The Milky Way was once thought to be "murky" or "milky" but is now c15y;k 6ees h4(q;svbtoadu 0monsidered to be made up oe1v64hk ym ;(sa tbd0qus o;e5f point sources. Explain.

A star is in equilibrium when it radiates at its surface all the energy generallfp a5.t(- ewted at its core. What happens when it begins to gefletl5(. w- apnerate more energy than it radiates? Less energy? Explain.

Describe a red giant stx9vnwgrg z:p3 j x13h5ar. List some of its properties.

Select a point on the H-R diagram. Mark several dibjwx3t l;xg34a 9 kpmicn4 q6;rections away from this point. Now describe the cnx4 3 jli4kx;pc ;m3g9qabt6 whanges that would take place in a star moving in each of these directions.

Does the H-R diagram reveal anything about the core of a star? xaa w q*/i6esy4ea-a1

Why do some stars end up asy07ghe *fbgb;m17dihb; i.ry white dwarfs, and others as neutron stars or black hhybbg0byei ;7mg.d*i 7 h;f r1oles?

  Can we tell, by looking at the population on the H-R diag;4mb qhf9 1ypgram, that hotter main-sequep1m4h;gb 9f yqnce stars have shorter lives? Explain.  ----待选择----yesno 

If you were measuring star parallaxes from the Moon instead gq.6rskx ;dn4+wk5x6w 7cgweof Earth, what corrections wouqwxe krw+g46 n.k7 gw;d6 xc5sld you have to make? What changes would occur if you were measuring parallaxes from Mars?

Cepheid variable stars change in luminosity with a c m9iy6 lx:r+ftypical period of several days. The period has been found to have a definite relationship with the absolute luminosity of the star. How could these stars be used to measure the distancexlc:r9+mfy6 i to galaxies?

What is a geodesic? What is its role insuzwm p(v k.-/ General Relativity?

If it were discovered that the redsj *yv*hxn0so6lbnr 5*)z i)nuhift of spectral lines of galaxies was due to something other than expansion, how might our view of the universe change? Would there be conflicting evidence?)ynb6n *x5vhuozs *n*il)0 rj Discuss.

  All galaxies appear to be moving away from us. Are w:a:e pwog5y*-vl dlnfg5s34 /a3em dte therefore at the center of the universe? Exwgaltdly:op*/ea 3-de:mf55ns4g3 v plain.  ----待选择----yesno 

If you were located in a galaxy near the :nk s*t;js9zbboundary of our observable universe, would galaxies in the direction of the9btk :n j*;szs Milky Way appear to be approaching you or receding from you? Explain.

Compare an explosion on Earth to the Big Bang. Consider su.2y u8f xd.wjvch questions as: Would the debris spread at a higher speed for more distant particles, as in the Big Bang? Would the de..2 8vfyxjdu wbris come to rest? What type of universe would this correspond to, open or closed?

If nothing, not even light, eqgzf 7a 8x0w 526(ylakir,ekescapes from a black hole, then how can we tell if one is therwgeaf (q7,08rixlzk52k6e y ae?

  What mass will give a Schwarzschild radius equal to that 0mo.hpdv eu3x;f+f o;of the hydrogen atom in its ground state?3xfo.;ve0ou f+;m phd M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion yeare2* ri26qt;8e qsv abns. Find that time on (Fig. Below). People have lived o6;s 2b enqer28q* ivtan Earth on the order of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosq+t9xnvq8bre4 rbf z,zr .hu4;.7vcp mic microwave background radiation is. Where does it come from? Wh . pr.qc4bbuz4ev7vrq ,;nr fx8h+tz 9y is its temperature now so low?

Why were atoms, as opposed to bare nuclei, unable a3nnfn 1vlu . q+cti05to exist until hundreds of thousands of years after tlqna5.vc0 ut1fn+n3 ihe Big Bang?

Under what circumstances would the universe eventually collapse bmjfh bwf:m,j,-3zhlh5 ndj4se,d) / in on itself?

  Using the definitions of the parsec and the light-year, shoz )d6s)w z8kk6ufmql2 ftd;apw 7 89ptb2(nquw that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.38 secondux+i py9w7. y f1q)i5w gudt:ds of arc. How far away is it? d =    ly

  The parallax angle of a 0+gxdr7keq9dcfq7d 57f 1p y zstar is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its parallax angle? hxs*8*w: xtrw
State (a) in seconds of arc,$\phi''' \approx $    ($\times 10^{-2}$)''
(b) in degrees. $\approx $(    $\times 10^{-6})^{\circ}$

  What is the parallax ang) (o,9ssl fu n-kvr,fule 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 s ++/un,zl. dv frp,pn nu+bea)oc(f*necond star, will the parallax angle of the farther star be greater or less than that of the nearer star? By what fact,+.e() un/l+pf, d cfo nzuvb nan+r*por?

  A star is 35 pc away. How long does it take for its light tbhope9 ;l o4v fb(s0g;o reach us?    years

  We saw earlier (Chapfbsz oe odh6,b m.)mk)ga6r+oh.02zpter 14) that the rate energy reaches the Earth from the Sun (the "solar coa.h6k.p+0o hzzm og2sfo be,br)6)mdnstant") 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 compared tw2 k- n c/b41 n(ssia;8cukx0ql+fnigi k88f co its nbf(s2skuxcn 18wi-+ ckflnq4g8;c8/ a ki 0ibrightness 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 woulzmmruus 9,hu 6 0 0z+oc3vehh)d subtend if observed from the nearest gaszouhuh u0zr c 6h0m,me3 9v+)laxy to us (Table 33-1). Compare to the angular width of the Moon from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes 1b o wnzlvc a nx5pbm.4z- lid-2*:v(wa red giant, what will be its average density if it expands out to thzc-b .4 da5i:-wxznbv (v1 po*l2lwn me 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 oy4q.3j duj7tabout the size of the Moon. What angular width will it subtend from the present dis47tjy.3 quoj dtance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of(m.mr,(3 22yt:vi3zi6x ev)zehc md2pace mf a white dwarf whose mass is equal to the Sun's and whose radius is equal to y :22,fex(mve( mazet3m)cd 2h.ii36rp vzmc 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. Cyg4 v+:ydmm7no v u8i,alculmyg , uiv+vm:7 dnoy84ate its average density and 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 rea s otji - ,qe1km4xtgsy0x8+vc8o(1 rcctions of Eq. 33-2. (The mass of the very unstablx4xrc 1siq0svom ojt-gck1t+8 ,8 ye(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 apuonm6n aux cgc8)qhgv6z.s-wz k8* 66parent 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 .u 287+ eo,bb ugvtdlro(m ,vlcluster are assumed to be about the same distance from us. Two such stars have spectra that peak2+(oglv ,o tbuu ml87,.dr bev 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 eebuyxai, sa72 nmx83z*/ol; a star with mass equal to that (a) of our Su i*/7b o3u ;amxxya,zee2n l8sn is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for ayw:m*ldn*ua n6n4v)z typical galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surfacn s2 ufvxf2jl 6fs.p50.v4 kww)mw)pse of a sphere, for which the sum of the ang2sf.2v p nwsfvsfwxm p5j 06u)wk4l).les is (a) 359º, and (b) 180°.

  What is the maximum sum-of-the-angles for a tris pe,4xa:,odjrpq(*fangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the spe qi2pngsk7:5xx. q,u5i xc:sfed of light, roughly how far away is it? x5 .fnx:qxp5 gii7kcs,: 2qus v =    Mly

  The redshift of a galaxy indicates a v( 7eawf:zz.ygelocity 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 obsi (3+ovol*n ueervable "edge" of te*ilo o3u+n (vhe universe, say 12 billion light-years away. v =    c

  Estimate the observed wavelength for the 656-nm line in the Balmer se4.kw(kl ;dtx k z.lq-qu8 atb 1viz4)fries of hydrogen in the spectrum of a galaxy whose distance fromt1 dt)i bxz u8.wq .l4k-;(fkvla4qkz 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 distance from us, if the wavelength forcjauwl0( jo26x 4toi/ the hydrogen line at 434 nm is measured on Earth as 6ao4cj /uiojx0lw t(2being 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 xrst;lu9h9 e ys48vj8galaxy with $z = 0.60$? v =    c

  What would be the reds n6g/1u vfm-*yj.qkoe(h9vg xhift parameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show tham+ qzh.sem spoym9).-lyy+ q/ t 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 at the peak of the m; p8il)l4qt+yoncv i+r hf8(blackbody radiation distribution at 2+n8lm)8 r(cyf q+v t;il4iho p.7 K using Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of the x 0:tbc 1r3vfiuniverse 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 beof yuhtzul5 7ewk+z(hgnc l m6 38(n)*tween galaxies) at any one moment is believed to have been3 6+7uz8metn( lkgul wfcz5)hy*oh (n 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 cooletj-z lhc7+7rrdcymx*7 ;;go td below the threshold temperature for 7-o*hzj7cx ;rt7ct;yml+dgrproducing
(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 r5 0yx qvds5:fcould undergo the three changes represented by the three arrows, A, B, and C,q5:r5df yvsx 0 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 ha3h22q*mre pfcl7yo )bve an absolute luminosity about the same as the Sun's. Their apparent brif3 ye)mbr7l*h2 poqc2ghtness, 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 velea937ar,yk1 dmaimv z2/ e*um ocity of a neutron star which has co 2aama evd zm/3y9ik*17mue ,rllapsed 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 kinetic energy change when the starpwppuz1i 9ua(2: ;b ay in Problem 56 collapses to a neutron sta w1b ;papu uia:2(z9pyr? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believed to brc,ms*a .d ncu rbu;,r 40amw3m7kl z)e a neutron star of mass 1.5 times that of the Sun, witl3 ),b4ark .a7rrs, zmmw; ucdcnm*u 0h diameter 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 to our Galax,cre n- -uqv/lwb, hn oy(e a;n7o9z7cy 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 critical density8d -5nh2fp* (fgvp ghekb2r5e to closef*2 e kpvdggp8bf (2 r5-hne5h the universe. 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, respectively, bq+, jvliqb7(q5 07mf 6u*ovh9etosnvoth 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 their diameters. [H s blt+ qj9vfvi 6,7*0heo oumv5(qnq7int: see Examples 33-4 and 33-5.] $\dfrac{d_{400}}{d_{600}}$ =   

  Suppose we can measure distances with parallax at 4h yas gf:3ds(t7vy c6100 parsecs. What is our minimum angular resolution (in degrees), based on this informdfa gs7c4yht 3v(s:6y ation? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from singly ionized hb3 lfbs6 0fil-wwe y,m+g4y8lokxhg+) x+) x gelium in a distant star happen to overlap with the Balmer lines from hydrogen (Fig. 27-22) in the Sun. How fast y,l wg+wxy43il6h +mexslbk g+)f 0ofb )g x-8is the star receding from us? v =    C

  What is the temperature(zr0h hn(nnp6eyw6i / that corresponds to 1.8-TeV collisions at the Fermilab collider? To what era in cosmological history does this correspond? [Hint: see (Fig. Below).nynrpnzh (66eh /(0iw] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotati2 uflc/8*k mjy0qf 1bwjz l+l5on of gas around what might be a supermassive black hole of b0l2lwuq*j8 1 +m/l kyf5czf jabout 2 billion 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 "e.q6* d5knhr bblue" hydrogen line at 434 nm emitted from the galaxy is measured oq.e *bh6d5nrk n 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 ev2 7b: o4qd7g 2ifuvdv: z r:gpjgn3u,jolution, a star (if massive enough) will begin fusing carbon nuclei to form, fdqvbd gr 2noi3z7j gfv27p::: ujug4,or 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 imdxf d7gn 6;9
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 it8v/v*) c wb ar-k+ahgrs density equaled the critical density of the universe,hk-cr aa*b)+vr8 gwv/ $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$