The Milky Way was once thought to be "murky" or4o i77qqmxl-w "milky" but is now considered to be made up of point soqi w7q4xl-7mources. Explain.

A star is in equilibrium when it radiates at its surface all the energy g8futs+ il . i60v/hih,jk )oloenerated at its core. What happens when itl )k.u6f vtj /8i iohs+io0h,l begins to generate more energy than it radiates? Less energy? Explain.

Describe a red giant star. List some of its po*m j10)aqgru roperties.

Select a point on the H-R diagram. Mark several dd7f8 us ksr+xxy1. *tairections away from this point. Now describe the changes that would take place in a star moving in each of ta+s1sk x tfu.*8rd 7xyhese directions.

Does the H-R diagram reveal anythinyo 7.op0 b-sevkqz. 2wg about the core of a star?

Why do some stars end up as white dwarfs, and others as neutron stars or bj (l,h6klj:akam tk) 5uf)ia0lack hol5 ik)a)(0kj:jm, k haalf6 utles?

  Can we tell, by looking at theabv6wdp-*v+ k population on the H-R diagram, that hotter main-sequence stars ha vb-vap+w 6dk*ve shorter lives? Explain.  ----待选择----yesno 

If you were measuring star parallaxes from the Moon instead of Earthf v)xj czos+-:, what corrections would you have to make? What changes would occur if you were measuring -c:fvx+jsz) o parallaxes from Mars?

Cepheid variable stars change in lvoq)k ;f+svj0sqec. 5rf h) ;5pnvh0wuminosity with a typical period of several days. The period has been found to have a definite relationsh h);)vj.nhrc05s v5esfk;q of vp+wq0ip 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 Relativitp) bhio:/4q mrc wfb*4y?

If it were discovered that the redshift of spcl1 r s3qfy.a:8: kbdpectral lines of galaxies was due to sop kl:yc38:b qaf1 .drsmething other than expansion, 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 therefore at tco3a50lkhwns uk.u7 2he center of the universe3al.oh2 nk 7sck0u u5w? Explain.  ----待选择----yesno 

If you were located in a galaxy near the boa8x6zr,zh-i l6frl 5 mundary of our observable universe, would galaxies in the direction of the Milky Way appear to be approaching you or receding froilz ra zlh,f6 5m6r8-xm you? Explain.

Compare an explosion on Earth to the Big Bang. Consider such que*8cftg9lf a :astions as: Would the debris spread at a higher speed for more distant particles, as in the Big Bang? Would the debris come to rcff9*tla8g a:est? What type of universe would this correspond to, open or closed?

If nothing, not even light, escapes frvtnkkx /p +)8 igb*qb;bln,q6 om a black hole, then how can we tell if obbt,6bnk qq8 k/*;+pin vlgx)ne is there?

  What mass will give a Schwarzschild radius equal to th m4v:su(0dvn ke;2) 7 pw2sz 7ctza70u tmyulzat of the hydrogen atom in i0nys;:t e0zu2 a (dv tmwvl7727uku4mszp)zcts ground state? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion yva )tzqa f.5r c ejgb7r0-lrgbvz 6-09ears. Find that time on (Fig. Below). People have lived on Earth on the order of a million years. Where is that on ag6 bt0lq-z)v.b5fc er07v9zrr ja- g (Fig. Below)?

Explain what the 2.7-K cos*:ub v*puf6o* zz63etudi 1 uxmic microwave background radiation is. Where does it come from? Why is ib3f 6eo z16*zi tuu p*xuu*vd:ts temperature now so low?

Why were atoms, as opposed to03unh waba2g*c3,o li bare nuclei, unable to exist until hundreds of thousands of years a0wuhon i3a,l32b*ag cfter the Big Bang?

Under what circumstances would the universe eventu zc*py z d,d1k6 bk6cqxsr:;f,ally collapse in on itself?

  Using the definitions of the parsec and the light-year, sfn,vh7mf45+bk l r-dl iot)e aec 14:lhow that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.38 seconds of arc. 6r ( bd*gl3nka9v/ pq 7dwx4es9xvq,aHow far away is it? d =    ly

  The parallax angle ojxsdbf(pp//s0buv2 5;zdf 7wf a star is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is i3tms08-gk l ylr0x ,wyts 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 s*48owcp lvtn )tar that is 55 ly away? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away from us ab86kg6 i:w( swev t3ujs a second star, will the parallax angle of the fareg:swj btk8w66u (iv 3ther 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 rowkc ;ryl25js 9m4vj2u pln. 2each us?    years

  We saw earlier (Chapter 14) that the rate energy reac6w0oz.nk0h7+ bhfy tthes the Earth from the Sun (the "solar conn7+hbt o00w ft6k.zhystant") 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+ dn(g0g+j* e/fuw pjo from Jupiter as compared to its brightness from Earth? (Jupiter is 5.2 times farther from the Sun than the guo *f wdje+/p(+0j gnEarth.) $\dfrac{l_{\text{Jupiter}}}{l_{\text{Earth}}}$    $ \times 10^{-2}$

  Estimate the angular width that our Galaxy would subtend if observedj kw-2x0hpg 6p s8w7qy from the nearestqp h62wsp0kxj-8 7gw y galaxy to us (Table 33-1). Compare to the angular width of the Moon from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red gindlw+.uyi) ll w 1evkad.831v ant, what will be its average density if it expands out to the orbit of Eartwe 3yl1dlku . )vdw8i+nl1va .h ($1.5 \times 10^{11}\ \text{m}$ from the Sun)? $\rho = $    $ \times 10^{-4}\ \text{kg/m}^3$

  When our Sun becomes a wt,a8hpw l 23n;fyfj1w hite dwarf, it is expected to be about the size of the Moon. What angular width will it subtend from the present distance to Eart1jlpwt;a2fh8w yf ,n3h? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf h .m. tkupckn x1*(7h5mbye+xwhose mass is equal to the Sun's and whose radius is equal to the Earth's. How matn pme.+bmx h*h u. k(y57xkc1ny 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. Cal * dj9pxvq.w wxsv-:bp:0q de-culate its average density and compare to that for a white dwarf (Pro:ddb0:-wesq p-xpv.j v q w9*xblem 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 thd8paio,,+v quk q z7y-o4ws8z e very oa+4vi7 8pu-skw 8,dzo,qq zyunstable $^8\text{Be}$ 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 samjqfon:a +++t we 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 a (x zxuzb 2vi94y1aao0ssumed to be about the same distance from us. Two such stars have spectr1x a0u9 xbiyzvo (4za2a 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 eqyhq go24ko9fakg3e hyk4 + +5nual to that (a) of our Sun isg5ok4yh49qk3 k+ nf2hagoe y+    km, and (b) of Earth is    mm.

  What is the Schwarzschild raol6ki,jolvm 2cd/9 r8dius for a typical galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surfa*s3nd 8 ,g*cwij+ sk-jlxvj;pce of a sphere, for which the sum of the an+s;jis3 -njk dwc,jp*gx*8lv gles is (a) 359º, and (b) 180°.

  What is the maximum sum.lhq19,7o ylluz do cs9o+ lj8-of-the-angles for a triangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the speed of li3qocsy(:/6rpefe,*i0g zc ugght, roughly how far awayf6gur e 0*,gq3op isc(:/yecz is it? v =    Mly

  The redshift of a galaxy indicates aamr14 umln ;w0 velocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of aegfl hv vfj/u2 6l9 hay5n.*c8 galaxy (relative to us) that is near the observable "edge" of the universe, say 12 billion light-years away. v feylhnc*hu6 /28.lv9gaj5 vf=    c

  Estimate the observed wavelength for t9f-dq hsiy32favrlg( 48 vu5b he 656-nm line in the Balmer series of hydrogen in the spectrum of a galaxy whose distanfvf gvr9s2-5 bqildua3y4( h8ce 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 frommsd)bne1,o) *hi j:c h us, if the wavelength for the hydrogen line at 434 od1)e:sij)h* b,c nmhnm 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 galaxy wdrh q9zj: 10gnn6rxhu7r 0-fbith $z = 0.60$? v =    c

  What would be the redsh h *w)u* bm be:f2xj,;l a/xk+pwibhb(ift parameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Doppler shift in wavelengt0u,ueaq191a hwfv;r u h is $\Delta\lambda/\lambda \approx v/c$ (Eq. 33-5b) for $v \ll c$. [Hint: use the binomial expansion.]

  Calculate the waveleng cf ;81uts7okkjd yi66th at the peak of the blackbody radiation distribution at 2.7 K using Wien’sj usc;ty 6 8kdk17oif6 law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of the universe qjk jbiyet: 0qw0(m(c k7e4;his $\rho_c \approx 10^{-26}\ \text{kg/m}^3$. State $\rho_c$ in terms of the average number of nucleons per cubic meter.    $\ \text{nucleons/m}^3$

  The scale of the uni (gvh9d xi/p2yverse (the average distance between galaxies) at any one moment is believed to have been inversely proportional to the absolute temperature. Estimate the size of the univerdxv2y(hi9 gp /se, 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 dmv 3jbbo)69 ecooled below the threshold temperature for pbevo6jd 3)m9broducing
(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 th0schyo tc56, rb7lqe 1ree changes represented by the three arrows, A, B, ant1eoc 7h0 6lbcq,5sy rd 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 absog pw9lifefx f8r*imd 4 :lgq+r4)41 jdlute luminosity about the same as the Sun's. Their apparent brightness, however, isir+9* ied:1gpw f4)lxqj rd84flg 4mf 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 r -r/-jy/ /,n6 k4rfl) gj8gkpzmeca ia neutron star which has collapsed to a diamete kke8rr-z/njima6j/lf y4cg)-/ pg ,rr 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 kinehqxsu 15zy6yg 97u(rxfui2 ,utic energy change when the star in Problem 56 collapses to a neutron st97iuuz xyxy16r5u hqgf ,s u(2ar? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believedudip: qsb*s798m*u-th1 qtn v to be a neutron star of mass 1.5 times that of the Sun, with diameter 20 km, is obsq hns1bisq- *tvm uup*dt:978erved 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 to our Galaxy ietbp-q4*/ps jqmgo /(uy e8a)s 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 (inck ysvh 8 f4j) hu.0bglr5e-h, eV) would provide the critical density to close the universe. A58 0-) f 4 js,hhkyleu.bhrgcvssume 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 40,bfct 0hd,zy40 nm, respectively, both lie on the main sequence. Use Wien's law, the Stefan-Boltzmann equation, ant fh,z,c04 bydd 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. What isb.++ ffdrm wlo 9lk,.q our minimum angular .+dqm,f.rlbk+ wo lf9resolution (in degrees), based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from sijayatran/fkgpfe,n +2p0+ j1 9o)r( xngly ionized helium in a distant star happen to overlap with the Balmer lines from hy+fnry( og9j+p1xna ft02)eaj rp, a k/drogen (Fig. 27-22) in the Sun. How fast is the star receding from us? v =    C

  What is the temperat hze-8k9wq s7,fm+fx*trgqq ( ure that corresponds to 1.8-TeV collisions at the Fermilab collider? To what era in cosmological history does this cog+f z9qkw 8*rsq,hm- qe7t x(frrespond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation of gas a526jf azz 8amtn8( maground what 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 ln a5a2mzft68 g(j mz8aight-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" hydrogen line at 434 ol* 2z 7;dkwj+tcq si/nm emitted from the galaxy is measured72 zlqjtk+*c /i; wsdo 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 evolution, a star (,8 r5s9dsw tyohbis a 5t+7bwpcn5m o*z20v -lif massive enough) will begin fusing carbon nuclei to form, for exaah vy5ospd+70r*2owct5tm s z 8si-b9 5bn,wlmple, 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 yc.hpa8gjv82dli8z. 8lpoo-m3mf6 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 beh u3ih1 ;avy (qhgu3krcv )la53*rg b9 if its density equaled the critical density of the univ9)r ha5vhy 3ruv;k* q gugbh3li (a31cerse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$