The Milky Way was once thought to be vtpkf184c jmq0c (io2su w8-f "murky" or "milky" but is now considered to be madekcjf0s 4 v2ft-8 wm8uo 1icq(p up of point sources. Explain.

A star is in equilibrium when it radiates at its surface arf+)a xor:e-q e6vim:ll the energy generated at its core. What happens when it begins to generate more energy than it radiates? Less energymr) ia- exv6f:+ :qero? Explain.

Describe a red giant star. Listij6i kb v5wli 9chvnbt.p aij8;;v-(6 some of its properties.

Select a point on the H-R diagram. Mark several diht2l2m dw*9v prections away from this point. Now describe the changes that would take place in d*2t92lpmvwha star moving in each of these directions.

Does the H-R diagram r un3 6 gjx**,e.v9/etn ivlpiueveal anything about the core of a star?

Why do some stars end up as white dwarfs, and others agpr+vsopl+t*zw ra cj*2;q8 m7()y s es neutron stars or black holem ec7jg *p)+8aspzqt v(yw+ ro2*r; lss?

  Can we tell, by looking at the population on the H-R d/bmqf*;jal:x/g u. uu ftw.+biagram, that hotter main-sequence stars have shorter lives?awbuu/g .+ft:fxj/ b *um;lq. Explain.  ----待选择----yesno 

If you were measuring star parallaxes from the Moon 9zn-d5xl+r cminstead of Earth, what corrections would you have to make? What changes would occur if you were measuring parallaxes from Mars5 +d9xlnm c-rz?

Cepheid variable stars change in luminosity with a typical period of sever oll 03c6ha+ge2cu3je; fm6ota/iw/: ebif) mal days. The period has been found to have a definite relationship with the absolute lumf/2ih+cb/ufja ei cel oglao;)6:6 w3e0 tmm3inosity of the star. How could these stars be used to measure the distance to galaxies?

What is a geodesic? What is its z8qy7 kpaku:nwni,1/ role in General Relativity?

If it were discovered that the redshift of spectral lines of galaxrz0iwom cqj 7m(;vc5l;)w sw 1ies was due to something other than expansion, how might 7)cw j 0(; o;zvmiq5ws1wcrl mour view of the universe change? Would there be conflicting evidence? Discuss.

  All galaxies appear to be moving awayw+vu4e1pd i1yjij+b4* p9y ka from us. Are we therefore at the center of the univers+kdy bwiv9p4+*4 1ujaijey1p e? Explain.  ----待选择----yesno 

If you were located in a galaxy near the boundary of our obseru,ntwqi g v vz1165xy)vable universe, would galaxies in the direction of the Milky Way appz1viwtg 6 nyv),1q5u xear to be approaching you or receding from you? Explain.

Compare an explosion on Earth to the Big Bang. Consider such h q +,banm1kj:3+hzuiquestions as: Would the debris spread at a higher speed for more distant particles, as in the Big Bang? Would the debris comnu 1+3mhhbaji , k+:zqe to rest? What type of universe would this correspond to, open or closed?

If nothing, not even light, * u;t8uld*c6. hqmy fxescapes from a black hole, then how can we tell if onexhcdu**yql8ftu ;. m6 is there?

  What mass will give a Schwarzschild radius equal to that of the hyde5t ;taund9 xp/kl2-ra6p)m u rogen atom in its ground sta)t;xerm-l9 utpd/2knp ua6 a5te? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion 6 f a6wcak 7 7y2x5z-d faa3diso+mqb0years. Find that time on (Fig. Below). Peoplc f-ka qd62s 70o6fa3+5wbz7yiaxmd ae have lived on Earth on the order of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic microwka,:uotutqq p69/g. e ave background radiation is. Where does it come from? Wh.q:egu6t9k,pauq t/ oy is its temperature now so low?

Why were atoms, as opposed to bare nuclei, unable to4/; rg-qmauhe exist until hundreds of thousands ofgm4areh-; /q u years after the Big Bang?

Under what circumstances would the universe eventually collapse in on itselfb07pqa6;c ygl ?

  Using the definitions of the parsec and the lighb d p,b+evi9mwj 98n/bt-year, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.38 se;1lqn3l 6dix3io l4.j.vuvz sconds of arc. How far away is it? d =    ly

  The parallax angle of a star isd :cgqtd:+0;xrgglm 5 $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its parallax h1eijy5hf)ss+ d ;mdk 0gas-p+7;qj tangle?
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 lc63is,2nq-dsvq r ;/b gur.pk y away? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away from us as a second star,o2sx8nksh;4 b will the parallax angle of the farther stans2ksh8x 4b ;or be greater or less than that of the nearer star? By what factor?

  A star is 35 pc away. How long does it take for its light t;+tvk+ qn; gz ps39vu2z-*hbudvlya.o reach us?    years

  We saw earlier (Chapter 14) that the rate energy reaches the Earth frop2ovr/ufmkl; 1fxp5; ly r6r0m the Sun (the "solar constant") is ab0vlym 6rf 1;pk/;u52rp roflxout $1.3 \times 10^3\ \text{W/m}^2$. 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 y,g7iqpe)-c c brightness of the Sun as seen from Jupiter as compared to its brightness from Earth? (Jupiter is 5.2 times farther from t7ig-qp )c e,yche Sun than the Earth.) $\dfrac{l_{\text{Jupiter}}}{l_{\text{Earth}}}$    $ \times 10^{-2}$

  Estimate the angular width that uz8os uy6pw4a aa)z:aq *-j,four Galaxy would subtend if observed from the nearest galaxy to us (Tabs8u6ozawa :yu-z qa,4)f paj*le 33-1). Compare to the angular width of the Moon from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes v5jgcubrk+ t/ ;p3n+sa red giant, what will be its average density if it expands out to the orbit of E+vrb/ ju c+3ngkt5ps;arth ($1.5 \times 10^{11}\ \text{m}$ from the Sun)? $\rho = $    $ \times 10^{-4}\ \text{kg/m}^3$

  When our Sun becomes a white dwarf, it is o54rv5r o7blj5+ 7 ux+obiwfdexpected to be about the size of the Moon.5 jforlbrdobo57ux7+w54 v +i What angular 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 ej 4 5-h(.kh0vls ;3gn nj,i7hu p8ovcmzoq1q mqual to the Sun's and whose radius is equal tuim8j. ljo (zsn-3k q0hg1 5vc4 7h;nhpmovq,o the Earth'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 solar masses has a radius of about 11 km. Care/ l0)7 08:wd re.lphg gvdstlculate its average density and compare to that for a white dwarf (Problem 13) and to that of nuclear ma/gwv :ld0 e0gr pr.set87) hdltter.
$\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-value ye* rcdslz9 1r 4ik.+zt/b+mss for the He burning reactions of Eq. 33-2. (The mass of the very un 49 czs bsk*rlr +mey.+tid/z1stable $^8\text{Be}$ 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 brigfk5(oyq-s0 4o mlky vik0+y)rhtness $l$ 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 certainy0maafh d+lss- 3k() y cluster are assumed to be about the same distance from us. Two sucam y)3k +l-s(0yhfadsh 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 radius for a star with mass equal to cta kst7 1)3q)cmr8bcthat (a) of our )mbqccs837t1)k rcta Sun is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for/zqk lzs./+ /eui,ag6+at he9n d )ieu a typical galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a sphere, for which teowut nh5(r(8p30 q chhe sum of the angles is (a) 359º, andp(ewun ch0q5 (83 ohrt (b) 180°.

  What is the maximum sum-of-the-angles for a trimj (x-a h8/ 3sgy.-7ntvz bvfvangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the speedwqmx h5 kunouek p2n5-x0t1/i qph82. of light, roughly how far away is it? v eqo1 8m50ux hk2n 2pq-. huikp/nxtw5 =    Mly

  The redshift of a galaxy indicates a velocitys sa/fq2u* f-d of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (relative to us*1 *0*haqdsryh gj - dy8htm(b) that is near the observable "edge" of 8jq1y**d(0 gyrs h-thmhba * dthe universe, say 12 billion light-years away. v =    c

  Estimate the observed wavelengrto*jkls 3(jam:;8 mzth for the 656-nm line in the Balmer series of hydokjs3rj :;az8 tml(*mrogen 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 dip-up7;;vr 5dql3owlostance from us, if the wavelength for the hydrogen line at 434 nm is measu-po5v73p l;qd;ulo r wred 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 galaxzny037uo rsv +y with $z = 0.60$? v =    c

  What would be the regktj 9/8vsknxcd7 - ;mzn5 ij,dshift parameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Doppler shift in wz6;oglr- 0 y(ye(dpnf.( rb ucavelength 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 blacc8xi ei5*mvh1 kbody radiation distribution at 2.7 K using8 v1h 5i*ceixm Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of the universe +:.d9*tp)w rv r hwpcfis $\rho_c \approx 10^{-26}\ \text{kg/m}^3$. 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 distv0rkr h spx+8ioyd63*ance between galaxies) at any one moment is believed to have been inversely proportional to the absolute temperature. Estimate the size 6xidr3 * hkp+ys8 v0roof 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 thresholnglvdn w uk;:5f 8)pe0 4j(jord temperature l w;e:g 4 rj nonk)f(p80jvu5dfor 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 could undergo the three chan-xgb)x / oac(;3 w.tgb9d/8sqvrwcloges represented by the three arrows, A, B, and C, in the H-R diagram of Fig. 33-28. For each case, describe the changes in temperature, luminosity, o bcx vw -cg/astgd83/rxlo9(q );.wband size.

  Assume that the nearest stars to us have an absolute luminosity about the 3+obf1kizfxet,4r 4 lsame as the Sun's. Thez34xl, tkr4ffo e1 +biir 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 angular velocitylmj 4bppq.tp.d j ,3u- of a neutron star which has collapsed to a diameter of 20 km, from a star whosetu3 dp4pqj-j .plb,.m 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 whbaznbxf9x*vk qj h-mvlc 229c0;8 vq ;en the star in Problem 56 collap*;qhk9vj-bv a08nv qxc;mf2 lx2 b9czses to a neutron star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believi.,pr2 2lqtyf ed to be a neutron star of mass 1.5 times that of the Sun, with diameter 20 km, is observed . ypq,2itlr f2to 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 mx. lx1tww + ( ts41w:dtidsl9Galaxy 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 critiiw;xgc n0,4 xhcal density to close the unincxi;0x gh4,w verse. 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, respectivu7 qkzb0c.;-1dwz qb gely, both lie on the main sequence. Use Wien's law, the Stefan-Boltzmann equation, and the H-R diagram (Fig. Below) to estimate the ratwbucz. ;g-k q z07d1bqio of their diameters. [Hint: see Examples 33-4 and 33-5.] $\dfrac{d_{400}}{d_{600}}$ =   

  Suppose we can measure distances l h1uz j04a4khwith parallax at 100 parsecs. What is our minimum angular resolut 104zhul4hkajion (in degrees), based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from singly ionized he ,s3t g/law:l ugl, an(xhnw00lium in a distant star happen to overlap with the Balmernanw0 wls/guax 3 l:0 lh(g,t, lines from hydrogen (Fig. 27-22) in the Sun. How fast is the star receding from us? v =    C

  What is the temperature that corresponds toh6/qtvwk yn(sbvdg00x yq +*7 1.8-TeV collisions at the Fermilab collider? To what era in cosmological history does this correspond? [Hinqdkb60+ytvnw70/ yqx h(g v s*t: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the o:/s-q(-qe j7. n 8+hdhhinbkhy (gmtrotation 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 60 lighte qh7t hhqiy:ns(-mh.nb / d+ g-o(jk8-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" hydrogen line at 434 nm iy -nzk8r:xcdyu:r- 4emitted from the galaxy is measured on Earth cxduy i n48: -ky-:rzrto 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) j bk/o kpo5**wrvbfo3 1(u kl+will begin fusing carbon nuclei to form, for example, magnesium: rf(l 5jou /ob3 1 wb*vokk*p+k
$^12\text{C} + ^12\text{C} \to ^{24}\text{Mg} + \gamma$.
(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 -7qfzt3o)gb z
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 ib(u .jao-t-qa ts density equaled the critical density of the univertaa-j-.u oq(b se, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$