The Milky Way was once n(j a8wr9bi.wthought to be "murky" or "milky" but is now considered to be made up of pojw(8 bni 9wr.aint sources. Explain.

A star is in equilibrium whejh4h34 gtpi .8 le1awfn it radiates at its surface all the energy generated at its core. What happens when it beginf 3ipwhg4.a8e1hl 4 jts to generate more energy than it radiates? Less energy? Explain.

Describe a red giant star. List some of its po7x h ofcn5 3,axitp72roperties.

Select a point on the H-R diagram. Mark several directions away fmm r c/. occj9o*35lmvrom this point. Now describe the changes that would take place in a star moving in eac*vm .3o mjl c9rc/om5ch of these directions.

Does the H-R diagram reveal ankp2.q pxvf:m 0ything about the core of a star?

Why do some stars end up as white dwarfs, and others as o4ucb 1rw-hr(xs4 9pqneutron stars or black holexu(1 c 9qrowb44 shrp-s?

  Can we tell, by looking at the populatir bwm++zgf5 ccbt 72+pon on the H-R diagram, that hotter main-sequence stars have shfw7b+zbc5 +g tc2+rpm orter lives? Explain.  ----待选择----yesno 

If you were measuring star 3ahafm, )6t-/w-2fu hmeufh t parallaxes from the Moon instead of Earth, what corrections woh-m /-6umwft )e,ht haf afu23uld you have to make? What changes would occur if you were measuring parallaxes from Mars?

Cepheid variable stars change ineak623e( si nc luminosity 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 to32kn 6(seeaci galaxies?

What is a geodesic? What is its role in General Relat- ihb;/, v2uli/wi bubivity?

If it were discovered that the redshift of spectral lines of galaxies wci;0 : r qz+k0fgln.epas due to something other th+cz rnq:0fg0e.p i;lk an expansion, how might our view of the universe change? Would there be conflicting evidence? Discuss.

  All galaxies appear to8u;k 3ss*viy l be moving away from us. Are we therefore at the center of the universe? Ex3u*k;v ssi8 ylplain.  ----待选择----yesno 

If you were located in a galx)+(8lstw u(/i wpn whaxy near the boundary of our observable universe, would galaxies in the direction of the Milky Way appear to be approaching +n8uw/stx( p ilwwh)(you or receding from you? Explain.

Compare an explosion on Earth to the Big Bang. Consider syuxd *+7 uc.syuch questions as: Would the debris spread at a higher speed for more distant particles, as in the 7sd* yyxc+u.uBig 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, t/)pn9ef qv u:uhen how can we tell if one is there?q) fv/unp :9eu

  What mass will give a Schwarzschild radius equal to that of the 5n3+0pwnob vhhydrogen atom in its ground state? Mow+ b0vhn5pn 3 =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion years. Figj)lo+x 0 c+su7ihdyt40, mgw7i .a hind that time on (Fig. Below). hos0xj + 7h74)um,g0wi+l.g tdyiia c 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 background radiatiaik2x* mnng/:on is. Where does it come2n/:m gn x*ika from? Why is its temperature now so low?

Why were atoms, as opposed to bare nuclei, unable to exin 1w )eba4f;gast until hundreds of thousands of years after the Big Bang?1aag; )enb4wf

Under what circumstances would the universe eventually co7b/d39xicikq dr,qf(sqo.: o llapse in on itself?

  Using the definitions of the parsec and the lighj d5 xf6rrh8ayh: n1,wyx9e r,t-year, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.38 seconds of arc. an4mqk; vw5;:m(z fry How far away is it? d =    ly

  The parallax angle of a stardx 0dl9 ty-1z u*y4vph is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. n; : xfqq)ej.*wrce5gWhat 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 for a star tu;n /w;lnrn ie4faqk; ( (bhe6hat is 55 ly away? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away fi2 zka7.us:1cletb eqqo ;/ o1rom us as a second star, will the parallax angle of the farther star be greater or less than that of the nearer qt7/ol1bcq .u2 ;ea:sk ozei1star? By what factor?

  A star is 35 pc away. b4 fz*ny .kng8How long does it take for its light to reach us?    years

  We saw earlier (Chapte13/n3 nfjk iptr 14) that the rate energy reaches the Earth from the Sun (the "solar constaki3pj3tfn1 n/ nt") 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 seen from Jupit 545 3vxjosnrber as compared to its brightness from Earth? (Jupiter is 5.v5sb5 3n4rxjo2 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 f(unre er,4;hu 0abt7from the nearest galaxy to us (Table 33-1). Compare to the angular width of the Moon from Earth.at uerhb(7;n re ,f0u4 $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, wh0p,q 1kz10kiqh ;a1onb -frv7qda -lvat will be its average density if it expands out to the orbit oq,;b0v v1 ha-11rfkkni70dpl-aq zq 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, -bj9kb o kpdh6yb-2(o it is expected to be about the size of the Moon. What angular width will it su (kbdy9- obp2j-6hko bbtend from the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whosf/mn-zmox n1( zs02 kq seqkhs,i*-g-e mass is equal to the Sun's and whose radius is equal to the Earth's. How many times larger than Earth's density(k-mo-f 0h s gqs*-q ez/k,2znm1nsix 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 m -k7arv (:z/cmim5q cmass is 1.5 solar masses has a radius of about 11 km. Calculate its average density and compare to that for a white dwarf (Proble:m7-m vrc im ka5z/cq(m 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 reactions of Eq. 33-2. (The0e+/lll car0)d. j. gfrble 4t mass of the very unsttl) rl0l+ fl ja e4/bd.0r.gceable $^8\text{Be}$ 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 apparendnd,n qtny n(13/)*zqim.kt st 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 distanc:wmr,ely;qidw1 v5)z a pft:2e from us. Two such stars have spl 2,;rv: )fyzat1wwpiq e 5dm:ectra 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 equalino3 t)5nm)v.cuxcbl+8i a y( ok0 wg6 to that (a) of our Sun+k5)(inlo8 o0. iawg c tc)vymbn x3u6 is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a +q0czll8btza . 6xdxm4fs6r8 typical galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a sphere, fop4vy+o+ hpq o3r which the sum of the angles is (a) 3+pyqh op o34v+59º, and (b) 180°.

  What is the maximum sum-of-the-angl5p vv 8u7c+:(t ;2 :hpfsv4yeiyeded tes for a triangle on a sphere?    $^\circ$

  If a galaxy is traveling away from usrkqul6k 8 g4r ucq81,s at 1.0% of the speed of light, roughly how far aw6qcr4l uuk 1,gq8srk 8ay is it? v =    Mly

  The redshift of a galaxy indica l of4 t.g)cz1pwxl63ytes 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 nearh)6 vw0mpon fg9f2 n.m1ezh:r the observable "edge" of the universe, say 12 billion light-years away. ehnfr: 296o1gm.0nmwpzhv )f v =    c

  Estimate the observed wavelength for t;n +v h30qjyw m (qz(+a 8w,w*urhzsajhe 656-nm line in the Balmer series of hydrogej(8wjhqmnah *yw(w+u vsz +a,r0zq ; 3n in 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 distanowj*9-u*h/o nqpn q5 hce from us, if the wavelength for the hydrogen line at 434 nm is measured on Earth ajo*-*hun9o /w5qn hp qs 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 ga z 4ldpjnf80(pm (ci2alaxy with $z = 0.60$? v =    c

  What would be the redshift parametep -10pzi z(e+i8tbyddr $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Doppler shift in wavele 9qy3 ;yb1c,umkqjubb9 ,u 7tongth is $\Delta\lambda/\lambda \approx v/c$ (Eq. 33-5b) for $v \ll c$. [Hint: use the binomial expansion.]

  Calculate the wavelength at ttq3b2lipg08g tw , q09bsjj;uhe peak of the blackbody radiation distribution at 2.7 K using Wien’s lu;jg ip90st8tbw,bq ljq 2 g30aw. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of the univek7e 12y9w jru 4:9mzpuu4b4qqn ehz5trse 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 r5s 4 ctiiv a,cm27vz1(the average distance between galaxies) at any one moment is believed to have been inversely proportional to the absolute temperature. Estimate the size ofc14 v7 ia, mcvzrit5s2 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 below the threshold s gyhkv();7+ub9vy6r ct.w gmtemperature for producyg(h wtu+ 7vgv9.kms)yb; r6cing
(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-sb9 t)7n:ul.)w js mdmdequence stars could undergo the three changes represented by the three ammwn7j)9d u:) dt ls.brrows, 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 have an absoluter kdz dto/xg4 op dz(5:)x2/wl luminosity about the same as the Sun's. Their apparent brightness, howpo/rl5xzwd:dx 2z k/ )ot4g d(ever, 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 vz1ne: zw.0t9 ii kibp8elocity of a neutron star which has collapsed to a diameter of 20 km, from a star whose radius was equal to that of npt0 kz8iw e:iz. 1bi9our 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 rotat przd9la.v/ 5gy+j u,eional kinetic energy change when the star in Problem 56 collapses to a n ug+ezj,d/p5l 9 rvay.eutron star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believed to be a neu vjni8+wn ,d u7*i8ba6gq6r rztron star of mass 1.5 times that of the Sun, with diameter 20 km, is obdg6ia+bwrz nj*iq nr,887 6uvserved 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 isiq d(buzg8o74x s y+h- 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 criticalc ;rhkjc nnsj+x6a7) 4 density to close the universe. Assume the neutrino density is, like phonj7x ck6s ; 4)ajhncr+tons, 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,x;n rdu5u* w1j4 : sbiqxiiz1.0vkfm 400 nm, respectively, both lie on the main sequx0s,:zq5f*b . u ijdm;iinkr11v x 4wuence. 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 ho6 yu2u x d3kfo;jig; lps*/-parallax at 100 parsecs. What is our minimum angulau/ o 3fdjlx-i 2*h psyou6kg;;r resolution (in degrees), based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from singly ionizgiq z*(i (z 3ve6dxl 3a3hfn.led helium in a distant star happen to overlap with the Balmer lines from hydrogen (Fig. 27-22) in the Sun. How f.6*3id3 avl xf(e3qnl zg z(hiast is the star receding from us? v =    C

  What is the temperature that corresponds to 1.8-TeV collisions at the F:va/z2qgse 5k.ur :,gor.dko ermilab collider2,q5.:k/de gr .s ok:uo agzvr? To what era in cosmological history does this correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation of gas aroundw wkzhu2yq5b6kv0d(0x s/g p2 what might be a supermassive black hole of abou6q zwvw5b2h/02 syxgd pukk0( t 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. The "blre n05snki;snj )1ua /ue" hydrogen line at 434 nm emitted from thkn nsrj)5ai1 sn;/e0ue 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 stellar evolutionu8ijt na; x.h48 bfpn(, a star (if massive enough) will begin fusing pn nhaix8b.uf;j 8t4(carbon 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 n2/xack3hoid l9;a2q
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 cf0kq5pli + :j5udsa+o ritical density of the universe, +j5 doq0+upk f5slai: $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$