The Milky Way was once thought to be "murky" or "milky" but is now considered toqn-(. crut2d d:w.b7ccxlv lw+kk9u k0i g; p3 be made up of point sources. Explail32kik d+ -pc90bx v(g .7wlc;dwtnr :kuq.cun.

A star is in equilibriulgg h drdbg1ja/x. -(;m when it radiates at its surface all the energy generated at its core. What happens when it begins to generate more energy tgg.- ;d r1hjbda g(/xlhan it radiates? Less energy? Explain.

Describe a red giant star. List some of z 3jbwgw4v;k4 its properties.

Select a point on the H-R diagrb*e05b+-kihhd x rl)f am. Mark several directions away from this point. Now describe the changes that would take place in a star bb5i+f- dlrh keh0)x*moving in each of these directions.

Does the H-R diagram reveal anythinm/r c:sfq4 wmbls:/03t2 zaobg about the core of a star?

Why do some stars end up as white dwarfs, and others as neutron g.a/0z dp:sn 1)slyg.zk1gzjstars or black holzk0 lg/d:1gygzzpj .) a1.s nses?

  Can we tell, by looking at the population on thpckb,. g)pp x;chk v,)e H-R diagram, that hotter main-sequence stars have shorter lives?, pcp)bh ,k. g)cx;vkp Explain.  ----待选择----yesno 

If you were measuring star parallaxes from the Moon instead of Earth em.nbgk p1 ps)k3t4 p.;up/kh, what corrections would you have to make? Whpbsepk;.4phm 3tk)un /.gpk 1 at changes would occur if you were measuring parallaxes from Mars?

Cepheid variable stars change in luminosity with a t(80 k afz;r 0/+aqudqko,md bwypical period of several days. The period has been found to have a definite relationship with the absol r0(0dq+/8aofzmdkk qb;aw,uute 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 Gene. ,gce7tanlm .f9jwh/ral Relativity?

If it were discovered that the redshift of spectral linuqqtk 4 +zi;8ses of galaxies was due to something other than expansi+qs4ikqut ;z 8on, 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 therefork d.fmec2 v(y:e at the center of the universe? Explk 2vef:cym (.dain.  ----待选择----yesno 

If you were located in a galaxy near the boundary of our observable un 1dbjk-bh: +w g.tktfp6t+pe4iverse, would galaxies in the direction of the Milky Way appear to be approaching you or recedbgtdhp1etf 4t k+w+j6.-bk p:ing from you? Explain.

Compare an explosion on Earth to the Big Ba qdc +dr)tkckajbup(*b,39ovl4p t-7ng. Consider such questions as: Would the debris spread at a higher speed for more distant particles, as in the Big Bang? Would the debrqk7p4(rjod bvpd)c lca u bt9,t+k 3*-is come to rest? What type of universe would this correspond to, open or closed?

If nothing, not even light, escapes from a black hole, then how cu 4 n15o-gfisvan we tell if oneno g45us -ivf1 is there?

  What mass will give a Schwarzschild radius equal to that of the hydrogen atomokp ux+4 ec8qc-o7o-00sqqe t in its gro-ox oq+u8qokq4se0 epc- 0t7 cund state? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion years. Find that time afk i1141jcfp on (Fig. Below).11f 1kijpc fa4 People have lived on Earth on the order of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic microwave background radiation is. Where doe/s0us use2zmh1:nq c*s it come from? Why is its temperature nz h:1sesnqu u2s /m0*cow so low?

Why were atoms, as opposed t6q eqljfbrby/4) */ cg4 17ahz5zv mcdo bare nuclei, unable to exist until hundreds of thousands of years after thec/frq*jvgq 1a ezl4dhm6c4b)ybz 75/ Big Bang?

Under what circumstances would the universe eventuallythx 0jjs24aa 24 rp3ey collapse in on itself?

  Using the definitions of the parsec and the light sm7kon; .w4,-6srexh cbq/dw-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 away is it? d = hwx).g y,eg) ro-l,td   ly

  The parallax angle of a s7 2x semd*zva u. dfqo/q0+no,tar is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. Whati6 ikdbu3p: u q9lfz32p*b7uf 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 for a svg( lw6 a:dzhgfvn69.tar 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 th2 (8z6:ryggzv*c u-wp fv5w wse parallax angle of the farther star be2wrv6*y-wcp5f gzw8:s z(vu g greater or less than that of the nearer star? By what factor?

  A star is 35 pc away. How lon1qda6t 8f:29bpxbp5sqonh5s7 q duw(g does it take for its light to reach us?    years

  We saw earlier (Chapter 14) that the rate energy reaches the Earth from thq90jl0s5( /*f9fdyl nd zavk3.u prlye Sun (the "solar constant") n 0pfkl 5 ( ql/jfv0sz*9a93rdyludy.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 fr :tej;/erm2mi xqg0 )e vvq9o9om Jupiter as compared to itvqej/0 2qoexv9;gmr) :tm9ies brightness 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 width tha a /8-)ehzydg8 1lqywlt our Galaxy would subtend if observed from the nearest galaxy to uy/l8)d wg qh1e ly-za8s (Table 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 densiyep 2qpjdi 15nf0 :x5lty if it expands out 5yx2 eq0 ljd pi:np15fto 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,o v6 tdbu rm29 )yv:el3kid8k the size of the Moon. What angular width will it subtend from the present distance odu3l2 :,evtm)6rk yd89 kiv bto Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whose mass is equal to the Sun's*b1r) hy* cs2 fdthoz7 and whose radius is equal to h)z2so7t **cb h1rdf ythe 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 mso7nl; iidmqpmf3- qx84js2z 62.s b+6fxm w1.5 solar masses has a radius of about 11 km. Calculate its average density and compare to that for a white dwarf (Problem 13) and to s os3imimpj m+ f.64 -q68x;7mzwqn dsf2xlb2that 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 (c)f1v.q x0xuflaa*v-2. (The mass of the fq(*ux0flvv x. aca1)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 apparewhxd0j*nx; b2a3 l9g knt 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 clustersa.qf,iva .k 6 are assumed to be about the same distance from us. Two such ssi.,qa.a6vf ktars 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 Schwarzschild radf0rxh1h/;1pkijb-yyt mf8mzv guik, u 2+)- kius for a star with mass equal to that (a) of our Skgfm;r1kh--2yiuxbm /p k0+fh1uy)ij v8 t,zun is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typical ga h; ; kwhhkivulq1lqs5 8)53ovlaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a sphere, for which the sum og 0 yr4e9+zrvqf the angles is (a) 359º, and (b0rygqv+r94z e) 180°.

  What is the maximum sum-of-the-angles for05x8ow.psr r sfnlu22rdvyy +(r:r.n a triangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the speed of light, roul5b1 wcc ;wn domo:8x5ghly how far away is it? v = 1wx5mo w5 clbocn:;8d    Mly

  The redshift of a galaxy indic z+w.6fobqm0 bvrsf()ates a velocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of aanpn, c9-lb9 oi*4nlp galaxy (relative to us) that is near the observable "edge" of the universe, say 9 ,*l lnpipobc49n -an12 billion light-years away. v =    c

  Estimate the observed wavelength for the 656-nfb8vaj l b6 yfy m-8d( 2p60;yal(navkm line in the Balmer series of hydrogen in the spectrum of a ga n2y fk(6bbap vfj8mldla(8 6vy;-ya0laxy 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 im 9ou i*d9 wpst ed)9sqqah5/.o:a0bz ts distance from us, if the wavelength for the hydrogen line at 49sbz09)5h*dtoa . ue/:q qwiop mads9 34 nm 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 j81 hw 6sl8kl5qrxz3 aa galaxy with $z = 0.60$? v =    c

  What would be the redshift param leo:bius3as; ) -1w9 xmg2hameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Doppler shift in wavelenv*laa,c;rxyqk bc 7,9gth 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 radiationp)hzdha)f l53 *ju7ev distribution at 2.7 K us 5 u)j3v*hafzldph e)7ing Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for-sjz)7qd )exrvw 9lonxs.e -2 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 distg 2fam:2cx0z6t. lo0bc z+9x0hbma myance between galaxies) at any one moment is believed to have been inversely proportional to the absolute temperature. Estimate the size of the unive09 lcm0m2.yx mfx bo2ghzz6c 0 a:+tabrse, 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 threshold te; rv1df9uw(bqmperature for producing ;wvubd(r19 fq
(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 three changes represe7 pr4:4y 4mkmvgsm* s*oi )rfanted by the three arrows, A, B, and C, in the H-R diagram of Fig. 33-28. Foro 4gras *m)7*i: ymp r4k4svmf each case, describe the changes in temperature, luminosity, and size.

  Assume that the nearest s*gn mpk av3-ls/0pzb1pk9 f7tas;4z j tars to us have an absolute luminosity about the same as the Sun's. Their apparent bria *jb;n91sfk 4z 7ltpmpz3p ag/ ks0v-ghtness, 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 n 7tfu,ys0s8pl6-nwp r2x/ csmomentum to estimate the angular velocity of a neutron star wcy6pwt0nur s lss7- x2f/p8,nhich has collapsed to a diameter 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 kinetic energy change when the star in Pro ag0aei zf/7 6u zr-adlz-5ca*ble u /7zaczzgfia5 edla0-6r- *am 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 lrlm vm3 w.3 oostp(i n,ja-f6r;3x)pof mass 1.5 times that of the Sun, with diameter 20 km, is obsep3xr l m(pr wai3sl.j)omt-v6,fo; 3nrved 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 Galax2dd2(ls*tom5 *p qn xr x0tm-yy 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 proqg8cc eclrqvfa64.: 8 vide the critical density to close the universe. Assume the neutrino density is, likq.r v8f46ace:qlgc c 8e 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, respecv(;y 6x-hiw jz mxv8w0tively, both lie on the main sequence. Use Wien's law, the Stefan-Boltzmann equ6wxm8wxvyzhi-v ( ;j0ation, 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 paralb2ou((grk)w *q-wflwx m2 um 0lax at 100 parsecs. What is our minimum angular resolution (in degrees), based on this informa2 0gmww) fx*(-2luuomr (qkbw tion? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the1fb63auva *mm Balmer lines from singly ionized helium in a distant star happen to overlap with the Balmer lines from hydrogumma*16b a3fv en (Fig. 27-22) in the Sun. How fast is the star receding from us? v =    C

  What is the temperature that corresponds to 1.8-TeV collisions aw(pml)+ sd9v9q es5jki+utyh4 + j)mut the Fermilab collider? To what era in c4m5+jdi ks +)9)9em jyh ts(puwuvq+losmological history does this correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recentlyq 8:lehdku 6tls6q8;+s9l aol measured the rotation of gas around 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 light-years, what Doqa;s o9 ul8t8lks l6dh+:6 elqppler 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 43 1mz)v: t4g uhe5knfyok0hy ,(f5gpl24 nm emitted fpgk:gfh(y 5h2t4k 1)l05fo ye ,vzmnurom the galaxy 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 be/bak t:sa x19egin fusing carbon nuclei to form, for example, tk1a b: s/xa9emagnesium:
$^12\text{C} + ^12\text{C} \to ^{24}\text{Mg} + \gamma$.
(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 reactioxobk18;wegm 5n
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 density of the u u/ 9jb8br stul5q 8oj*aojk32niva25*o/ us8j8u oljbb3k9tqjrerse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$