The Milky Way was once thought to be "murky" or "yk ;.+2smdy7kfj 8kdymilky" but is now considered to be made up of poin;ykd+kyfk y7. s djm82t sources. Explain.

A star is in equilibrium when it radiates at its surfa tb4; ot2sxqc0qp r8b.ce all the energy generated at its core. What happens when it begins to generate more e2b tr;pbqo.04s 8cq xtnergy than it radiates? Less energy? Explain.

Describe a red giant star. List some of itsy7ui .m8/jf0 ww7uos z2ug, fi properties.

Select a point on the H-R diagram. Mark; tjppsyb/) poy u.81/czj+xi several directions away from this point. Now describe the changes that woo.p)/ y px;jc1t 8bypijzs/u+ uld take place in a star moving in each of these directions.

Does the H-R diagram reveal anything about the core of a s 6qcmdtmur, 6v/w q8a1tar?

Why do some stars end up as white dwarfs, and others as neutron stars or bz*:1*lwqudcyer0z 6nlack hol0quel*rn:z1ywz6dc * es?

  Can we tell, by looking at the population on the H-R dia -0wg33dc h+ff5 e-nlq8vgyj lgram, that hotter main-seqevhj l338 ln w-qyfc0 dg+gf-5uence stars have shorter lives? Explain.  ----待选择----yesno 

If you were measuring star parallaxes from the d+k5e3sd*+n +o rweeg/ :prok Moon instead of Earth, what corrections would you have to make? What cha:oo e5kp egns+w3 ++*d der/krnges would occur if you were measuring parallaxes from Mars?

Cepheid variable stars co wafii+f -br: gp:w,/hange in luminosity with a typical period of several days. The period has been found to have aa - :w/b:f +porgiiwf, 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 8jle eq-xab .3bp)wci+m+hco-a8f:t its role in General Relativity?

If it were discovered that the redshift of spunwk3fy/* /dqmy: g hxa24u1vectral lines of galaxies was due to something other than expansion, how mig*3 4 1qh yd2/auxugnf ywv/:kmht our view of the universe change? Would there be conflicting evidence? Discuss.

  All galaxies appear to be mulp:y6 kpk1j pk,9ul4 0/2ekutu3abooving away from us. Are we therefore at the center of the unj1,e4ula / yuk3o upp90u t2:k6pklk biverse? Explain.  ----待选择----yesno 

If you were located in a galaxy near tyuv +b j(0o.xv3oquly7(;(axlpo md)w sk62ohe boundary of our observable universe, would galaxies in the direction of the Milky Way appear to be approaching you or receding l3+a(sdy7)ukobpluy. ; o oxvxv2m(j(0qw6o from you? Explain.

Compare an explosion on Earth to the Big Bang. Consider such questions)v( vp3nn ,r0,jht(ptqr q9ajv6b 1ac as: Would the debris sprr hbjt( ,a 0vnjp93)vvp6,ta qcq(nr1ead 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 or closed?

If nothing, not even light, escapes from a black hole, then how caum2y 3;f+m jpdn we tell if one is the jf+ ym3;pm2dure?

  What mass will give a Schwarzschild radius equal to that of the hydrogen atom immjndjpzj3rj/w2 8-wy2ha7e t 18ke/ n its ground st1 n z e jkdr/jhatmj- 2p8wewm7yj/283ate? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion years. Find that time on (Fig.-l shfmyo9x0q3s8y;1 jtqhz : Below). People have lived on Earth on the order of a mys 9yo1 hl3hj8x- 0 sq:mqtfz;illion years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic microwave background radiation is. Where does 77aq nf1b7rjrf/ i394liulgo wjh 9v( it come from? Why is its temperature now so loi9 uqalfbv7gi1 lor4 f 9(3/h 7rjnwj7w?

Why were atoms, as opposed to bare nuclei, unable to exist until hundreds of 2gqm)gt z:g+p thousands oft zm ):g+2ggpq years after the Big Bang?

Under what circumstancesesr 8-vw r*o6 dfko;2s j8ypw-jw:w)z would the universe eventually collapse in on itself?

  Using the definitions cwhn9 asubx+)sk,m m*2 l qn06of 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 of arc. How far away qtz prcr.n*(hpf 9+;g is it? d =    ly

  The parallax angle oekc.*a *ar-gzwqw +7o)*gr tdf a star is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its parallaho6c01g/2lghgqmu),gad +vl)k f4 z g d5l*dqx 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 that is z+ lobg ,,m k6voq*tadxh193p55 ly away? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away from us as a second st07 hhwypjm55c ar, will the parallax angle ofmjhc h0py5 7w5 the farther star be greater or less than that of the nearer star? By what factor?

  A star is 35 pc away. How l gzk*kxe+ j:0iong does it take for its light to reach us?    years

  We saw earlier (Chapter 14) that the rate energy reaches the Earth from the Suu qzep 8 ,/.7dispe+.2 nlt;auu ngzpdd(t i6-n (the "solar constant") is abs8d qeup- .duz+e(;2 6p .ignz 7,piutdalt/nout $1.3 \times 10^3\ \text{W/m}^2$. 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 bi+mxm,9 gn9 ; ypycxa81;g/yd )no fwarightness of the Sun as seen from Jupiter as compared to it;and ym ;ga)xfopmyx/ 8 91iy9c,w+n gs brightness from Earth? (Jupiter 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 wougy7kx(vmee40ssl0gc1f y( 7p ld subtend if observed from the nearest galaxy to ufs1e(cmgyxy470g p 7 lekv0s(s (Table 33-1). 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 denhlk(9 /-s:d5e z qsdlusity if it expands out to the ordqz: 5/s k -u(l9lshedbit 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 , 87du qz/azk7m-bxiye0l cv1is expected to be about the size of the Moon. What a 0xycqz 7/id7l v-k ,muze18abngular width will it subtend from the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whose mass is equal to the Sun's and fy ep.3bcck.0whose radius is equal to the Earth's. How many f 03cc .pkeb.ytimes 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 solar masses has a radiusb2kyg+ht k;bbrnjqf5 6w.623m:s xzc of about 11 km. Calculate its average density and compare tob;yg bz6 kh:w +2t.3 q6srj2n5kc fmxb 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 reactions of Eq. 33-2. (Tw4cla/o nke9slx3ag(k1 -d -ol1qtt, he mass of the very unstabtl-, xa1o4e csltd ko-3/ ga1l9(w nkqle $^8\text{Be}$ 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 brightnekt e,hg/fism1cl( .8tss $l$ 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 certaiy*j l 8 (m-fjmlvu wr+uw65:tpn cluster are assumed to be about the same distance from us. Two suluw m m:j *jfwt+56py(lvu-r 8ch stars have 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 rads u- 8;o,cq3ht1wcx/z s4uc epius for a star with mass equal to that (a) of our Ssq/ xuhu8-c;ts1cpze3ow c4 ,un is    km, and (b) of Earth is    mm.

  What is the Schwarzschild raes;jek4/ q-yi dius for a typical galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawpk jga1x as 1tt2z2l9 rzh78k)n on the surface of a sphere, for which the sum of the z 19 2htx1z7l tkak2 8a)rsgpjangles is (a) 359º, and (b) 180°.

  What is the maximum sum-of-thm qh--e x tp87vrc,fp(e-angles for a triangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the speed of light, roughly hfmr44u3ke tgnp,s6-u1pnh * yow fauhe4 k gp,fnyus-4 1r6n 3m*ptr away is it? v =    Mly

  The redshift of a galaxy indicates dy-piivck3)pn::x 5ta velocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (relative to us) that *muz8rh m*usz f n1i;v 3gk(4eis near the observable "edge" of the universe, say 12 billion light-ye;h34 *zm1 uurv*(nzkfimgse8 ars away. v =    c

  Estimate the observed wavele 4nykc.; at t1 paeg6/4z2ilwangth for the 656-nm line in the Balmer series of hydrogen in the spectrum ia w tgan.6 zle p/k;4ay4t12cof 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 6yqw6 5yj9qih6 5h lltgalaxy, and its distance from us, if the wavelength for the hydrogen line a6556 hq lyq 6lwyj9thit 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 galdh q1 hi x:f .ib-i/9c+v/aeihaxy with $z = 0.60$? v =    c

  What would be the redshift parbl mq76ro2p1 mameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Doppler shift in wavs3zv6 zhlz jpcp2v/,1 elength is $\Delta\lambda/\lambda \approx v/c$ (Eq. 33-5b) for $v \ll c$. [Hint: use the binomial expansion.]

  Calculate the wavelength at thqedbt89 ,8b upe peak of the blackbody radiation distribution at 2.7 K using Wien’s8puq9tedb , 8b law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of the universe ik v - ;a0u2nvxdqn )7mr4wb0zzs $\rho_c \approx 10^{-26}\ \text{kg/m}^3$. 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 distan+u q)t+fr3a0sllef mo f r2r5,ce between galaxies) at any one moment is oqse r, +25lrt+m3f)aluff0 rbelieved to 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 the threshold temp h4g)l(q/hi yaerature for producin(h)ghq l 4y/aig
(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 couljl1lbge st*-b0otao787 *lib.fom/ md undergo the three changes represented by the three arrows, A, B, and C, in the H-R diagram of Fig. 33si-j77*.of0b81*lb matl o /olbtm ge-28. For each case, describe the changes in temperature, luminosity, and size.

  Assume that the nearest stars to us have an ay+m8h a8apx8,we j7fhbsolute luminosity about the same as the Sun's. Their apparent brightness, however, is a aj+ why 8p88amefx7,hbout $10^{-11}$ 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 abc a+(bw4e/r m neutron star which has collapsed to a diameter of 20 km, from a starb +4(c erbma/w 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 70q b hp-yfn5iwhen the star in Problem 56 collapses to -nq0bih5y7fp a neutron star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, belie4 1d5s i1k nt/fe2jp),1mvhcgv ccx*uved to be a neutron star of mass 1.5 times that of the Sun, with diameter vfn)m sx ,p41 kgu tj*hc5cc12d/1ive20 km, is observed 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 oulp7i.qgvv: ;z r Galaxy 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 pm,p5bhs z3s y;rovide the critical density to close the universe. Assyp,35mbhss ; zume 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 spect3pz /l i5e0sk-.hhrnyra 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. Below) to estimate the ratio of t0-erp/hkz3s 5iy.nl h heir diameters. [Hint: see Examples 33-4 and 33-5.] $\dfrac{d_{400}}{d_{600}}$ =   

  Suppose we can measure distances9 hzh :woej.. sfjn;7y with parallax at 100 parsecs. What is our minimum angular resolution (y njw .f szhhj.7;9e:oin degrees), based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines im 2b46 )--dbgvvkasonkd 4* ufrom singly ionized helium in a distant star happen to overlap with the Balmer lines from hydrogen (Fig. 27-22) in ths4kgo2- 64vb-)md*b kiav n ude Sun. How fast is the star receding from us? v =    C

  What is the temperature that corresponds to 1.8(eh-dh bi l4;(j fw0in.)gpfz -TeV collisions at the Fermilab collider? To what era iw0-i;gf nzp b ji)d(f.h(h4 eln cosmological history does this correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation of gas arou ,qryn,j u+,gund what might be a supermassive black hole of about 2 billion solar masses at the center of a ga q,,yu,+ugjn rlaxy. 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 Earemssgsbb.8 axl 7p7/: th. The "blue" hydrogen line at 434 nm emitted from the galaxy is measured on8 :7l/ ag bxemp.7ssbs 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 ev) g(noi8mq;sp olution, a star (if massive enough) will begin o;i8( mn sgp)qfusing 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 reactior*djf/v mhxy );jo j-bu1 w:9cn
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 nj k0 ns jg4u 76x(8jky-,ayzdits density equaled the critical density of the universe, ,yk kxy 7a(zjnus-04j86jdn g$\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$