The Milky Way was once thought0am76r,)sv-wz umpjz *eks1b to be "murky" or "milky" but is now considered to be made up of point sources. Expl*vze7u0a-) mmss6zkw1pbj,r ain.

A star is in equilibrium when it radiates at its surface all the , mhyfwew90e5 energy generated at its core. What happens when it begins to ge hwmefye0w ,95nerate more energy than it radiates? Less energy? Explain.

Describe a red giant star. List some of iq bwcru/*t.ieo 1p3/w ts properties.

Select a point on the H-R diagram. Mark several directions away from this point.w,3v8bp roza6 Now describe the changes that would take place in a star moving in each oop 8 wv,r63abzf these directions.

Does the H-R diagram reveal anything about the core of a;+s 1zrk,;p 1dyj*v mybile:q star?

Why do some stars end up as white dwarfs, and others as neutron stars or black3 u yk156yn pi9mc00*jexsum1ee8odk holm 05*j6 e1y8syoekn3md u0pe 9kuci1 xes?

  Can we tell, by looking at the population on gk-/c 1. ho 0r.qx;bc5nq oslythe H-R diagram, that hotter main-sequence stars hah0g ;q-ocrc.xylnq 51o/b s.kve shorter lives? Explain.  ----待选择----yesno 

If you were measuring star paral.1 xvv+p:oz0h+v w xprlaxes from the Moon instead of Earth, what corrections would you have to make? What changes would occur if you were measuring parallaxes fvrvh +x0z:v xpo+ 1.wprom Mars?

Cepheid variable stars change in lumino 9vobyxh, xg0tptuc)k)w/; 2 jsity with a typical period of several days. The period has been found;2w0h) x,9 yuc)t/vkpjgtb o x 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 inqr2s a/n qivd):pn7igdfg-+n+x p.m5 General Relativity?

If it were discovered that the redshift of sps 8iz*/fa8n xy(g u,6wvxxl4oectral lines of galaxies was due to something other than expansion, how migh(4y,v8s a*z oi8x fxng/6xu lwt our view of the universe change? Would there be conflicting evidence? Discuss.

  All galaxies appear to be moving away from us. Are we therefore ath1 n; emucb,v 4x2sjyuove s),9vd45p the center of the universe? Explsep,4j 4v u5v9s)umx2,ocyd;n 1evbhain.  ----待选择----yesno 

If you were located in a galaxy near the bound xkm2naxlc2--fziru7rb.4 n*ary of our observable universe, would galaxies in the direction of thufilr.x 74 a 2n--n* m2bxzkcre Milky Way appear to be approaching you or receding from you? Explain.

Compare an explosion on Earth to (wy4 mm ) 9s+5tjggj g rf,3lr54s5oh5hmlnggthe Big Bang. Consider such questions as: Would the debris spread at a higher speed for more distant particggghw5 to,5 m+hrflg54nr 5yg(l)94 smjsj m3les, 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 hows+pkq6a( q 2nf can we tell if oqs6(p+2n qkfa ne is there?

  What mass will give a Schwarzschild radius equal to gkf q +plqf5in7k-:u2that of the hydrogen atom in its ku2fg:q+pk5l q f7-n iground state? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often gzad+o t+2 gji;iven as about 4 billion years. Find that time on (Fig. Below). People have lived on Earth on the or;todjza+g +2 ider of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic microwave background radiation is. Where does it cpj kie+-xqpo 6k8kh 59t5xy ,tome from? Why is its temperature no+qe9oy i 855,-kpx tkj6thkxp w so low?

Why were atoms, as opposed to bare nuclei, unable to exist until hundreds ofg3 1z( o9jgu*/z kx2hgj+iogw +whv y, thousands of years a3ox1*woy2i+hju9gk h /jv g+zg(gw z,fter the Big Bang?

Under what circumstances 3va2.a yv7pg ywould the universe eventually collapse in on itself?

  Using the definitions of the parsec a(5ur/v -m almind the light-year, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.38 seconds of e5 s(uq)xl )otarc. How far away is it? d =    ly

  The parallax angle of a star u ns6o -ry21p6- b3eoiffv;obis $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away.) ikpln lxsoni +1*u09m.*wxr What is its 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 vubx5pd:o, 8y 2o c6vsai5h5e2x(xmpangle for a 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,hz5 .qidasw : *u t*f/5iwwe;i will the parallax angle of the farther star be greater or less /.ew ;dt wfa ii:zihu*5w*5s qthan that of the nearer star? By what factor?

  A star is 35 pc away. How long does it tada+zydu48 ,i8offlm 8ke for its light to reach us?    years

  We saw earlier (Chapter 14) that the rate energy re nz4gu(7qd u(;rtpf/wdkb4 3laches the Earth from the Sun (the "solar cdzudpf k wg34u7;/4btnqr ( l(onstant") 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 Jno( 0xg1;k snsupiter as compared to its brightness from Earth? (Jupiter is 5.2 times fs;g1xkn (0 osnarther from the Sun than the Earth.) $\dfrac{l_{\text{Jupiter}}}{l_{\text{Earth}}}$    $ \times 10^{-2}$

  Estimate the angular width that our Galaxy would subtend bk6/mtew i*)mif observed from the nearest galaxy to us (Table 33-1). Compare to the angular width of thekm/) 6m*bw eti Moon from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, what will be its average de.mxica::8 n*jg va g22cbgn5pnsity if it expandsa:na 2g xm*8 gn5ivgjbcc2:p. out 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 expected to be about the size of the h)1qh3 cge ht7yn6kaw* /gz *sMoon. What angular width will it subtend from the present digz*/)ns*3th 7w6e hqh a1 cgykstance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density ofhwvqq0:9/ ,6l tu ;gw ydsnc9qsccd.* a white dwarf whose mass is equal to the Sun's and whose radius is equal to the Eatcq s9h d wcug.vsn; 90y6,lqq/d:cw *rth'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 rfp 0ewv df: octaf,8)4adius of about 11 km. Calculate its average density anatf )wdp: 0fo8vfc, e4d 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 reactions of Eq. 33-2. (The mass of i:*8nlcrx 6g )2kwlpfthe v*lik 8cpnrx6f wgl2):ery 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 apparent brigh-yjdyqua xl9 ,l5k-)+a uzr 3btness $l$ 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 aboutn/a8 t0vp sx+k.rc81 9/bdsp vxbhc *j the same distance from us. Tpsacx0r c+.dv*ptjks9/ h/nbbv 881 xwo such 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 that (a) of o .kn.)yixc* oaur Sun is.)cnx io*a.y k    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typical gal ,p3 t3ix2oup)n*m aavaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a sphere, for which the sus)o6 qvs1i1 zem of the anglesevz6qi o 11s)s is (a) 359º, and (b) 180°.

  What is the maximum sum-of-the-anb1yd) qypqvxbza5)+7gles for a triangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the speed of li ld*l-724byv) ztgu wpws12dfght, roughly how far als)2d24bp u -wl7 tfvz *ydg1wway is it? v =    Mly

  The redshift of a galaxy indicates a velocgdg/ggk u:qz-48 z-icqifb2 1 ity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (7n6 gyd7:5 ln ugvdo4xrelative to us) that is near the observable "edge" of the universe, say 12 billion :645uy7g7l ndngxvdo light-years away. v =    c

  Estimate the observed wavelength for the 656-m1pckjcy6 i31nm line in the Balmer series of hydrogen in the spectrum of a galaxy wc 16j1i 3kpcymhose 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, , tf.za u+l)jgo sx(x0and its distance from us, if the wavelength for the hydrogen line at 434,ogfsl txj() .u0+ azx 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 t+ur)8 4otb fagalaxy with $z = 0.60$? v =    c

  What would be the redshift parameter /8.b aoisc.mkz 85lw8q ae.3:x t; ptzurw/cw$z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Doppler shift in wavelength is d84 ugrtrap5*ng;uh w(+- xru$\Delta\lambda/\lambda \approx v/c$ (Eq. 33-5b) for $v \ll c$. [Hint: use the binomial expansion.]

  Calculate the wavelength at the peak of the blackbody radiation distribu/jm6,-l0e. sfz,c5s ykco7ysdqd l:ftion at 2jlqyk,z 7yfsm0lc/df,5 .d-o sce6 s: .7 K using Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure o g n;svwv ,dkj1uhtbtl)mg-5a4+m ,f(3d/qjzf the universe 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 (ea+yz p xwndf523hr2;/fx*s wnjrke7))pv; qthe average distance between galaxies) at any one moment is believed to have been n5 2efj+ spx wenz7r)qwah ;v/3pf)* k2dr;xyinversely 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 tim450 qxz3fdwvvwl5wj ) 3qhr *ke had the universe cooled below the threshold temperature fr*qqfv4 l3 wj5kw)v 5 z3whd0xor 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 changes represeg yi ,d6e,p t8g12m14sah1 b -kgbpaxdnted 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, lumspahi18eb d1dg-xg,b m,a46yg p2 k 1tinosity, and size.

  Assume that the nearest stars to us have an absolute ln 5a/4dt--y bgqn9ffiuminosity about the same as the Sun's. Their apparent brightne dag-yn5/if 9f-n q4tbss, 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 velocity of/*q.f jgr6qctb1:x h w a neutron star which has collapsed to 1qwc*/:gb6xfq.h jtr 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 star ) 7ht2wvjl x*y/3lnaiin Problem 56 collapses to a neutrv3anl/)wxh2i lj* y7t on star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believed to be a neutron starp:bl2uj+ t*ypia 2t 1s of mass 1.5 times that of the Sun, with diameter 20 kma*l 1t+pjy2usi2: pt b, 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 our Galaxy is . zckos8 .uiw) i:vuo4k):xqp 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 y4ri.j6 :uz3zfcxv uyi+6 y6 pprovide the critical density to close the universe. Assume the neutrinocr+yzy:j u6i .pzxy3 vfui646 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 spe ta9zu2k(d z -xy4bxfe c/b)r2ctra 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 estizruf2/dxcb(2 exb-tz ak y94 )mate the ratio of their diameters. [Hint: see Examples 33-4 and 33-5.] $\dfrac{d_{400}}{d_{600}}$ =   

  Suppose we can measure distane -w44p+fk7wueg0zgq ces with parallax at 100 parsecs. What is our minimum angular resolution (in degreez7 gkwfw-0p4+4e queg s), based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from singly io5dw5xn+6)g ci wvs-fh nized helium in a distant star happen to overlap with the Balmer lines from hydrogen (Fig. 27-22) in the Sun. How dh)xg5wf-n+6s v5 wi cfast is the star receding from us? v =    C

  What is the temperature that corresponds to 1.8-TeV collvosxzgoj cs . ;r51l19isions at the Fermilab collider? To what era in cosmological history does this correspond? [Hint: ser.1j gz1ssv5x;l9oco e (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation of gas around wse 8yt t j 8(b)8im tjp1keo/8+mimkcquuw-65hat might be a supermassive black hole of about 2 billion solar masses at the center of a galaxy. If the radiupo8i5 /ttmw(ijq61m8) m ek+-j8uktcy ubse8s 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" hydrogen line at 434 n-1x oii *na /f4qeh-pvm emitted from the galaxy is measured on Earth to be 6e-xh -1/ f*naqipvoi4 50 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 o9w *edxw ;lo;kf stellar evolution, a star (if massive enough) will begin fusing carbon nuclei tod;wlow k*e 9x; 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 ;gr toj4 h10cnmle:s+
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 i3usow vf:,w /kf its density equaled the critical density of the univ3w/ f:vw ks,uoerse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$