The Milky Way was once thought to be "murktjn++0yox0 ebe7 auav/l-fqp, s 3 1cey" or "milky" but is now considered to be made up of pol bnqee,p/0s1t3-0 j ea+yuvfao 7c+xint sources. Explain.

A star is in equilibrium cm b+4em:hkf*(ffvx9 vz +gx1ij3+po when it radiates at its surface all the energy generatee+v:fzjm4+oxfvg i 9bkhmp 3f+*cx(1d at its core. What happens when it begins to generate more energy than it radiates? Less energy? Explain.

Describe a red giant star. List some of its propekz*) w nn+km0jrties.

Select a point on the H-R diagr e *x6;ipgvystp88v,gam. Mark several directions away from this point. Now describe the changes that would take place in a star moving in each of these d6ye gvtip; g*v8, xp8sirections.

Does the H-R diagram reveal anything about the core of a sta;8zn0vqcs l l.+yc3wz6o p bj9r?

Why do some stars end up as white g,5 0onb;a rcdw,*jykdwarfs, and others as neutron stars or black hownb,yk5;* ajcg0o ,drles?

  Can we tell, by looking at the population on the H--hv8 ow8(rc- e7 i4z6p0pxcdi*iq nrn R diagram, that hotter main-sequence stars have sq-zdip4in6oivrx (p807h-n*c 8wcerhorter lives? Explain.  ----待选择----yesno 

If you were measuring star paral6jax)g ofr q0p,((*i-uvreye laxes from the Moon instead of Earth, what corrections would you have to make? What changes 6x(fogvjepa rryq,u-0)*(e iwould occur if you were measuring parallaxes from Mars?

Cepheid variable stars change in luminosi2)hkrf(w bx:c :zydc4lk3hc .c(0 ysity with a typical period of several days. The period 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 g r:csc 0cby2(ci.yh x4zl3wk )k(fh:dalaxies?

What is a geodesic? What is its role in General Relativicwmm1.*;a92a-r-rx izoc szwty?

If it were discovered that the redshift of1fis-beysf7e- 0 d (vb spectral lines of galaxies was due to something other than expansion, how might our view of the universe change? Would there be conflicting evidence? Discussvfi b-b7 s01(efey-ds.

  All galaxies appear to be moving away from us. Are we therefore at the cente/q ), 8kb3e-b( k ly4wc7hwqqlm io)nhr ofh -oy73mh l)qi)n ,qw(wb8kc4b /klqe the universe? Explain.  ----待选择----yesno 

If you were located in a galaxy near the boundar l7x+o i(bse8fy of our observable universe, would gala bixfl eo(s+87xies 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 s2;oi/mra w ne0uch questions as: Would the debris spread at a higher speed for more distant particles, as in the Big Bang? Would thrao0m/;enwi2 e 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 tellm7i k:+i/loug7xhao off+vvgc4z th9. w4)k 4 if one gf:.zw9g)v/4um lxo h7++t 4o4akf7cviio hkis there?

  What mass will give a Schwarzschild radius em6akg0/z mdff3 -dbq+ qual to that of the hydrogen atom in its ground state? M = d0 6f3m/gbzmdqk-f+ a    $ \times 10^{16}\ \text{kg}$

The Earth's age is oftd;hjnf tht 2rl1nl, l qoua 93ye8g5/.en given as about 4 billion years. Find that time on (Fig. Below). People have lived on Earth on the order of a millionqeo.rh1ul da5, t2g9;t l3/f nn h8lyj years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic microwave background radiation is. Where does it1a cbvwux xqq8c b*vu+h3yt ,9tg333n come from?tav3u u1+8qhbv q g3,ct9xn*3cxwy3b Why is its temperature now so low?

Why were atoms, as opposed to bare nuclei, unable to exist until hundreds of thxi.f-xeb 78mpn(n*y42 xv dww) i6cysousands of years after the * 7w 4d- s.n bxxpc6y2 i8mnx)(wvyifeBig Bang?

Under what circumstances would thass,hjr 2b.fs4,(r.cj,ucloe universe eventually collapse in on itself?

  Using the definitions of the parsec andom:j4j y/2spr 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 aruh34zp kn-y6ni9ciu k.u5g- w0b . syway is it? d =    ly

  The parallax angle of al4d uw4c h6.kr star is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc awayd,e zjdg(1k5 b. What is its parallax 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 *nm5:fiu zdz qt*g o8(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 secoz::08 6foh ippuuvd1ynd star, will the parallax angle of the farther star be greater or less than that of the neaz8vh0pu: d:yf6 upo1i rer star? By what factor?

  A star is 35 pc away. How long does it take for its light t/v4h ( m9fludl 0j(vujo reach us?    years

  We saw earlier (Chapter 14) thpjzv7u:6 ua79mc3vnmnfj; 9gat the rate energy reaches the Earth from the Sun (the "solar constant"mnj7fv: j 9a; cpum 7nuz9v3g6) 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 brightn7g:g*jt (.a 6tnt(h9 pmlvuk2o )azctess of the Sun as seen from Jupiter as compared to its brightness from Earth? (Ju9 agt:zp(n ugvo6jttk)l ( m.ah7ct2*piter 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 subtend if observed from twtlm- :i;jie a(y8)o ohe nearest galaxy to us (Tabl :jtl imo ;)(ayw8eoi-e 33-1). Compare to the angular width of the Moon from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, wha 5 yd+oi+k3rpat will be its average density if it expands out t+r o35pk+dy iao the 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 expected to be aboum 9nuy1-k(mj ut the size of the Moon. What angular width will it subtend from the present distance- mkj( uy91mun to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whose mass is equal tqcn4.x+o. nmj o the Sun's and whose radius is equal to the Earth's. How many times larger th4.nqx+cj.on man 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 solarfb)-x s(2weae masses has a radius of about 11 km. Calculate its average density and compare to that for a white dwarf (Prs -)(bf 2exaewoblem 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 bubk7x* -j 7bjggrning reactions of Eq. 33-2. (The mass of the very unsta7- *jb7ggkjbxble $^8\text{Be}$ 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 thjtj7 g4zx r p/o ,wj0g8qu;uz3e 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 cluster are assumed to be about-5p plme d*+zn the same distance from us. Two such stars hae +md- ppn5zl*ve 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 st*(hoi.z v6 xm49bs oznar with mass equal to that (a) of our Sunh.n zo (s9x4 *6vozmbi is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for, yeyxzl d45 2uy)9(tmt)h84vmk vstm a typical galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a sphere, for which the *y t8dsn-tca;9cq/ rm . dmo0dsum of the angles is (a) 359º, and (*c n/m 0yr dsdtmto9 ;ca-8dq.b) 180°.

  What is the maximum sum-of-the-angles for a vsych2 m2tjbc0.d)x5 triangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% qs -17t mksr4*,c y:dw//xi znw gncv:of the speed of light, roughly how far away r-1*x zki 4q7 :n vs,tc ycsw:ngwm/d/is it? v =    Mly

  The redshift of a galaxy indicates a velocitypsvx-y i4 iag. a5)uatsc: m.4 i;r1zu of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (relative to us) that is near thecph d9/ bu4z.l observable "edge" of thez udcl.b/p4h9 universe, say 12 billion light-years away. v =    c

  Estimate the observed wavelength for the 656-nm line in ti8tix r6q6q r7he Balmer series of hydrogen in the spectrum of 6 tqriir7x6 q8a 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 fc/y wzp-jh :ov-n +1f t:ir4cwavelength for the hydrogen line at 434 nm is measured on Earth as being 610 nm. pft-zi n4v yofh 1 :w:r+c-/jc
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 galaxyaktoxf-/wf* r09fx3s6sxgved60tv , with $z = 0.60$? v =    c

  What would be the redshift pycsb0yrw z-+ 8y6sq v,la5 cny2 *hbe9arameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, nfv1zxb41t;u y30xlcnom 0t4show 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 radiation distributi hgc1dn4g;c a,on at 2.7 K using Wien’s law. d1ac,gg c4hn; $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closurej3c98, izlxc kzu t.l+ 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 averm5z(j;f2l kf uage distance between galaxies) at any one moment is believed to have been inversely proportional to the absolute temperature. Estimate the size of the universe, cou;fm2( k 5lfzjmpared 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 threshold te c+qzv+o5ps6imperature for produ+ p cqs+5ov6zicing
(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 mai2vsl rrcag3+ga;m u7+n-sequence stars could undergo the three 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 temperat7l3rgr cu;2+agasm+ vure, luminosity, and size.

  Assume that the nearest stars to us have:vlis .jn4auizn3+,q an*s m+ an absolute luminosity about the same as the Sun's. Their appare ij+:+v3n4sun *qna las iz.,mnt 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 angular momentum to estimate the angular velocity of ad 18adgy mrk dd---rb) neutron star which has collapsed to a diameter of 20 km, from a star whose radius was equal to thdgbd-r1- m dyd8)-ka rat 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 when the star in.ej*llw :8 mwtfnos8 2tmxi 30 Problem 56 collapses to a neutron setw8.mxj: *lm0nl w 8tsiof23 tar? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believed to be a neutron stazhk 2ig ym )b0z0+j;ssh;q(r hr of mass 1.5 times that of the Sun, with diameter 20 km, is observed to have a rotatihh0khg)2s0+zbiyj ; ;zr (msqon 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 Gal(ovr8zv (5wukb/oog85zvc r, axy 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) wo145l-bxte;rje ib; h huld provide the critical density to close the universe. Assume the neutrinoi re5-h eh;lb4; tx1jb 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 spect+a 6b me;ple-kjmi8s r9ix17fra 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. Br1 i8a 7-;j+me6xibl fpeskm9elow) 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 parsecs. What is our mi zj :,t/bd i,yzl;;kbdh+xjy 9nimum angular resolution (in degrees), ba/+t hyk bidzz9l:jj;,;b x,dysed on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from singly tx9cijlv4zq:ae t3 01ionized helium in a distant star happen to overlap with the Balmer lines from hydrogen (Fexvtzi109qjlc4 a 3 :tig. 27-22) in the Sun. How fast is the star receding from us? v =    C

  What is the temperature that corresdbd0c ;yvaosn xc )84:ponds to 1.8-TeV collisions at the Fermilab collider? To what ersnx4c b8ca d;y0o:d )va in cosmological history does this correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently8 vlfcrc;) ahtecc1.+ measured the rotation of gas around what might be a supermasclavrec1fc) +.h8 ;t csive 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-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. Thtddkx46 89kmn e "blue" hydrogen line at 434 nm emitted from the galaxy is measured on Earth to be 6ndtk4 kdx86m950 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 +: -*zewm f84ni-mgpe /cnqrcof stellar evolution, a star (if massive enough) will begin fusing camec nnm:fqwcg-p+-iz4 8r/e* rbon 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 reactio*r*mjtp: .xh ds s(iqu/rt 6a2v.w0lrn
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 c 4/ 9 p(qs5:izvoou6r/gbhkx equaled the critical density of the universe, iro(xbcog /5zuvq s 4 6:9hkp/$\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$