The Milky Way was once thought to be "murky" or "milky" but is now considered to72a)mogm /hft s4d0io be made up of point source/go4af m0md2ith s )o7s. Explain.

A star is in equilibrium when it radiates at its siw(nr,w9p7,pbc k: uyurface all the energy generated at its core. What happens when it begins to generate more energy than it radiates? Less energy? Ex,,7(: rpwwy9n c buikpplain.

Describe a red giant star. List some ou s4 8+jldeq e./dtq8df its properties.

Select a point on the H-R diagram. Mark several directions awa1e8 nim/ n8jwwy from this point. Now describe the changes that would take place in a star moving in each /wij8n8 w1nem of these directions.

Does the H-R diagram reveal anything a,j( :0yih9soq nbt-ey bout the core of a star?

Why do some stars end up as white dwarfs, and others as neutron stars or rkscj); b.w4gql 3t) cblack holesc ) r.3qlbj;s) 4wctgk?

  Can we tell, by lookizm5xq*0+bk, f*6t qxjr 5 qhwung at the population on the H-R diagram, that hotter main-sequence stars have shorter lives? Explain. 5r0uh+ 5wqft,*6xq qk*zxmj b ----待选择----yesno 

If you were measuring star parallaxes06l0a(9j jaaxa-wso7k8wcz * w b7mza from the Moon instead of Earth, what corrections would you have to makea09jo7-kj b *xsz lza6ww8ca0m 7wa (a? What changes would occur if you were measuring parallaxes from Mars?

Cepheid variable stars change in luminositkxvv kn7msc8j6 4e 5v:y with a typical 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 bn5x6sce:j4km 7vk8 vve used to measure the distance to galaxies?

What is a geodesic? What is its role in General Relau.fiea 2,; tdotivity?

If it were discovered that the +i g7sfq/vz cim9c 7s2redshift of spectral lines of galaxies was due to something other than expansion, how might ouzsmi9c7i/ sv gq+7c2f r view of the universe change? Would there be conflicting evidence? Discuss.

  All galaxies appear to be moving away from us. Are we therefore at the cent/lf-l ea6o 4pfer of the universe? Expll6 ffe- 4pal/oain.  ----待选择----yesno 

If you were located in a galaxy near the boundary of(2zg ot;.dh(c1lz* mty:4bq +oibz mr our observable universe, would galaxies in the direction of the Milky Way appear to be approaching you or recedinoz ot2bc bz:qgi. tz1l4m+ yh d*r;((mg from you? Explain.

Compare an explosion on Earth to the Big Bang. Consider such questcxo:1dv4rj 7ce0p *erions as: Would the debris spread at a higher speed for more distant particles, as in the Big Bang? Would the debris 1r*e ocxjp07rv:4ec d 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 can w bewja:a5 sd)b 0q3vr7e tell if on0 evjd5a 3b:sr7 )abqwe is there?

  What mass will give a Schwauv2 ewvb6 m6hd. l:8hurzschild radius equal to that of the hydrogen atom in its ground state? M d 8w.e66lvb2h:v uum h=    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion yea:0 wwm3,t+fibw jrju (rs. Find that time on (Fig. Below). People have lived on Earth on the order of a million bwjwtr+:w j i, (uf3m0years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic microwave background radiation is. Where (+f/pm/)q + spaahtcedoes it come from? Why is its temperature now schm t p+()//fep a+asqo low?

Why were atoms, as opposed to bare nuclei, unable to exist until hundreds xcd /: t/x2e0y23,ekojmne0/ v vvdhzof thousands of years a,ho2d/0 / y 0/t xd j2cve:3envzkevxmfter the Big Bang?

Under what circumstances would the universe eventually collkmeuvo/xqdy m wb7 2g8e8907f apse in on itself?

  Using the definitions of the parsec and the light-year,:x4;djwzi,;fu 9dm b+matjuu9b o;(f show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a paralbrq( )z8/ a 5qfj)ptxolax of 0.38 seconds of arc. How far away is it? d =    ly

  The parallax angle of a stap*)x+ . cgb7t+fyvh;bfjq tc-r is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What.akh 67fbsbu4 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 angle for 8fv /93x)wwe)bs;xkgwbpaq 7 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 seconjoq3 c /riaofl5e(7 -xd star, will the parallax angle of the farther star be greajleao(ocx5 3qfr7i / -ter or less than that of the nearer star? By what factor?

  A star is 35 pc away. How long does ix n7h ki(k4ql5/jw9kw t take for its light to reach us?    years

  We saw earlier (Chapter 14)dou :/c+dnpj t-aw ku.w-z(4p that the rate energy reaches the Earth from the Sun (the "solar c(p4j.ktnu uc-wz/ dp-wad o:+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 brightnes a(lopvez m4tvc l s0h4)un2xwr3.9w+ s of the Sun as seen from Jupiter as compared to its brightness from Earth? (Jupiter is 5.2 times farther from the Sun v3o+.exrlw9 h( tc4anmz2pl)wu0v s 4than the Earth.) $\dfrac{l_{\text{Jupiter}}}{l_{\text{Earth}}}$    $ \times 10^{-2}$

  Estimate the angular width that oub4me+:dmj 4gur Galaxy would subtend if observed from the nearest galaxy to us (Table 33-1)e4bdgm:jm 4+u . Compare to the angular width of the Moon from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes di47 ww2bm 3zja red giant, what will be its average density if it expands owijm437wzd 2but 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 dwa:r cw9ot2m*-laiphv( cjp5 akpk:(8orf, it is expected to be about the size of the Moon.cpv* or2mthok kaaip9:lc (p5 w8-(: j 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 equal to the Sun's mku*s1. zl l0yand whose radius is equal to the Earth's. How many times larger than Earth's densit*u0z1msy l. kly 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 masxi k0re*3 .kph,-pdk zses has a radius of about 11 km. Calculate its average density and compare to that for a white dwarf (Problem 13) anddzkx , kkp- .rpi30eh* 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. 3jf bih8t.7;b76gxv dkz6n y*n3-2. (The mass of thei;fbdvz76 k7 8gh.n b ntjxy6* very 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 thez *e fotd* 0,ljsb9i6i same apparent 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 ceh5todyzxh51b2 k6 8dq rtain cluster are assumed to be about the same distance from us. Two such stars have spectra that peak at y5521db8qkdotx zhh 6$\lambda_1 = 500\ \text{nm}$ 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 stpo7 i.o h/q+6q7dr ea.7yzsur ar with mass equal to that (a) of our eroq7. s.y d6ua+o7/qiz pr7hSun is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typical galaxy (i9xotfn 89 tb.7bp 9qxlsek3(like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a -e(2e aq cenq9,-;ox sserd *kd/;hissphere, for which the sum of the angles isse,n;ear ;s q-/oe*i e2xd (h-kcsqd9 (a) 359º, and (b) 180°.

  What is the maximum sue+ bq 5w-gq+mdm-of-the-angles for a triangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the speed of light, rougakp 584(ad6 m :(9wnfkiymsfh hly how far away is it? v = yi(a 6f:h(fsd8 ma5mk4k 9 pnw   Mly

  The redshift of a galaxy indicates a v(e+vxh.vfs+t*m p*ffo- 3h b pi0.mzwelocity 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 o7 +r;vb-qoyi cwop tis(bm;0pi;u4mwx/. tq .bservable "edge" of the universe, say 12 billion light-years apt(q m40cw .qi; m/is-.b +vbopyoit;ur;x7 wway. v =    c

  Estimate the observed wavelength f5snj jo85+5d* vq wsqwor the 656-nm line in the Balmer series of hydrogen in svs w55woj8dqn j 5q+*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 distance from us, if the wavelength fo)owpknn0d/ s mds9apl0p c/8gqv051zr t5s0)mp 8ckagd ln /q n9v s10dw/opzp0he hydrogen line at 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 xl0id*zpqi 2lph 4y;l*4tw3 za galaxy with $z = 0.60$? v =    c

  What would be the redsd9mlrd.bz i.7 hift 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 wavelengg.g ge-keq)rco vd;*r xxb3)6th 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 blackbodyk 9q y (jch3 ,5dnz3thi2er)ji radiation distribution at 2.7 Kn 33rh2zqdt9i,)j jeyc(i5kh using Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closg:w m5/q,f wdxure of 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 (the averag -datxw.c8(aie distance between galaxies) at any one moment is believed to have been inversely proportional to the absolute temperature. Estimate the size of the universec8(ad- wi.a xt, 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 thresho 8wcr /;dwx3uqld temperature for produc;dx q38u w/wrcing
(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 44yx9(,v cxzl djc 6perepresented by the three arrows, A, B, and C, in the H-R diagram of Fig. 33-28. For each case, descri4jl cy6x(4x9 cdz,pvebe the changes in temperature, luminosity, and size.

  Assume that the nearest stars to us have an absolute luminosity abouta* 85a*zg qgmf the same as the Sun's. Their apparent brightness, howe*g zga85m*q afver, 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 a fa 7li,..7:g txnztmpneutron star which has collapsed to a diameter of 20 km, fri flt7:.zpx, n7.tg maom 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 in Prna204 me/as uyoblem 56 collapses to a n0/ 4amusa 2yeneutron star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believed to be a neutron star o46 qh9gab9o le-ahdnn(g//wz;- bmqt0 eecx 9f mass 1.5 times that of the Sun, with diameter 20 km, is observ 9mw0n tg-;4cx/ hg h9-dob(qla 6eene/9 bqazed 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 ouz sgaf 1prsd6v85 d;q: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 pro9 bv)lk5wm):rm e w3wivide the critical density to close the universe. Assume the neutrino density is, like photons, are b9 iw5k:3m)mw wvl)bout $10^9$ 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, respectiveo nag* );ml 2b(ekwkxrsb15h;ly, both lie on the main sequence. Use 1 )( xbakgonbhs*52 em;rl;wk 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. What ; 7lc rkigp03mis our minimum angular resolution (in degrees), based on t307grl pki c;mhis information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from sing5l3./imy(i ot f*vgcbly ionized helium in a distant star happen to overlap with the 3.imtci gb(/ov*yf 5l Balmer 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 to 1.8-TeV collisions at they398gw 0zn1cu eoh*,3focf pv Fermilab collider? To what era in cosmological history does this cor3nhcoy* 8c0 o1ewpv,ufg zf3 9respond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation of gasttakf:pit62*b/rut-f* o e7c around what might be a supermassive black hole of about 2 billion solar masses at the center of a galaxy.2totr6*:ka t ebc/ u 7ipft*-f 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" hydraiamj r)yf*gby9 8 8bs1r3ka 9ogen line at 434 nm emitted from the galaxy is measured on Earth to be ) 1b9b38rg*mfsj9y 8kia yaar 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) will ggq)zn0r*4jjaq tl/ 1begin fu0g/t gjrl jz qqn*)a14sing 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 reaction qw:;-tk r-jle
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 critiut2vl c11 1u;-j mvbt/ r8j)bfnv/ nllcal density of the universe vcv/jtruf 81 1m-/n u1jl bn2ltvl;)b, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$