The Milky Way was oncei:joyrw f/ea r7g +:9fph,9v g thought to be "murky" or "milky" but is now considered to be made up of f9e hao/:gjp i r9gvw,:+7 rfypoint sources. Explain.

A star is in equilibrium when it radiates at itteox s1ug iel z22)u1s z,2s8hs surface all the energy generated at its core. Whatg28 zs)u2 h1x,lisee2st uz1o happens when it begins to generate more energy than it radiates? Less energy? Explain.

Describe a red giant star4/lw 0stoc3cz 2* szgt. List some of its properties.

Select a point on the H-R diagram.b 6ur tv.sih6- Mark several directions away from this point. Now describe the changes that would take place in a star moving in each of these dv66 th bris.-uirections.

Does the H-R diagram reveal anythip d91zxz6)sl zql b8-nng about the core of a star?

Why do some stars end up as white dwarfs, and others as neutron stars or e;w0wp xty*8gblack h0*8 wg;pywxetoles?

  Can we tell, by looking at the population on the H-R diagram, that hotgkakat/ (:* 7-cxk6ksu u:lw vter main-sequencex6g7tc /lukuw :k( a a:kk-*vs stars have shorter lives? Explain.  ----待选择----yesno 

If you were measuring star parallaxes from the Moon inste j) ou e+y2e(vveus3nt9i3z;c 3*e gziad of Earth, what corrections would you have to make? What changes would occur if you were mee)eiot c(3z+ euei2 393v;nszg*yj uvasuring parallaxes from Mars?

Cepheid variable stars change in luminosity with a typical pit f3yv 96t7ugeriod of several days. The period has been found to have a definite riyg3fv t79 t6uelationship 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 Relativvr bs 2rt3 ;sup0,cuf8hww 2tii h33)eity?

If it were discovered that the redshift of spectrab 6olg/ rk/:fil lines of galaxies was due to something other than expansion, how might our view of the universe change? Would there be conflictin:/lo6gbi rfk/g evidence? Discuss.

  All galaxies appear to be moving away 3x9m8rp7 *zdda4knglfrom us. Are we therefore at the center of the universe? Expln 7pgldmx3*4rz8 d9akain.  ----待选择----yesno 

If you were located in a gala7 zlkv8wt43co xy near the boundary of our observable universe, would galaxies in the direction of the Milky Way appear to be approaching you or receding from you? Ew74kc3vt8z o lxplain.

Compare an explosion on Earth to the Big Bang. Consider such questions as: Wo8 xf 0;4lu i;jox3s vpvfua7h wrg*(d:uld 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, o:pf u;;70sfh8lio3 au dv w4x( j*vgxrpen or closed?

If nothing, not even light, escapes from a black hole, then how can we tell ifoka ags.cfq t6n5*auul0c1r +s16 0ka onek6u nqcf* aaascgk1 a651sl. 0+t0rou is there?

  What mass will give a Schwarzschild radius equal to that of the hydroge62qde.gop0uyb2 r0nk1xl h4ln atom in it0bn4d2e r k plohqguylx602 1.s ground state? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion years. Find that(9u q)pb 8)fcpjxuo xz d7dj5, time on (Fig. Below). People havex pb q)upo9,udx( d 75)cjzj8f 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 isnye8ww tg ;3+-z;xuxad6 -7kr 8gkvxz. Where does it come from? Why is its temperature xuwk;kvg-z6-g3+w r 887ny ;xat dez xnow so low?

Why were atoms, as opposed to ba lkqy9evo(,h.re nuclei, unable to exist until hundreds of thousehk,qlv .9 yo(ands of years after the Big Bang?

Under what circumstances would the universe eves 5e/ao2b3/( smpt:c1oz8xtwa /pwb vntually collapse in on itself?

  Using the definitions of the parsec and the light-year, showi ; d9it3,tcnh that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.l3 *do2b25etzjin5e7,jfi o g unz4/z 38 seconds of arc. How far away is it? d =    ly

  The parallax angle of av ed9y)muw. tzw1;xa / star is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its paramjll bmj6z:)x5d9v w+w:efi 2 llax angle?
State (a) in seconds of arc,$\phi''' \approx $    ($\times 10^{-2}$)''
(b) in degrees. $\approx $(    $\times 10^{-6})^{\circ}$

  What is the parallax angi.lco u n+g9drfd442x le 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 af2l - wk :dzhu3ot1px. h9s5l*d;mghos a second star, will the parallax angle oo9u:phw3 omx1h. sgt- fh;z*5kldl d2f the farther star be greater or less than that of the nearer star? By what factor?

  A star is 35 pc away. How2h hs-ht9/ ts+y5prjyzlqz h*1*t sx+fc wj() long does it take for its light to reach us?    years

  We saw earlier (Chapter 14) that the rate energy reaches the Earth from the Sc ;ztk7b6i*8vodapr : un (the "solar constant") is abo;pcrb *ovd 6atz 7i8:kut $1.3 \times 10^3\ \text{W/m}^2$. 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 asxl,f //soh tc) compared to its brigh/sh)cto,l fx /tness 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 would subtend if l n6)o,ooz( 2 u5nqbc4nq:xmxobserved from the nearest galaxy to us (Table 33-1). Compare to the angular width of the Moon from Eart2u:,bn nolnm q( xqx)64c5ozo h. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, what will be its average de- ymu1iw+h+seva: i( mnsity if it expands out to the orbit iam+ 1we -ui s:h(myv+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, + ;cdeola1v/8zs s)p: oji+id it is expected to be about the size of the Moon. What angular width will it subtend from the present dio p8o++is1/ ) d;dsjlizec av:stance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whose mass is equal to the Sun's 8os;iv cux(be. .kvf 9zm+lzzr6 z9s1and whose radius is equal to the Earth's.6c +ovb 9zilz;v xu(zks 8fe.9z1mr 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. Ch, kmmq9ce; 094iwjomalculate its average density and compare to that for a white dwarf (Problem 13) and to that of nuclear matter. mh9k;c,4j9iwome qm0
$\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 +wuulu(t zu1s)m9pz. mass of the very 1)suz+l (zmuuuw9p.t 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 appar6pyyf7jf(5c,o su3h:h hu+qo/yuy9 j ent 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 asysp /r+;f h-ycsumed to be about the same distance from us. Two such stars have spectra that peaf- rcsyph; /y+k 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/0etx.p9onax 5vetd o- 1cvo0 radius for a star with mass equal to that (a) of our Sun is0n-oc vvd1oe ex5/ox0 t9a.tp    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typical galaxy (like ours)?t/ja7(f4g:x9tju xmm R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn ofe;- ql:gf0z w/ aplz)ffz1v, n the surface of a sphere, for which the sum of the angles is z zpg/,;vq ewlf 0f1f- ):lfza(a) 359º, and (b) 180°.

  What is the maximum sum-of-the--sfa9g a(nk)zp+g e4 (bgnj*4stq0pz angles for a triangle on a sphere?    $^\circ$

  If a galaxy is travelingl7s7;2zstj,n/h o ouz away from us at 1.0% of the speed of light, roughly how far away iolj;t 7hoz7 , usn/zs2s it? v =    Mly

  The redshift of a galaxy inditgcwhl9qjh 8kkk*7 4 *cates a velocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a gl e+h+ahs0 ra/2 k/2rd+o0s dniqx+aralaxy (relative to us) that is near the observable "edge" of the universe, say 12 billion lighdd2eqa+20ia hl0s +okha r+rrn +x//s t-years away. v =    c

  Estimate the observed wavelength for the 656-nm line in the Balm sl,rlrkgogllg 03h 4i6(z 2:aer series of hydrogen in the spectrum of a galaxy gr(o ,g2:slzg0r63 lll ai kh4whose 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 o kmfsq)c6r0f8;ik1a ahzd w). f a galaxy, and its distance from us, if the wavelength for the hydrogen line )s. hr1;8) ak 6ffickzmq dw0aat 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 w yoeh av6wqt-8.jb66pith $z = 0.60$? v =    c

  What would be the redsh6cdr7el)jany4 + mol0ift parameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, shoqtcd l )(r9/xpw that the 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 at06d gf22u q3gvasz) l xs*z/a0esrer) the peak of the blackbody radiation distribution at 2.7 K using Wien’s gz2uz0r2))a r6df/lse3s*0egvqx as law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of the utdm e9 uch* oah.vd*(3niverse 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 between galaxies) :mvw -)6y;0bjb r3mp8h pvks(du 3-pd8huuhu at any one moment is believed to have been inversely proportional to the absolute temperature. Estimate the size of the universe, cobv8;rh80363hu:m kppdp)hwb - y ujmu(- dvusmpared 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 hjglfl8vj 53ntm1o1 wg4vnp98ad the universe cooled below the threshold temperature for pr8jfn mljt3pg1 4vlow18 n v9g5oducing
(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 s ke(hbvz wf1d1*-2hrptars could undergo the three changes represented by the three arrows, A, B, and C1 fhb -*12pk vh(rzdew, 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 hxa de78h)5nw uave an absolute luminosity about the same as the Sun's. Their apparent brigh8n)5h d7w axuetness, 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 vgxl k(6)n uo9angular velocity of a neutron sxnlo( v )6g9uktar which has collapsed to 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 ki ju*jwz: lcf8a ,tpo qs9:9+ghnetic energy change when the star in Problem 56 collapses f za*:+:u989,thwo lqjgpcj s to a neutron star? $\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 tim7fkgk ks+ a1frs 0 2zb6-wthe1es that of the Sun, with di2f7+ be kzsg1rfwakhks-t601ameter 20 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 tm1qaj( n ), y8 7:n*z4niqhv,uywvtoa o our 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 provide the 1gpyml1 bj k 47vh7+jht;zqt(critical density to close the univeh+tpyj 1lmkj4zh; t (g7vq 7b1rse. 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 ax.3k fgs81 5ee8cch wq(ll9p nm, respectively, both lie on the main sequence. Usekeg( f q98hcp1.w 3elx5lc8a s Wien's law, the Stefan-Boltzmann equation, and the H-R diagram (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 100 parsecs. Whaty5bml:jvu wsn-ml10 3u*ir-f is our minimum angular resolution (in degrees), based on this informatiofwnmm jirsy bu* lu3:v-- l051n? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from ss1qh(ykg.u0 uk xq .)aingly ionized helium in a distant star happen to overlap with the Balmer lines from hydrk s() .k.hxuugaqq0y1ogen (Fig. 27-22) in the Sun. How fast is the star receding from us? v =    C

  What is the temperature that correspo 7rmr.9jdvu2 toezw-m zn /8kki/*c3xnds to 1.8-TeV collisions at the Fermilab collider? To what era in cosmological history does this corresp*w9zm 7 kj.cudr vm-xnzo k2 tei3/r/8ond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation of gas ag7n dru8t(2*b l(1an7fnnmfz. r 8 ogaround what might be a supermassive black hole of about 2 billion bt2nzl7u(mrg(.7*ao1 dn n8rg naff 8 solar masses at the 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" hydrogen line at i,gq jnl7ts2b944gtq 434 nm emitted from the gal7qiggt j qn49,2l4b staxy is measured on 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 evolmvt y5kb 06ym1ution, a star (if massive enough) will begin fusing carbon nucleibvym 0ty5mk 16 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 semjw 52 6a7du
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 density of tuiy p p9.h/o .e/07nl j1x6tksbssr z)he univ. j6s 7)bn/yse/. o hisktup1plr09xzerse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$