hdjp ;ixb o?

  Can we tell, by looking at the popu, z:m ku4(* er-zy(t htsffvb,lation on the H-R diagram, that hotter main-sequence stars havekz sb,vyrufmh t,4tef *((z:- shorter lives? Explain.  ----待选择----yesno 

If you were measuring star parallaxes from the Moon instead of Earth, w* ex-cu.kt+iihat corrections would you have to make? What changes would occur if you were measuring pari.xce+ it *uk-allaxes from Mars?

Cepheid variable stars change in luminosity with a typical pe+u +*qi t;kr5zqh vo2d;/tn o8f x.rnjriod of several days. The period has been found to have a definite relation;5qhrf tu/ d i+ko .tqx;v8z n+onr2j*ship 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 Rej+b7 ej -px wuq2rew::lativity?

If it were discovered thagc m/h(7b7 cxpt the redshift of spectral lines of galaxies was due to something other than 7 p7hmg/c( bxcexpansion, 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 a1cdd3i)u0 1+ y- .nfe tzdktbht the center of theh1+1eu .dkfdyt0- tnc zb)id 3 universe? Explain.  ----待选择----yesno 

If you were located in a galaxy near t3hrry5 o 8nxq2he boundary of our observable universe, would galaxies in the direction of the Milky Way appear to be approaching 5 r283yrnqxoh you or receding from you? Explain.

Compare an explosion on Earth to the Big Bang. Con4h0pde5t -d)bfqm*bgsider such questions as: Would the debris spread ab5ptq)d- ge 4fb 0h*mdt a 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, escapes from a black hole, t7gx, meyazvc .gy a;1xqd+-e+hen how can we tell if one is th a-c,yy dmg .+e gx17q+;zvxeaere?

  What mass will give a Schwarzschild radius equal-y4.d+1 k3b5lm xvhb bbe 1kkx to that of the hydrogen atom in its ground state?bxbkkkbh d4.+ 3y xe 11bl-m5v M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion yh h(yfeq. kt5t1b v41 hd6ib+nears. Find that time on (Fig. Below). People have lived on b6.be4hktf dy+n h11it 5qvh(Earth on the order of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic 7kmuo;, gp8xhmicrowave background radiation is. Where does it come from? k g8, phxmu;7oWhy is its temperature now so low?

Why were atoms, as oppmmca aq.oi6da9g 2a( pl( f: cw7c/7wfosed to bare nuclei, unable to exist until hundreds of thousands of ye :a(mcfdglo w/cwfam7 aqp2a c6.9i(7ars after the Big Bang?

Under what circumstances would the universe eventually collapse 8bh s)539g .fmr 3z3a qacj15.b i7tzkjvnkpcin on itself?

  Using the definitions of the paelwzvv8zj9qn0 k v1mri+7(f0rsec and the light-year, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.38 seconds of arc. How far awqyt7z/kzz hu- g+ oygba 3;4z/ay is it? d =    ly

  The parallax angle oi/na2o g/n jq.f a star is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its parallax anglp ,j4/8 tm*el:ufei ca 2id5bhe?
State (a) in seconds of arc,$\phi''' \approx $    ($\times 10^{-2}$)''
(b) in degrees. $\approx $(    $\times 10^{-6})^{\circ}$

  What is the parallax angle fet8c jra--ml 7gjo96sor 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 sta2vwch 21iqz9,qsv9mdiz*9 8y7ee (ja *pnro ar, will the parallax angle of the farther star be greater or less than that of the nearer qi221daz9,sny9*(eae wvvh c8 zrop 9q*7mji star? By what factor?

  A star is 35 pc away. How long does it take 8 po.0y t07r lqqry3aufor its light to reach us?    years

  We saw earlier (Chapter 14) that the rate energy reaches the Earth from th0e w1s)4c qct9h*42njqpxyn3 gh2vjk e Sun (the "solar nn0 9wckvge2pycq h4s3x1)h*j4jt2 q 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 Su;d ldoptt-hs 0 t-f4hdg)7un45z6 laun as seen from Jupiter as compared to its brightness from Earth? (Jupiter is 5.2 times farther from thet7n-6g4;ud l0) hh-tdpl4 tdzsu oa5f Sun than the Earth.) $\dfrac{l_{\text{Jupiter}}}{l_{\text{Earth}}}$    $ \times 10^{-2}$

  Estimate the angular width that our Galaxy would subtend i5rpv 3jwd3y( tf observed from the nearest galaxy tp3ry dj v3(5wto us (Table 33-1). Compare to the angular width of the Moon from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, what will bgi-yq*e/xx)/ x1 *oig xw,/cae)vx ii* i1loae its average density if it expands out to tcix )-*i1*ia igw exlxo/ a1yeqio*gx,//xv)he 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 esc w04l-m;dyz xpected to be about the size of the Moon. What angular width will it subtend s- ;w0dmy z4clfrom the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a whitym j uvyd:a4r5 yi2r8.e dwarf whose mass is equal to the Sun's and whose radius i.yjy5 a rmur2dy: iv48s equal to the 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 . 06ih u(so/xkwam/ow11 km. Calculate its average density and compare to that for a white dwarf (Problem 13) and to that of nuclear matter.( /0mwoswxk h6/i .uao
$\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. (T vbrw68z:,7gz/1xa wsvd+d gdhe mass of the very unsw s+x,wga b7d 1z8/v :rdzgdv6table $^8\text{Be}$ 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 thme nd1bg 1.zqxr3+p amk/9xjit162n ue 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 clha,b*v un80 fkuster are assumed to be about the same distance from us. Two such stars have80*unb hv kfa, 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 radius149pm a8pi f(la.vg nu for a star with mass equal to that (a) of our Sun i.apf(p84amlu1n 9vg is    km, and (b) of Earth is    mm.

  What is the Schwarzschildgmqdub.o ,z g-hj l5+jr/ :f+u 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 6q;uod)q k2jl2)j wtpthe angles is (a)dujow)q;q kj lt 6p2)2 359º, and (b) 180°.

  What is the maximum sum-of-the-angles for a triangle on a spher09mpzpu/)m q5oww9ot6gz 2t +fi h8qge?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the speed of: eg,5d amfq*oo in:7t light, roughly how far away *ma ng do7te:f5i,o:qis it? v =    Mly

  The redshift of a galaxy indicates a ; 6u4ov3je)xbn hai 8nvelocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (relative to us) that is nea agv3h9,khhh 3r the observable "edge" of the universe, say 12 billion light,3hahh9 3khg v-years away. v =    c

  Estimate the observed wavelength for the 656-nm li0.d: n syrt mc/.:t9j )tbghihne in the Balmer series of hydrogen in the spectrumr bsc.)h jmi: th: .dtn0g9/yt 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 ofqbc eyr*m 2ven0qilq5j87-x / a galaxy, and its distance from us, if the wavelength for the hydrogen line at 434 n*xqvyecb - 7qeim rq/8 5j02nlm 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 galaxxm2269rvb nb zy with $z = 0.60$? v =    c

  What would be the redshift m3r.t9*g( cimeard+c parameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Doppler sc yf;am/;f4 jdhift 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 th/ . pwkf zt9z t; syv0cwlr2/qloc/(4xe peak of the blackbody radiation distribution at 2.7 K using Wien’s l0ft.v;lzcw o pyltz ( /9r4q/xscw/k2aw. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for clodapk4,y 79al psure 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 (tha:,l/;ljva .tnhgb 8se average distance between galaxies) at any one moment is believed to have been inversely proportional tot lnaj/. ,8alg :v;bsh 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 w*bylfrm8r5 um sd; as1326yvtime had the universe cooled below the threshold temperature for produ365l;rbf2* mrwymu 1ay8 vdss cing
(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 chan6h+2sz6eb wd hges represented by the three arrows, A, B, and C, 6zhs wd2+h6 ebin the H-R diagram of Fig. 33-28. For each case, describe the changes in temperature, luminosity, and size.

  Assume that the nearesto,g (t c1mp ga03hheto.0/vth stars to us have an absolute luminosity about the same as the Sun's. Their apparent brightness, hoc vtt, gph g o/0.3tea0ho1(hmwever, 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 moment6ng h1;u+vwg6ekze0 yum to estimate the angular velocity of a neutron star which has collapsed to e+g 6eg 6;uzyvh1kw 0na 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 rotationmx5,s 61 at:.gmgkjo nal kinetic energy change when the star in Problem 56 collapses a6.omgg, xks mntj5 1: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 mass 1.5 times that of theg9bc pqh4ct: 7 Sun, with diameter 20 km, is observed to have c: tph9cg7q4ba 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 c7 ;kgmr2:y /odgfdn(k u1. kois 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) would provide the critical density to u;j (yht-* urrclose the universe. As*-j(;ru uhyr tsume 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 peaktrgo2 e)v) l+x 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 estimate the ratio of their diameters. [Hint: see Examples 33-4 and 33-5.] +lrx )eo)v2gt$\dfrac{d_{400}}{d_{600}}$ =   

  Suppose we can measure distances with parallax at 100 parsecs. n 4 j ka4r+ik7.zy1bnd+2gbmwqqae* 2 What is our minimum ankqad.+74 yw1 mjq2b +4anzkb*egr 2in gular resolution (in degrees), based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from singly72s9 p i3sg)uvi3qh, qg -(hg xqxhce7 ionized helium in a distant star happen to overlap with the Balmer lines from hydrogen (Fig. 27-22) in the S3gu gqq 2x3 xe vi-s7,qh)gh7ciph(9 sun. How fast is the star receding from us? v =    C

  What is the temperature that corresponds to 1.8iqhvi *6(o a0s-TeV collisions at the Fermilab collider? To what era in cosmo i6s(hq0iao*v logical history does this correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured;9o1rey w;h4js*k 8bberq 8zx 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 radius from t8;8b9z 1q jr obxys;ke *h4wrehe 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 lin8ib) kuiuy 9( qgj,cp5e at 434 nm emitted from the galaxy is measured on Earth to be (qb89ikjc g)p5,uui y 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) will beg3afs0tv csk+6sz2 y+a in fusing carbon nuclei to form, for example, magne0s2a3vz+y c tfka6 s+ssium:
$^12\text{C} + ^12\text{C} \to ^{24}\text{Mg} + \gamma$.
(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 -k bfq k12c7rj
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 critt+ yvn.uk6k2 y(ej;w1s0prh hical density of the univ+12w.vu0sekptj ;ry6n hk y( herse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$