The Milky Way was once thought to be "murky" or "milky" but is nol.1l oz ajh),ew considered to be made up of point sources. Explz)1eohjl .a l,ain.

A star is in equilibrium when it rz,0a+ pt s4ksd13js.;u:qq g)upoecz adiates at its surface all the energy generated at its core. What happens when itkq4jtazoep+s q0z pu;csgu1d: 3 )s, . begins to generate more energy than it radiates? Less energy? Explain.

Describe a red giant star/kaeqnofyw. * u *l4c:. List some of its properties.

Select a point on the H-*.k0xk7p h1sy o hl9nqR diagram. Mark several directions away from this point. Now describe the changes that would take place in a star moving in x9 0kyknqphol .*h71s each of these directions.

Does the H-R diagram reveal anything about the core of a so55qqb 6bn +,syhi/h ytar?

Why do some stars end up as white dwarfs, and others as neutron stars orhj+k7d9 6otpc black holes7d+o cjkpt9h6?

  Can we tell, by looking at the population on the H-R diagram, that hottel-s g26mtp lc) o v.9(bmx(yqst /lyj:r main-sequence stars have shorter lives? Explain. -xjcb sltm9q(ol :gvmy6pyl(/.2t s)  ----待选择----yesno 

If you were measuring star parallaxes from the Moon instead of Earth, whacnm/j sdha.k f)/ioaf4+0jw 9t corrections would you have to make? What changes would occur if you were measa+o 4.ndwcmjs/ 9fhka i0j /)furing parallaxes from Mars?

Cepheid variable stars chan. 8af 4p9 chmkx6h( fwk+;drxr,hi:qxge in luminosity with a typical period of several days. The period has been foundrkhx(pi,mkhc6+. qhdf8 x; wxr 9a4f: to have 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 General ujs(1q3 t qp2:sp1 lhagq-v,xRelativity?

If it were discovered thatn7od3 zr8u f9s the redshift of spectral lines of galaxies was due to something other than expansion, how might our view of the universe change?fr97o 8 usnzd3 Would there be conflicting evidence? Discuss.

  All galaxies appear to be movigl8 ;uhqs5s*l ng away from us. Are we therefore at the center of the univeul5s s*;g8q hlrse? Explain.  ----待选择----yesno 

If you were located in a galaxy near the boundary of ourlb/ ( bwj*+z zkjz/6tv observable universe, would galaxies in the direction of the Milky Way appear to be approaching you orzb +6wjk/ *zltzb(/v j receding from you? Explain.

Compare an explosion on Earth toyiha(.u) qu:g 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 type of universe would this corqay:ui ()ugh .respond to, open or closed?

If nothing, not even light, escapes from a black hole, then hos(h(lfv1ei14 iid4 yiw can we tell if on(ysil4i1(14df ieh ive is there?

  What mass will give a Schwarzschild radius equal to that of the hydrogen zxkkr/p )r u0v-;7gr catom in its ground skp0c; urx)vr g-7zrk/ tate? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion ;u3ing 1 ,fjl pfl2+lpyears. Find that time on (Fig. Below). People have lived on Earth on the order of a million pf3 ;1pl,+llijgfun2 years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic microwave background radiation is. Where does7:w c:ex us8az it come from? Why is its temperatua e78:zsxw uc:re now so low?

Why were atoms, as opp sjl jujp239 3g;8oiftosed to bare nuclei, unable to exist until hundreds of thousands of years after thesuot2p i j9jl3f;g8 j3 Big Bang?

Under what circumstances would er-: d 6+.buydaj frf3 lx 65ojtlj7 9dm0al3athe universe eventually collapse in on itself?

  Using the definitions of the parsec and the light-year, show that p,hdd9pr )t2j $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.38 seconds of arc. How far away is it? d z4pl2phu bi /jfn5(f. =    ly

  The parallax angle of y0qh/xq c9+tziov: r:)i;ysj a star is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is i :h5 un*gsdg-m45varxts 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 s;6e.;: da d)ha dz.gw k vjhh:p.rlg.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 second star, s/2m c b te*p5h6on;gywill the parallax angle of the farther star be greater or less than that of the nearer star? 2mbt sn5 eyhg p;oc6/*By what factor?

  A star is 35 pc away. How long does it vl uz0,i; mnz0take for its light to reach us?    years

  We saw earlier (Chapter 14) that the 58chax )k,4 sa1pah ijrate energy reaches the Earth from the Sun (the "5)4 ,ik1cph xa8aj hsasolar 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 Sun as seen from Jupiter as compagq i io,idks)dy8n -65red to its brightness from Earth? (Jupit)g8-qni6dy o d,ikis5er 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 Galb oszfes*g(by j+i uvx 3(*//maxy would subtend if observed from the nearest galaxy to us (Table 33-13s*ixebs (o/vb(/u *z m f+jgy). 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 ave6 d64;leiimo8a0t karuwu. 5 urage density if it expands out to the orbit of Earthli otu 4m duawrk;866ue 5a0i. ($1.5 \times 10^{11}\ \text{m}$ from the Sun)? $\rho = $    $ \times 10^{-4}\ \text{kg/m}^3$

  When our Sun becomes a white dwarf, it is expected to be about the size om m d0z9,mc1eb,:p1h ouqbc*yf the Moon. What angular width will it subtend from the pru 0mo19m1hpm,* dqz y b,cecb:esent distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whose mass is equal to the Sun's andr dge-u 64q)sa whose radius is equal to the Earth's. H-4d)su 6rg eaqow 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 ier,k9szfhpqux7:p;.fwf+mm o9b -- is 1.5 solar masses has a radius of about 11 km. Calculate its average density and compare to that for a white dwarf (Problem 13) andi+b;mp7:f- exf.-ouhsq f pz9,wkmr9 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 bupj2p29ev :mme 6ltnx*rning reactions of Eq. 33-2. (The mass of the very unstabl2 nj *9pxleep6tv2:mm e $^8\text{Be}$ 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 apparent brightness )qlh: grqbt(5 $l$ 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 clug+9gc+jukox6 ster are assumed to be about the same distance from us. Two such stars ha96jug+o+ xk gcve 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 equp63pxx vocj zc-t6d-5al to that (a) of our Sun jcdx6 -53tz-v6oxpp c is    km, and (b) of Earth is    mm.

  What is the Schwarzschild t xwc vx96ek5uk7kfv -m46(pq radius for a typical galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn k7: inj rzt50non the surface of a sphere, for which the sum of the angles 5ntj0rz7n : kiis (a) 359º, and (b) 180°.

  What is the maximum sum ah2c x5t5;6c joq/(9 gn3qgn*zdun cj-of-the-angles for a triangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1s n*a3tqw86ln .0% of the speed of light, roughly how far68nt w lsa3nq* away is it? v =    Mly

  The redshift of a galaxaveaqh.l ll.yw6;5 . e3*z-knv:eau sy indicates 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 near the obse a zh+4ah( af; /uiwh2xkmg15jrvable "edge" of the universe, say 12 billion light-years awa;ahmu/1h 2i (z5w +ajak4xgf hy. v =    c

  Estimate the observed wavelength for the jx4: e0whma7bofy po;4+i3q y656-nm line in the Balmer series of hydrogen in th axh:yfo;3+me oy 7iwp4jqb40e 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 +(0hicb1w x xq:ly 6meits distance from us, if the wavelength for the hydroglx6mw0 :ceyqih(b+1 xen line at 434 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 galaxy wwpzg kn:n+ ck1+4nctpw +.6 uiith $z = 0.60$? v =    c

  What would be the redshify-,s a9rkx z8pkin) g-c9g+qjyq9 3cst parameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the ,6 onkz8trjoz.z4wfa2ur; s /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 radi ir*(q:0tgkze ation distribution at 2.7 0egz k :r*tq(iK using Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of the unive kvdcotky) t:a6ori/bh*:1x ;rse 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 avmbqlp6+/ esrv5m 9y 6;f xjm8cerage distance between galaxies) at any one moment is believed to have been inversely proportional to the absolute temperature. Estimate the size of the universe, compared to today, at pflv8 sre 66y9x5 c/mbqm+;mj
(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 ):f3b : hwv(l8ivo4b-e obyveuniverse cooled below the threshold temperature for producing -: (i ovbweb e3:)yho4flbv v8
(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 u8x,q-lu 2p yxv-f(uk nndergo the three changes represented by the threuyx-8k p2vu-nxq ,f(l e arrows, 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 ab j-)fu; uqr3*fdkv ld(solute luminosity about the same audfr(q*jd kuf-;3 vl )s the Sun's. Their apparent 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 /g: x8,1p kuldtv3 jfhg; j4rwangular velocity of a neutron star which has collapsed to a diameter ofwxpkgu/,41j3t;d 8fg hvlr j: 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 tcsu2e(1plx5m;3szs u0n )wp hhe star in Problem 56 collapses to a neutron star? up 2s( xs1snm h lec3;p)zw50u$\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 timo0(x,qzyt og e:5vgrqf 3/en+es that of the Sun, with diameter 20 km, is observed to have a rotation speernq 0/(e,q:o3o e+gy5z tvfgx d 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 lw4rpm1j77n0v ( e9;7auzl.nc i hj bcGalaxy 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 crit +mxo/pwp23fub +0qddical density to close the universe. Assume 0 3pfxpmbq2w+dd +o/uthe 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 6qzp8 1c8poicqnz67 )r00 nm and 400 nm, respectively, both lie on the main sequence. Use Wien's law, the Stefan-Boltzmann equation, and the H-R dia)ppcqzcz o68q r8 1n7igram (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 hb5-m zn(a-z 9xitigelz10*z100 parsecs. What is our minimum angular resolution (in degrees), based on this information? ei h zmxb9-l(zn 1z- 0i*tag5z$\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, 2v pz 9q*gzat76e-urb/o ws5othe Balmer lines from singly ionized helium in a distant star happen to overlap with the Balmer lines from hydrogen (Fig. b2 oz-pztrv9oue a s6q5/w7g*27-22) in the Sun. How fast is the star receding from us? v =    C

  What is the temperature that corresponds to 1.8-TeV collisions at the Fermilab,l a4ugi4hy39xysf j 0 collider? To what era in cosmological history does this correspond? [Hint: see (Fig. Below).] T 9 g43f,yhxs0liu a4jy $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation of gas around what might 46eew1:9hw;m nibnfupl*r 9 rbe a supermassive black hole of about 2 billion solar masses at thmwbl nwr :;ipe9r 1e*9hnuf64 e 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 "blue" hydroh/jqn*cv,k mmw0)ef 3gen line at 434 nm emitted from the galaxy is measured on Earth v3/n*cqm j0f ,)emhwk 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 enough) will nn;o7xlrk( kbp8la./ begin fusing carbon nuclei to form, n o.rnlkxa 8k( 7;pb/lfor 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 ( g-./qt xfq8p8p:vusr:t ni c
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 equale*v: x;xoug:m,hplev2 (gvs i1 d the critical density of the univeoi(v m vx,p1e:*vsh;g:lx2ugrse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$