The Milky Way was once thought to be "murky" or "milky" but is now considerwb(g2v,m ks2 red to be,mb(s22k vrg w made up of point sources. Explain.

A star is in equilibrium when it radiates at its surface all the energy gen0.z 7 t zp2pgrhlw0s6eerated at its core. gl ph6.r0wz0 pz27estWhat happens when it begins to generate more energy than it radiates? Less energy? Explain.

Describe a red giant star 2 do3o;vo:ptb. List some of its properties.

Select a point on the H-R diagram. Mark several directions away from tst ll 69nnu1,pn d;ujn7/ kzo /5uub)ehis point. Now describe the changes that wo k td)/on l,59n;lp jen61unubu/u7z suld take place in a star moving in each of these directions.

Does the H-R diagram r 5nt,taksy; e(eveal anything about the core of a star?

Why do some stars enn.ns5 ,yzj0cz d up as white dwarfs, and others as neutron stars or black holes?n,5y.0nzczj s

  Can we tell, by looking atl rt, .h5gid o:y8pcl9 the population on the H-R diagram, that hotter main-sequence stars have shorter lives?tl:,9 pg ily58c.r odh Explain.  ----待选择----yesno 

If you were measuring star parallaxes from the Moon instead of Earth, ,,8-uodg2 sc7 y 7ixd rkpo2gzwhat corrections would you have to make? What changes would ou, s o 27ki7d2,8 gproyd-zcxgccur if you were measuring parallaxes from Mars?

Cepheid variable stars change in luminosity with a typical period of several da r53n,;pi)vvdj ztnx(ys. The v zn5,vd3 ;p xr)jtn(iperiod 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 i1 r ju1gsratz:8:7l ues its role in General Relativity?

If it were discovered that the redshift of spectral lines of galaxo/4ilu fj di:8ies was due to something other than expansion, how might our view of the universe change? Would there be conf odij84:u fil/licting evidence? Discuss.

  All galaxies appear to be moving away 3)k6on afduanw868r y from us. Are we therefore at the center of the universe? Explaioda 6kfua)6r3wy8 nn8n.  ----待选择----yesno 

If you were located in a galaxy near 36d 7t8nyegfc the boundary of our observable universe, would galaxies in the direction of the Milky Way appear to be approaching you or receding from you? 7e gy6nc3dt 8fExplain.

Compare an explosion on Earth to the Big Bang. Consider such qs*m8x3wd -phxv4o0 ehuestions as: Would 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 universe would this smpx38 e* d0w xh-hvo4correspond to, open or closed?

If nothing, not even light, es2n1x6a)an f phgz8kx ,capes from a black hole, then how can we tell if one is ther,8gxx61k ha2)npfn zae?

  What mass will give a Schwarzschild radius eqf0j vjswq(6q4dx5 5pf ual to that of the hydrogen atom in5q4v q5fd0wjjsxfp (6 its ground state? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about / s8 rwmniq whhlo:6g: y6z9lb;sb8q54 billion years. Find that time on (Fig. Below). People have lived on Earthng ls: s h89i: 5 oh6w68;wlqmq/ybbrz on the order of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic microwave background radiation is. Where does itf8 gm1kw3kwz/ come from? Why is its temperature now so log8k 3mwkf/1wz w?

Why were atoms, as opposed to bare nuclei, unable to exist uk-x1keu *8 dibntil hundreds of thousands of years afte 1b8uk-dikxe *r the Big Bang?

Under what circumstances zp65xap/xo3 i mgb-j7would the universe eventually collapse in on itself?

  Using the definitions of the parsm,vy,2zsb (1kr:bn js 7zd+ltec and the light-year, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax o;n:/70y md2chiappo gf 0.38 seconds of arc. How far away is it? d =    ly

  The parallax angle of a star v0-v/mgt1irae,ar2n is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is itswvz r,j 2gfm44 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 that is 55 ly away9d72wbzm:e * rvho+zzxt, *sm? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away from us as a second star, will the parallax a2fz; hivb5x yx+d)q 2cdk) -8a7fbde yh)py/ ungle of the farther star be greater or less than that of the nearer star? By what fadc y)qf)f85v;2h7+d/ yi)b2eh px- kz ybduxactor?

  A star is 35 pc away. How long does it take for ii ;(tcu4.sboodj / 3rqts light to reach us?    years

  We saw earlier (Chapteab bn n +779jt8af( k0vgsjlt+r 14) that the rate energy reaches the Earth from the Sun (the "solar constant+a9a sbtgb nlj7nfvj+t70(8 k") 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 compared to il4 bc e1;3wwegts brightness from Earth? (Jupiter is 5.2 times farther from the;l cewb431 weg 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 from the ne7eii jn2fg0/fxmnl(8kp4 5 l tarest galaxy to us (Table 33-1). Comparmi0jlnf( t knx/4pg58l ei72f e 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 6 h7k.nxomr cnt/s 6x84qhx:e 8rz,t+nad/ hxdensity if it expands out ktxh64nh+6/.z nxxh as78 mxc/8:r,qdnrteo to 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 white dwarf, it is expected to be about 9jd hejx, e7r8the size of the Moon. What angu xhe8jr7jde,9lar width will it subtend from the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whose mass is equal to kt2(q2;mnwhoc l,wx / r4 y:lg5qixw.the Sun's and whose radius is equal to the Ea;x5: yl. hwgt wx/k2o(,nlw2qrcm 4iqrth'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 solar masses has a radius of about 11 km. b sjy-s5w *n8rCalculate its averag b-8rn5y*s jswe density 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. (eby75 jgd dd:; nt.jm*k4pwqap*rs 5 f.rl ;v-The mass of thkddtlnv4gd. pjs*jrb5;wqe7 a. yf;: -5r p*m 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 ovh 0ygy2 )m5iw 48l+dfq:c4j(ib p sgthe same apparent 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 certain cluster are assumed to be about the same distance fr / k6n3f ujge)nnxgdnek3):/som us. Two:)kn dkxn/6gf 3ejg en3s/)un 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 Schwarzschildh2lrro2 c4*5(ng3dda 6o u qqj radius for a star with mass equal to that (a) of our Sun *4 qujo(rdqdc l2hrag6no52 3is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius(fr5 iyt )w+xaj18f pg 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 sum of the ,t9hj40a c: ul)t,o+fq rqbqmq-2gagangles is (go,)q ug ,bqft0larcq :t -4am92qh+ja) 359º, and (b) 180°.

  What is the maximum sum ayi *;7dj5ujtamwr* 1-of-the-angles for a triangle on a sphere?    $^\circ$

  If a galaxy is traveling away from6q0aljpd b* 4n us at 1.0% of the speed of light, roughly how far awa0n6 dqap*jb l4y is it? v =    Mly

  The redshift of a galaxy indic37x bf7fn mw4cates a velocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galy 5wog+j0b6 u q,z02grybki)q ; :j 1(qqmpljqaxy (relative to us) that is near the observable "edge" of the universe, say 12 bi5u bwg61 j;)igblkyo2,y(0 +jq zq:rjmqp0qqllion light-years away. v =    c

  Estimate the observed wavelength for the 656-nm line in the Balttl1vbf 3)4 qemer series of hydrogen in the spectrum of a galaxy te vf1tb4 l)3qwhose 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+v1kbyn6x)tcb3l ,x8yww0e l distance from us, if the wavelength for the hl,x vc6)nt 8kxyb10 ebl w+wy3ydrogen 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 aeo6 )cuxln(7b/m q gm fpr0aq4m z-n06 galaxy with $z = 0.60$? v =    c

  What would be the redshift parameter - yh87xwpez5,:1 gh wc1vkogn $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33 i253)qkzmy fk-3, show 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 wavelengl;lkmo 6csrg7 w- tq//th at the peak of the blackbody radiation distribution at 2.7 K using Wiekt7/l/gq6s-cm;ro lwn’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for cli qom(40; p8)djz/crwkhfyy 6 osure 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 distance betweh7 p nf4v 4g6: k4d9xfsw-zqqwen galaxies) at any one moment7 v:4zfwsk9 xgn q q4fhp6-w4d is believed to have been inversely proportional 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 universe cooled b4l cow q(9ix 1pryv6(oelow the threshold temperature foxy(pi6o w l(rc 4vqo91r 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 z:al-1zcsjp zhhm n* zo14u(26yqg; j/ *jpoi stars could undergo the three changes represented by thejz o snz(z;j2gho4 z :ap-m1c 1yilh *q/pj6*u 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 size.

  Assume that the nearest stars to us have an absolute luminosity about the ; jis*cjvmx2i/7u tu:same as the Sun's. Their apparent brigt2 xviu7jm*is /;ju:c htness, 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 angnek 6n1n*i1amvqc v. 8ular velocity of a neutron star which has collapsed to a diameter of 20 km, from a star vi1 n vk1me8q.6an*nc 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 kineticjsqo+0 z8rdg+ energy change when the star in Problem 56 collapses to a neutj q8+ 0+rsgzdoron 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 tha-4kbj8 jlc/o 2knxegsw. -0nat of the Sun, with diameter 20 km, is observed to have a rotation speejwo- 2xkl/bns kj.e 04a8gc-n d 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 Galhhf5mo )yh(. ese xp*,axy 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 critical density to cpokc4 jy1r1; dlose the unio41 ckyp;rj1dverse. Assume the neutrino 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 on-lewj qz 7mp+1r50a ya the main sequence. Use Wien's law, the Stefan-Boltzmann equatioa q1lmawjzyp75+- e0r n, 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 at 100 parseu ybsg*bz9u3. 75 tnuzv 3qwor*q4v v,cs. What is our minimum angular resolution (in degrees), based on t s*5zgv .,owq3ut r7 9bq*3uz4un vvbyhis information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidemh+ /jg5ols29 l4.hf m ) i41nucvxbysnce, the Balmer lines from singly ionized helium in a distant star happen to overlap with the Balmer lines from hydrogen (Fig. 27-22) in the Sun. How fast is the star rece4lob 4x.us2iymm/h hvfg+ lj1 )5n 9csding from us? v =    C

  What is the temperature that corresponds to 1.8-Teldvp)e3ez i yh3l3q +a3w//wkV collisions at the Fermilab collider? To what era/3l evqw+kpz w333 e)dlhi/ya in cosmological history does this correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation of gas around whtdf )a1 olg ,b6zpcm;e:l:l+lat might be a supermassive black hole of about 2 billion solar malo e d);,ll:z m:alp6g1 tcb+fsses 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" h* is nf1z6 qlz*8tsof6ydrogen line at 434 nm emitted from the galaxy is86 lzqsfoz*n6fit*s1 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 evolupe2( q* .hhmj,qhywy8tion, a star (if massive enough) will begin fusing carbon nuclei to form, (yhe* 2mh py.w qq,h8jfor 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 /nqmps3qd pq lscp(w18i (ts*g0) l i)
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 cri(pbi6a4 ktz nd1 upo((( 8kfud( ftws6tical density of the universe, opt(6f(n ud8p1tf(a(b w(zi6ks uk4d $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$