The Milky Way was once thought to be "mrt 6nj3q6 h cp6llr279at-7carkaju2urky" or "milky" but is now considered to be made up of point sources. Expl h2 lja76a7ar-2rc l6jn96 3tptucrkqain.

A star is in equilibrium when it radiates at its surface all the energy), ii*g0;sqy 5, riggjt8cio k generated at its core. What hatc yioq)j,5,sg0g ;8i *iik grppens when it begins to generate more energy than it radiates? Less energy? Explain.

Describe a red giant star. List some of its pr(vigu ij,oj06 ys)*uf operties.

Select a point on the H-R f6hc, cl,h88ufa mfa; diagram. Mark several directions away from this point. Now describe the changes that would take place in a star moving in each of theslc8cf fm,a ,68ahh; ufe directions.

Does the H-R diagram reveal anything about thxq*xd dbbg: eoe /9 ia1hi8,d4e core of a star?

Why do some stars end up as white dwarfs, and others as neutron stars2.-nu okji (bc or black hole-j k.n(bi2 ocus?

  Can we tell, by looking at the population on the H-R dilh2cn )p 0rrb:agram, that hotter main-sequence stars have shorterp: )b2n0rlc hr lives? Explain.  ----待选择----yesno 

If you were measuring sta*w g:2;xv9tuo:msun w nu90exr parallaxes from the Moon instead of Earth, what corrections would you have to make? What changes wouvnu wxu 2t;0x9:e *mn :gso9uwld occur if you were measuring parallaxes from Mars?

Cepheid variable stars change in luminosity witplhawewu98r4ig/9sd y;m, )jp; 1 uq dh 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 measu;uag 8,9hqwp/1j e9sdr)piml 4wduy;re the distance to galaxies?

What is a geodesic? What is its role in Generv7qqs ehw5 +2qm20w5yan 9w tkal Relativity?

If it were discovered that the v9qa cfomj+(6redshift of spectral lines of galaxies was due to c ojfvam9(6+qsomething other than expansion, how might our view of the universe change? Would there be conflicting evidence? Discuss.

  All galaxies appear to be o 5o4p*rqud d86zejf+up;xr 3moving away from us. Are we therefore at the center of the universe? Ex zdpr;rdopo+6q 3fuuxj 8e54 *plain.  ----待选择----yesno 

If you were located in a gala6y-u r7 k o7o/rna ,pu6hlc)b i*kxp-jq*,ohjxy near the boundary of our observable universe, woukojp6cuoi barq y-*-j7*onu k 6,)rph7hx/,l ld galaxies in the direction of the Milky Way appear to be approaching you or receding from you? Explain.

Compare an explosion on Earth t/+q duycd+1j io the Big Bang. Consider such questions as: Would the debris spread at a higher speed for more distant particles, as in the Big Bang? Would the debris come to rest? What qyu1i/+jd+cd type of universe would this correspond to, open or closed?

If nothing, not even light, escapes from a black hole, thenmhw glm8sky*: +jv9.x how can we tell if one is there?.vhs m89 k* +mwxjgl:y

  What mass will give a Schwarzschild radius equal to that of the hydrogen xa*6-pa+lvp;nwlgm 6atom in its ground state? x6*;amapn 6w+-l vplgM =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion years. Find u i0 )kvaumq 25q8p7z 9vp;ozbthat time on (Fig. Below). People have lived ona7 pb 05vk2 iuuv8pqzq m;9zo) Earth on the order of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic microwave ba;j)kh+i5eigr99)mmfyot f , lu1xsv1ckground radiation is. Where does it come from? Why is ig1o9f 5)myems1kufj9xl i) ,h+tr ; vits temperature now so low?

Why were atoms, as opposed to bare nuclei, unable to exisdjo 6abd.( v0w 7xfho*t until hundreds of thousands of years after the Big da.oxhvbw d( o*j67f0Bang?

Under what circumstances would the univeryieoy ,7 rlv* +eq)b.+i0n:r*mdvn x mse eventually collapse in on itself?

  Using the definitions of the par;msb 1hftwlcv6d 7p g;;7kg9osec and the light-year, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.38 second69zkljvmim tafps 6u8qc3/4 4s of arc. How far away is it? d =    ly

  The parallax angle of a shgye3zr3 e q953hmi gc6y/k-y/qi*f b tar is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its parallax ang2bl 1artknw uznzm 3;30wy9d- le?
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 ufg(8/mwsr 3es,m oyua7 jt349dk0qk ly away? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away from us as a sec .swdhpco ;sj+u4 : p4w9liv7dond star, will the parallax angle of the farther star be greater or l.dl: +jdiwp;9hvp u4 os 4c7wsess than that of the nearer star? By what factor?

  A star is 35 pc away. How long does +x:os2 3o ,uies whl5qit take for its light to reach us?    years

  We saw earlier (Chapter 14) that the rate energy reaches the Earth fp 8vu(k:3ejm lrom the Sun (the "solar constajm8(k:le pu3 vnt") 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 Jupiter )z osv 5 rjm0.f:fo8p5a5j bpras compared to its brightness from Earth? (Jupiter is 5.2 times farther from the Sun tha.j5 )sp8pvrarj 50z:fo5mbof n the Earth.) $\dfrac{l_{\text{Jupiter}}}{l_{\text{Earth}}}$    $ \times 10^{-2}$

  Estimate the angular width that our Galaxy would subtend if observed from ,ird,169yxc:gfiblfz ahl9) the nearest galaxy to us (Table 33-1). Compare to the angular i:lc9)r l1g96,yfzbha,fi d xwidth of the Moon from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, what will bkj:3eav d4ce1e its average density if it expands out vd:ca4j ee3k1 to 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 expe y;ztth-gt(t3cted to be about the size of the Moon. What angular width will it subtend from the present d (t tght3-zyt;istance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whose mass is equal to the Sun's and wfy1ygg,/ro kk34r2r those radius is equal to the Earth's. How many times larger than Er1fy2/ ky34gkogr ,t rarth'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 mb ;d7j l;wwogqbf9 :g+asses has a radius of about 11 km. Calculate its average density and compare to that for a white dwarf (Problem 13) and to that of nuclear 9qo7:l+ gw;w;g b fbjdmatter.
$\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 burniuh spvs5tlj4 .j.34je ng reactions of Eq. 33-2. (The mass of the very unsjjpl3h4j4 .e5vu .ss ttable $^8\text{Be}$ 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 saoay+ bh)2 x,j9 lg5bitp:am-z me 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 chh *om(*3uv df 6vz,afertain cluster are assumed to be about the same distance from us. Two such stars have spectra that* h odvva6hf umf3z*(, 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 that ,05yrqkafuk . o3kn/j(a) of our Sun is 35nrjqa0.fo kk / kuy,   km, and (b) of Earth is    mm.

  What is the Schwarzschild ra0bh*v uyv3;9a( zb9mbjxu r4udius for a typical galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on thkldd)-m k,7 gke surface of a sphere, for which the sum of the angles is (a) 359º, and (gd7kdmk ,k-)l b) 180°.

  What is the maximum sum-of-the-anglei: 5g qnzuyiw8ca i;z-0oeg 7suz6 86qzh0e;ms for a triangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the speed of light, 9 + gxv6aiu.wrroughly how far away is iur+wivxga9 . 6t? v =    Mly

  The redshift of a galaxybb* ufh dokvd 7hl)u:f/-i q+nw. c(8k indicates a velocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (relxsbs- xg,gjm ef0:(j0 ):abki ative to us) that is near the observable "edg:essb:0gxkb)jm-f i0 a,g jx (e" of the universe, say 12 billion light-years away. v =    c

  Estimate the observed wavelength for the 656-nm line tl ;m2*gebi)qin the Balmer series of hydrogen in the spectrum of a galaxy whose distance from us it; 2l*q)egi mbs
(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 th8ydmpi e4u2wkpu 91 i8e wavelength for the hydrogen line at ed28wp8ypk9i ui4m1u434 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 galax uo 3)ykuc0dbm8ak(8 0nzhsjqf4 zh/*y with $z = 0.60$? v =    c

  What would be the redshift paraz0+0rnidpeh44ge: e p g*6c c)2crfcn meter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the o/q2 rg5(pibw 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 distribution atr4 j3njzt;; f6ytnynp b xyw0,*uxt2* 2.7 K using Wien’tjtnznn x36 wy y b04 *tr;,;yj*f2xups law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of the unik;cn 3: rzu3xpverse 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 galaxies)cfcqjr/hd,kh8 1d ;2o +doq-s at any one moment is believed to have been inversely proportional hcr/sfojcq ; hd d+dq-ok,821 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 below the threshold temgi 68a:97( gtjpg jjkpperature fo8a k(:pijp 7tjgjgg96 r 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-sequ t)w/y) )teohy jlq)q3y /gd+pence 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 cl )y tytyq/))p+jo g 3hde)wq/hanges in temperature, luminosity, and size.

  Assume that the nearest stars to us have an 6qxwuazy+xz;(c c2 mg+4q6t zabsolute luminosity about the same as the Sun's. Their apparent brightness, w6z2+cgqxq64+xzy atmz(; cu 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 velocitnoa -x0k,vopu3 o*wc9 y of a neutron star which has co 0koo, o9c-uxv3a*pnwllapsed to a 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 rotational kinetic energy change when the s e-y.4m qnd4rntar in Problem 56 collapses to a neutr-4eq.rn ydm 4non star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believed to be a neutron star ofj4h1zgvku . k7 mass 1.5 times that of the Sun, with diameter 20 km, is observed to have a rotation speed hvg.4zk7kuj1of $1.0\ \text{rev/s}$. 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 is kpc:3 u-ns cz3+7ks+iua5 r xpabout $2 \times 10^6\ \text{ly}$ 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 x6.mv9l6r )w xzwn nf. uyj*0vdensity to close the universe. Assume the neutrinolnwf).vvm * uwnzj.669 x0 yrx 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,9c hyb pvozuoou -0v03f7d51e04 wftx respectively, both lie on the main sequence. Use Wien's law, the Stefan-Boltzmann equation, and the H-R diaw1 4fvzf-e97pou0yd03ot xvu05h oc bgram (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 distancespmwfy) f jm0.dy3;f .s with parallax at 100 parsecs. What is our minimum angular resolution (in degrees), ba;w fyy3s fp mmd.0j.)fsed on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lixc5 .-8upqnuqv;m3ne+r t o)ones from singly ionized helium in a distant star happen to overlap with the Balmer lines from hydrouqm;vxor8 ecu3 -pn 5. )qn+togen (Fig. 27-22) in the Sun. How fast is the star receding from us? v =    C

  What is the temperature th 6r51/us 6eyjbb:,yub t*hn-g inxq5rat corresponds to 1.8-TeV collisions at the Fermilab collider? To what era in cosmological history does this correspond? [Hint: see (Fig. Below).] enbyy5nxb61q:ru-5 h6ijr/sg*t u,bT $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation of gas aoh5 2h;soj ;42,)f zjslf xtpiround what might be a supermassiv4xhfs22 pl;tj ,i)jo;zf hso5 e 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.b 6gf;g ljbr 01kkz4 b;qpeszdq;7 b(. The "blue" hydrogen line at 434 nm emitted from the gala s;6.;ejdbz( ;kbfq7 b qzpkr4bl0g1gxy 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 evolution, a star (if massivhofa6j 4o(dhd,m:s qx7 ;+ahoe enough) will begin fusing carbon nuclei to form, for exa j:fd7qosh ,oxad+o4m 6h(h;a mple, 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 q u+w(- 0 r+ohxaua:zg
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 density o1h 9:iki 8nxwndu9of qj.51ut f the univi 9.h19u8:ijwq5fnoxn1tud kerse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$