The Milky Way was once thought to be "murky" or "milkk a+a(/ ofiku/17ihuty" but is now considered to be made+/(1at/okaihu7 ik uf up of point sources. Explain.

A star is in equilibrium when it radiates at its surf2kt7kj k 2tt+qace all the energy generated at its core. What happens when it begins to generate more energy thtq jt+k27tk 2kan it radiates? Less energy? Explain.

Describe a red giant star. Lm r 2r9hh+bvy0 ia6 g49mmo.ioist some of its properties.

Select a point on the H-R diagram. Mark several directions away fwjj8 s ah/ii 4g//vwvbnf) +j*rom this point. Now describe the changes that w j/jnw4 /wg i/sj)vi8* afvb+hould take place in a star moving in each of these directions.

Does the H-R diagram reveal anything about the core of a stae yrf )-x55m w/9btueyr?

Why do some stars end up as white dwarfs, and othyj qj;oac 0.q;ers as neutron stars or black holq0oy.c; j;qj aes?

  Can we tell, by looking at the population on the H-R diagram, that hotter mainn ep+dy d,-y(x-sequence stars havep,(xe-y n ddy+ shorter lives? Explain.  ----待选择----yesno 

If you were measuring star parallaxes f x bndo p/d4+7c9:z6 hhxrq fvs.8;jqirom the Moon instead of Earth, what corrections would you have to make? What changes would occur id.nz b/:8ix q649f;+ho chsjpv rx7dq f you were measuring parallaxes from Mars?

Cepheid variable stars change in luminosity wit +zite09;:y7cs0 bs3 dexxkalh a typical period of several days. The period has been found to have a definite relationship with the absolutetai0y zdx7sxl :+ec39 0ksb ;e luminosity of the star. How could these stars be used to measure the distance to galaxies?

What is a geodesic? What idqjt3 +s5n 2+z mz;b sigp,shm7*s9tbs its role in General Relativity?

If it were discovered that the redshift of spectral lineio 3 wdb a1uz(0m6n u*kc)vzz)s of galaxies was due to something other than expansion, how niz ukv6m0o3 dawu)z )b c1z(*might our view of the universe change? Would there be conflicting evidence? Discuss.

  All galaxies appear to be moving away from us. Are we there)*hk /egkwr80obs,.az-3dsmg 5 ssoofore at the center of the universe? )0 aroo-k8 g/z sgdsw,s es3hbm* .5koExplain.  ----待选择----yesno 

If you were located in a galaxy near the boundary of our observable universe,(am f9ctc ge37 would galaxies in the direction of the Milky Way appear to be approaching you or receding from you? Explain.tf(ac3 me97gc

Compare an explosion on Earth to the Big Bang. Consider such questions equ 0k0:jeubs:d5 wt0as: Would the debris spread at a higher speed for more distant particles, as in the Big Bang? Would the debrut00ed:5 0wkubsj eq:is come to rest? What type of universe would this correspond to, open or closed?

If nothing, not even light, escapes;1lc4yuqn c r+ from a black hole, then how can we tell if one is there?1qy 4ruc+cln ;

  What mass will give a Schwarzschild radius equal to that of the hydrk-1.,zqw e h:l:joor eogen atom in its ground qe,o-1r : h.:weokjl zstate? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion years. Find that time on (Fig;0 bny*sr6apcj8 y,zp. Below). People have nc s0ry,j;6pp*bzy 8 alived on Earth on the order of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic microwave backg t8 ypz 89602gher:i.vowfwah round radiation is. Where does it come from? Why is its temperature nozp6oywf. w vh rea988 0:h2gtiw so low?

Why were atoms, as opposed to bare nuclei, 8/z fnok 8m3.g w0fa0l6ldvop/s u2mqunable to exist until hundreds of thousands of yearssdz/a m /60.wqn320v8goku8f lfp oml after the Big Bang?

Under what circumstances would the unive)g1t9rl+-bc v7c np z0cy2o murse eventually collapse in on itself?

  Using the definitions oe( 5;p.q6cun x lgql5 5tsu5-pp8wpuwf 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 awayuc +6-j8nlek5g3pc hr is it? d =    ly

  The parallax angle of a ste(g(r1eh m 85 sf.7 kk6isobwcar is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its paralla: c:m eeqe-nq ft)*r6px 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 foun -16r 4vwqagn3)ddo wrf) c5r a star that is 55 ly away? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away from us as au,) k 6fsam0iej 4ry2ki,ei 5m second star, will the parallax angmy ) e2iurfjk4sa, 56 keim0i,le of the farther star be greater or less than that of the nearer star? By what factor?

  A star is 35 pc away. How long does it take for its light to fzh.aa *.6xpcyvd +4lreach us?    years

  We saw earlier (Chapter 14) that tw02f ,a5-hyn4w-tb4d qrq4xnn pqr4 yhe rate energy reaches the Earth from the Sun (the "solar constaxyb4 qn-q4ryn4pt 0rw 4q2aw,f dnh- 5nt") 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 Jupitek6af3+ie )el gr as compared to its brightness from Earth? (Jupiter is 5.2 times farther from the Sun than the Ear+ie k 6algfe3)th.) $\dfrac{l_{\text{Jupiter}}}{l_{\text{Earth}}}$    $ \times 10^{-2}$

  Estimate the angular width that our Galaxy would subtend if observed fromh-etd:wh4e ptpsk3yq(.11g cf5t- x j the nearest galaxy to us (Table 33-1). Compare to the angular width of tpes- jd3cgek.14(f tpqyx-wt t1 :hh5he Moon from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, what will be its average density if*yxi /6prsu vzopn(21oq2o ;a it expandsnyu;ixp/rpv o oz2 *1q(as 26o out 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 a 9yn.f iprd46obout the size of the Moon. What angular width will it subtend d9yfr.p46 oinfrom the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whose mass is equal tk2 w f6cl;b/wto the Sun's and whose radius is equal to the Earth's. Hwf cwb;kl62t/ ow 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 sol.b)uqk/011;cd nnl l,nw ij rfar masses has a radius of about 11 km. Calculate its average density and compare to thatjnr. kblnfqncw1,)u01 / ;dil 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. (The mass of thkj :k)i 2askl2v(yp6p e very unspiyp a) l62(j:k 2kkvstable $^8\text{Be}$ 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 brights)25g*usefg t *7hsdyness $l$ 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 an w +u h6jsr;.k x7 kyo9xmbv6lq12+yxbout the same distance from us. Two such stars have sqywj6vl;y+mx+xs r21nkhb k7 u. 6 o9xpectra 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 ouou5 ;,ai;s iy*jn .tiqr Sun is iiqasn*, u5y . oitj;;   km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typical galaxy (like ourb0a6wxo)w 8uvs)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a sphere, for which wmdba/oc)f7 ( /w :qlwthe sum of the a(abmo/www 7fqlc:) /dngles is (a) 359º, and (b) 180°.

  What is the maximum sum-of-the-angles for a tr.)hatt6)e8ip , svbui iangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the speed ofc nijbr8h5(0 p light, roughly how far away is it? (c5jn0b 8phir v =    Mly

  The redshift of a galaxy indicates a velocitp/m3w d ju*1cly of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (relative to us) thaif)+vbij 7p3kl xr sd+.+v*bat is near the observable "edge" of the universe, sivvx f+ )*las.++rip3b k d7jbay 12 billion light-years away. v =    c

  Estimate the observed wavelengt35 tdi6 waxed.h for the 656-nm line in the Balmer series of hydrogen in the spectrum of a5e3i a6 tw.dxd 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 distance from us, if the waveleznr 0tz+eksr- 3) zw4zngth for the hydrogen line a )nt0zk-+zz serzrw43 t 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 g xt.(3ub hokx,alaxy with $z = 0.60$? v =    c

  What would be the redy:jiedi9/ ch/)1 qpw)vwt,xk shift parameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show thkhy yrdj)0f,q(; ey-l fxnj6-at 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 peak of the blackbody radiation distrg95b pt o5i.9 ui 5d4koxl3jqmibution at 2.7 K using Wien’s law. x5 tkiq3j49ip59m od.ulo5g b$\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of the universe is )ngb-)x+t *jmv j5k:hz7ki mm$\rho_c \approx 10^{-26}\ \text{kg/m}^3$. 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 mom yze+ im.r .we:+;ogfcj:v-l ir;gn7aent isglroer a-.;7y.;w+ ncz i :im ej:fgv+ 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 below the threshold temperatubzm wg sdp7 8i)ruo+m:n 2*h8ffw 96avre for producing 8z+bi6r mnwsh a: dfo29vp7guf8)w *m
(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 undergo the three chan3h zcw g x4x8evr/t1/kelv 47cges represented by the three arrows, A, B, and C, in t 4v/xv 8 43tee7zgr1wl/c kchxhe 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 hmtjfb21 wv9g+ave an absolute luminosity about the same as the Sun's. Their afmt91jvw bg2+ pparent 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 ajjvs8a4 + mck8ngular momentum to estimate the angular velocity of a neutron star which has collav +j ks8mc48japsed to 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 kinet d;85cjs9 qxgoic energy change when the star in Problem 56 collapses to ;dj89s o 5qgxca neutron star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believed to be k *8jr ah6d ((4lhvpfj zo1w-ea neutron star of mass 1.5 times that of the Sun, with diameter 20 kmjevzj1- h8l4f(k(d a6* owphr, 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 galjd,* lh( dy2xejn z,bzan5t*;axy 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 rest mawb*,ts:o m ;e x.:yoehss (in eV) would provide the critical density to close the u:h,yx w*;me o.: eosbtniverse. 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 spe30plj3+ nbpy fushk.9 ctra peak at 600 nm and 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. [Hint3nk3f9jh p0u+py b.sl : see Examples 33-4 and 33-5.] $\dfrac{d_{400}}{d_{600}}$ =   

  Suppose we can measure distances with parallax at 100 parsecsjtck.m8eb0 m+ . What is our minim 8k+m b.0jetmcum angular resolution (in degrees), based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Bzr pm *sw8ru+5almer lines from singly ionized helium in a distant star happen tw p+*8m szr5uro overlap 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 corresponds to 1.8-Tew .hay0(i7 jmjV collisions at the Fermilab collider? To what era in cosmological history does this correspond? [Hint: see (Fig.0 7i m(whjj.ya Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation of gas around w/5l*e.vi * 1*qv .ezf* k xs0qffvygkn:wb*fphat 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 light-years, what Doppler shift q 1z*fgnp*f.*ye biw * v e5vkqv.0lff*s/x:k $\Delta\lambda/\lambda_0$ do you estimate they saw? z$\approx $    $ \times 10^{-3}$

  A galaxy is moving away from Earth. The "blue" hydron:kyic1x(p:xx. (ov mgen line at 434 nm emitted from the galaxy is measured px (::c(vmx1okyxi . non 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) wd j;wv;*nwgt,)x*c m88xxjo uill begin fusing carbon nuclei to j8w;u*)v 8*xnx otx wc g;,mdjform, 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 ;d/ph7+ gp)3lpkfl e-;au8f * pqyzk v
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 critical densityk1s iy.qu i62p)c.y k szl-b9w of the univ u..b 1)pwkk2lic s6 qiz9s-yyerse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$