The Milky Way was once thought to be "murky" or "milky" v:l7p; *q6i;u;gouocakw .f q but is now considered to be made;ouw;iq : fc6 ;qaovp7uk*lg . up of point sources. Explain.

A star is in equilibrium when it radiates at its surface al j k 2w*prc 4h5l9eo;4kkrg3pkl the energy generated at its core. What happens when it begins to generate 5 3jpc kk2r;hp wko4g 9kl4*remore energy than it radiates? Less energy? Explain.

Describe a red giant star. List some ofvdkkbv1dco3 d 5 +(5fa (hik/ t*ynub0 its properties.

Select a point on the H-R diagram. Mark severalu7l8xgyml 0.f;ai+ zw directions away from this point. Now describe tg0xa .zm7;8+ lwiyflu he changes that would take place in a star moving in each of these directions.

Does the H-R diagram reveal z *:d1g.zey* k t3vstdu4id;vanything about the core of a star?

Why do some stars end up amcde6(y* ,d hos white dwarfs, and others as neutron stars or black hol6m (ohcdd e*,yes?

  Can we tell, by lookjd.m/4g boddqf6 bau-h:7m 46 z hcf:jing at the population on the H-R diagram, that hotter main-sequence hdczq. 6d-b dm o::h 6f44gfuj/bja7mstars have shorter lives? Explain.  ----待选择----yesno 

If you were measuring star parallaxes jmo l(xjh02m )vp,i 1vfrom the Moon instead of Earth, what corrections would you have to op)xj0lv21jmh (imv ,make? What changes would occur if you were measuring parallaxes from Mars?

Cepheid variable stars change in luminosity with a typical p8y6or/iv uu j: )cn u4dtdj9tv98: teleriod of several days. The period has been found to have a definite relationship with the absolute luminosity of the star. How could these stars be used to measure the distance to galaxivdu: jt9yio8c9 jn/)ut l64:r vdu8tees?

What is a geodesic? What is its role imaalfczjx/ 29qu *)o 3n General Relativity?

If it were discovered that the redshift of spectral lines of galf a+4tpjwdu 1:axies was due to something other than expansion, d4utf:j1wpa +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 the cex qe)t1 ;u7g/yqfwc. enter of qw;/cfy)e gxe.q tu17the universe? Explain.  ----待选择----yesno 

If you were located in a galaxy near the boundary of 60f,ctm2akcl l gpg: gi *c2j xm4v+u,our observable universe, would galaxies in thexitj, c,c: +06cmm *4g 2 algpkuvg2fl direction of the Milky Way appear to be approaching you or receding from you? Explain.

Compare an explosion on Earth to the 5* ;r qy1eis7bccg,stBig Bang. Consider such questions as: Would the debris spread at a higher speed for more distancty ;g*1,ie s rbs7qc5t particles, as 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, 4 n j e:1zsu3onnb0.clescapes from a black hole, then how can we tell if one i. b0 1n3n zujclne4so:s there?

  What mass will give a Schwarzschild radius equ :bd7eh r:pd*o(kb+p1d r;gzpal to that of the hydrogen atom in its groundb(z1;hbddopr:g+d * 7p:r ekp state? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion ye5v:pcs;wl( o+vcxj*kd9- suv ars. Find that time on (Fig. Below). People have l;wdc*v(svou-9 :vspl c+j5 x kived on Earth on the order of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic 0kxmhga s hcv bx7 dfj84lsg :42/6pv.microwave background radiation is. Where does it come from? Why4s6/f kavxh hbc0 gl4m vjxd7.sg28:p is its temperature now so low?

Why were atoms, as opposed to bare nuclei, unabq)jx-*kyjh-eh d*sh9mz7 wk 5le to exist until hundreds of thousands of years afterq-h7hk h x*j *-kedz5swmy)9 j the Big Bang?

Under what circumstances would the universe eventually collapse in on it )nhddl2h(gz: pb)*/rdev)ex d 6-dttself?

  Using the definitions of the parsec pcvb(tdb: 1;m67f2gw q 0o lyrand the light-year, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0xg 80wix4bh/ x.38 seconds of arc. How far away is it? d =    ly

  The parallax angle of zzyl+a+s*qq)na v5e) a star is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its vl dr4ucfa7j+h7 p*o9 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 azh mv1j(1nxt*5p( tyerwf*1w 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 paralfitftw 6y oy(,l2 1cp0lax angle of the farther fyl,t(1 yfto6 2ic pw0star 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 reach 6 vkduf7o4pj/ us?    years

  We saw earlier (Chapter 14) that the rate energy reaches the Eart)mam5rq xwuap 8p,0f3h from the Sun (the "solar 0 )qaa3uw mr8 pfp,mx5constant") 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 Jupit/hnxmmaa.t st.:qa-. er as compared to its brightness from Earth? (Jupiter is 5.2 ti.:x/q .h -.astmtnmaames farther from the Sun than the Earth.) $\dfrac{l_{\text{Jupiter}}}{l_{\text{Earth}}}$    $ \times 10^{-2}$

  Estimate the angular width that our Galaxy would suxi k,jwntg:g9y,hm04mpk86 r btend if observed from the nearest galaxy to us (Tableh p8i ym6 :tgk gn049,kr,jwxm 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 ip am.;( -7/f7bzvtgequ b6hgats average density if it expands out to theha v gm6 q7(upgfzb-7 ba;et./ 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 about th60frz485q7idmhm a/bl xd:ex l0 dw9oe size of the M6 r /zhwd0iqddo ex4m790b f8ma 5llx:oon. What angular 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 equal to the Sun's and whosyvhq1pam)co9bzh 4o 01w k1c*e radius is equal to the Earth 9hohw o*1140zqby1a) mpcvc k'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 b9vgc :uvto ox5m--0g1.5 solar masses has a radius of about 11 km. Calculate its avera0gtx:o -o -9m 5gcvbvuge 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 Eq. 33-2. (The3fcj(9mb3lb ixqb . hdi97v-c mass of the9bxhb -l7m b33 cij.9vciqdf( very 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 the same apparentdjyua vhg;un15ypq * +5d:gn3a 6st4s 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 assumed to be about the7k )8m4mk96:m-yd szpvxf.*twboiv u same distance from us. Two such stars have spectra that peak at i)x6o*7ky98vs zfbk:p.m m-w u t4 mdv$\lambda_1 = 500\ \text{nm}$ 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 tdhht81snqvp *52 uo*phat (a) of our Sunn5ph *s 2*p1qt8vhdou is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for arrv(9 4d3aktku 0l/wq typical galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the 1d )6v rljsy4-b s3becsurface of a sphere, for which the sum of the angles is (a) 359º, and (634je)y sdr-s bv1lc bb) 180°.

  What is the maximum sum-of-the-a xv-uokg 2+)hdngles for a triangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% os3fkr(,d*l e 5c0dv6p rwr8wkf the speed of light, roughly how far away is ir*0clvksw8 pfk 53 ,rdwre d6(t? v =    Mly

  The redshift of a galaxy indicates a 9yfmv5.lsu 9; dzms.nd5zxj+velocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (relai7cgey2 7 ek0o za:t v /z0jeju)b;3uotive to us) that is near the observable "edge" of the universe, say 12 bill7 oa)oj0v2 /egek 3u ceibzy:tz0 uj7;ion light-years away. v =    c

  Estimate the observed wavelength for t x,8oxy:sg4j hhe 656-nm line in the Balmer series of hydrogen in the spectrum of h,xg 8xs joy:4a 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 z+543 5hrfdm5yve eu7 rrxg*yfrom us, if the wavelength for the hydrogen line at 434 nm is measured on Eavrzdu5e+y*4 ehx 3gmr5r7y5 f rth 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 ab2ed1;/ 8gnud1 v22vptbo3p-wd (v m 3fngvws galaxy with $z = 0.60$? v =    c

  What would be the redshift parameteri,i)d/an 7b1i:q6 chiefk -nt $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that t q ,xae7ybhn*(k-d,9l9wp mvahe 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 wavele1lw3 r; shnwr*ngth at the peak of the blackbody radiation distribution at 2.7 K using Wien’s law. r;rw13nhwsl* $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density fo2t,t zxin)ox7 r 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 average distance between gaywmpeth o(6v s -b3j+3zaos1sqyz .02laxies) at any one moment is believed to have been 6hayj3 moq 02w.ssto 3-ysvzez1p(+binversely 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 thres(g.ca:a rg 6gyhold temperature for producag yra.:6g( cging
(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-sequenc/.m oyc)rn 7u)pvb wz:e stars could undergo the three changes represented by the three arrows, A, B, and C, in the H-R diap.:yro uc m)bwz7 n/)vgram of Fig. 33-28. For each case, describe the changes in temperature, luminosity, and size.

  Assume that the nearest stars to us have an ab oi, x/ (3i)tvuqxbop9h l6mv(solute luminosity about the same as the Sun's. Th9t,hv) vx(oxibilmoqu ( p 3/6eir 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 esiulok/,jx 3: ctimate the angular velocity of a neutron star which has collapsed to a diameter of 20 km, from a staro,i3 l/kjux c: 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 8jeawc2kg t;txfb v* e4np-.uc4 3 6jgenergy change when the star in Problem 56 colla-*kwjb 4c j4 tev.6ug3;pfc x8ega2tnpses 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 mass 1.5 times *;es*j+: v;fk ;wycq (zpiz uethat of the Sun, with diamu; k +*; pvzi f;wqcj*esz:ey(eter 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 to our Galaxytayme 0gt; eq: 8 9o,w.alqhe9 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 dcgso2hs 7 d (wpt1j-iu1h*2b iensity to close the universe. Ashws2-j t s7u2*hdico1gp1ib(sume 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 j6 3;wj btp+qaj3/fa f9epv f2u d1eb.nm and 400 nm, respectively, both lie on the main sequence. Use Wien's law, the Stefan-Boltzmann equation, and the H-R diagramqj f6;vd pje92fbf. 1 b3t/eauwp3j+a (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 t+ 4d 5tgqsd8)qi4ijf100 parsecs. What is our minimum angular resolution (in degrees), based on this information?4dd +qijg)5t 4tifq s8 $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from singly ionized helixegpz,j s y49vlbd0t5e y;2yh5b i*(cum in a distant star happen to j ;dlgsyxe9 *54 ztb iby,h02 ypv5e(coverlap 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 corresp(m ;ya c(ci:cw+0mashonds to 1.8-TeV collisions at the Fermilab collider? To what era in cosmological history does this correspond? [Hint: see (a chac+iw ymc(m;:0s(Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation of gas around what might be a su)n cug.dq 1hv,permassive black hole of about 2 billion solar masses at the 1vun, ).chdg qcenter 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 from Earth. The "blue" hydpr5 x p,2.l wz/dd;pddakr0j5rogen line at 434 nm emitted from the galaxy is meas,r/ drkpd50;d a .zjdpw2p 5xlured 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,omcryl wrm +7v +7,bk; 4-sw0 fq6wwhx a star (if massive enough) will begin fusing carbon nuclei to form, for example, magnesium: fw7lo7 s-my0m;+6 q w+bw xck4v,wrr h
$^12\text{C} + ^12\text{C} \to ^{24}\text{Mg} + \gamma$.
(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 reactionqo s)4a4b)av3ot6c:r brz- b h
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 critica k-0hg0qcp 3vv;g +olll density of the univerqv0-;ck llo 0ggh +v3pse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$