The Milky Way was once sbqfyso ce 6yck+52;mw,k7f)thought to be "murky" or "milky" but is now considered to be madf+,75k6 qc)by se w;so2kc mfye up of point sources. Explain.

A star is in equilibrium when it radiates at its surface all the energy generate;o3 ; dmizzbxl*.q9lc d at its core. What happens when it z m l;q*zb dl9.3;iocxbegins to generate more energy than it radiates? Less energy? Explain.

Describe a red giant ssql 8.ja9dss.d5 195fmtd1/ppyg9b osl ,y z ytar. List some of its properties.

Select a point on thel tmghprxxj z+f.,szw1(v b,;,-1b te H-R diagram. Mark several directions away from this point. Now describe the changes that would take place in a star (-x ,lbj, zp wtrg.efvht+,1s zx1b ;mmoving in each of these directions.

Does the H-R diagram reveal anything about the core omby u;lw/).- ggj.ljk/vs v8nf a star?

Why do some stars end up as white dwarfs, and others as neuzxb 2drpgvi)o4 6 xmg.c,kk97 tron stars or black h7bvgrz2k pcxki9go ,6md.x) 4 oles?

  Can we tell, by looking at the population on the H-R diagram, that hotter m,0t--ki6zhg 6qd xfcqain-sequence stars have shozq dtgq0,6-fi -6 kxhcrter lives? Explain.  ----待选择----yesno 

If you were measuring star parallaxes fu )r3;)h ,ededapq(o drom the Moon instead of Earth, what corrections would you have to make? What changes would occur if you were me eedou)3d;rdh q ,(pa)asuring parallaxes from Mars?

Cepheid variable stars change in lu4,z1/lk.a fio p r1osominosity with a typical period of several days. Theo o/s.i4a r 1fkl1zo,p 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 distance to galaxies?

What is a geodesic? What is its role in General Rde *zb j5*l)hzelativity?

If it were discovered that thei21a g/g-p*c+dck sgv redshift of spectral lines of galaxies was due to something other than expansion, how might our view odg akg -p 2+cvg/is*c1f the universe change? Would there be conflicting evidence? Discuss.

  All galaxies appear to be mo/hf h 9p-( f f-3y;bqzrnd9xeqving away from us. Are we therefore at the center of the universe3 x -ndpqrq9 (h-f9 hfe/ybfz;? Explain.  ----待选择----yesno 

If you were located in a galaxy near the *n d,nb8mcwz bk5a:lm 2ad:2mboundary of our observable universe, would galaxies in the direction of the Milky Wayc528ba2 a, bdmzm*dkn:m :lwn appear to be approaching you or receding from you? Explain.

Compare an explosion on Earth to the Big Bang. Co e:0ib 0if2px8bb/;gnbu 7b oensider such questions as: Would the debris spread at a higher speed for more distant particles, as in the Big Bang? Woue/e7 20ubb fbo8x 0 :nbigpib;ld 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 how can we tell zj5 2uq 0uhe+gif one is ther+h0u g qz25juee?

  What mass will give a Schwarzschild 4m a7g0a7n;q,t 5foun 70x9y uxy( w sjvpraf/radius equal to that of the hydrogen atom in its ground staaq(puf0 x9owx/,0 ysum5jva r747;7afn ny gt te? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 bi+ k1o 3xsqgx4illion years. Find that time on (Fig. Below). People have lived on Earth on the order of a mil x+x3o4 igqs1klion years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic microwave background radiation is. Where does it6b z oads6(bv0 come from? W6dv6 bosazb0 (hy is its temperature now so low?

Why were atoms, as opposed to bare nuclei, unable to exist until hundreds of tuupu/43a xd7 chousands of years after the Big3uu4 pa 7uc/dx Bang?

Under what circumstances would the uni*2m t9glojk5g0k b3mk verse eventually collapse in on itself?

  Using the definitions of the parsec and the light-yeap0f 3xaba3n(bz. n.rzr, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.38 secondsx .-v xh*1+knppokks2 of arc. How far away is it? d =    ly

  The parallax angle ocowlss+a; b7lwidd99q8 0r* to. k z2df a star is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its parallax aoy6 nd i-7oin4 -xrf-jngle?
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*4 5ib, )9tnkojl1t 6ltxo cfe that is 55 ly away? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away from us c:wnp p:w+ryu**+a:ol pxx* x ixa+5m as a second star, will the parallax angle of the farther star be greater or less than that of tpynpa*p awmw+x x *xx rc::i:ol*5++uhe nearer star? By what factor?

  A star is 35 pc away. How long does it take for5*fm*xo zi 48 g92 jzhvfrobw- its light to reach us?    years

  We saw earlier (Chapter 14) that the rate energy qh( 0h )fkh8 4bsm .6f6p 3ttngrjzvg)reaches the Earth from the Sun (the "solar constant") is about k fbfq30)vjr (hphmt8.sg6z4 tgh 6n)$1.3 \times 10^3\ \text{W/m}^2$. 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 brightnessjt5a,uyh*ca vmvb8:jk : .w 5zl m/mr3 of the Sun as seen from Jupiter as compared to its brightness from Earth? (Jupiter is 5.2 times farther frov kblmurym.:5c vt8h,*amw:/z j j53am 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 observed frolm hid1au577 xm the nearest hlm xa71d7ui5galaxy to us (Table 33-1). Compare to the angular width of the Moon from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, what will be its average densitkhsp) 2geks+p3bwk ).y if it expands out to hkgsksp3 k2w b.e+ )p)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, ny+/f ,looml white dwarf, it is expected to be about the size of the Moon. What angular width will it subtend from the prf, ooml,nl/y +esent distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwar ,n)4 4r vpxc3fk g ng6eod()kj)n,vktf whose mass is equal to the Sun's and whose radius is equal to the Earthkv 4p)) 4r3(e), jdvtg xnn6k knfgco,'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 sol;h: eblf ,b9gmar masses has a radius of about 11 km. Calculate its average fe:hl9;gb,bmdensity 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 reactions of Eq. 33-2. (The mass of ugll.u as5czm .500pk the ve .5ulku.m5 scgpl0z0 ary 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 appqd. 0w)-f8 ddvp* fi rvm*8 )mh:egwjtarent 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 certainx7e cjp*m6s7ud4 cdq. cluster are assumed to be about the same distance from us. Two such stars have spectra thamx pd7ec dj.4s*u76cqt 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 n -wtxx/2)kj ea star with mass equal to that (a) of our Sun is-x /)tjnwkxe 2    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius fb e.w ml,y+i6sql7lyv )+i-n for a typical galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a sphere, for which b,9 ianh;sz.evqae*8 the sum of the angles isaeb;.s aeqzv*hn 9,8i (a) 359º, and (b) 180°.

  What is the maximum sum-of-the-angles for a triangle on a sphe9y krdrm61(tz re?    $^\circ$

  If a galaxy is traveling away fr m-tlvu j/t3. cho)/brom us at 1.0% of the speed of light, roughly how far awayh3r)bmjl-/.t uotc/v is it? v =    Mly

  The redshift of a galaxy indich/ mroz3 g9 9fs,h1fywates a velocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (relative to us) that is nex d ,-,*va iy,cvlbm(rar the observable "edge" a (xr vc*,dyl, mi-bv,of the universe, say 12 billion light-years away. v =    c

  Estimate the observed wavelength for)ydc8w1wr v+ l4x7ys b the 656-nm line in the Balmer series of hydrogen in the spectdrw x ys1bv78ly4 w)c+rum 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 wagu7rcpgy0 *a9velength for the hydrogen line at 434 nm i9 uyr*gg0ac7ps 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 b;sf2a+ ar / /lyyj/fdgalaxy with $z = 0.60$? v =    c

  What would be the redshift parame+ yrv8+ aeqch7ter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Doppler f7tjw+6-v bt(ut hd:qshift 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 blackbody radifrx /10y8qlk*h -mq jmation distribution at 2.7 Kq0 /jl8*kmq m yrh-1xf using Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closur1k)0 ( /c ho e,o3dhf2dogpiqp;o7gp6vke6 nae 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 average d8/n5 bn rnbkkz1;g sl.istance between galaxies) at any one moment is believed to have been inversely proportio s g8nkk;1/nb5lzn .rbnal 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 umf8 q.,ia:aeb3j rh -eniverse cooled below the threshold temperature ib.:ejq-a3fa8 ,hm refor 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 rep,(k9.t l zddn n.ulw)g ak)o,:cil;ljresented by the three arrows, A, B, and C,lan:jd ,; z.lo)w9 )kli k(t lcdu,g.n 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 have akt :uc:n,pa y,n absolute luminosity about the same as the Sun's. Their ayk: n,ap: utc,pparent 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 ang*8to x.4d+xak 335 tpqikfnw aular velocity of a neutron star whix nk 58atixf td3wo+a4 .q3p*kch 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 t/e ) lvzmy/a5r)wk(rg 5d n8whhe rotational kinetic energy change when the star in Problem 56 collavd / 5g(n)8rwrym5heaz/ kw)lpses 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 af7vgk .0fhkr53a-o6 fkj1ho of mass 1.5 times that of the Sun, with diameter 20 km, is observed tr7h ha oa fov k3f.6k1jfk0-5go 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 Galaxbs4xj a mk 4;pn,qph/*y 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 th)+s m2mmj jto:e critical density to close the universe. Assume the neutrino density is, like photons, 2mjjt+ sm)om: 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, .a:w8vv/3 bbs;vo 25bqfdo.*j zw 0mx b5qvlarespectively, both lie on the main sequv5o.3qw2xb/lbavz fq*owja0.sb : ;m5 d8 vvbence. Use 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 atxytpoz- -k:8g)4c c)dit*zqn 100 parsecs. What is our minimum angular resolution (in degrees), based on this xz )-i kz*ocp:t4dytgn )c8- qinformation? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from singly ionized helium i ;thbi zzgi6)2n a distant star happen to overlap with the Balmer lines from hydrogen (Fig. 27-22) in the Sun. How fast is the star receding frhz )i2zg;t6i bom us? v =    C

  What is the temperature that corresponds to 1y,ixr.o 5sob4 .8-TeV collisions at the Fermilab collider? To what era in cosmological history does this corresponyi ,osb54.x rod? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation of gas around wh19st yar,0 bizat might be a supermassive black hole of about 2 billi sybrit01, a9zon 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 atchr- u(4cbj r7 434 nm emitted from the galaxy is measured onh-4(c r jbr7cu 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 evolution, a star (if massive enough) will be;uo 192nqfrqnbvb63 agin fusing carbon nuclei to form, for example, magnesium: 6bna v;qo3n2q9 fu1 rb
$^12\text{C} + ^12\text{C} \to ^{24}\text{Mg} + \gamma$.
(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 .( hctni) z/lf
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 dw/-kkj:yu *dnx n kyw j08l+q.ensity of the unive kux kwyj*8:0-dk+./ yn jnwqlrse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$