The Milky Way was once thought to be "murky" or "milky" but is n5 jiv-kz7 ld )8 r+s9cedulaqw+ dqje-7i 40huow considered to be mad jiw5 z9r dl7e8-vu++l4aqdhsq0 - kd 7ui)jcee up of point sources. Explain.

A star is in equilibrium when it radiate;5a76iobc tmjs at its surface all the energy generated at a5omic j;t 76bits core. What happens when it begins to generate more energy than it radiates? Less energy? Explain.

Describe a red giant star. List some of i jrkv+(bbfbm:k m fg (w09-l9fts properties.

Select a point on the H-R diagram. Mark several directions away from t 80ro pi0a rsalzn2ur25;.zqghis point. Now describe th ;iaraq gn 25u2rlz0p0sor.8 ze changes that would take place in a star moving in each of these directions.

Does the H-R diagram reveal anything qq 4k.l2spev,about the core of a star?

Why do some stars end up as white dwarfs, and others as neutron stars or blacr3k/10e )vnq v3zjyr sk holes?1zvyrnr3v qsk)3 j/e 0

  Can we tell, by looking at t3 ;b(3.j iwqzzqq5jnd(qi(y0g p w6gnhe population on the H-R diagram, that hotter main-sequence stars have sqdi; pqzgw6i3jq (5( z0qn.y3jn w gb(horter lives? Explain.  ----待选择----yesno 

If you were measuring star parallaxes from the Mqot3 wn9 mokcs.6.st3 oon instead of Earth, what corrections would you have to make? What changes would ok3w. tn3m9qssoot6 .c ccur if you were measuring parallaxes from Mars?

Cepheid variable stars change in luminosity+ue wr(yg.2dq 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 usedr+2uywgqe (d. to measure the distance to galaxies?

What is a geodesic? What is its role in General vkslvtj9wey8vx u;-( :a.fy)y1q*wqRelativity?

If it were discovered that the redshift of tj;6vnny2e o4 spectral lines of galaxies was due to something other than expansion, how might our view of the universe o;4 jvynn2t e6change? Would there be conflicting evidence? Discuss.

  All galaxies appear to be moving awagjtf+siwy , / 8-qmulr/s: zk9y from us. Are we therefore at the center of the univeru- kf8/ +mjs9isg:zty r/ ,wlqse? Explain.  ----待选择----yesno 

If you were located in a galaxy near the b xn;v;npu- wf uvaky.qjw6-kp 1,xh 93oundary of our observable universe, would galaxies in the direction of the wp;fq3 vv1k n,wx.9huj x6a;p -ku-nyMilky Way appear to be approaching you or receding from you? Explain.

Compare an explosion on Earth toy8 ;5y(t(8br8q w,z)8tf qu+znxmyh( koy fko the Big Bang. Consider such questions as: Would the debris spread at a higher speed for more distant particles, as in the Big B8f5x,mow 8uf+y qbqyyzhy8k(o(;) t8nt k(rzang? Would the debris come to rest? What type of universe would this correspond to, open or closed?

If nothing, not even l2qq:;rnsf0vybchdf rd85/ 0k ight, escapes from a black hole, then how can we tell if one ih2nsq0 :yf8fr;r/ 5qvd0dbk c s there?

  What mass will give a Schwarzschild radius equaqs /j3ng2fw9zgaxxlu,9j is +xz/5wja)39 fll to that of the hydrogen atom in its ground state? /igjns 9fxja5+uw l/,zslag99f z x 3q)w2jx3 M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 4g96e9b md e:z6:na ,upoytfu4szb6 gbillion years. Find that time on (Fig. Below). People have lived on Earta 4fg ,: 694 6oyzemnp:6zdeuug t9bbsh on the order of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic miv9vc -*6nnzbgcrowave background radiation is. Where does it come from? Why is its tem9z 6ncgn vv*b-perature now so low?

Why were atoms, as opposed to brtr jm;(pjzjik +3*zod 7 3j;pare nuclei, unable to exist until hundreds of thousands ofr;tz 7 om;k3jjpd (*rjzi3jp + years after the Big Bang?

Under what circumstances woul jqe:p ov.60 5ddb4nopd the universe eventually collapse in on itself?

  Using the definitions -a;jli 4 ogf+pof the parsec and the light-year, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a par8qxix6+/a glz allax of 0.38 seconds of arc. How far away is it? d =    ly

  The parallax angle of a stao ev9as ()bwl5r is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its parallax angle? kin/:vuhs5m7y g5n-o
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 is 55 ly aw6f) h snin;d)7e6p ocmx,jz;e /apti+ay? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away from us as a second star, will the parallpuvz+yv u v448xlzp3 2ax angle of the farther star be greater or less than that of the nearer star? By wh vuyp8 x3 zp42+uz4vvlat factor?

  A star is 35 pc away. How long does it take for its light to reara/)g +(6d v1qyp q*vrk,hno gv6bv*s66cgqech us?    years

  We saw earlier (Chapter 14) that the rate energy reaches5q+bxes2x j+b1+bmeg : x .zd*+ghkes(l tfj3 the Earth from the Sun (.x+j+be(m1+l2qx5*k eghfjxs: sbz+ tgd eb3the "solar 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 brig,se0rg8 fpkf:l+uhj 5 uz79s(h yvrku n522orhtness of the Sun as seen from Jupiter as compared to its brightness from Earth? (Jupitev5fulsrfs07 r ku8oh z uy 2:k+g rejnh,95(p2r 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 observedg he z5m:ye:44-czv nf from the nearest galaxy to uv5ez:f4g c: ye-hn m4zs (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, : fzjwue *g2g s-r129xbc/uxdwhat will be its average density if it expands out to b2d*z/9x sfwxg: -1uuec r jg2the 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 about th jtggvw+ -09c-n9+a 6mgzfqh2 f oy6oae size of the Moon. What angular width will it subtend fro6yc692afznmgho w9q-gg tf + avo +-0jm the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a whitp 8a,wlz7irasfe ;mpv(8/-4dv nxd:qe dwarf whose mass is equal to the Sun's and whose radius is equal to the Earth's. How maamd-ae( zw /4pln;7: sqdvrvx8f i p8,ny 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 mass6idpqxrw8t mt:. *,g *z3dqus is 1.5 solar masses has a radius of about 11 km. Calculate its average density and compare to that for a white dwarf (Problem 13) and to that of nucleg t*pwtxd :d.rq*m, zs38iqu6 ar 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-valuezh+c rnw8/ 0cgi h(ux5y;g+cjs for the He burning reactions of Eq. 33-2. (The mass of thej8 5 gccxnhru+h/z 0iw +c(gy; 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 the same apparent brightnes;,c 9 *uzoro;dqzxga3 cau u80s $l$ 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 assumerm r9b7vy* dp+d to be about the same distance from us. Two such st9 prd7br+vm y*ars 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 Schwarzs+qwrnae9ugm2z,3b qk.k5,pf child radius for a star with mass equal to that (a) of our Su,a. qf+5,uzk krgbq9 3 2pmnewn is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for.pedmpl8gy8 - a typical galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on th9d:30un c 1)ng tobej)r wvbwu:3i* nve surface of a sphere, for which the sum of the anglesct *ev3)r1w ninu0b)jdbv:no:9uwg 3 is (a) 359º, and (b) 180°.

  What is the maximum sum-of-the-angles for a triangle on a sphebnfqx6; drg tb8k3 -3cre?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the speed of li77cclflh2d /zght, roughly how far away is itzlc2 /c d7f7lh? v =    Mly

  The redshift of a galaxy indicat:7b w.u7adqt mes a velocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a gala3w3c0ztaqg sx3ot :9hxy (relative to us) that is near the observable "edge" of the universxgh0s9atzqoc t w:33 3e, say 12 billion light-years away. v =    c

  Estimate the observed wavelength for the c -av- ts)p86ktyq:ibv;5t/srs y, rf 656-nm line in the Balmer series of hydrogen in the spectrum of kpst 8:rty5 bsq,;v-v6s/ti- fc a)ry 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 diy0cr 5qqgr 1-jstance from us, if the wavelength for the hydrogen line 5q0c rq ygj-1rat 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 )nlfd*xh g4s:ith $z = 0.60$? v =    c

  What would be the redshiftxl.k xr9/ ;ivujls( y; parameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Doppler shift iv ,2xw 5)hkfjmb 3c-sbn 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 radiation cl6a2dms 80xuzuq8h ouzk.,1distribution at 2.7 K using Wien’s lak.z0 qcu,alz16288hxou du msw. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closy7*iiebt1 ezkx y;x 8.ure 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 univer,en1 6 venryn. t0k5jlse (the average distance between galaxies) at any one moment is believed to have been inversely proportional to the absolute temperan,50tj l6 enkvne1ry. ture. 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 univ-zqi,hbwtx4 wt/ o *b:dh r/8verse cooled below the threshold temperature for producxrz:bbth/i,- t*hd8v/ow 4wq ing
(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 un6c)t g2mwgh/: atx5 lxdergo the 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 temperature, lumin agw562xgcxlhtmt/ ):osity, and size.

  Assume that the nearmdq 5o +df4hys*w72 buest stars to us have an absolute luminosity about the same as the Sun's. Their aos2b7d45dw fh+qm* y upparent 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 anguleo+9wqm/ bk 8q8hsq1wdv;*ztar velocity of a neutron star which has collapsed to a diameter ofs+ eq wk 1h8b;9dt8*/wqvzo qm 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 star in Pro/zk,3n pyh h-.t:c xm-lrp**c/em knk blem 56 collapses m:mke hc/ptc-k -r*l3kz/,pn ny.*x hto 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 times that ,l2mjv9v*+w s0qlvs fof the Sun, with diameter 20 slvjv*+v 2,lqwsm09fkm, 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 Galaxy is abo:77csiw z9w 2qc pcir6ut $2 \times 10^6\ \text{ly}$ 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 r kb gi,dv:82rnest mass (in eV) would provide the critical density to close the universe. Assume the neutrin8vb kirdg,n2: o 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, both lie .( pv* nl:smveon 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. [Hint: seeepv:vs (*nlm. Examples 33-4 and 33-5.] $\dfrac{d_{400}}{d_{600}}$ =   

  Suppose we can measure distances with parallax at 100 parsecs. What is ou+c z.o3y**e:lotvyqv r minimum angular resolution (in degrees), based .oyc+3tv*z lve*: oy qon this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from s(0w dlx3q2dsfb9 it,pingly ionized helium in a distant star happen to overlap with the Balmer lines from hydrogen (Fig. 27-22) in the Sun. How fdld(tq, w 3sx0fpb9i2 ast is the star receding from us? v =    C

  What is the temperature that corresponds to 1.8-TeV collisions at 6fq6n61zbgl1 2/ihgj-jmk nw the Fermilab collider? To what era in cosmologicag hqj1/kw- 62j1lmi6z ngb n6fl history does this correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotatio)dq q) )k/jzbcyhz +r2n of gas around what might be a supermassive black hole of about 2 billion solar masses at the center oh)/yrd+)c kqjbzq2)z f 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 fromv jgt. (9r 3psnzmrd+, Earth. The "blue" hydrogen line at 434 nm emitted from the galj3d.,ntg(sr9r vmz + paxy 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 evolution, a star (if massive enough) wit9fr3ox8l ie9jmsk9oj 2 r :dyb,a;xxq1ho7;ll begin fusing carbon nmld8 ho3terx1ax ,99iqsjo; f;j r2x:7b oyk9uclei 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 h6jlcay l*k27
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 equaleli8 i +p8*3r nfvh6rop +le jcnpq**z:d the critical density of the universe, ji :* lf8z o*r+vrp6 ne*i+3nlqcph8p $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$