The Milky Way was once thought to be "murky" or "milky" but l 8 ,aggstl.d5qfsu ad18m*8eis now considered to be made up of point sources. Explaugf5add1, qs.el8sla t*8m 8gin.

A star is in equilibrium ld*6n d:r aw5dwhen it radiates at its surface all the energy generated at its core. What happens when it begins to generate more 5dna d6w: lr*denergy than it radiates? Less energy? Explain.

Describe a red giant star. List some of jr-vfnp5c 7as*e9 tw c)lf fz1+/-vl ,rudfs9its properties.

Select a point on the H-R diagram. M44ffbeugv69 f ark several directions away from this point. Now describe the changefg6bv e49f 4ufs that would take place in a star moving in each of these directions.

Does the H-R diagram reveal anw8q58 k(53rd alfyr g f ,sj2 8,rcxdts--ddjiything about the core of a star?

Why do some stars end up as 5o(btoud8 3 iuwhite dwarfs, and others as neutron stars or black huoo bt i(u385doles?

  Can we tell, by looking at the population on the H-R diagramejo/+j9 w)cd r3ipx g0, that hotter main-sequence stars have shor+)godw/ c ir0e xjjp39ter lives? Explain.  ----待选择----yesno 

If you were measuring star parallaxes from the Moon instead o6regjke;am 2f5s p,6o f Earth, what corrections would you have to make? What changes would occur if you were measuring parallmfor5g6 ee2a6j ;pk,s axes from Mars?

Cepheid variable stars chaq9n 9 jh5nh8ftnge in luminosity 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 be used to measure the distance t hnh 9q8fnt9j5o galaxies?

What is a geodesic? What is its role in Generalp; ll* bd0;aal Relativity?

If it were discovered that the redshift of spectral lines of galaj;rpa// l :-pmb0og:9by gc byxies was due to something other than expansion, how might our view of the universe :cb0 /ogbyl/pjg-;mb 9p y:archange? Would there be conflicting evidence? Discuss.

  All galaxies appear to be moving away from us. Are we txa(d p8m2c9 sdhxp s6aj(,z(therefore at the center of the universe? Explain. xa9s ( ( dph28mpadzc,tj(6 sx ----待选择----yesno 

If you were located in a galaxy near the boundu9 b7.eznie *w2 0k6:tgtzdo(nmv, bfary of our observable universe, would galaxies in the direction of ieo7,(nf z 0g nb*.uwebd6z :k9vt2tm the Milky Way appear to be approaching you or receding from you? Explain.

Compare an explosion on Earth to the Big Bang. Consider such questions as: Wi+/xepy kdiy *.me2 a(ould 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 univpdei2.i yxk/m* (e+ayerse would this correspond to, open or closed?

If nothing, not even light, escapes from a black hole, then how can we tell if om)roc*h9d gi:o 0ai8mne is thag mioo)9c *dh8m ri0:ere?

  What mass will give a Schwarzschilx+ 9zqj10oe gvj c6 )/ 8ernuun50hcskd radius equal to that of the hydrogen atom in its ground ste+j0cno 5/)1qj uv 6u08xhknsgrc 9ezate? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion years. Find thath 0 )d*u+9 xhivojwuk: time on (Fig. Below). People have lived onjhvu u)ko+ 0dih*9:xw Earth on the order of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cokrd 1sfhl62( esmic microwave background radiation is. Where does it come fk rfeh2l6 (1sdrom? Why is its temperature now so low?

Why were atoms, as o xt o3,aiy;ws9pposed to bare nuclei, unable to exist until hundreds of thousands o,9twxya3i s; of years after the Big Bang?

Under what circumstances would the universe eventually collapse in on ihqybxs9 f:8ajr /g2*itself?

  Using the definitions of the parsec and the light-year, show tha3mc+v ; zsx -w vx/-wrap/j8ypt $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.38 seconds of arc. How far away is itdd6-x6 -r fsdy? d =    ly

  The parallax angle of a star is plep:5n.t r062e+ wt e5lnsww$0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its parallax angle? xch v3p ksfva:7c/86g
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 that rsxw 4u ywmou/ yyg*k15dv;(3is 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, will the parall:vo+yl *) yqhzuhwf:.ax angle of the farther star be greater or w: :y*hy)z+ulofv hq.less than that of the nearer star? By what factor?

  A star is 35 pc away. How long does it take for its light toc: -9srueethny4sz: 2; 1tyiopi j33gb:xh l/ reach us?    years

  We saw earlier (Chapter t cn6d3jo0agm; mdo7*fytmy2q 5p20j 14) that the rate energy reaches the Earth from the Sun (the "s5t n*jj203m;of pd70 yqdot2am6c gymolar constant") 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 /*-/vaayh zvs s x/15p q0ohhfbrightness of the Sun as seen from Jupiter as compared to its brightness from Earts x1h/0/ -vzosf5h/ q*hapayvh? (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 /z/1-f zgubpfwould subtend if observed from the nearest galaxy to us (Table 33-1). Compare to z/bgpf-/ zu1f the angular width of the Moon from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a b9-ua8v qzhaw;(pgu .red giant, what will be its average density if it expands out to the orbit zwpb(qa u8.;uvag9 -hof 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 dwarf9jgsd5ch/ ,fz*orxv8y: s jk/ , it is expected to be about the size of the Moon. What angular width will it subtend ff okxh8 d,jy * 9/:5cs/vrjzgsrom the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whose mass a .h2fl501s ncx 0wx:qpoiw3 uis equal to the Sun's and whose radius is equal to the Earth's. How many times larg w3h5 piu. xwa0102q:xlcnosfer 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 i2a8x tbjp6vh8s 1.5 solar masses has a radius of about 11 km. Calculate its average density and compare to that for a white dwarf (Probj2 p8vtxa h6b8lem 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. ,pwoh1;qe k j;33-2. (The mass of the very p,k1;oqw; ehj 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 agi ozap*cl /. -.a/2glzo(rzjpparent 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 cet6;,yempegx a *q9/ ykrtain cluster are assumed to be about the same distance from us. Tw 6a qe9ytmx;ek*y/p, go 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 e ,(9e o*v 2vg/xxwbdnevg2i+w; tvy-wqual to that (a) of our Sun is x,*g 2(v;-/onywtvgedw9+ve2w i bv x    km, and (b) of Earth is    mm.

  What is the Schwarzschild rad l yi5afrfkd1a hv7j:pq ;a6y(l,y /*zius for a typical galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a sphere, fob7 n gwilig :4qe;,0nbr which the sum of the angles is (a) b gw7lig;i qne0 :n4,b359º, and (b) 180°.

  What is the maximum sum-of-the-angles for a triangle on a sc2q- p 1bbh nfciv*89uphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the speef13yl pd c)nymvv. 19jd of light, roughly how far away is it? v3cp)yv.9ljm f 1dn 1vy =    Mly

  The redshift of a galaxy indicates a 1jdmj n3 /z6tqb c*3ov2,ibyovelocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a gzy. .xog9yd rr9 haq.i7,7gogalaxy (relative to us) that is near the observable "edge" of the,.d z77o9.rayriqg gogx y.h9 universe, say 12 billion light-years away. v =    c

  Estimate the observed wavelengts;ppm7kp4 r13zj2o 9nzbmpr3h for the 656-nm line in the Balmer series of hydbn p3 3jpprr9 1 7m4o2;szzpkmrogen in 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 waveleneo7jh1tz(04w4wbii vpc5gai 3rh )2ygth for the hydrogen line at 434 nm is measured on Earth asrgyhej1 ii4p(b37zc4 ita w5 wo2v)0h 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 ef9pq5h8 bc e rn77r+icj4h*u: mm4lf a galaxy with $z = 0.60$? v =    c

  What would be the redshif(urcb mx *-be(t parameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the (d.22sqbcm 4oy; nwsz2m qp3 tDoppler 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 peakusb h 6hsi/:8t of the blackbody radiation distribution at 2.7 K using h6 u8sbsth/ i:Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of t+fmst5zg9mot ;ohz a4.(x c: ku4u)d8j; oveu he 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 distance between galaxiea594wh p, bdihq q0x-ys) at any one moment is believed to have been inversely proportional to the absolute temperature. Estimate th4wdx ,pqyh b0iqh-95ae 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- 5arszo6i)o tdvk(5c cooled below the threshold temperatu oio5a5z6)kc(vrstd - re for 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 thj2x2 xdei71tr1 gjmy z-p.m4 ze three changes represented by the three arrows, A, B, and C, in the H-R diagram of Fig. 33-28. For each case, describe the changes in tr4mmdyizz2g-xj1 1p2x.7et jemperature, luminosity, and size.

  Assume that the nearest stars to us have an absolute luminosi:e ve-)m .ds b7xhtyx;ty about the same as the Sun's. Their apparent brightness, however, i:e.m;t d- v)yhs7xe bxs 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 angularj7x1 wrjohap/9.3 l vn velocity of a neutron star which has colllrh7jnj1xaw 3. v 9op/apsed 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 energ,;x)p cmx;9or+upylwy d tx:3y change when the star in Problem 56 collt oxm ; ,lxuc)d:;39wyyxpp +rapses 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 mascr8s x *jolb c(2cmwxp54,rh 4s 1.5 times that of the Sun, w(hcj 4o4wx l sp,xr8cm2cr5 *bith 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/(tdro:i7m- myv(hpzv -cq :wy 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 criticaa63d3y,z i og au9l q6o,rbc.tl density to close the universe. Assume the neutrino dens, ,ail.3q9u3 ty 6 z6crgdbooaity 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 andy dnb*3 ent.skw *wk5* 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 estimate the ratio of their diameters.ty.nw5k b ek*sd* n*w3 [Hint: see Examples 33-4 and 33-5.] $\dfrac{d_{400}}{d_{600}}$ =   

  Suppose we can measure distances with paralqn,ej+c(w*l llax at 100 parsecs. What is our minimum angular resolution (in degrees), based on this w qn(,l+l* cjeinformation? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from singly ionized helium in a eeo t cngjw:/2q.x:t4 distant star happen to overlap with the Balmer lines from hydrogen (Fig. 27-22) in the Sun. How fast is the star receding from us? c4j:ot2 wt enqg:/ ex. v =    C

  What is the temperature that corresponds to 1.8-TeV colliatx0 ;0e1m /xnbws6f lsions at the Fermilab collider? To what era in cosmological history does this correspond? [Hint:sbl f6xmt 0 ae01x/n;w see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation of gas around what migwodo 2l r9q ww +ke((-aez806k2mkpmxht be a supermassive black hole of about 2 billion solar masses at the center of a galaxy. If the radius from the gala 2q(ke8wm (m w k+w-alr 2dp0xkoe9o6zctic 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" hydro.db4iup5ck. vgen line at 434 nm emitted from the galaxy is measured on Eart4i 5k.cv u.pdbh 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 .-/obje/ b:dcfws+xy lyoyj7qf 7)/e of stellar evolution, a star (if massive enough) will begin fuslj7yyo )fb / y/d/sefo qxwc-+7j.b:eing 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:q:fmuprnqi dl7) xsl85mjr .2/8ckv
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 denzyvny 9ag6 :l5j5za(1(zful wsity equaled the critical density of the un wvyag (j5:zfl9a zu(zlyn561iverse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$