The Milky Way was once thought to be "murky" or "milky" bub)my y4 9g yajm4jd;u7t is now considered to bmuyb jj;a 74)dy9gm y4e made up of point sources. Explain.

A star is in equilibriuscq k fica2,,w8 nze;dfmh.23m when it radiates at its surface all the energy generated at its core. Whatshziqfc3fc,; ,82a m .d2nkwe happens when it begins to generate more energy than it radiates? Less energy? Explain.

Describe a red giant star. List som5 kppkc56b wa3e of its properties.

Select a point on the H-R diagram. Mark severalv.n:0xege xqy-x4vb/zy d91w directions away from this point. Now describe the changes that would take place in a star moving in each of thesxg/q.:nv xvz 0 -byx 4wyee9d1e directions.

Does the H-R diagram reveal anything about the core of a sta 4 n(r vg( k3 qo64qpyy(zx.f9pqn9tdmr?

Why do some stars end up as white dwub+*iry.rcfn1q3i;ujz m1) q arfs, and others as neutron stars or black holes? bqiz; u)f3q1*1rumcjn yr+.i

  Can we tell, by looking at the populaw s*rp: 9cs;s4g)a*qrdcjn/ ution on the H-R diagram, that hotter main-se9s* nducrc)q: /gwpr4s*j a;squence stars have shorter lives? Explain.  ----待选择----yesno 

If you were measuring star parallaxes from the Moo-prfmwyk9 v+q w a:)4tn instead of Earth, what corrections would yr-k wq pf9y +4wavtm:)ou have to make? What changes would occur if you were measuring parallaxes from Mars?

Cepheid variable stars change in luminosity with a typical period of several d //q; gbtwohb/ays. The period has b/b wbtq g;ho//een found to have a definite relationship 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 rov;4k f4f49q qyjeya9yn 5nh4 ele in General Relativity?

If it were discovered that the r:5zbt:pqprbos a(je+w .1/szedshift of spectral lines of galaxies was due to something other than expansion, how might our view of the universe change? Wou zqps.a r o1tw:j+p /b:sez5b(ld there be conflicting evidence? Discuss.

  All galaxies appear to be movi3dg+dsj;,.9bpvmwbc ng away from us. Are we therefore at the center of the universe? Exp wsm.vcpg9,;d+dbj3blain.  ----待选择----yesno 

If you were located in a galaxy near the boundary of our o.s6 o.6o(vphvf , raybbservable universe, would galaxies in the direction of the Milky Way ao,pf6hsvrov (6a.y.bppear to be approaching you or receding from you? Explain.

Compare an explosion on Earth to the Big Bang.99kt6x uu e0cl Consider such questions as: Would the debris spread at a higher speed for more distant particles, as in the Big Bang? Would the debris6k0 ux9tlc9eu come to rest? What type of universe would this correspond to, open or closed?

If nothing, not even light, escapes from a black hole, theqi/)v za,0oa eao/e*kn how can we tell if one is there)*//akq iaa,ev oe zo0?

  What mass will give a Schwarzschhg* uoj c5oio7j5kz7.92 j beaild radius equal to that of the hydrogen atom in its ground sta.e oo72g ho5a5b *zk97juic jjte? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billi;8p5.tz7 sr0wofxq y:kn .tfz on years. Find that time on (Fig. Below). People have lived on Earth on the order of a million years. Where is that otn75.f8k:0qp s;yfr. xtz wzo n (Fig. Below)?

Explain what the 2.7-K cose ( -kpc6c9fr2.;tgd fkilqw8mic microwave background radiation is. Where does it come from? Why is its teqckw k-pf(.lite9 d r2;fcg86 mperature now so low?

Why were atoms, as opposed to bare z0i 8cn vt5.*v 8nctdunuclei, unable to exist until hundreds of thousan8tc*vi c58 zduv0n t.nds of years after the Big Bang?

Under what circumstances wou8hyv vo.ij0z9ld the universe eventually collapse in on itself?

  Using the definitions o n c qpkduvmf+/q1k*o; vhhsm e(1.-)nf the parsec and the light-year, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.38 seconds of arc.l+scsy- ku0m5 How far away is it? d =    ly

  The parallax angle ofljdj p*0xwif8)b d4f7 a star is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its parn;qi-,kxeu tk) (qn0(b9kct g allax 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 fh6yxj7w 1qs j)or a 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 xv: ;w wibmn)s/s85olstar, will the parallax angle of the farther star be greater or less than that of the neareo ns;bxmww/ 8 sl)i5v:r star? By what factor?

  A star is 35 pc away. How long does itn1 ulbny2 lc**ij)n* z take for its light to reach us?    years

  We saw earlier (Chapter 14) that the rate energy reaches the Earth fr4fpt9w1k xna 8om the Sun (the "solar k94wtx81n f paconstant") 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 b/30ishx,7psuhd 0 v1jbno uv)rightness of the Sun as seen from Jupiter as compared to its brightness from snio 1s3 h,/ u7xh0vd bupvj0)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 t si6 /dso4:r+a8f.yd*dpl up fhat our Galaxy would subtend if observed from the nearest galaxy to us (Table 33-18/.6:+ 4d*pplfsuao fddsy ri). 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 averaffbz8j3d5ul ,a 5b ,mdge density if it expands out f,b bmld85 a5ju,zdf3to 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 s*woy10cx, 16hntook is expected to be about the size of the Moon. What angular width will it subtx, kn 1co o*1y0ostwh6end 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 Sukhz;jl ws+5,y5 x3xh;y nsig1b 0 bp0vn's and whose radius is equal to the Earth's. How many times larger than Earth's density is this? ,5 bng;sxy5v0 zh+y1wlbxiskj;0ph3
$\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 y+9 jym5w:fr:5a xypx1.5 solar masses has a radius of about 11 km. Calculate its average density and compare to that for a whiy pxamy95ywj: 5xr:+f te 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.q/jr:/3m ovaq 33-2. (The mass of the very una:jo/rq/ q mv3stable $^8\text{Be}$ 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 suf j;7d740tqt xqqpw.ame 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 as -(wshoxq* b,nkzw(+u -yn- masumed to be about the same distance from us. Two such stars have spectra that peak at - q(osw ba-m(wyuxn-k+*hnz, $\lambda_1 = 500\ \text{nm}$ 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 stac(cz)rj g5mj 3cjw1ix13 niq..ygqu8 r with mass equal to that (a) of our Sun .yj r 3j8mx31.ci5czuj (qgw1q )igncis    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius forq lplcrpk5 -n sxq22qny9i,3+ a typical galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a sphere, for which the sum of vileybb b09)8 the angles )bly90ebv i 8bis (a) 359º, and (b) 180°.

  What is the maximum sum-of-the-angles for a triangle on a sp,h1md*k yf m0ohere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the spe-(im)y kqih/0 bbfn)jed of light, roughly how far away is j f)h) /imq-b kny(ib0it? v =    Mly

  The redshift of a galaxy ina6a9-qkt d9a :yvdz,g0dak3vnk:6u gdicates a velocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (relative to us) that is near the obsi -rpsrxr; 8z4wc9ls 2ervable "edge" of the universe, say 12 billion light-years away. -2ri984lssw ;r czp rxv =    c

  Estimate the observed wavelength for the 656-nm line in the Balmer m1h)fyy76 5rvyill8 xseries of hydrogen in the spmyylyf) 7i 65vlxr h18ectrum 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 ;5fxd : qrl0tnus, if the wavelength for the hydrogen line at 434 nm is measured on Earth as beinn;d5r fql0x: tg 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 wf8,4wr5uhc (g6t (pt* emdsxqith $z = 0.60$? v =    c

  What would be the redshigi*zo 3s(0 q gxzp(bp*dk 1bg*mjw8b) ft 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 wavel njpv5.p,eejk 7 5afk-pug x6x l..mz+ength is $\Delta\lambda/\lambda \approx v/c$ (Eq. 33-5b) for $v \ll c$. [Hint: use the binomial expansion.]

  Calculate the wavelength at *6j+lvysa;cy54szo c the peak of the blackbody radiation distribution at 2.7 K using Wien’sz4+s6y o;ac yvlj5 sc* law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density lzj rj ;.bts117, d*:c ehswywfor 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 galaxiesqn7t,; ab(gw z) at any one moment is believed to have been inversely proportional to the n;z(t aw ,gqb7absolute 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 ;(7lerv ;-m6v)mjl n0zny1lsipx) mi cooled below the threshold temperature s 6xn-i)r;e)m7p(lnvl ly; zm10vmj ifor 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-sequenc n d7ef9g9gv:we6jrc 0e 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 temperat:wr0vfn9g7 ej cged9 6ure, luminosity, and size.

  Assume that the nearest stars to us have an absolute luminosi k ha06k ccz.r67-jk/ u4jldedty about the same as the Sun's. Their cju47-rddkkl k.c6hj 0za/e6apparent 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 s8f3f- 2swf 0 k+qsq:r8uc gxgx fun5(angular velocity of a neutron star which has collapsed to a diamete:gxxng02 k uff-rqs3q 58sfwc+uf(8s r 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 chanfy z7046;eeju1 rg.fc.jc jolge when the star in Problem 56 collapses to a neutrrjlzu;.f4j c. 7fy e61 ogej0con star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believed to be a g1ee*bgoblk67f,ru, qtyw :+as/7c uneutron star of mass 1.5 times that of the Sueg,ua gw u6 o*k7,1/rtb beqcf7l:y +sn, with diameter 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 o1qd i 4ssqh)igsw d7;,ur Galaxy 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 neutri4tojux4l 11xy ujh 0:ono rest mass (in eV) would provide the critical density to close the universe. Assume to1x0 :u4tx1uyjj4l ho he 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 400 nm, respectively, both lie on t8lpi.ug*0f aos 3gp /80xgv xzhe main sequence. Use Wien's law, the Stefan-Boltzmann equation, and the H-R diagram (Fig. Below) to estimate the ratio of their diameters. [Hint: see Examples 33-vps8.0 g3gxzoa0xl 8up g/i f*4 and 33-5.] $\dfrac{d_{400}}{d_{600}}$ =   

  Suppose we can measure 0a-/m bk g(- lm*jcqgxdistances with parallax at 100 parsecs. What is our minimum angular resolut- x (l0/ckma gb-j*qgmion (in degrees), based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from singly ionized helium43u9e u n4 k9xkow:lni in a distant star happen to overlap with the Balmer lines from hydrogen (Fig. 27-22) in the Sun. How fast9l:n4k9 iu4o 3xnkweu is the star receding from us? v =    C

  What is the temperature that corresponds to 1.8-TeV collisions a syz r4j*;mvd9c-nlp 0t the Fermilab collider? To what era in cosmological histor; yd-z490mpls*njc vry does this correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation of gas around what mi yn;-2xv3naey 8 6kgo/opc :mtght be a supermassive black hole of about 2 billion solar masses at the cent6:yk 3pmgxv/-aec2t nnoy 8o ;er 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 f7qkfqolb-y +4qllz+vf po)69 rom Earth. The "blue" hydrogen line at 434 nm emitted from the galaxy is measured on Earth to be 650p6 k f9b-lq4yl +ov7+ozq)qfl 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 evolutiq,8 xiv5ulix*on, a star (if massive enough) will begin fusing carbon nuclei to form, for exampllvi q8,xxi5u* e, 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 2rf9vgf0mrv8w)y (c j
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 iy:9yb pa/3 qhj.a,+ e, 7xsf;ug)a ,zmk cbesgts density equaled the critical density of the univej yh s p+m;g/bzcx,ea9 gb),.kqesa,fay7 3:u rse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$