The Milky Way was once thought to be "murky" or "milky" but is now con0 fuz2ov irm*q. pw*ue,(h: gom2u;nwsidered to be made up of point sources. Ex2(*ozf wop m:niu;mu v.0*2g erh,qwuplain.

A star is in equilibrium when it radiates at its surface a 2 avn0 :wobmn-t9an.ell the energy generated at its core. What happens when it begins to generate more energy tha.nv2t:a ba -ewo9m0 nnn it radiates? Less energy? Explain.

Describe a red giant star. List some of txtc3lz(h5v w3e), eu its properties.

Select a point on the H-R diagram. Mark several directions away froyx,h681pus06pwulz1ng 4 x c4wia r o)9h :wbom this point. N1o 0i:r6y8xgu4 zlhw n 4paw)cwo u6xspb9, 1how describe the changes that would take place in a star moving in each of these directions.

Does the H-R diagram reveal anythinhci fh+ 4b3jep+j 5yr3g about the core of a star?

Why do some stars end up as white dwarfs, gh qq8y 2;f9;zhra6sg* 8 hncdand others as neutron stars or black hol98a2ng; yq6h8drghzhqfc *;ses?

  Can we tell, by looking at the popuq 8b,bp1juk jxq9w. s,lation on the H-R diagram, that hotter main-sequence stax.b,qkj8 jb w sup9q,1rs have shorter lives? Explain.  ----待选择----yesno 

If you were measuring star parlmb 63lh 22wfgallaxes from the Moon instead of Earth, what corrections would you have to make? What changes would occur if you were measurw m22b63lflg hing parallaxes from Mars?

Cepheid variable stars change in ln-,9.8t on/ny kztdt ouminosity with a typical period of several days. The period has been found to h/ too.zt ,9ntndn-ky8ave 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 its role in Gener4vqn/ dc,; +cmw1pddy al Relativity?

If it were discovered that the redsue4g(q:byk *m hift of spectral lines of galaxies was due to something other than expansion, how might our view of the universe change? Would there be k ugby*me(q4: conflicting evidence? Discuss.

  All galaxies appear to be ma12kvrldn atogbc*:;dhl4 k0e i -8* moving away from us. Are we therefore at the center of the universe? Explaia2albcn*d0:r 1d*kegm l-khv;4o t8in.  ----待选择----yesno 

If you were located in a galaxy near the bounugwx 6ygm7b 6k t;5)kjdary of our observable universe, would galaxies in the direction of the Milky Way appear to be approachi uym6) 6xk7g5j ;kwtbgng you or receding from you? Explain.

Compare an explosion on Earth to the Big Bang7z- x5(e (gyiwa:y 2da )ezhoo. 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 type of universe would this correspond to, open w5ed o2)7 zo( egyyhaia(-x:z or closed?

If nothing, not even light, escapes from a black hole, tkz tq9:a( o9srhen how can we tell if one i:99( orqkaszts there?

  What mass will give a Schwarzschild radius equal to thatbhh0p 7lhapy+a la:o a.;,z9q of the hydrogen atom in its ground sta9+b0:hl aoza ahpp. hyl7q;a,te? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often gp 6uqpzugl .:6iven as about 4 billion years. Find that time on (Fig. Beloupu.6 g pzql:6w). 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 radiation is. Where does i29b ensss1jt)y.hy) m t come from? Why is its temperatury.e by s 9sn)2shj)m1te now so low?

Why were atoms, as oppx+mqh4jdi - u4zf:n+posed to bare nuclei, unable to exist until hundreds of thousands of years af- 4j :4mid nqzpxuf++hter the Big Bang?

Under what circumstances would the universe eventually collapse in on iio:w. qbcf*i;i1+ u owqe0t atqmx 50.tself?

  Using the definition7k vf(q.+:4yrpp edi ss of the parsec and the light-year, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.38 seconds w64wabmui ;. sof arc. How far away is it? d =    ly

  The parallax angle of (2de,bucm 2q4olb88iga n vw5a star is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its parallax angleynov 72 mqs66 nbj.),; crplyk?
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 starn2f3wxi*7k ff+x sps )lng j 3dhm8b7- that is 55 ly away? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away from us as zs/q r/q scb.5a second star, will the parallax angle of the farther star be greater or less than that of the nearer star? By wb5 zr/s.cqqs/hat factor?

  A star is 35 pc away. How long does it take for its li( dri3f+1i0 ts io;qcight to reach us?    years

  We saw earlier (Chapter 14) that the rate energy reaches the Earth fheg/) *bn /jl*d;fmh lrom the Sun (t/*ehmlfdg/jb) *;nh lhe "solar 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 brightness of the Su7p ov ivec vb2*)mw;y-n as seen from Jupiter as compared to its brightness from Earth? (Jupiter is 5.2 times farther from b)2mvco;yevv p*w 7i-the Sun than the Earth.) $\dfrac{l_{\text{Jupiter}}}{l_{\text{Earth}}}$    $ \times 10^{-2}$

  Estimate the angular width that our Galaxy w:;lz6 kr s(zlkjirl +3ould subtend if observed from the nearest galaxy to us (Table 33:zlk 3 l(+rskz6lirj ;-1). Compare to 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 density if it expandb6ra s4 0ye1ufs out6y bf ea401urs 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 whi uvm3yfp;1-zl8 7hpirpci61ote dwarf, it is expected to be about the size of the Moon. Whatci63po1 -8plpy z7 1;hfrvui m angular width will it subtend from the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwna6ara+r 1ib0yi72 uqi o)(tk arf whose mass is equal to the Sun's and whose radius is equal to the Ea i7k+ a0r ion621ti ()qraubyarth's. How many 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 s7a.e1 2 vjn ;bis:pixtce3c: holar masses has a radius of about 11 km. Calculate i3.2c:1in 7j xeiascpt :e;bhvts 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 reactionj5p (rm/*hy fx +8dkojs of Eq. 33-2. (The mass of thoh 5x/ rjkfpdm+y8*j(e very unstable $^8\text{Be}$ 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 apparent6y2ex8d ohcd 1t gw/w8 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 thm( cv:t 76tlpce same distance from us. Two such stars h7(t6vpccm:t l ave 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 that (a) oflkys+5 djmru- q2-,wc our -s 2qmyl5jd cw-+k ur,Sun is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typical galaxy (2 g:u)ahfh*ef*0b bj tlike ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawng y-tp7uh3ia)o q1kk 3 on the surface of a sphere, for which the sum of the angles is (a) 359º, and (b) 1ugy)q- hok p37ikt3 a180°.

  What is the maximum sum-of-the-anglesm* vjvfvr7 2;nod1vo7 /t f*hd for a triangle on a sphere?    $^\circ$

  If a galaxy is traveli2n p uc3:7xidk. ad1xung away from us at 1.0% of the speed of light, roughly how 2 7dau .xkin cd:p13uxfar away is it? v =    Mly

  The redshift of a gala9la gq i8:hs8nxy indicates a velocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of wylfaar07/hb vp,u g y6;0 5ugfyc0g3a galaxy (relative to us) that is near the observable "edge" of the universe, say 12 billiobu/05fp3aya v;0gy ggych ,uwfr6l07n light-years away. v =    c

  Estimate the observed wavelength for the 656-nm line in th b8(6t yls oumat/h8ey 9xi,t 4md09une Balmer series of hydrogen in the spectrum of a galaxy whose distance from usby9yo 8d t0us4i/,tnmt exha9(6 u8lm 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 ga(s*nl(fqc x:,gk b ) csx3w::qnr9d btlaxy, and its distance from us, if the wavelength for the hydrogen line at 434 nm is measured on Earth as beinq(:xf c3lxr 9)(,:wbsncqs* kb dn :tgg 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 (7v(b lwv+sq7x .x ksogalaxy with $z = 0.60$? v =    c

  What would be the redshift parame im*zqajh k.qs,;u/h*r- d8ejyj-0gx*-uwheter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Doppler skcj d*utrn js5my*z2e,)x3- vhift 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 ra ,u3- oqo;nmy3nf qq3bdiation distribution at 2.7 K usi y;oqo,b-3n fqumq3n3ng Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of the un9t06gzso1pahouk oqb, 9-nw6iverse 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:bt:qm )o 9q)sv prz-drm)rt. between galaxies) at any one moment is believed p9r:z:.)qm mrvqr o) sbd)t-tto have 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 universe cooled below theu vri4wjhv8 oj/*0lr2r(d o ;e threshold temperatur0e j/(v *ljho4uirrdwv; o2r 8e 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 d tafgv.*9p 9f3ltkmne1f1dv7r97 h7i tv) hwcould 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 thm fr k7gn7tpdl91 1 f9ht d39twivv7ef.)va *he changes in temperature, luminosity, and size.

  Assume that the nearest staq.h;ad3pa g9 yrs to us have an absolute luminosity about the same as the Sun's. Their apparent brightness, howd q 9phay3g.;aever, 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 angulardms4 mp9jh2-9amgj it/sewb k -din0/x,:w5m velocity of a neutron star which has collapsed to a diameter of 20 km, from a star whose radius was wdisbx/nm-a0 5i -,: d / hmmtmegp9jjsk2w 49equal 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 c(aubn.,8yvb3;54lba 3g zs8nsqrz m when the star in Problem 56 cyv ass;4g83 q nncubz8 5rb.(abl mz3,ollapses to a neutron star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believe im-a9kxqus 9)d to be a neutron star of mass 1.5 times that of the Sun, with diameter 20 km, is observed t) qui9ksm9-xao 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 is aad0gcg svt,4npi5 8tks18 ;e,ldvr. l bout $2 \times 10^6\ \text{ly}$ 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) w9rc*0lrq((zmm anu) y 7r6fv rould provide the critical density to close the universe. zc97a6n r)*frr( mr(vl0uqmy 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, respectively, both ;s4auyr86e vbq8epr )rs8l. alie on the main sequence. Use Wien's law, the Stefan-Boltzmann equation, and the H-R diagram (Fig. Below) to estimate the raevqa6;ela r8pru4 ) s.88yrbs tio 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 parse0wmfg.0k , nmrjr4+rxcs. What is our minimum angular resolution (in degre gj.0wr,0+f kmnxr4 rmes), based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Bd l 6e5i8a2oyfd2z2kzalmer lines from singly ionized helium in a distant star happen to overlap with the Balmer lines from hydrogen (Fig. 27-22) in the Sun. How fast z2ofy5e822kl i6d azdis the star receding from us? v =    C

  What is the temperature that corren ; bm2r s75o5+ uvqens8x(metsponds to 1.8-TeV collisions at the Fermilab collider? To what era in cosmological history does this correspond? [Hint: see (Fig. Belos vsnt27re(o85eunx5q+bmm ; w).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured tht314 osa.fqhk e rotation of gas 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 6s4h 3q a.1koft0 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 "bluy12m e/sdp yit/nx db,8-uk1w e" hydrogen line at 434 nm emitted from the galaxy is measured on Earth to be 650 s n8/yxd-b iwk1m1typ de/u ,2nm.
(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 srl61 olv/ouqvg 03fg) tellar evolution, a star (if massive enough) will begin fusin6vo)q vo /glg1l0ru3fg 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 4 jfx89ac fyibe,+ jqgn7/s)7p 0wb ux
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 lrrd ( zi-fr)7density of the uni(drrz )-r 7ilfverse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$