The Milky Way was once thought to be "murky" or "; uqk2twv -+knmilky" but is now considered to bewk;-n+t 2v qku made up of point sources. Explain.

A star is in equilibrium when it radiates at its surface all the energy -;7f+ jmy5mj 9scuyzppdjkl 8f21a9ubh2s;m generated at its core. What happens when it begins to generate more energy than it radiates? Less energy? Explaikjcd 29hayfp7uj 2- ;u+8s b1 syml5z; 9jmmfpn.

Describe a red giant star. s)d509 okwcqsm u,ua4List some of its properties.

Select a point on the H-R diag gni- i :ixn oy4ul2cn,+;tc.a0ab-wxram. Mark several directions away from this point. Now describe the changes that would take place in w:galnn-.4i+oa c2xcb 0yi i ;,ut xn-a star moving in each of these directions.

Does the H-R diagram reveal anything agq5;m dhh )w(igz,bz 1bout the core of a star?

Why do some stars end up as white dwarfs, and others as niflwb; 6)dro2;ru+ ofeutron stars or black holesf26bowr+oi;d r;)fu l?

  Can we tell, by looking at the population on the H-R diagram, tis9mv1vmt6f1/ ymb 4jhat hotter main-seqmvmms1v4 t f9b /1jy6iuence stars have shorter lives? Explain.  ----待选择----yesno 

If you were measuring star parallaxes frb8 ;* qp:xiszqom the Moon instead of Earth, what corrections would you have to make? What changes would occur if you were measupzxi 8 s;*bq:qring parallaxes from Mars?

Cepheid variable stars change in luminosity with a typical periodi5r 1ik d7qe)p of several days. The period has been found to have a definite relationship with the absolute luminosity of the star. How could these stars q17pk5 i di)rebe used to measure the distance to galaxies?

What is a geodesic? What is its rfrz8o -rnl3 +gs;*pfrole in General Relativity?

If it were discovere nuw 1wu0z1ujw*h9u2* o4hs iud that the redshift of spectral lines of galaxies was due to something other than expansion, how might our view of the unw 4 hz wswiohn01u9u2juu1** uiverse change? Would there be conflicting evidence? Discuss.

  All galaxies appear to be movinwt5x 2 x18ngl veb)qi+g away from us. Are we therefore at the center of the nx2) 1ibvgwte +lq8x5 universe? Explain.  ----待选择----yesno 

If you were located in a galaxy near the boundary of our ov 2*wefvnu89c4a, k qxbservable universe, would galaxiesv,uwaqfk*n8ev2x9c 4 in the direction of the Milky Way appear to be approaching you or receding from you? Explain.

Compare an explosion on Earth to the Big Bang. Consider such questions as2we uu xnvu4h;(ixq1z6(dr (r: Would the debris spread at a higher speed for more distant particles(zd;vhw(4 6ir( exnuqu x u21r, 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, sfpu(k1 zazo+o7-suj+, 01ilkg pb-cescapes from a black hole, then how can we tell if one is there?-ual f(+0s1p+,-zbuk7 i1poos jckg z

  What mass will give a Schwarzschild radius eqmlmw.4ovo w: uzw: 4nq9-gpy8ual to that of the hydrogen atom in its ground state?:uy 8mq:p.gnw4 9v-owmz4lo w M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion years. Find that time on (Ficf+zien:, ;ilk-/yco3z*np ag. Below). People have lived on Earth on the order of a million years. Where is that on (Fig. Beoylca/+ ;nfe k, -*cin3ziz:plow)?

Explain what the 2.7-K cosmic microwave background radianw+ 2mqym 43*.adtv yps791ebcbkd m5tion is. Where does it come from? Why is its temperatpm39+w14d7* bmmqetc 2 5nsabk y y.vdure now so low?

Why were atoms, as opposed to bare nuclei, unable to exist until p6:p)z2qu (cuj*iav d hundreds of thoua)v6 czp *d 2pujuq(i:sands of years after the Big Bang?

Under what circumstances would the universe eventually collapsse d9ax8c 9c md3p1u7 8v n2cdhs9cac(e in on itself?

  Using the definitions of the pard( w .a:) xhs5z0fnafvsec and the light-year, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a pag 9jhu;)h tvm2rallax of 0.38 seconds of arc. How far away is it? d =    ly

  The parallax angle of a star is-m. uecwka)k ; $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its parallax angle3yr :u 2c4doxc?
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? ksx; i d4 cbq+,-mmmx/$\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far e0h 2idy6j4jbaway from us as a second star, will the parallax angle of the farther star be greater or less than that of the nearer star? By what factor0 yih e6j42djb?

  A star is 35 pc away. How long does it take for its light to reach us 5ig3ne: odvq)xdmfit.u7e 7 8?    years

  We saw earlier (Chapter 14) that the rate energy reaches the Earth from the Sb)n:; apwa 6 zch0mrs+un (the "s0zam ;nbp+h6a w):crsolar 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 brighn*)k mqrn, ev*rh3po 9tness of the Sun as seen from Jupiter as compared to its brightness from Eanrrep nv)o qh* k*,39mrth? (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 G( b,nvqy8b,xhvwf 81r alaxy would subtend if observed from the nearest galaxy to us (Table 33-1). Compare to the angular width of the Moon from Earth. vb1bhw,yrf q8xv(,n8$\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, what will bewv ,ty:geqj(3d0cm 9 em (:tox its average density if it expands out to 3:tod(g9(x, c m:mw eyv0t eqjthe 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 eo8rd2)c n.* rsmge9vm xpected to be about the size of the Moon. What aonr8ed9.2)m*ms cr vgngular width will it subtend from the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whose mass is equal to the Sun's and who1 jw /k)ud41zy3ryq stbqh)n3se radius is equal to the Earth's. How ma13uyw)dtjbn3q) yrzks/h 1 4 qny 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 l*tcu25t gjs :.s0hlu of about 11 km. Calculate itsgu 2 .tslu05:lthcs*j average density 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 He burning cb4kvpta* ip9j,qbljl649e 9 reactions of Eq. 33-2. (The mass of the very ivpb ,4j99lp k b6j4q9cle*atunstable $^8\text{Be}$ 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 appar9n.fwkmd,9kq0ip ; qtent 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 disq zte3nk 5hp2 /.+ykiwtance from us. Two szk3/.5q2kehip+ w ntyuch 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 5v8d - j, f+n4ej4rdlu clcdr/that (a) of our Sun is rdjvl / ddl48r,ejnf+5c -4uc   km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typical 0 ui-rbye nx mah8hrc:6sn -*4galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a sphere, for which thv7r+drdm sin1e0g 0a6e sum of the angles mde1rav sn+r 6gi0d07 is (a) 359º, and (b) 180°.

  What is the maximum sum-o,hsqlei v:kj(a,1al; 0 9 cgymf-the-angles for a triangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the speed of light, rou:w);ttebcq8 b0nd ( oy)k5 v.)u zsqvbghly how far away is it?v8e)uv.; t0nqdtz5 ):wb(b qsyb k) co v =    Mly

  The redshift of a galaxy indicates a velocity w89fy -cut7vftg6v4vx(lf8 tx7 q or1 of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed ofy0 3jt)j)m 4 rwkyr,crnw9nxc k3sr;0 a galaxy (relative to us) that is near the observable "edge" of the universe, say 12 billion light-years away.nx3,r w0)ksm3w9k4c0yjty c )r;rrjn v =    c

  Estimate the observed wavelength for thc c- jebljjch39 /h+8ye 656-nm line in the Balmer series of hydrogen in th c38clch+bhy/j je9-j e 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 galaxjy(, w 9l9snz3amdz/7 gvkls2g1 rn.ky, and its distance from us, if the wavelength for the hydrogen line at 434 nm is measured ognn wz9, 73jz/ rk(lsls.a12vgky 9 mdn 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 ofsr2k:hd1/lb7 skgm q 8 a galaxy with $z = 0.60$? v =    c

  What would be the redshift paramet/cf2n6e(/h nxr1ns l cer $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Doppler shift inh0 ls,y*f(+f u(c cqtm;wl4un 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 bhwt x:c z)drya-* .(mthe blackbody radiation distribution at r.y(m:)ht zwb*c da-x2.7 K using Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of the univers9pph; ej v6nvv75dn(se 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 h xsot4v;hws:)kx71a -z;wgmdistance between galaxies) at any one moment is believed to have)mxsk7g4 wtzh: 1o;;wh av s-x been inversely proportional 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 und xk*;e qvbb,nrx 3*p5i+kl4diverse cooled below the threshold temperatur*q, 5nird;*+pk x x3d bevl4bke 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 three cythiapf(2 g/ ;6w0c un/i tqz*hanges represented by the three arrows, A, B, and C, in the H-R diagr2tfzqi/;wyn ghi0t6a* (u c /pam of Fig. 33-28. For each case, describe the changes in temperature, luminosity, and size.

  Assume that the nearest stars to us have an absolute luminoskn;eutj hln37 b5fsg+uv. t,j*kpuszu-, ;:dity about the same as the Sun's. Their apparent brightness, howe;,b u3*d.u n,g+k5teun ;ksts j-pz7vf:u hljver, 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 angulark uc --z )e4dp,f,dzxd velocity of a neutron star which has collapsed to a diameter of 20 km, fr zc -d)zu4xk ,-pfe,ddom 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 en5yhe3kk( j a4vergy change when the star in Problem 56 collapses to a neukyeh 3v4k(ja5 tron 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 the 6pu7fg a )tuj.Sun, with dup.fuaj) g7t6 iameter 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 galaxy to our-*/0e oltzo arm ib.i; 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 provide the criti 9m:l.efkkp. tcal density to c9k:. .kmlfetp lose the 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 at 600 nm and f ve:o2 xlks4xf- o2p8400 nm, respectively, both lie on the maifk-el v8p2 4 2o:fxsoxn 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.] $\dfrac{d_{400}}{d_{600}}$ =   

  Suppose we can measure distances with parallax at 100 pa8oa:xc-rj qd6z -0can- 3iooj rsecs. What is our minimum angu--do6noxcr q c0:izja -3 jao8lar resolution (in degrees), based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from singly ionized helium in a)s hx*tvthxf3( g5gd( distant star happen to overlap with the Balmer lines from hydrogen (Fig. 27-22) in the Su sgtx) vf3g (hd(xth*5n. How fast is the star receding from us? v =    C

  What is the temperature that c;dvr /kdbwgupn.1 u5g 41q qk)orresponds to 1.8-TeV collisions at the Fermilab collider? To what era in cosmological hi v4qpuk5ggk1)/udnb rd1 wq.;story does this correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation of gz -dx (r* f79letb9vun54a ikgas 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 is 60 light-year9k u(4t 9 dgrvbl efi-*5nzxa7s, 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 nm mm16 i*:lah/j3fujvs( b.; ku m 5aqgeemitted from the galaxy is measuviaf ku3ahmslq65.m*jb:m / ;g(e1u jred 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 evolution, a star (if massive eno5;qbp xs7tzl2gg+ /l en *,fx g8jlq0zugh) will begin fusing carbon nuclei to form, for example, magnex;q *gs2pllgxltqz87gb0+/z,e fjn 5sium:
$^12\text{C} + ^12\text{C} \to ^{24}\text{Mg} + \gamma$.
(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 oqfjfaem8g,ivr+-ao. 6r .gw+uja/ 4
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 densf2 .2jxpe*wrs55w ekk9c+k i o5iy xv7ity of the universe, 7*srew5 2x2.xk v f5kipwycij9oek 5+$\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$