The Milky Way was once thought to be "murky" or "milky" r nc )vb6)jeov-d0isch1 dl6; but is now considered to be mav d-r)bi;cno6l 06sh)e jv1cdde up of point sources. Explain.

A star is in equilibrium when it radi0 fkqt 7;g4i 2zanua7/yv by:mates at its surface all the energy generated at its core. What happens when it begins to generate more energy than it radiates? Less energy? Explg fy/ 40;bz7uyaa:7imtqk2 vnain.

Describe a red giant q2e-f fyvc2(qhui/7istar. List some of its properties.

Select a point on the kju -roua,. q.ymou2 4jm 3n-vH-R diagram. Mark several directions away from this point. Now describe the changes that would take place in a star m v.4qn.2o,kja-ymu3o j-ruumoving in each of these directions.

Does the H-R diagram -g vh mucts q68m)4:hlreveal anything about the core of a star?

Why do some stars end up as white dwarfs, and others as neutron st qv(ilng,id s-sjeq l3y9d; 2;ars or black h,s s3;iqq9gdijy-dl2v l e( ;noles?

  Can we tell, by looking at the populat4aui-v-/x, 2awx 45 v 5(e7t jaxbjz6s bzxwhoion on the H-R diagram, that hotter main-sequence stars have shorjxwi6v,zjbasxvux t- 27w-x( z4 aaob5h e4/5 ter lives? Explain.  ----待选择----yesno 

If you were measuring star parallaktgx.3 tkh *3h;jp8e axes from the Moon instead of Earth, what corrections would you have to makeg t3*tk;j hpahke38x .? What changes would occur if you were measuring parallaxes from Mars?

Cepheid variable stars change lk.-; 5jt/zzj: yyntq in luminosity with a typical period of several days. The period has been found to havej z-ytqjyl;k/ t.5n:z 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 is itznr4rr7y e/) /m,ldwrfdqq2vf6 3ul-s role in General Relativity?

If it were discovered that the redshift of spectral lines of galaxies6x 6jvje 0sd1 8en-lko /im( :mn/hnql was due to something other than expansion, how might our view of the univer -68 jo enl vm:m6qk1/xhnid/ejs0(lnse change? Would there be conflicting evidence? Discuss.

  All galaxies appear to be moving away from us. Are we therefore at 8xlawxew 31/l/rqfrl31c)r dthe center of the univx3 /q cl3xd r1r/r)1wleal wf8erse? Explain.  ----待选择----yesno 

If you were located in a galaxy near the boundary of our observable universe, wok0hkk/ ; wp-s*4r .jwh;ir qcquld galaxies in the direction of the Milky Way appear to be appr ip0wkrrkqh sjc;;kh-*4q./ woaching you or receding from you? Explain.

Compare an explosion on Earth to the lv51gd0 sl0t jBig Bang. Consider such questions as: Would the debris spread at a higher speed for more distant particles, as in the Big dv0 ll0s51gj tBang? 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 brmydq3 r)6cgy.i - -(xsc6jmblack hole, then how can we tell if one is gs x.dq 6m(y6r)ji3rb -cmcy -there?

  What mass will give a Schwarzschild radius equal 3v ezh4*j) iejto that of the hydrogen atom in its ground s z)h3ev4jei *jtate? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is oftgkfud :dl(, n4en given as about 4 billion years. Find that time on (Fig. Below). People have lived on Earth on the order of a mil (d,gfk 4u:dnllion years. Where is that on (Fig. Below)?

Explain what the 2.7arguxkiq2x fv22.v - 2-K cosmic microwave background radiation is. Where does it come from? Why is its temperatu2i.x2fvqr ga-kxv2 u2re now so low?

Why were atoms, as opposed to bare nuclei, unable to ex3uve 4,u,kuqxa.g) fbist until hundreds of thousand4bfv.)3ka,quue xu g,s of years after the Big Bang?

Under what circumstances would the universe eventually collapse rveivb pxlc 7l9rf9sjhz9w /h0 8dj5np8 ,u++in on itself?

  Using the definitions of the pkj1 ga4;orma-a/ u4fn arsec and the light-year, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.3d (nc1(xrhy3n 8 seconds of arc. How far away is it? d =    ly

  The parallax angle of a star is+.ov0rw0rwxe+ ig t,l $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is itpklo( -w rwv. r8ow*,ss 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 al, +yl9(oiyw/cxi ya)ngle for a star that is 55 ly away? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice osn.ux)q 5d0 r x0u-knas far away from us as a second star, will the parallax angle of the farther star be greater or less than that of the nearer star? B0dxnoqns x- 0.5kuru) y what factor?

  A star is 35 pc away. How long does it take for its light to reach udj8ajr; 8+t5tx uw 3ezj* rzp)s?    years

  We saw earlier (Chapter 14) that the 0hh-swuf z.r8/+qfweq qv.o/ rate energy reaches the Earth from the Sun (o wq vh+ -hfqw/./rf8zuq 0se.the "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 brightness of the Sun as seen from Jupiter as compared 5dudlw8er,uh2m( icsf6 oci.8+p -vsto its brightness from Earth? (Jupiter is 5.2 times farther fromih-l d csov2udsc im( 5pew8 fu.r8+,6 the Sun than the Earth.) $\dfrac{l_{\text{Jupiter}}}{l_{\text{Earth}}}$    $ \times 10^{-2}$

  Estimate the angular width that our Galaxy chg233yyouuy4yc: y2 would subtend if observed from the nearest galaxy to us (Table 33-1). Compare to the angular width of the Moon from Earu2y4 yuhc3c:o3yy g2yth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, what will be i..dz .scq hn ewqh/o-4ts average density if it expands out to the orbit of Eecn./4zhod q..s qh w-arth ($1.5 \times 10^{11}\ \text{m}$ from the Sun)? $\rho = $    $ \times 10^{-4}\ \text{kg/m}^3$

  When our Sun becomes a white dwarf *0mcy8,s4s fdj k p2cg3(ghbs, it is expected to be about the size of the Moon. What angularp4f3s,hjy8 s m(gsk cc*gd0b2 width will it subtend from the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a whi k/e7i usxvrur r5(9v.2fq /cpte dwarf whose mass is equal to the Sun's and whose radius is equal to the Earth'sx.q7rp fr(/2 i9/ ucv5r euskv. 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 a i3e+/ pvzgt:ebout 11 km. Calcul/epv:t+izg e3 ate its average 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 E)6pe2 s /jcgcqq. 33-2. (The mass of the very unstqc cp jg6)/es2able $^8\text{Be}$ 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 brightixw* 4fj,v ch8ness $l$ 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 assumedjl9pg:p ay ai3w)tn-y .3tg09ef(yeb to be about the same distance from us. Two such stars hav0.fle b)3t an99yyjgpa:ip-yetg3 w( e 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 equal to that (a) of ou-nte c h7tz g:)*bt8c jv3/nc5g(gjsyr Sun is tg sn-thjg*3z :ybt /5cnc(cj7e)g8 v   km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typical galaxy (like re2i,umfnp+ s 28 ;bz/ffneo+ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surfacd5(18aj*( q vx qryqjze of a sphere, for which the sum of the angles is (a) 359º, and (bvdra*j(q xqyz8 qj15() 180°.

  What is the maximum sum-of-the-angles forqq ;v8z-af*2 jiksz)t *dae(d a triangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the s)r,b vm7iaj-a(s x zkf(5gk4npeed of light, roughly how far away i4b kia )mk v5njr(xf as-zg,7(s it? v =    Mly

  The redshift of a galaxy indicates z/u csaag*j9/a velocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (relative to us) that is near the observa.w5r hpk1j 9m6n oij;*vq0mvra )h nb a07ndj(ble "edge" of the universe, say.0 vrjdnn6(am)v5 ar h i;jbq91wh mp7no0*jk 12 billion light-years away. v =    c

  Estimate the observed wavelength for the 656-nmfs afu6+ 5brt8 line in the Balmer series of hydrogen8b fs5rt+6 fau 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 i si: q+ 7vvw1nv;dr*ddistance from us, if the wavelength for the hydrogen line at 434 nm is measuredrvdini; w*qvv 7:1 s+d 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 witx4wykq8(5jcw ,0uxs yh $z = 0.60$? v =    c

  What would be the redshift parameter ypl1 n b.nlo3;$z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Doppler shift in wavey2 q8fd4scizbs xs 166length 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 radicstl1;)/g4 bzt3p;zt 8ode l oation distribution at 2.7 K u)/ bsc l1logz4ttod;;p8 3eztsing Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of the y c7s.5- k)0t+ rlhe4hhul,i myxla)k 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 ai,7v8 06sunik*m mz (q 9jinqdistance between galaxies) at any one moment is believed to have been inversely proportional zj v 6(n 8im ,u0qaikns9m7q*ito 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 univp;b7u od)z )5 iupcg*x 5m5awf;/0pj aoulxy1erse cooled below the threshold temperature for produciw b0 ci5f)o7u pxa;1xagjpuod5m)5uzl *; /pyng
(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-sequenchfw/sp1nww8: 6dweg q5og+e; e stars could undergo the three changes represented by the three arrows, A, B5p6hggwweewf os 1qd; /wn8:+, 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 neark,:72b yv8 s-hsis7;b ghz vydest stars to us have an absolute luminosity about the same as the Sshv2z dbi -k sh:g7;8,7bsyvyun'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 momx(:0/lnzqzh bentum to estimate the angular velocity of a neutron star which has collapsed to a nl q/b:0(zzhxdiameter 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 csz :( g3ry*njin Problem 56 collapses to a neutron stacys(:r znj*3gr? $\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 y. f.uqi pmtyhki7y*nq 4r2* 9of the Sun, with diameter 20 km, is observed to have q.i2y*u4 tmp kfq*hyy .97nria 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 Galqje.tuujnl u 1emf*gy*s++. *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 densit*j/v,a1 pygaa y to close the universe. Assume the neutrino density is, like y ,1a /agvp*ajphotons, 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,7+1l gbh0;6 ay x 2daqy;uiutq respectively, both lie on the main sequence. Use;76 +1 2ui g0;tlq ubdhaqxyay 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 at 100 parsecs. n ph: sn*y82ur2g qj)oWhat is our minimum angular j2 go2r)yqs:n8up h*nresolution (in degrees), based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from singly ionized helium in a g3fxpkm + 4ien6)a w7zdistant star happen to overlap with the Balmer lines from hydrogen (Fig. 27-22) in the Sun. How fast is the star receding fromgf37pz6xa mwn )k+ie4 us? v =    C

  What is the temperature that cbw3-zsp k g0* b85xmcf+oq (sxorresponds to 1.8-TeV collisions at the Fermilab colli qzs*( b+kpxb0fg85 so3xc-mwder? To what era in cosmological history does this correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recenmf6,c -giir o3tly measured the rotation of gas around what might be a supermassive black hole of about 2 cfoi gri- m,36billion 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 fr7zqyns3 n 4iibc:1,v 3,jwegcom Earth. The "blue" hydrogen line at 434 nm emitted from the galaxy is measured on Earth to be 65i4cywn:3g 1,e 7 i3vsjnz,bcq 0 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) will begin e,yd(*qf0le d4) asi8ew roz+fusing carbon nuclei to form, for example, magnesium:dziewye sar4)d, 8*0 elf (qo+
$^12\text{C} + ^12\text{C} \to ^{24}\text{Mg} + \gamma$.
(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 nn y:, 7zmdpj:+mm rk/
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 eq )reg, 1ttb vrdg:m1r.b 40oy:z9svmbualed the critical density of the unive v91toe ,y0bmv:zrbmsg1gdt r. :)rb 4rse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$