The Milky Way was once thought tgica 2ki11z(5np poy4 ubbr1(o be "murky" or "milky" but is now considered to beirn2io1p1z4up (5 g(by1 ckab made up of point sources. Explain.

A star is in equilibrium when it radiates at its surface x t3 ns vy93mtvh*8aw*all the energy generated at its core. What hap xt9y vah8*3s 3w*tmnvpens when it begins to generate more energy than it radiates? Less energy? Explain.

Describe a red giant star. List w gooa7a:zjz ,-o88bnazyan 4p;j9f ,some of its properties.

Select a point on the H-R +ro.pe q n3pnqj3z )2rdiagram. Mark several directions away from this point. Now describe the changes that would take place in a star movinenq.2p)ozpn+r3 3rj qg in each of these directions.

Does the H-R diagram reveal anything abo+l )xa-dxcm 6mfh a34zut the core of a star?

Why do some stars end up as white dwarfs, and others as neu,c52n x6umxf-6 v1:iy o vqteytron stars or black hole-61:vc foiymyxuq6v25te ,n xs?

  Can we tell, by looking at the population on the H-R diagram,fu,ib,wv;lbi r 9w5mp6 t8mb, that hotter main-sequence st,,6 tbmu wwi ,i;8bpbvm5 rlf9ars have shorter lives? Explain.  ----待选择----yesno 

If you were measuring star parallaxes from the Moon instead of Earth, wi.k 1-3rqxssk hat corrections would you have to make? What changes would occur if you were mekk .rqx-1is3sasuring parallaxes from Mars?

Cepheid variable stars change in lumineoz uz1(ng,x;osity with a typical period of several days. The period has been found to have a definite relationship with the absolute luminosity of the star. How could the(1;nze oz,xug se stars be used to measure the distance to galaxies?

What is a geodesic? What is its roleg vokih- ae(9vlho*,7 in General Relativity?

If it were discovered that the redshift of spedt 0q/iz;ak-y oes,- cctral lines of galaxies was due to something other than expansion, how might our view of the universe change? Would there be conflictin-qty-;kc d,oei0 a/szg evidence? Discuss.

  All galaxies appear to be moving away from us. Are we the zwe9dan;m1 0ek3o 9girefore at the center of twen d;9k a39ig ome10zhe universe? Explain.  ----待选择----yesno 

If you were located in a z. bx3b rsuo7nbfoo:4yam zzh8; + .cs7ax1*sgalaxy near the boundary of our observable universe, would galaxies in the direction of the Milky Way appear to be approax3 zonr+ :a4u* hyx7s .o b78a.bboms1cs zf;zching you or receding from you? Explain.

Compare an explosion on Earth to the Big 7 8u-kg x) a;cqjg/qqoBang. Consider such questions as: Would the debris spread at a higher speed for more distant particleuog /;cjqq8aq )xkg7- s, 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, escapes + /d9v7-ic 0s8y+ hdkotdwjuq from a black hole, then how can we tell if one idijdo9c0v 7yd+h -8k/wqst+u s there?

  What mass will give a Schwarzschild radius equal to that of tclq-vk:b .(* wm*ngw hhe hydrogen atom in its ground state? ncw:.*( *-blhvkgwqm M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 bi)l vh2rv2*vq/ qg* ntallion years. Find that time on (Fig. Below). People have lived on Earth l/ 2)g*vtrvvh2 *aqnq on the order of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic microwave background radiation hqt01ht*4 laru dc7z (is. Where does it come fro lh1r ut7a0t*q (4chdzm? Why is its temperature now so low?

Why were atoms, as opposed to bare nuclei, unable to exist until hundre w2d6zfl,qi1pgrj7ped aw2, 0*ibfm 7ds of thousands offfm2lr dgj6wz a *b7,2i71wi ,p0qpde years after the Big Bang?

Under what circumstances would the universe eventually collds1jfarv o fw- r3ut*k9*xw,)apse in on itself?

  Using the definitions of the pa:2og p7 )bh:*itrlnmqrsec and the light-year, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a paralk o9jl*c0jr v;lax of 0.38 seconds of arc. How far away is it? d =    ly

  The parallax angle of a star is 6,um 9nnh6nc ( h)ybsq$0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its parallf-owel/o k/ leh s,:-9zco1r4ut c6siax 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 star that is 55 z r 8+9 wi12tzlqd),hu bwby6wly away? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away from us as a second u rx;ce igx+ y )b9b8flj/:x(dstar, will the parallax angle of the farther star be greater or less than that of the nearer star? By what f9rj;(xf :) i x c+x8blgeb/dyuactor?

  A star is 35 pc away. How long does it tak), z9bfi jbiwgey)jb nf9 e,76e for its light to reach us?    years

  We saw earlier (Chapter 14) that the rate entdornlj7(b ) 0ergy reaches the Earth from the Sun (the "solar constant0n(b)t orj 7ld") 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 Jupiter as compaifo8bn+ :gn/q red to its brightness from Earth? of:8i n qng/+b(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 width that our Gs sy1;02,. dywhymspw alaxy would subtend if observed from the nearest galaxy to us (Table 33-1). Compare to the .,yswd p1h y0wssmy;2 angular width of the Moon from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, what 9u-uag(otop- .vau n;will be its average density if it expands out(o- ap ta-.guuvuon; 9 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 about the size o22 gz5yd: spqa6opk0sf the Moon. What angular width will it subtend from the present distance to Earth? z ykps2pqo d0: ga52s6 $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarhzi (c*pa jdl+d i 7wc0o(b61gf whose mass is equal to the Sun's and whose radius is equal to the Earth's. How many1o*hl i(zj(c dgcpbw 70a +id6 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 a, wqym +z-d.o x)4 wum1g)nbqobout 11 km. Calculate its average density and compare to that for a white dwarf (Problem 13) and qouno wb4)x)gz-+.1mqyw dm, 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 reaction,ndd;46azi c3od 5smsi(o ,h mnmt2y6wq:)o gs of Eq. 33-2. (The mass of the very unstablezn(m2)c6nm ds;a ,wqs4ih d5o,d36 g iyotom: $^8\text{Be}$ 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 duhp q+wxb ,1ltq *,xa64b7rh 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 assumw,bv:p zz7v( m e* krdu1;yk/med to be about the same distance from us. Twk: pmyerzv(/w;dvz , k17*bumo such stars have 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 Schwarzsc i3uq:c ef- dm(l0o8irhild radius for a star with mass equal to that (a) of our Sun idiic(f rqo 80 3u-le:ms    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typicabtnaup (con0- 5d6n,al galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a sphere, for which the5aqh ldset vdtgvk2ar40h-.o ;4-+l e sum of the angles is (a) 359º, and (b)kt;4dgar2 oh.lqtd lv-0- e +5esvh4a 180°.

  What is the maximum sum-of-the-angles for a triangle on0b z+l;bbf9qqh,0 bn k a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the speed of light, roughly )9)k u 1 40c.yejzr wr3equxahhow far away is it? vr ej.4eqkuc0ra)x9)z uy1 w3 h =    Mly

  The redshift of a galaxy indic zjxla7,kupqjyo*y:dp 7q*j; m+h. 3eates a velocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (relo :v:f6l kx /s3n2a upjos;b0lative to us) that is near the observable "edge" of the universe, say 16;:bpfjn0/3k vlooa: s 2xul s2 billion light-years away. v =    c

  Estimate the observed wavelength for the 6561b9aopbfwf*k1 i 6a4d-nm line in the Balmer series of hydrogen in thea bd4i9f61 kafobw1*p spectrum of a 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 +y rik4+1zjh xwavelength for the hydrogen line at 434 nm is measured h4+ rz kiy1+jxon 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 gala7gw3 2h kni 2v8/vuebqxy with $z = 0.60$? v =    c

  What would be the redshift p3 .y+0+wx k3uf2z)ebaqpkj-k fd 7pujarameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show thaq2 8bsonu; ,ltt 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 radiationssyx6p*trro +: ,8pak distribution at 2.7 K using Wik,:6y+xp rrs8sp *oaten’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of the unive46 u*5-j0bzhwjnom.pkn.e ijo (9yvtrse 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 dist 0l9dc+wq /cykjr9ii 5 )cu2ydance between galaxies) at any one moment is believed to have been inversely proportional to the absolute temperature. Estimate the size o)ry/dc0c5+uqijdc9lik 2y 9 wf 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 thetn6n (x5 -uufczrb s2: universe cooled below the threshold temperaturn5z uurc:t nf26(x-bse for producing
(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-sz0a11 omeauo bx.uu3 7equence stars could undergo the three changes represented by the three arrows, A, B, and C, in the H-R diagram of Fig. 33-28. For each case, describe the changes in temp3x7a1mouz0u ue.ba1 oerature, luminosity, and size.

  Assume that the nearest stars to us have an absolute luminosity about ,txk; kz*n7dtj (hzhg s1u.6h the same as the Sun's. Their apparent brightness, how ,t7hz16kh gk (nj*tuzs .hd;xever, 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 pkkt f*(8x b e7q :)l/bdx7aybthe angular velocity of a neutron star which has collapsed to a diameter of 20 km, from a star whose radius was equal t)tpkk8b/*dfxl7 :e q b(xbay 7o 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 change when the star n(s:xcc*tmh3oo9i 5 z in Problem 56 collapses zcx5so3 ihcnm(* to:9 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 timr e xqszdlees v:jtj/l5b.34 ,j8y.g)o8v v;des that of the Sun, with diameter 20 km, is observed to have a ro,ovxjs)8ev:3 yr.4;.qjl l /5dgjdvt szb ee8tation 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 Ga s5lwr cg7xw-jbt82 yw+u /mb1laxy 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 prov+. /nr.bc+5kaqe k bk9rm/j bkide the critical density to close the universe. Assume the nrej+amb .kkc n+b rb5./k kq/9eutrino 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 400 nm, pjosfb0ti . ruyu2 9(h2) l3uurespectively, both lie on the main sequence. Use Wien's law, the Stefan-Boltzmann equation, and the H-R diagram (Fig. Below) to esti.22y (lus 30hu9iufujp r)tobmate 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 is our ;ki.rx ,xxnmk(bu/+kminimum angkx +b,.; ikkxun(x/mrular resolution (in degrees), based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Ba/a,y9 :kt 3d1:ttt1e matbc rdlmer lines from singly ionized helium in a distant star happen to overlap with the Balmer lines from hydrogen (Fig. 27-22) in the Sun. How fast is the star receding from us1re1tmykcddtt:t,t :ba93 /a ? v =    C

  What is the temperature that corresponds ::0sq 6 aekxfh8p ,n)yp cut-jss(q.sto 1.8-TeV collisions at the Fermilab collider? To what era in cosmological histp f e8cn,.s(qsjyush)a kq0s t6::xp- ory does this correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation of gas around what mig gxx9(oww x.o8*zy 15ai q-jsvht be a supermassive black hole of about 2 billion solar masses at the center of a galaxy. If the radius from svay i* .x 1-x85xjw9owq(ozgthe 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 fromgy tf(z7/ag3.p;hbu i o8slx2 Earth. The "blue" hydrogen line at 434 nm emitted from the galaxa/3. big yxfltsh;g(o82u7z py is 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 evolution, a star (if massive enough) will,3azru 4xqm 0x h68fdk begin fusing carbon nuclei to form, for example, magnesium: uk3ad4 rqxxz,m08h6 f
$^12\text{C} + ^12\text{C} \to ^{24}\text{Mg} + \gamma$.
(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 reactioh 0v6-*4voxlg r/ chmwn
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 crgvx6gg ( q80kvitical density of the universeg0x(8vggqv 6k, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$