The Milky Way was once thought to be "murky" or "milky" but isbnl *g8keo)6f now considered to be made )8gnl6oe f* kbup of point sources. Explain.

A star is in equilibrium wheno +m0w* aw:bhr it radiates at its surface all the energy generated at its core. What happens when it begins to generate more energy than it radiates? Less energy? Explwa+:wm0h*b roain.

Describe a red giant star. List sh0/qe. 3uec,sz q ae1wome of its properties.

Select a point on the H-R diag.y 5 ;fv7am1*:ig4ovep d vaairam. Mark several directions away from this point. Now describe the changes tha p ;af5dy4a*oie 7viagmv1v:.t would take place in a star moving in each of these directions.

Does the H-R diagram reveal anything about the core p5 5 g4*y veu)bgyapddii0 vv8)qo/a1 of a star?

Why do some stars end up as white dwarfs, and ql7fp/jg3n (k-c fa cfo+1dv*others as neutron stars or black holes nq7g fc+*c flp (kajv1/fo3d-?

  Can we tell, by lookm n8a/f75u njging at the population on the H-R diagram, that hotter main-sequence stars have 8gu/ nn75 fmjashorter lives? Explain.  ----待选择----yesno 

If you were measuring star parallaxes from the Moon instead of Earth, what correyfo fo6 ,4q*+i.hhmse1e )pgpctions would yoo,f .) gpqy1ehp*fe 6+ s4omihu have to make? What changes would occur if you were measuring parallaxes from Mars?

Cepheid variable stars change in luminosity wi )bsjc8:x;v imth a typical period of several days. The period has been found to 8 s:m)xbvj ;ichave 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 its role in General Rln 7zgn;:jid0 elativity?

If it were discovered that the redscth;t-b lt-ls5c45 za6k 8npehift of spectral lines of galaxies was due to something other than expansion, how might our view of the universe --hntb6za8 ptkll45ecs ;5t c change? Would there be conflicting evidence? Discuss.

  All galaxies appear to be moving away froc )jwp*p/vrfmnv9:spy sq 3mg usy-f2o-1d27m us. Are we therefore at the center of the gs -yu3fpsq1mw2rvd mnycf/9v)p * osj7p- 2 :universe? Explain.  ----待选择----yesno 

If you were located in a galaxy near the boundary of our ob)bphb2 *b )m:t+oywpzservable universe, would galaxies in the direction of the Milky Way appear to be approaching yo)by zptb +mh2wp *)o:bu or receding from you? Explain.

Compare an explosion on Earth to the Big Bang. Consider such questiow+1ndwo comv 2o y-;p5a8kgb1ns as: Would the debris spread at a higher speed for more distant particles, as in the Big Bang? Would the debris come to restow; 2bmckaovy8 od15g wpn+-1 ? What type of universe would this correspond to, open or closed?

If nothing, not even light, escapes from a black h kmh,p)x1/.wlmm7lwk69nhi99 b6k : q evunm iole, then how can we tell if one mn1wkv79 m,hw9 pi6.qun i xk/b:m6l9m )k helis there?

  What mass will give a Schz* wxj.o4go d+;o gl5jwarzschild radius equal to that of the hydrogen atom in its ground state? o+ x.jz*ogolg ;j54 dwM =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given ;kh 7+-ac jx)by jew/6xc)gkwas about 4 billion years. Find that time on (Fig. Below). People have lived on Earth on the order w;7)xejcc/xk+h)kya w 6- bgj of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic m65mqf e (tq3ql-luv+l 2l,+,vkiv uneicrowave background radiation is. Where does it come frouv+e lq52qifu6 e,,q(vll mk3t- l+vn m? Why is its temperature now so low?

Why were atoms, as opposed 72r5u56pi 9lk6bv7-gns ;rmqzk msknto bare nuclei, unable to exist until hundreds of thousanb q kk5lvin66szmrp; m9ru2 5k n7-7gsds of years after the Big Bang?

Under what circumstances would the uniaxyl5 l5(9- 8 *igezrkx- qhhyverse eventually collapse in on itself?

  Using the definitions of ynmabsv7p:g -c;)t 9vthe parsec and the light-year, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.38 seco0m* 4js n mw;;wgjj.-0yep pxgnds of arc. How far away is it? d =    ly

  The parallax angle of a star i nzu y4g58g bws(k(zyw+*3ndxhe:p y .s $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its p 7m3*f16hozxqt8so:oqtk9 s aarallax 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 f0cg5x4pb od s1e6*l,vt k)agw7nya5 b or 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 a second star, will the par(zee1:;(r lx -v0 lzq3tgsge uallax angle of the farther star bveeqezs ;l3tg(-:zu l xr01(ge greater or less than that of the nearer star? By what factor?

  A star is 35 pc away. How long does i zm 2o*x w1mo-uaq6chpa)n99it take for its light to reach us?    years

  We saw earlier (Chapter 14) that the rate wdy, l-)/bnfxenergy reaches the Earth from the Sun (t)b -lnd,/xwy fhe "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 ogmi2.xtlis/f0zh( 80 s* ncbas seen from Jupiter as compared to its brightness from Earth? (Jupiter is 5.2 times farther from theot .s 2imizn8l0 fbhg(sc/x0* 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 z:hc+o* fw fo t7k)ru*from the nearest galaxy to us (Table 33-1). Compare to the angular width of the Moon from Earth. ftfc+zu o*)o7 hk:w*r $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, what will be its aver0s:b a5sqojo9 age density if it expands sjsoq :oab 950out 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 whrwk)her7eu 6 c; gstjr)+g:c4 ite dwarf, it is expected to be about the size of the Moon. What angular width will it subtend from the present distance ts:j gec 4r)u rt;7+h)gwk e6cro Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whose:gf *s wz.fo-u-ct g6i mass is equal to the Sun's and whose ra-w*f.:s-cg oit zugf6 dius 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 mass is 1.5 solar t.p ef.0e/l1tkp3omm masses has a radius of about 11 km. Calculate its average density and compare to that for a whi p.l3ep1m0e.om t kf/tte 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 :n0 s:6uz9e e9pmprcne+s*iq. 33-2. (The mass of the very ucn:ee u6m pzn0es: p9s 9*riq+nstable $^8\text{Be}$ 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 appar6n afsps t03;tent 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 a( 0yd8qm fy;4z5r( (f0 +bskdzqrteko ssumed to be about the same distance from us. Two such stars have+zt( 5((b4f0syk0 md 8edyo kqr rfq;z 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 qxhur a44s9+bwith mass equal to that (a) of our Sun is+srq4b9x au 4h    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a tyl g9;0xxvy9i,-m2d0ow2 b8puiq tx lgb e yv.,pical galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a sphere, fowpwn l3s..xog; z(o7zr which the sum of the angles is ;s(x.3pol.7 zwzw n go(a) 359º, and (b) 180°.

  What is the maximum sum-of-the-angles for a triangle on a sphere:7*kdw ms d uaw4v0)rki:fj 5s?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the speed of ligh:)c zyb/qv9tct, roughly how far away is it?y:z/c)vct q 9b v =    Mly

  The redshift of a galaxy indicates a velocity ofqhe h1:f)fsk+ $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (relative to us) that is near the observable "ej1s/+ e6 uobqedgjusoeq b+16/ee" of the universe, say 12 billion light-years away. v =    c

  Estimate the observed wavelength for the 656-nm line in the Balmer seriesl +xxh*gz7.j cem(bqna 3r/x0 of hydrogen in the spectrum of a galaxy whose distance frg*x0xejb 7 nx 3.ar/+mchq(lzom 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 5q / mu7ps-fkf4f8ov lthe wavelength for the hydrogen line at 434 nm is measured on Earth as4 ff5/ou 7-fqmskplv8 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 galaxka9 rlq.:o-lcxoe uz :pzg*9;y with $z = 0.60$? v =    c

  What would be the redshift paz/5nu sg2bs4;r7:p d3qmp7nb lfojx2rameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33- rkm8:7ijz5c z3, 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 wavelength at the peak of the blac 3ptsfh)+sc0h kbody radiation distribution at 2.7 K using Wien’s p+h)3 f s0hsctlaw. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density i 7 ,/v ti 1qlidhblm((3*e*pzx okbj0for closure 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 aver)q;n7oi c d,rsage distance between galaxies) at any one moment is believed to have been inversely pro;ni )7,qcsod rportional 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 thresholozb /;dpwcle2 g/m): gyzom:/d temperature for producing )2::e b gp/gwmzlc/mo /o;yzd
(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 scf(3/cq *6dcpr83 9qhfmm ufatars could undergo the three changes represented by the three arrows, A, B, and C, in the (f uahmqdc 9 3*mrcf3/cf6qp8H-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 luminw 8: a01hzp,va9xnczmosity about the same as the Sun's. Their cz :,a m vxh091w8azpnapparent 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 angulayrvfpzzmi3 1ue8 4k9udb50c70 xfj v8r momentum to estimate the angular velocity of a neutron star which has collapsed to a diameter of 20 km, from a star wxbuc8ey f jv7r0imfp109uz 34vz8kd 5hose 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 changefvw71ye yd4( v when the star in Problemwdyy vev4f (71 56 collapses to a neutron star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believed to be a neutron star of maea4oqh7 vo (f5 v3)a7aw-/tjlm0 tdcrss 1.5 times that of the Sun, with diameter 20 km, is observed to hor7h4( v wtl-tamoca3 /)fe 05j7v aqdave 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 is0o z.lk(+yqgm d9p a(z 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 densimc01zbz45gfnk q(km 7+-ysgou z94oxty to close the universe. Assume the neutrino density is, like photons, abouz5 xmko1q 7ub+ 49gogzfn y cksm-40(zt $10^9$ 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, bothg 5b,.4fq iwju lie on the main sequence. Use Wien's law, the Stefan-Boltzmann equation, and the H-R diagram (Fig. Below) to wf,5i q. gbju4estimate 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. Wh/0ptfpi* i,y8vgk+k qat is our minimum angular resolution (in degrees), based on this infoypq0vpk+ f igik*t ,/8rmation? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, t);, f1 gegfvgscz6tu (he Balmer lines from singly ionized helium in a distant star haz,et 1 v)g(g6fu sgcf;ppen to 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 corr3m/x( 8njb56ifx0t whzh 1xf iesponds to 1.8-TeV collisions at the Fermilab collider? To what era in cosmological history does this c56f( wtx mxbxji0ni8h1f/z 3horrespond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently mm31 2xn6zb2il)4 qrvdgas rk6easured the rotation of gas around what might be a supermassive black hole of about 2 billion solar masses at the center of a galaxy.drxkbgqrzn43 a26v 6 )il m21s 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. Thed+*gpp 6mfz3zjwn31*6npk9zadr -v q "blue" hydrogen line at 434 nm emitted from the galaxy is measurednp1 a*z+jd9zzpn*vd-3rqm3wpf g66 k 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 evqdem /n. 8o3bh0 /il1erl )dwqolution, a star (if massive enough) will begin fusing carbon nuclei toboe/e83w)0 hlqr1ldqn m./ i d 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 k r)g lme 3 qiw)emho3fyo,ra/5bt27 3
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 -d*1ulb3 l vwsp5g j1zits density equaled the critical density of the univers dlvglu11s 3jpz b*w5-e, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$