The Milky Way was once thought to be "murky" vc pv;c/a8ai8q3xx7a r1*pgq or "milky" but is now considered to be made up of point sources. Explagr;3vqivpcxa1a8/ a7 c p*x8q in.

A star is in equilibrium when it radiates at its surface all thebfqa: *,fml598g 10n mjsg rrz energy generated at its core. What happens when it begins to f,nb m01f8m*qslg5 9:rrgzaj generate more energy than it radiates? Less energy? Explain.

Describe a red giant star. List so f(da af0g0)a3c fppn9me of its properties.

Select a point on the H-R diagram. Mark several directions away from this point.wk35mqfs qwjno:t: 5- Now describe the changes that would take p:n-5:qt5jfokm3w sqw lace in a star moving in each of these directions.

Does the H-R diagram reveal anything about the core oovcwfb8 y8 mzrn,+63 hbkn2 r yeii,zkb9g08( f a star?

Why do some stars end up as white dwa)-je vc.fgfg bc89 iw+rfs, and others as neutron stars or black hol fci+f9eb8j-vg w )c.ges?

  Can we tell, by looking at the population on the H-R diagram, that hotter ma zy.v 0xv4r2 srtdukx1h(ysdt//9fe 8in-sequence stars have shorter lives? Explain.r/(v81zfxvs0t 9/ 4kyh r usetdx dy.2  ----待选择----yesno 

If you were measuring star parallaxes fromazfiri 8 ty9a3;h/g(v the Moon instead of Earth, what corrections would you have to make? What changes would occur if you were measuring pa(a g atzhii 3rv/;fy89rallaxes from Mars?

Cepheid variable stars change in luminospe0l/pzj5i 8 9lktx*tr9*xk jcp 9 8fwxon7+jity 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 sta889n pok9+c07r/ *lke xi zt j*xtxjj9fp5pwlrs be used to measure the distance to galaxies?

What is a geodesic? Whan z8 edgs2,4k 6.qjrzmt is its role in General Relativity?

If it were discovered that the redshift of spectral lines of galaxii66,ijy q2qqm0p l3xn ;z4.)acbyhsies was due to something other than expansion, how might our view of the ux, b.;c64s2yqa3ip)nqq y0hml j zi6i niverse change? Would there be conflicting evidence? Discuss.

  All galaxies appear to be moving awayu62ec.jvb;nx from us. Are we therefore at the center of thc;n2u .xj 6vbee universe? Explain.  ----待选择----yesno 

If you were located x)e zr-5zp,qbwi1 y)r;p t6v96aor r iin a galaxy near the boundary of our observable universe, would galaxies iywxr9)rto,;b1a6ipr iz 5eqp r) zv -6n the direction of the Milky Way appear to be approaching you or receding from you? Explain.

Compare an explosion on Earth to the Big Bang. Consider such qlj:m zo )vijp44;cav0uestions as: Would the debris spread at a higher speed for:ivvm jac4o4zj )pl ;0 more distant particles, as in the Big Bang? Would 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 b6mfa b(kgp(c-jg.uyf+q : o7if one iqby-cjf(g +mo7(p : 6afukg.bs there?

  What mass will give a Schwarzschild radius equal to that ofkuc7la n)a3:v the hydrogen atom inckv 7a:ul )3an its ground state? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion years. Find om fe;r2y2k0cljefe u1(p r;zbdbhq* ;,;k 6ithat time on (Fig. Below). People have lived on Earth on the order of a million years. Where is that on (Fig. Below)?f yr;dh 6(0u,fkzi;ce jr;12pl kme e*bbo2q;

Explain what the 2.7-K cosmic microwave background radzsu)tlsz:k66 fd v.cxb-/b( m iation is. Where does it come from? Why isssb)czx(:b - tu/zl6fmd6k .v its temperature now so low?

Why were atoms, as opposed to bare nucleqony/z s/+. b+7m-/ttk fmmt/mq 7wx zi, unable to exist until hundreds of tho7wz tq+/f+m 7 b . txokty/mm/z/sn-qmusands of years after the Big Bang?

Under what circumstances would the u7j ;fomv8q5b92qdt) fjmg-j nniverse eventually collapse in on itself?

  Using the definitions of the parsec and0fmk tbe+ /f x)j*d,cb the light-year, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a paral1afz;3/nyj 8 vc ydd+ylax of 0.38 seconds of arc. How far away is it? d =    ly

  The parallax angle of a star 2 he 24:glypmdo vbsozs9br8 30qmo; 7uxy./ qis $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is itsvn gswb*es ; -2xs:li/ 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 a star .8s q-oevi0,snm5hh9qh. jygthat is 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 paralk-ik* k-dzmv 1lax angle of the farther star be greater or less than that of the nearer star? By w-- km1kz *ivkdhat factor?

  A star is 35 pc away. How gf/c- ,wqbxf )-n8 dbplong does it take for its light to reach us?    years

  We saw earlier (Chapter 14) that the rate energy reacheb 3rj8n6 9frnvs the Earth from the Sun (the "solar constant") 98n 3n jr6rfbvis 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 ofp z)/k kd7-kobq6i ;ok the Sun as seen from Jupiter as compared to its brightness from Earth? (Jup k/oiko-d6b;7q)pkkziter 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 wou q/oiggpc;x-+vd5b.*,g l da fld subtend if observed from the nega-g+dv5io/;fgd l *,pqcb .xarest galaxy 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 density if it e 7h rtjdj9c65kxpands out to the orbit of Et95dk jjr6h c7arth ($1.5 \times 10^{11}\ \text{m}$ from the Sun)? $\rho = $    $ \times 10^{-4}\ \text{kg/m}^3$

  When our Sun becomes a white dwarf, it is zqxsu49:6 lko2k,huex 0gw :sexpected to be about the size of the Moon. What angular width will it subtend from the present disu42k sw0kxe u:zo:xlh,q96g stance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whose mass is equal tou;kkkbezrjh; 7m;ejwf1 *.- b the Sun's and whose radius is equal to the Earth'sb.1f - mju7kbeh k;w rz*k;;je. 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 m.vmrq7u4d . d1.5 solar masses has a radius of about 11 km. Calculate its average density and comp vu4qmd..7rdm are 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 reactioa/*hzikc w2 smc zu 6xlth,0/z/n-qa 3ns of Eq. 33-2. (The mass of th qc2/x3k*u/hnalzz, /tmws60 -iahcz e 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 brigh7.:vd q gu bvx6j/s-m7fp; n1wni g+abtness $l$ 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 acilx5kmmqsjrq72-47 yj3 ,r hssumed to be about the same distance from ukjrl3 cis5yjxq7r24-7qm mh, s. Two 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 Schware 5/znn m vfjq(.q2,lrzschild radius for a star with mass equal to that (a) of our S(ql/ 2eq5 ,vjnrzm.fn un is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typical galax 0a+3f;bgmgo9qpzqi.wt*czm*cr3j l+k +)p vy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the suwr 1kk)j 2nt7jrface of a sphere, for which the sum of the angles is (a) 359º, and (b) 1t2nkk 1jrw 7)j80°.

  What is the maximum sum-of-the-y+ajz) 7q5 xxvlh-o 8sifg7 f1angles for a triangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the speed of light, rougr2w. rx9 q rb5j8s4i9ppd *yk7 vtowy8hly how far away ip5x98b 2r 9tiwrj.74 qws v krydoy8p*s it? v =    Mly

  The redshift of a galaxy indicates a veloci,3ll6/qn vrahty of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (relative t+1m /qpj.tn0yl,8 dqa ml b;cso us) that is near the observable "edge" of the universe, say 12 billion light-years away. ymm.q+j; ltp0/b s8ndcqal,1 v =    c

  Estimate the observed wavelength for the 656-nm line in the Balmer sa *qk-(4aj yyu/ned:r eries of hydrogen in the spectrum of a galaxy whose dista4/aank:d y -eqy(*jur nce 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 wpp8ks*2*fbvr)95 *wpesj pgu avelength for the hydrogenvwe2fps*prpg**bus5 k 8pj 9) 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 a galaeocw 6uj*4(2 yiby glb5q1t(h xy with $z = 0.60$? v =    c

  What would be the red dpns fg3)z) tzjz-h13shift parameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, showy5u/(yz,xfjce h4om- v f4t.o that 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 p5dqt;px 9a rm6xma5+peak of the blackbody radiation distribution at 2.7 K using p pta mma6qx95r5d;x+Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of the universe isaq3 (2hq*:jxwm *g enl $\rho_c \approx 10^{-26}\ \text{kg/m}^3$. 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 galaxies) at any one m21oootkhze 9q6pdj+r 2/9 ukt oment is believed to have been inversely proportional to the absolute temperature. Estimate the9o zkko dpt u2+q t/jh96e2r1o 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 cooledpr j;mty1e gu 0x2jz-9 below the threshold temperature for pr ru1j;mjyg2 tx p9z-0eoducing
(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 maint*23 kxtk6 f9qf6o9h yjh*j 5otsv ug)-sequence stars could undergo the three changes represented by the three arrows, A, B, and C, in the H-R j koy)xt5 j9to9 fs 26t3uhfhqvk6**gdiagram of Fig. 33-28. For each case, describe the changes in temperature, luminosity, and size.

  Assume that the nearest stars to us have an absolute lumin,08z x sr-pa0qudz :oposity about the same as the Sun's. Their apparent brightness, haqps,xo -up00 r8:dz zowever, 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 nomdulthd u 9w:,)o-k -+bs 3gneutron star which has collapsed tosotub 9:-m )o kdgunl+w,d -h3 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 star in Pro khb lf5;aid6-jwcn5 rq 7m(c86;gyqr blem 56 collapses to a neu6jf 8 d;g-bmqi 5k6r;( cqahlyr75wcntron star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believed to be a neutron starwqnqy:f2 01m k/h 0dqfhh 4:wa of mass 1.5 times that of the Sun, with diameter 20 km, is observed to have a rotation : wq4fqw:0n 0f 2mh1dykqh/haspeed 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 galaxzo).d )hp.v e,8nqiuo sn+)omy to our 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 rht/) mua:2br oest mass (in eV) would provide the critical density to close the universe. Assume the neutrino dentm:rhb o)ua/ 2sity 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 abn(5 oupnpw n-*vu ;t)nd 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. [Hint: see Examples 33-4 and 33-5.n n*)utw bp(;5 v-ounp] $\dfrac{d_{400}}{d_{600}}$ =   

  Suppose we can measure distancesa5 xgg, 5mu/3)gq*uxkt s cbh 0c5(9hqddo ue0 with parallax at 100 parsecs. What is our minimum angular resolution (in degrees), based on sd5/*hoba5ce g txgqum 305u, 9h x(u 0ckqd)gthis information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidea1 ;b+vf 2h+aly4v1/nii sidynce, the Balmer lines from singly ionized helium in a distant star happen to oh+invfblis 2 vda;+ y 41a/iy1verlap with the 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 corren,f8bgcgd2 bt*10f zf 53pbissponds to 1.8-TeV collisions at the Fermilab collider? To what era in cosmolobbgg5 10pzn sbi fc,f d3f28*tgical history does this correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation of 0zpbzl8 ;l )qkpum3bl+85 hqd gas around what might be a supermassive black hole of about 2 billion solar masses at the center of a galaxy. If the radius from the galactic center to the gas clouds is 60 mk+3 u;ph bzqlp lz 8b8d)5ql0light-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 at 434 nm em,1 l +qr:tplkyitted from the galaxy is measured on Earth q lr1y, pt:+lkto 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 stellvv4z r h9n4k9tar evolution, a star (if massive enough) will begin fusing carbon nuclei to form, for tvrk49h9nvz 4 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 kna) 9j)f xpf/
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 i yxfpg/a (me8c.1 taxhwwov6u4b(/ u5f its density equaled the critical density of the univtoa4x xc8u yevapu1 w/w(5f ./bgm(h 6erse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$