The Milky Way was once thoug q6b:z ,ox-zfkht to be "murky" or "milky" but is now considered to be made up of point source,x:zk-zqfo6 bs. Explain.

A star is in equilibrium when it radiates at its surface all the dr, ,fzlis1(benergy generated at its core. What happens when it begbi 1f d,rz,ls(ins to generate more energy than it radiates? Less energy? Explain.

Describe a red giant star. List some of its prqbi75)qu j up8operties.

Select a point on the H-R diagram. b; )bo2jiyz vj/qhj7n t08v.j Mark several directions away from this point. Now describe the changes that would take pl2)jj.8 jjbn0 btyvvh;7 /zoqiace in a star moving in each of these directions.

Does the H-R diagram reveal anytnl2)w kuwe 6p9hing about the core of a star?

Why do some stars end up as white dwf a t-r2wmj)x .w)9 q3t,dsgehsz1p2aarfs, and others as neutron stars or black holes? 9 tg-fwq xa pj2hdsst.w,m)32z1)rae

  Can we tell, by looking at the population on the H-R diagram, th5zy ;ciyl )r7 g5qz p6*vxy7rxat hotter main-sequence iv5 yr6xg5y*zxrl)z7cp ;7qy stars have shorter lives? Explain.  ----待选择----yesno 

If you were measurind6iaux-t35 v2 vt c,haq(wd 1wg star parallaxes from the Moon instead of Earth, what corrections would you have to make? What changes would occur if you were measurdau1v,-vq63(cth 2wa tdx w5i ing parallaxes from Mars?

Cepheid variable stars change i9 gao8. 4p z)y6 ynz7md7vuyafn luminosity with a typical period of several days. The period has been found to have a definite relationship with the .4yyazmngo )u778fv9p6 z ady absolute luminosity of the star. How could these stars be used to measure the distance to galaxies?

What is a geodesic? What is its su w(lsa;c6fl:n5. cb k:y ,pfrole in General Relativity?

If it were discovered that the redshift of spectral lines of galaxiesbivo6 kin.. c 92a v;usbf2x 1nw.uzu9 was due to something other than expansion, how might our view of t .uboin.uuvn9a2c.w2s6;b x 1 9 zfikvhe universe change? Would there be conflicting evidence? Discuss.

  All galaxies appear to be moving away from us. Are we therefore 9o;6zju-cm5 mqsp/ v kat the center of the universe? Ex69 jsc mkzm-/u5qo v;pplain.  ----待选择----yesno 

If you were located in a galaxy near the boundary of oubxiv53-odiy3r8 o8 wir observable universe, would galaxies in the direction of the Milky Way ap w5oi-3idvy38bri o8x pear to be approaching you or receding from you? Explain.

Compare an explosion on Earth to the Big Bang. Considerk f7yrc *:) yqm*yj0ik such questions as: Would tkq*yyr:cfm yk*i)j7 0 he debris spread at a higher speed for 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 fror*k(h1qr 4tm zm a black hole, then how can we tell if onetqr*mh1rkz (4 is there?

  What mass will give a Schwar7g bxofau6u3k2dr 3g :zschild radius equal to that of the hydrogen atom in its ground state? 3a 3brugk2u:of dgx7 6 M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billiohm34uqvtn 2 cpnw50l 9n years. Find that time on (Fig. Below). People have lived on Earth nvl h4 m25qn 3pcwt0u9on the order of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-Kt6bldm zyc+).jws: i + cosmic microwave background radiation is. Where does it come from? Why is .s md ++yctbizw6lj ):its temperature now so low?

Why were atoms, as opposed to bare nuclei, unable to exist untip*)9 5vwji;v 6dxz hbkl hundreds of thousands of years after the Big Bang5p*idxvk)zwb 6 h ;9jv?

Under what circumstances wouldhc -qyb *yk0 8jw,w0nv the universe eventually collapse in on itself?

  Using the definitions qfbn4r5z/8z 6m p 4lu s5h2zsaof the parsec and the light-year, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.38 seconds of arc. How far away is nz,o7 lwc)i :ccx q n2bp3dc.:it? d =    ly

  The parallax angle of a star37sgjodvj (1 x ixt3+rkyhgz-j7b/9h is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. Whaou;o,51zt l y kv3dm pf9b:ll:t 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 a star thatjpjq( b2 ew8m6)39fr5eis w om is 55 ly away? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice kem/ h d;dt 04bk9(dbmas far away from us as a second star, will the parallax angle of the farthddk;/bdtmb4 h(kem 9 0er star be greater or less than that of the nearer star? By what factor?

  A star is 35 pc away. How :jqhus j1l00z* 7gz,w ax lql7long does it take for its light to reach us?    years

  We saw earlier (Chapter 14) that the rate energy reaches thes9n ym, 2ksqwa- ox -h9ie;: ,v0rnsio Earth from the Sun (the "solar constai2,s -wsor9yxomq:;ieash 0 9vn,- n knt") 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 brightness of the Sun as seen from Jupiter as comp4 9ewr2us 0rhj,+dzl kared to its brightness from Earth? (Jupiter is 5.2 times farther from the Sun than 4dl,wjrrh 0+9zues 2kthe Earth.) $\dfrac{l_{\text{Jupiter}}}{l_{\text{Earth}}}$    $ \times 10^{-2}$

  Estimate the angular width that our Galaxy would subtend if obserfojtyf)*jq:7(k1-cr cgk36 (qcz rds ved from the nearest galaxy to us (Table 33-1). Compare3ckr) 6jf dfscygq(*:j r-ktcqo 71(z to the angular width of the Moon from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, what will be,reb/wbg3o w+hw 1m,v its average density if it expands out to the orbit of Ear/ , w+ohm3,bbg ww1evrth ($1.5 \times 10^{11}\ \text{m}$ from the Sun)? $\rho = $    $ \times 10^{-4}\ \text{kg/m}^3$

  When our Sun becomes a white dwarf, it is expectp;a r- 9a pv*(a;go -.st0 wajgljv,hwed to be about the size of the Moon. What angular width will it subtendvlg j, vr-*a09whap.-s atw p;jag(;o from the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a whitee wzb5aqt* 4b0hv2 q72/nxopbhje1 p( dwarf whose mass is equal to the Sun's and whosoq q*a4zb(hv5xn0bt2p b/2w j7eh1e pe radius is equal to the Earth'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 mas-ni8qhdc ; i1is 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 nuclear matter. n-i ;ci 1hdq8i
$\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 2xf v-:qd y9duc*hak6o,kn ,cof Eq. 33-2. (The mass of the very d 2h-6oc9fk,kx:ncd,q u*ay v 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 brightnewax7w0,+qyvb ss $l$ 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 assume yn4vkur-*,7iddh+p gd to be about the same distance from us. Two such stars have spectra that peak au+rhni*pyv4dk7 ,-dg t $\lambda_1 = 500\ \text{nm}$ 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 aar yagfu7pmu-ye,7 q69 dv 9(mass equal to that (a) of our67-dvf ep9 qur7(amayy,u9g a Sun is    km, and (b) of Earth is    mm.

  What is the Schwarzschild rj p5l4fqs+j65ye,u,xr 2gbabl0)s ddadius for a typical galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a sphere, for which the s :ds6 p0nzq -gd)etc;fum of the angles is (a) 359º, and (b) 180°.fqgc6s-;d ):td e0 pzn

  What is the maximum sum-of-the-angles /h;hppt.uziaovl5 2wran3* ( for a triangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the speed of light, roughly how y2af;takz52(q 4(( nfajq idj fadk(2z24f(qaa 5tna qj(ij;y fr away is it? v =    Mly

  The redshift of a galaxy indicates a vvz7 hupl)* 6e; xix(vu;jyxn: elocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (rela:i jt+cst.bg fn:3d/ ttive to us) that is near the observable "edge" of the j .b cf:sdtni/+g3t:tuniverse, say 12 billion light-years away. v =    c

  Estimate the observed wavelength for the 656-nm7;ascvsv*lz41cr 1q r1 sbja.mptf0* line in the Balmer series of hydrogen in the spectrum of a galax fsavs0a pmc;1t71lsqb ** jr.1rc4 zvy 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 e8 o*o tpov8s +pzg7*qfrom us, if the wavelength for the h*ezt8o o8 g7pqs op*+vydrogen 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 gpuk 9die1zg45(t a7)fbgdn r4 alaxy with $z = 0.60$? v =    c

  What would be the redshifz1 )b fg);5)/oyml jggizc4aat parameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show thatrzm5pzx6 4.stqw -vuc:o l9i,(i m sa) 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 wavelengthg8v,dt,0c9.w op d zdmliqyh m*9(f(m at the peak of the blackbody radiation distribution at 2.7 K using Wienpq tl.m(hmd , 8zddiywmv,*o9 9g(f 0c’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of0 (ahad1 yxg5q 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 unipxf;p5jm r6k. verse (the average distance between galaxies) at any one moment is believed to have been inversely proportional to the absolute temperature. Estimate thpf5 r; 6pmj.xke 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 cooled below the thr clm96xtop6lo +g xm8/kht*+leshold temperature for pr+xk9t*6hocl t6ml 8pxl/o g+ moducing
(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-sequenc 2lks-isl0l g0e stars could undergo 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, luminosity, and sizels 2gls-i00lk .

  Assume that the neare6z:rrpv02 pduk x s1zxwg3c0p.mi3c 5st stars to us have an absolute luminosity about the same as the Sun cpidr1gpk2zv:x303s0 .pux m6wz5r c's. Their apparent 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 angular velocity of a n ek94;64fdj(hnxdm pz(zto2c ac9i+neutron star which has collapsed to a diameter of 20 km, from a star whose radius was equal to that of our Sun 4;n9t(n(+ dz hc2edocjiz4 m xpak6f 9($1.4 \times 10^9\ \text{m}$) 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 rotationar sf4)tgjexwl88f2w ; l kinetic energy change when the star in Problem 56 collapses to a neutror)w8gwf; f4jxt l2se8n star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believed to be,ubg mi43ram8.7o3 t 4yc:z ghdftt8 f a neutron star of mass 1.5 times that of the Sun, with diameter 20 km, is observed :3ghcmy,zt4u f t8.o a ib7trd3g4m8fto 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 9+s4vzz3uoo 8am)id sv+ uy0bis 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 thetnwa1c4v1(i o critical density to close the universe. Assume the neutrino density tocn 1w41ia( vis, 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, respectp8t/a;rgrv,w ively, both lie on the main sequence. wrgp /v,;tr8aUse 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 oeoogxb7vd .)* 1, vvd( fcdxf7k)izy,uy;y 0at 100 parsecs. What is our minimum angular resolution (in degrees), based on this ink;1i ,v(xdd)v, bxf0* ufz7d)y. yoocoevyg7formation? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidencen10 0rui,gzuq tbuzk,/lo/s *, the Balmer lines from singly ionized helium in a distant star happen to overlap with the Balmer lines from o* u0l 1tug q0sur,/zizb /,nkhydrogen (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 the Fermilab cs a0mz avm;::zt1sq cd/ma1 2follider? To whasamf2cd0mtsqz/ az1 1a:;v :mt era in cosmological history does this correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recentlv). 5g- gkshdwr*ws /sy measured the rotation of gas around what might be a supermassive black h sgsgdr-5v/w.h* wks )ole 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 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,pcj0e :v rbf.-tv06 ng .9cu ,wewpui. The "blue" hydrogen line at 434 nm emitted from the galaxy is measured on geb6v:. wr 0vf9.ei-, ujpwt,upccn0Earth 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, afte-;pore ;m+o1qs9v star (if massive enough) will begin fu 1 +tsqrmpe9o-;;vfe osing 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 jrf um ..5d;ty
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 equk0 w8mm+e e r;no;tdke9:obt-aled the critical density of the universe, o m0+d8bo m9te; wkk;-e:er tn$\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$