The Milky Way was once thought to be "murky" or "milky" but8/2a ggd nayf0 is now considered to be made up of point 2 nyfdgag8 /a0sources. Explain.

A star is in equilibrium when it radiates qy)k (6 a)hinxat its surface all the energy generated at its core. What happens when it begins to gene)an(q6 h)ix kyrate more energy than it radiates? Less energy? Explain.

Describe a red giant star. Listw+*x qcxw8 ly7 some of its properties.

Select a point on the H-R diagram. Mark several directions away fromzn 0jrw/dvf cdg1 p8g/cf3 (0f this point. Now describe the changes that would take place in a star moving in ea 0jf8dncpc/zdg fw(g 1f0rv/ 3ch of these directions.

Does the H-R diagram reveal anytgb3swrbhrw,a+ bto xn.l:) /:hing about the core of a star?

Why do some stars end up as white dwarfs, and others as neutron stars or bla q.mg q,y(slp+ck hol.+l qp,gy(qm ses?

  Can we tell, by lookr2:msoh+/wd ning at the population on the H-R diagram, that hotter main-sequence stars have sho: 2osrn m+hwd/rter lives? Explain.  ----待选择----yesno 

If you were measuring star parallaxes from the Moon instead of Ear o7mtprsv1-/rth, what corrections would you have to make? What changes would occur if you were measuring parallaxtpomr-v1r s7/es from Mars?

Cepheid variable stars change in luminosity with a typljg /zfj9bgvc7a im7+/vjezz7: x96w ical period of several days. The period has vcjb a7m/xj9: 6 e+j7lfv/wzzig 9gz 7been 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 is its role in Gec1b /ckiqdks a 8u,:4oneral Relativity?

If it were discovered thaqgu 2umj5x mijl;(r( :t the redshift of spectral lines of galaxies was due to something other than expansion, l :mrj((u 5g2jmx iqu;how might our view of the universe change? Would there be conflicting evidence? Discuss.

  All galaxies appear to be moving away from us. Are we thereforentd ;h6v s1so9 at the center of the std69 nvo1s;huniverse? Explain.  ----待选择----yesno 

If you were located in abe. qo7wv)wq -(5zcyra-8njk galaxy near the boundary of our observable universe, would galaxies qr-joy- 7eqaw n5w.z8kcv) (b in the direction of the Milky Way appear to be approaching you or receding from you? Explain.

Compare an explosion on Earth to the Big Bang. Consider such queg 4q l bcp4oljr(.ii:0stions as: Would the debris spread at a higher speed for more distant particles, 40iiqg4oc .jrb(l: lpas 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 from a bladb; dd2 nspua) af-x9bfa. 7y(ck hole, then how can we tell if one is afb9;pb.-(daudd)xsa 7 f2n ythere?

  What mass will give a Schwarzschild radius equal to that of the hydrogen atomvgrzq)8 ;y-ejz+xfb*d w3/*d * i wypo in its ground 3ovrd**;wfw + jyx -z e*dy)bz/pgq8istate? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion years. Find that time on (Figgqv2 iwsx68ww u 1d4o0. Below). People have lived on Earqg1iv642wu 8d x0wsowth on the order of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic micr6q0+ex xlw y*dowave background radiation is. Where does it come from? Why is its temperature now so low?lw +*xeyd6qx0

Why were atoms, as opposed to bare nuclei, unable to escjb.0ig pz3n .y2 x,exist until hundreds of thousands o ejy cnis30z.x .g,bp2f years after the Big Bang?

Under what circumstances would the universe eventually collapfvb45 uj1x/j 1ipni /p;aa n1e5cui-nse in on itself?

  Using the definitions of the parlw uv,w)m6rbnzu0n x6; v2 c0isec 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 aw2i,h7 sdxc(08yqwoz qay is it? d =    ly

  The parallax angle of a star is , 7 9z+ o.lm* 4k /erkyxhvzs,eo1fyha$0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away.s8;v6t1l s9 5s mklzjc What 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 fo zhriouz 3z7*50d,zjo r a star that is 55 ly away? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away from 0*+z. gb+e vr i,y1 som+k;qrkqim9ovzfg0s8us as a second star, will the parallax angle of the farther star be greater or less than that of the nearer star? By what f0f+yv1i0mbk;z,.g 9os rik*z r +gv8moqeq+sactor?

  A star is 35 pc away. How long does it tajaipt, l1 6ak,ke for its light to reach us?    years

  We saw earlier (Chapter 1487 g1euzc4 ki3mawp)u ) that the rate energy reaches the Earth from the Sun (the "solar congi81uw 4zmacekp3u )7 stant") 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 znyjqcaru /9 ; +e0j+useen from Jupiter as compared to its brightness qc;jr9+/nz0y+u e jau from Earth? (Jupiter is 5.2 times farther from the Sun than the Earth.) $\dfrac{l_{\text{Jupiter}}}{l_{\text{Earth}}}$    $ \times 10^{-2}$

  Estimate the angular wsr7ry3p*.z m u7;-/yf jnno uhidth that our Galaxy would subtend if observed from the nearest galaxy to us (ou-n*rm7yj3;uf n zy. p/hsr7Table 33-1). Compare 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 densityey7+l(hg 5yaw if it expands out to theha w+7ye(l5gy 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 exg)b/fjrbvizoe *, r (5pected to be about the size of the Moon. What *, )zebo5rr/(jifbg vangular 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 equs apwf s37:k dg43i;geal to the Sun's and whose radius is equal to the Earth's. How3asf73 swpk;eg4i g :d 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 8 54 bjwt4m(/ mcrw tj2)cejh hzae.6amasses has a radius of about 11 km. Calculat2h8/w mc54ea)bm(tjjjh.wz e4ca 6 r te 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 thgebv+aty./ *hsq)q*q e He burning reactions of Eq. 33-2. (The mass of the veb.+se )qqh/tg**q ayvry 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 thi v.cgh ,bsm-4e 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 assum39r-cf8nf0xpp pa( .ueu 331fxvsn dled to be about the same distance from us. Two such stars have spavf( 9r1 p3-.8f u3u0pxsfneln3 dpx cectra 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 ouzvva/:+wi8y) 7hw4 zu+ivzb pr Sun : iya/w7h +ivuvwv)8 zbz4p +zis    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius e x;qp6vi6i 3ifs0e*mfor a typical galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a sphere, for whic jib8vd k5t;;sh the sum of the angles is (a) 359º, an dsik 5;tv8j;bd (b) 180°.

  What is the maximum sum-of-the-angles for a triangle on a sphered*tp p 6s8b7zbx4cak4?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the speeddk 1e 3(av.0 h.1/ubdprpv sto of light, roughly how far away .bpks/(ota1v 1dd h.0p 3rvueis it? v =    Mly

  The redshift of a galaxy indicates a velocity of wo*ah6 dd* 5th$3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a 6; qk wuj7 xp+yhi*y:igalaxy (relative to us) that is near the observable "edge" of the universe, say 12 billion light-years away.6hj+ qyp uxk;7 iw:y*i v =    c

  Estimate the observed wavelength for the 656-nm line in thei3 j a/r i*,9sxqnnnfvv c/)w; Balmer series of hydrogen in the spectrum of / vn* 3a i/srncf9jwx,)v; inqa 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 wavelength for w3mq0x,la5qlp 4t mc7 the hydrogen line at 434 nm is measured on m0a 7pq5tlcq w,4lmx3Earth 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 witpygv)mr 606tbg )ryt)h $z = 0.60$? v =    c

  What would be the redq6rqondq vd503)f l*dshift parameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that thew5q:a /vy tn), jny b-+vn9dzd 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 wavelengtbd x i(3*v4qywh at the peak of the blackbody radiation distribution at 2.7 K using Wieidx (bw4*v3qyn’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of3w.mq kz )2nmv 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 averaj qvl3tney/jcb17 pi( bb-;7wge distance between galaxies) at any one moment is believed to have been inversely proportional to the absolute temperature. Estima;b bpb3-ejj ni/y17wcq t(7l vte 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+xg; u6z huleg(ky80d 4vnk* r universe cooled below the threshold temperature for produr *(kuk+ez8l6 ug0v gn;dxhy4cing
(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 thr np vi90.zxai+ee changes represented by the three arrows, A, B, and C, in the H-R diagram of Fig. 33 .p+iixn9vaz0 -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 same a2l51myq -ms3k5fksb ms the Sunbs-5 3ysqmkl2m1 5m kf'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 neuhseo :d6qjd yg, s4 k(djh)e: 891gb,uchcto 2tron star which has collapsed to a diameter of 20 km, from a star who46ug) jd k1:2hto:qhhsey9 djgc8(se o,cd,b se 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 rotationa9n4huk;b. (y 6spvnkcr(ey yi7;)zsb l kinetic energy change when the star in Problem 56 collapses to a neutron st4(cyvu zikh ;.n7y( p ks ny;r6esb9)bar? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believed to be a neutron star of mass 1.emafo 1iw53 y25 times that of the Sun, with diameteaf 51ye3m2iow r 20 km, 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 galaxy i15tjqh a.07cr ku :cn9tjx9xto 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 mass (in eV) would provide the critical densitr 0wxs:drg /krq j34y(y to close the univer ( /j3r4s yxd0:wkgqrrse. 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 ao a*m78bv6t rm 7xjk1bnd 400 nm, respectively, both lie on the main sequence. Use Wien's law, the Stefan-Boltzmann eqmb1v778t*oj 6 xrbmakuation, 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 paralla-6p ;bja3c66g0vi mpu tt1p nsx at 100 parsecs. What is our minimum angular resolut 1a np30mtb6j 6p-putg;6sciv ion (in degrees), based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from singly ioniz( eve3(gfp80d(w7bhd pak-rued helium in a distant star happen(p d3w 8f apve((dkrbe-g 0h7u 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 corresponds to4khyf : e*o1ae 1.8-TeV collisions at the Fermilab collider? To what era in coee* ok1h4:ay fsmological history does this correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recentlyb+h(fr4) iw azd8e;kv measured the rotation of gas around what might be a supermassive black hole of about 2 billion solar masses at the center of a ga)vkwzf8(h4; + irdebalaxy. 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" hydrogexjx )7g0fqgy (n line at 434 nm emitted from the galaxy )f j(xg0 gyxq7is 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 mndkjxe0o kf: m fpjt-.g 5,0aoi;7)aevolution, a star (if massive enough) will begin fusing carbon nuclei to form, for example, magnesium: ao0k;f f7neo5a d.x -ip0j,k)jmt:mg
$^12\text{C} + ^12\text{C} \to ^{24}\text{Mg} + \gamma$.
(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 reactioz)dl6rtrdmz9m2k;b 8 n
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 denwh9v y6k0ue-gh+( a5d zkdop 7sity of the universe9yd-evkgk a6u70h(zpw5hod + , $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$