The Milky Way was once thcscvag( 288sx4 dg:fy ought to be "murky" or "milky" but is now considered to be g(s8x4d8 2 ccav gf:ysmade up of point sources. Explain.

A star is in equilibrium when it radiates at its surface all the energy generatr(mzo65h i2 .cm*x ekged at its core. What happens when it begins to gener52.rxogmze *6 c( mkihate more energy than it radiates? Less energy? Explain.

Describe a red giant star. Lix9li thckhhkib 6.+2y3.vw9 g st some of its properties.

Select a point on the H-R diagram. Mark st( x9me trikj1i (;+fe+yw6ikeveral directions away from this point. Now describe the changes that would take place in a star moving in eaei+ tx+ywk j9 (;i(ir6tkfme1ch of these directions.

Does the H-R diagram reveal any)x0 a4m6e gdsvc9jn0gthing about the core of a star?

Why do some stars end uyp8q yrzi2l*3p as white dwarfs, and others as neutron stars or black hi8rzyqyp3l2 * oles?

  Can we tell, by looking at the population on the H-R diz8pr .kvzh0h,7 sca w6agram, that hotter main-sequenc, zzkh87. vsp0whcra6e stars have shorter lives? Explain.  ----待选择----yesno 

If you were measuring star parallaxes fromk pejkcol2;ggc-0pk (l inf3y(k, 0a( the Moon instead of Earth, what corrections wfpplik0 og c3 c (a;(- jn0(lkg,2kekyould you have to make? What changes would occur if you were measuring parallaxes from Mars?

Cepheid variable stars change 2a5lo)jzg t,: x co7i:d:tehu in luminosity 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 thd al, xtozg5ic2:7e :oht:j) uese stars be used to measure the distance to galaxies?

What is a geodesic? What is itsyrnu3k+ vd2k1 role in General Relativity?

If it were discovered that the redshift of spectral lines of galaxies was due 0+79(fv kwmcq4p d-sh,bz jm(4 pdewsto somethin4pwksm0e mvd7c4p bq( j-hz(9d+w fs,g other than expansion, how might our view of the universe change? Would there be conflicting evidence? Discuss.

  All galaxies appear to be moving aanjd9v rrorv.w.n m7 c( o(s19way from us. Are we therefore at the center of the universe? Explam1a r. jnsco(rd7( 9nv9vw or.in.  ----待选择----yesno 

If you were located in a galaxy near the boundary of our observable univlfbwl/f :68wyhpae1 *n(-oyyu ) (prqerse, would galaxies in the direction of the Milky Way appear to be approaching you ob 8) l(r-efpyyq n/w :pwh*y6u l1(afor receding from you? Explain.

Compare an explosion on Earth to the Big Bang. Consider such questions as: Woul0o.(qofd2r v3m lvds /d the debris spread at a higher speed for more distant particles, as in the Bigq/.0vsrlo odvm (df32 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 black hoztdpd 7)m k7q-le, then how can we tell if one is tqpd7tdz -k 7)mhere?

  What mass will give a Schwarzschildm m.gav;lpnp/ y24r:*qe lf2p.0b zac radius equal to that of the hydrogen atom in its ground s 4bq / la2.:l.cfrvgamz;2ney0 pmpp*tate? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion yeao)iegq,b 4v f+rs. Find that time on (Fig. Below). People have lived on Earth on the order of a million years. Wheref,gi bo)e +q4v is that on (Fig. Below)?

Explain what the 2.7-K cosmic microwave bnkr1v.wzdp(q 4skpy 3v *u58background radiation is. Where does it come from? Why i54dynbv3w8v(qs *k1pp. zukr s its temperature now so low?

Why were atoms, as opposed to bare nuclei, b21w kg ;7beh3a m(pkxunable to exist until hundreds of thousands of years after the Bm3ehb b1px;kwg( 72akig Bang?

Under what circumstances would the univre1ew o k4f*k5r 2ral2w 0tda)erse eventually collapse in on itself?

  Using the definitions of the parsec and the ligh46t -ip- a7jnhlw iazf29sn 5et-year, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.38 seconds +wx.*ql )eryfihd.-) yx; ituof arc. How far away is it? d =    ly

  The parallax angle of a whaob 9i4 s43zc4zbs4star is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its parallax angl55c6xp7 2e,zm 7o3(7xh jskotunafj.k fl0bk e?
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 k-ai uh9b,0 tostar 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 paralluou ;dev *c38oax angle of the farther star ooe *uc3d8uv; 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 reack zna ,m/i* s*+quimfxy9b7:ah us?    years

  We saw earlier (Chapter 14) that the rate energy reaches the Earth from the Sun wm7xjp5+ky u 1:26dl bgbgyb: (the "solar constant"7w+uyby jgb 526mlgb1:xk dp:) 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 compareuss.fal++mm-fv.- *4akd hh td to its brightness from Earth? (Jupiter is 5.2 times farther4.huds mlmst*fk-ah+f-a v+. from the Sun than the Earth.) $\dfrac{l_{\text{Jupiter}}}{l_{\text{Earth}}}$    $ \times 10^{-2}$

  Estimate the angular width that our Galaxy woulz1qon7o (ze(v )diemcj.pw 51d subtend if observed from the nearest galaxy to us (Table 33-1). Compare to the angular width o.zpc1w )(on o5ezvjde1q 7mi(f the Moon from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a re;)hj sg + i/mt48 *im6mihxkmyd giant, what will be its average density if it expands o6imimx/ms;+t8ymh4)gj i *kh ut 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 thek7hw x1t 04 jb*1o*nrqnhi st9 size of the Moon. What angular widthjn n101i*o shr4 tx*7kqt b9wh will it subtend from the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whos( :)2aw)kyt7rqzwt;;(kely hlec ad.e mass is equal to the Sun's and whose radius is equa l)wah;c7y() a(: k2kt; ltzwdqy.eerl to the 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 1.5 solar masses+su s;k,m8 ctx has a radius of about 11 km. Calculate its average density and compare to that for a cxtms 8+;usk,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 Edkutz :.vg, v3q. 33-2. (The mass of the very unsta.gu,zv :d3tkvble $^8\text{Be}$ 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 * 0d3i37muu z zt)gk73y iidsathe 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 assumed to (w:32+ha.sr ee ;h prx d(xn,j-lbbkobe about the same distance from us. Two such stars have spectra thanr3e hkde:l;h - jp+(.xbb(sw, o axr2t 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 Schwarzschilx 9b 6oy vj 8u3fpl2vzap*l+b.d radius for a star with mass equal to that (a) of our Sun p6.jxp l3of8a v2*u by+zv9 lbis    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typical galaxy (like ours)? 1c+xiu w*,(8tee2 ujlf f4yikR =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a sphere, for which the sum of thz1hln:o6cecgy o9 gs,3q 8 : m2ywkv8rdl2 w0ee angless y:32kz,:o 0mdhc yregocl81 69e 2vl8wgqnw is (a) 359º, and (b) 180°.

  What is the maximum sum-of-the-angles f. *m6: svgenbxor a triangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the speed ow1; 07 vtek i-6-t9csewpttpbf light, roughly how ; s1-evtcwpb6 pe9w0tt7-t ikfar away is it? v =    Mly

  The redshift of a galaxy indicates a velocit e284-y vg*w0k;jk wg0zfhqlwm:d p. qy of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (relative to us) thqtyc hu n091nv+: 1x/qw.kna fat is near the observable "edge" of the universe, say 12 billion light-years away.qn+c nknh:vx/q0.yf a1w 19ut v =    c

  Estimate the observed wavelength for the 656-nm line in the Balmer serie q(4sv ijj/hr:o(hdr+ s of hydrogen in the spec(jir:4ovd(h jhqs/ r +trum 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, u fc)s1l/ 1 -a(mmjqwf./ui epp(qw4iand its distance from us, if the wavelength for the hydrogen line at 434 nm is measured on Earth as being 610 n fqcuw) awi/(l / msmpe1i(4qp.fj1u-m.
Eqs.33-4 and 33-5a v $\approx$    c
Eq.33-6 v $\approx $    $ \times 10^9\ \text{y}$

  What is the speed of ahd j m pu6.88qzdsvp1: galaxy with $z = 0.60$? v =    c

  What would be the redshift parameterj 7 j xwsm0/7pz mr3tnk,g4qw4 $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Doppler ,vuzzjt2f 3 jz;lo)s*ur: 1jb shift in wavelength is $\Delta\lambda/\lambda \approx v/c$ (Eq. 33-5b) for $v \ll c$. [Hint: use the binomial expansion.]

  Calculate the wavelenged5 *zvg*ucx82ud f7p bbic 7,th at the peak of the blackbody radiation distribution at 2xp*7,egc u*c5zv7f i dbdbu28 .7 K using Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of the universe isnyt)kz*63weclpq93tq/ t1 ad $\rho_c \approx 10^{-26}\ \text{kg/m}^3$. State $\rho_c$ in terms of the average number of nucleons per cubic meter.    $\ \text{nucleons/m}^3$

  The scale of the universe (t,7ylzfi,/fre he average distance between galaxies) at any one moment is believed to have been inversely proportional to fr,ly7 /efi ,zthe 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 t62j:ph4o *jm rvh 1mds/qk-kthreshold temperature for produkh o6tpk*/:-h 2 m4vsrdjqmj1cing
(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 th4 0w1a 3rnmuytree changes represented by the three arrows, A, B, and C, in the H-R diagram of Fig. 33-28. For each case, describe the changnw1ryt uam 403es in temperature, luminosity, and size.

  Assume that the nearest stars to us have an absolute luminosity abtl nkd / o,g) xe)7u7zuqz6c)bout the same as the Sun's. Their bc6 tnoq7),g/zkxd )l uze)u7apparent 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 angularu se3;(ub k3,sqlc5dn velocity of a neutron star which has collapsed to a dilus5,(sud3k nc ;be3q ameter 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 kineti5p5a s(/ qfhlmc energy change when the star in Problem 56 collapses t5 5/pha (fqmlso a neutron star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believed to be a neutron star (z. c.gc;kx z 6y6 t-(bgbblyxn)9m lpof mass 1.5 times that of the Sun, with diameter 20 km, is observed to have a rotatiy c)t-.zngly( 6.lkb9b zg6c( bpmxx;on 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 is ab +wqko pb5- djzhcp4;*xph:j6 out $2 \times 10^6\ \text{ly}$ 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 (9t ni:*opggvy4uh5 uft392ih in eV) would provide the critical density to close the universe. Assume the neutrino density 2 pgu:t o*hn39i h5fytg u49ivis, 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, respectively, bo y qrvx70x;4tvth lie on the main sequence. Use Wien's law, the Stefan-Boltzmann equation, and the H-R diagram (Fiyxv4x q7 ;r0tvg. 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 is q+-hsw d f4pm5our minimu -sdh 5w+qp4fmm angular resolution (in degrees), based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the h7u .,t,m zwn6bol* jf2wsld9q 75ozxBalmer lines from singly ionized helium in a distant star happen to overlap with the Balmer lines from hydrogen (lxd oqo5wu9 n2b,j,l 67mw*7 t.szhzfFig. 27-22) in the Sun. How fast is the star receding from us? v =    C

  What is the temperature that corresponds to 9ph1rr79 dy1 fss qes( w**hfu1.8-TeV collisions at the Fermilab collider? To what era in cosmol9hs1*9sq1(wuf *yrdfeshpr 7ogical history does this correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently mvu1s,pil i0x +bq 8ld4easured the rotation of gas around what might be a supermli + vx0u4dqspb,8i l1assive 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 Doppler shift $\Delta\lambda/\lambda_0$ do you estimate they saw? z$\approx $    $ \times 10^{-3}$

  A galaxy is moving away from Earth. The "u:2ua 78 ,zhlox b,ejmblue" hydrogen line at 434 nm emitted from the gala:o2 ubl7euh8,jzxa , mxy 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 evolyakbfp6sq1o jd ./ut,-g3-unution, a star (if massive enough) will begin fusing car .y qb3p -1tus/onajd ,gu6kf-bon nuclei to form, for example, 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 reactionc0f)2xaf +- gemhtvynlh 1 9b/
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 0m 2d.mklrfo 3critical density of the un2k3.r fm 0dmoliverse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$