The Milky Way was once wl)whi 5 +(ga6cwer1s+ei)ci thought to be "murky" or "milky" but is now considered to elge( )c5+6si+ ir ia cwwhw1)be made up of point sources. Explain.

A star is in equilibrium when it radiates at its surface all the enerv fsh1l u004mpgy generated at its core. What happens when it begins to gener1v l0psum0 fh4ate more energy than it radiates? Less energy? Explain.

Describe a red giant star. List some of its properties.zlixq :+y ae h4w.xe24a c/4ab*wc.sj

Select a point on the H-R diagram. Mark several directions away fro-f/hpc9urfs 2 m this point. Now de9phfsr -/f2 cuscribe the changes that would take place in a star moving in each of these directions.

Does the H-R diagram reveal anything about the core:yuwb2 76c rznqu(ww 1 of a star?

Why do some stars end up as white lb.b. 9xtkn/t dwarfs, and others as neutron stars or black holes tn9./b.ktxl b?

  Can we tell, by looking at the population on the H-R diagram, that mwrv8 l xgwk+)l7fnky3n dw9x82 x6+rhotter main-sequence st+ mldkwxl+ry92w7xwvn)gfk r86n 3 8x ars have shorter lives? Explain.  ----待选择----yesno 

If you were measuring star parallaxes from the Moon instead of Earth, what cormgk6n ec h9w). p(a6rr4hjo8zrections would y n rch.4k6o(wz)e9jgm86 rphaou have to make? What changes would occur if you were measuring parallaxes from Mars?

Cepheid variable stars change in luminosity with a typical period oybh/wlklmk v as 9j0)y2e1:+q f several days. The pe:y9ljlyavm1s wk/e)hb+2q0k riod 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 bt;;1l( 9o ;+xmisdqen(io euits role in General Relativity?

If it were discovered that the rem0l6gw*v pyw 6dshift of spectral lines of galaxies was due to something other than expansion, how might our view 0gwy* pv m6wl6of the universe change? Would there be conflicting evidence? Discuss.

  All galaxies appear to be moving away fro( byaf /wxx;k.m us. Are we therefore at the center of the universyba wx. k(x/;fe? Explain.  ----待选择----yesno 

If you were located in a galaxy near the boundary of our observable q6clb n0x 2/dovf,4 cduniverse, would galaxies in theco6cdlvx q 0, nb24df/ direction of the Milky Way appear to be approaching you or receding from you? Explain.

Compare an explosion on Earth to the Big Bang. i eqw.q r4y /pbym5/s2Consider such questions as: Would thpmi/qr bsyye.2q5 w/4 e 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 this correspond to, open or closed?

If nothing, not even light, escapes from a black ho1llhrj)l-izkd n;6 dl8.w5k xb895cn.cbaj l le, then how can we tell if one is dnl-llrz;jlcxc1b j na8kd. 5.89hwb6 k)i 5lthere?

  What mass will give a Schwarzschild radius equal to that of the hydrogew9cm ltakq,8uw8 t *+an atom in i,lc qak8a +wmtu* w89tts ground state? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion year)xe4qt)oet9y4 j1t gc s. Find that time on (Fig. Bejoxetqt)gt)1e 4 94y clow). 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 backgroundm (gb5o 7;fkwt radiation is. Where does it come from? Why is its temperature nmowb 5(gft7;k ow so low?

Why were atoms, as opposed to bare nuclei, unable to exist until hundreds of ns3m a1+6isbd thousands of years after thd3m6 in+s1ab se Big Bang?

Under what circumstances would the uni-zmn8q uq8s41ou py3ku ,9giyverse eventually collapse in on itself?

  Using the definitions of the parsec andd w3 y;kwm71 ls(kl)cgkvy: sp)j:m7n 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. H.f1 /4mf x9(j3ocs i59 qp6kafynmuae 0xv,aqow far away is it? d =    ly

  The parallax angle of *t/l -,dq8gprci: oiaa star is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its p8- fcxxtck. ;(axviod*b (;pfarallax 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? tgir5m4 *b3li$\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away from us as a second star, will the paralla/dar6 ,.w7;c hgc,g*nib:hprjzv f8mx angle of the farther star be greater or less than that of the neicvdh7:g bcz pa./,;jr6mh 8g* nw rf,arer star? By what factor?

  A star is 35 pc away. How long does it take for its light to rearld1u+n/h 1n kch us?    years

  We saw earlier (Chapter 14) that the rate energy reaches the Earth i*m-) v3ht zvxr8i176h ids rjfrom the Sun (the "solar con v36 sri ti)8hrvhz1x -7jmd*istant") 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 s ,h*vz(h( sdq62lveyceen from Jupiter as compared to its brightnh*s,el(dch6 q2v v zy(ess from Earth? (Jupiter 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 Galaxy would subtend6x.g9m as c x+kuc;xa+ob i7j/ if observed from the nearest galaxy to us (Table 33-1). Compare tik+ x umaabxg+;6s.9c joxc /7o the angular width of the Moon from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, what will be its average densitywg o- bec p) : -;m2bpaw-bnkq,cj1ic9vna 3d2 if it expands out to the orbit of Eart b2cpiwd ;wc c- 31-n, qb2enp9:aob-a)gmvkj h ($1.5 \times 10^{11}\ \text{m}$ from the Sun)? $\rho = $    $ \times 10^{-4}\ \text{kg/m}^3$

  When our Sun becomes tyw.(cf7.xzh0-j suw a white dwarf, it is expected to be about the size of the Moon. What angularc. xw-.(jtf u 0h7ywzs width will it subtend from the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the densit/6zwrjohdgyx l /*2 ys* xv)l2y of a white dwarf whose mass is equal to the Sun's and whose radius is equal to the Earth's. How many times larger than Earth's d2/)syhlx gz*wv/r* yjl62 xd oensity 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 ha,b 9v j+n1zeawjot9j4s a radius of about 11 km. Calculate its average density and compare to that for a white dwartzjw vaej99+nb4 ,o1 jf (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 ; cul(jwl.sa9jt8 p: buj0cw7hc .ck-He burning reactions of Eq. 33-2. (The mass of the very un 7.8ck p. hjbscj :0cc9jul uwat-w(;lstable $^8\text{Be}$ 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 aj 0ulgw 9rq+.3h-ojyqpparent 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 dpd a90v dppx(y9 689(oqjgt(jw4ulhaistance from us. Two such stars have spectraphoawu vq( 6gyxj 09 4dd8p(pj(ta9l9 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 fo 2tuuee44 :. l+hhffj+q aj-mqr a star with mass equal to that (a) of our Sun is 2t+ heqja+ljq4:u -f 4uh m.fe   km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typi19 j:3lblu 8 tklqpjt71fes o-cal galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a sphere, for which the sum of the11 t-z yf)m;)hx pfcqy;jos7g angles s tx)f1qmzy; gc1pjy7 f )h-;ois (a) 359º, and (b) 180°.

  What is the maximum sum-of-the-angl1ubzwvk30obkzmqeae8 -k:9 8 es for a triangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the wka1-n) sisj3l/-smp speed of light, roughly how far awayj/ k p)n-smalw s1i3-s is it? v =    Mly

  The redshift of a galaxy indicates a velocity of5:, bx qdv)s kiku6*wl $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (ro/.ug +ylv-pz elative to us) that is near the observable "edge" of l/zgo v.py +u-the universe, say 12 billion light-years away. v =    c

  Estimate the observed wavelength for the 656-nm line in thf4rhf*(ig joh,ml/ 0pe Balmer series of hydrogen in the spectrum of a galaxjmofpfg,h 4 0/ril(h* y 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 d4y (uaeuho,bly (3 /2npmf,nus, if the wavelength for tyulh( 2donmea (p3y4fb,u/ n,he 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 of a galaxy withg+2*c) b) weargk0gll $z = 0.60$? v =    c

  What would be the redshift parametir*ti d:luui3,j f. 0mer $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Doppler shift zppb;1 wj5ttqp s8+fxo5,3j u in wavelength is $\Delta\lambda/\lambda \approx v/c$ (Eq. 33-5b) for $v \ll c$. [Hint: use the binomial expansion.]

  Calculate the wavelenpy,g7wu lk8t ylmk +,+6ogw2k gth at the peak of the blackbody radiation distribution at 2.7 K using Wien’s law. k+w ,klw l7tgmgok2 y6u8p y+, $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for ilf9+p6 m bs*yclosure 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 galaxiesj8b2l gp1vk(n,g ye/n ) at any one moment is believed to have been inversely proporti2bgnnvpkjg(e,1y 8l/ onal 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 belowh ykb:x5z1zxy3tkck+)if /7u the threshold temperature for izx/c5bkhk13)+fzk yy x:u 7tproducing
(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 un093z4 pbmm7gw irn;cw rsbc3,dergo the three changes represented by the three ar4 3cg c7wnw mr;mp3,b09si rbzrows, 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 nearest stars to us havew2yb3 8rg7 z/nf aur6s an absolute luminosity about the same as the Sun's. Their apparent bri rwngs b7y za2fu8r/63ghtness, 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 a ne z 85zw-+od*eg xts5mqutron star which has collapsed to a diameter of 20 km, from a star whose q 8mtoz+ *5sd xg-zwe5radius 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 kineti +hs(o xvcbol6.g8: spc energy change when the star in Problem 5ssg oc8b.6l pvhx:( +o6 collapses 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 timyg o3,zhs90 gwdz0z4 nes that of the Sun, with d3zh ,49gd0 zyow0 zsngiameter 20 km, 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 gala16s tm w*ls m;r17cen3mlx-aaxy to our 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) would uwvp7l52p33kr2 im h mprovide the critical density to close the pu3 73 k rmv2imwh2pl5universe. 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 at 600 nm and 400 nm, respza+qv;h jy7.rxwv/ g 3ectively, both lie on the main gv;qaz w7 3 j+yrx./hvsequence. 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.] $\dfrac{d_{400}}{d_{600}}$ =   

  Suppose we can measure distances with y+ rc :3cetfi *)t2naoparallax at 100 parsecs. What is our minimum angular resolution (in degrees), based on this in*ce:fr2yc o+3 )tt ianformation? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balrnwh,gt/,u; vv2cz9 emer lines from singly ionized helium in a distant star happen to overlap with the Balmer lines from he utwv;v,zgc/92,r nh ydrogen (Fig. 27-22) in the Sun. How fast is the star receding from us? v =    C

  What is the temperature that corresponds to 1n-lc1t n7ke8mom: 8fnisu 9 ib38(xmh .8-TeV collisions at the Fermilab collider? To what era in cosmological history doeskf-iin(e o8mtl 8mnbuh n7 m:189xc3s this correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation of gas aro*jbuu4 mfc6x9f ojj-sm:z*+9tc b o - x0zt4oxund 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 is 6 cbtf0ujsjx-z: x 4ocmbox- j 4m*u*oz6f99+t0 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 line at 434 ..cikupp i 3a /6kz.tjnm emitted from t .c/6.jk. kapp3iuztihe galaxy is 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 stelc6 nx eq8yi. 0hell .si/(/ nrtj6im+ilar evolution, a star (if massive enough) will begin fusing carbon nuclei to form, for exampli6/+n .crhl.jlmi6 ste/0nie xy( i8qe, 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 reactionf*:pl8l;t wkbakx4a t1* 7icj
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 critical densit(zjk-v9q b2 s2w2hof xi1n.sdy of the universe, ( 21j.w2i2nbos xhz9sfdkv- q $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$