The Milky Way was once thought to be "mu:t5 3 uhu 7s/nb0outgjrky" or "milky" but is now considered to be made up of ptgsbn 7/:ouu ju0h5t3oint sources. Explain.

A star is in equilibrium when i6ivk 7,ror kf 0fu(gz,czw mg0i342vz4wmz a1t radiates at its surface all the energy generated at its core. What happens when it begins to generate more energy than it radiates? Less energgz1i v 7marg4o,rzk0iwzu406f (k2f,vzcw3m y? Explain.

Describe a red giants0vg bqm b9l.;3l msd- star. List some of its properties.

Select a point on the H-R diagram. Mark several directions away from7olh 4s, m-d9+n g5sfmtd6hk h this point. Now g d t+o n9h h47fs56d-mlksh,mdescribe the changes that would take place in a star moving in each of these directions.

Does the H-R diagram reveal anything abvvpv 0y2/ f8o 4xpsfa3a9 x:ylout the core of a star?

Why do some stars end up as white dwarfs, ky 5.4kuo9i(ozas v)fand others as neutron stars or black holess4vy) i9k.zafoo( ku5?

  Can we tell, by looking at the popugxf/elbc 1)e(lation on the H-R diagram, that hotter main-sequence)l e(cx g/b1fe stars have shorter lives? Explain.  ----待选择----yesno 

If you were measuring star parallaxes from the Moond taptcaw6qs 9 /o9,n5 instead of Earth, what corrections would you have to make? What changes would occur if you were measuring parallaxesa a5sdc,wn9p /ttqo 96 from Mars?

Cepheid variable stars change in luminosity with a ti 98 b -xfgc5zyd0z1hfypical period of several days. The period has been found to have a definite relationship with the absolute luminosity of the star. How could these stars bf -x1z9df0hizg5c8ybe used to measure the distance to galaxies?

What is a geodesic? What iae 3czt1wk*bh8 0c7aok, v*cg s its role in General Relativity?

If it were discovered thatnwyoxf1u--) q8z hkv6*zp,y v the redshift of spectral lines of galaxies was due to something other than expansiovkpv zx) zyyw8 -uq,1-6n*oh fn, 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 th;u3rrcp 7ffdh q3d-a0e center of ta3uc 3f0q fd-prr7 hd;he universe? Explain.  ----待选择----yesno 

If you were located in a galaxy near the boundary of 5/ybe2 z bv) u+ufsrz1our observable universe, would galaxies in the direc/zb)e5 zfu yr1vb2s +ution of the Milky Way appear to be approaching you or receding from you? Explain.

Compare an explosion on Earth to the Big Bang. ql jsg; q*ltjn52;8ix Consider such questions as: Would the debris spread at a higher speed for more distant particles, as in the Big Bang? Would the debris come to rest? What type of universe woxqntjs g2;ji8 ;ql*5 luld this correspond to, open or closed?

If nothing, not even light, escapes from a black hole, tzd8m k v-m(ql n3.+2mqw* vhndhen how can we tell if one is therh+ kdqmvm3d2lnq* nv8( -mw. ze?

  What mass will give a Schwarzschild radius equal to w(x hasgnt 11 j/v1+dcthat of the hydrogen atom in its ground shn 1+tv1x/c1a g wd(jstate? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion years. Find p)pg9ilg4 (jx that time on (Fig. Below). People have lived on Earth on the order gx )4 ipglj9(pof a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic microwave backgj ui+ (m bwc39tvtt+pdtui35/round radiation is. Where does it c++ 3c5 pvuw(t idtj t9mut/b3iome from? Why is its temperature now so low?

Why were atoms, as opposed to bare nuclei, unable to n iia+pty5-4dexist until hundreds of thousands ofi5aytp4d+-n i years after the Big Bang?

Under what circumstanceumgyr ( w5ddfo,fwl/7 ox)8 u-s would the universe eventually collapse in on itself?

  Using the definitions of the parsec9v (bjkc) 7ud3x. svgv and the light-year, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallz0 ubr j1(tqvyc hx:n5:0. mnlk8de,fax of 0.38 seconds of arc. How far away is it? d =    ly

  The parallax angle of a sucb+c 4ogn h*be+e 2(ytar is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away.g1ehbp fs0m:. What 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 ane9 hl*p 9++iio:ams gcgle for 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 star, will t, erv1n7w 3) r,v:nann*ny jmzhe parallax angle of the farther star be greater ornv, e yj zar n,w3*n7v)n:n1mr less than that of the nearer star? By what factor?

  A star is 35 pc awayhw2n0;wp*j)sv7 5 n -jyy rxym. How long does it take for its light to reach us?    years

  We saw earlier (Chapter 14) that d7wf eg64( dtas+a4vkthe rate energy reaches the Earth from the Sun (the "solar cotva+dga f4sd (w7ke6 4nstant") 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 relativewjk a x-*0zgb7 brightness of the Sun as seen from Jupiter as compared to its brightness from Earth? (J-ag*k bw7 xjz0upiter is 5.2 times farther from the Sun than the Earth.) $\dfrac{l_{\text{Jupiter}}}{l_{\text{Earth}}}$    $ \times 10^{-2}$

  Estimate the angular widtpcjlo4zktmb d,2(4/gz 4ec.wh that our Galaxy would subtend if observed from the nearest galaxy to us (Table 33-1). Compare to the angular width of the Moon from Ewecld j24.o gcb z,t4m(pk/z4 arth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, what will be its average density if it j 8vt0(:okrui0 ste 2rexpands out to the orbit of Eart 0:ovr(u tr ej2tik08sh ($1.5 \times 10^{11}\ \text{m}$ from the Sun)? $\rho = $    $ \times 10^{-4}\ \text{kg/m}^3$

  When our Sun becomes b5-uuat g0ix- a white dwarf, it is expected to be about the size of the Moon. W-0ta-ub xugi 5hat angular width will it subtend from the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf sd v 43k-p1oqe6drtg1f*- mnx whose mass is equal to the Sun's and whose radius is equal to 6s-fqgp-1v* m n 1rkexo3t4 ddthe 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 ho; i/vlvs-i5bas a radius of about 11 km. Calculate its average density and compare to that for a white dwarf (Problem 13) and to that of nus5 iol;- /ivvbclear 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 zvy)snyguq,+ d,:j7br*wa w,pi zg )6for the He burning reactions of Eq. 33-2. (The mass of the very unstably*pvb,,+)i wqsaw r)y6 un7d g,zz j:ge $^8\text{Be}$ 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 apparentrmh6kcwr6 6 1j 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 cert:xq0s ec(,f t9w1 kzuyain cluster are assumed to be about the same distance from us. Two1 ,wqte( yuz 90s:cxkf 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 Schwarzschild radius for a star with mass equal to that (a) of )gj p ehv6l23j,pisb1ourp,g 2 j)3 hvbij6pe1sl Sun is    km, and (b) of Earth is    mm.

  What is the Schwarzschild rag+2, u qj:p,,0.+is; wzlffwejgchm wdius for a typical galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a ss1f o b73r20ds5iyisah5t 9zwphere, for which the sum of the angles is (a) 359º, an 32ast9w5h5r z1ds7o bf0s yiid (b) 180°.

  What is the maximum sum-of-the-anglkta pyp hf.80s 7s-,dres for a triangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the speed of light, roughl5f. cnvp;1iw7 m 8ssxay how far awaa f 8x.s5s wp7v;nimc1y is it? v =    Mly

  The redshift of a galaxy indicates a velocity ofn yghh-ojx ,11m5z; uf $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (relative to us) that is near the obe 4*amrnxu rdh-:1c/nnuo5/yservable "edge" of the universe, say 12 billion light-years away. 5en //4n :mra rxoyu*ud nc-1hv =    c

  Estimate the observed wavelength for the 656-nm lisz, kl-sr/pd s)(*e iwa t.oakp; 9b6yne in the Balmer series of hydrogen in the spectrum ofky;6 rsk (itazosa) 9bpdw, -p*e/.ls 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 diwhi ly8ny 82,ws 0ntj6stance from us, if the wavelength for the hydrogen line at 434 nm is measured on Earth as being 610 nm. y8,w68nl0ts2nj wh iy
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 wia,.u7d/3 lu mtwfv meyx5* o*fth $z = 0.60$? v =    c

  What would be the redshkx232*,s frggx8 te wryebe ;l671 hv:iejtd5ift parameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Doppler shift:u( llzd-+k 4ydc g.j4a q0+mxh;oppk 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 blackb3ozbpk qm1:r) ody radiation distribution at 2.7 K zr3:qkmo1 )p busing Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of the unk8 h+kzd 77y8yt9h ngiiverse 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 galayw : vg)c7vv8ky5ewn0(wc/qhxies) at any one moment is believed to have been inversely proportional to the absolute temperature. Esgkcwy nv8hyve0 5c(/ v7q)w:wtimate 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 threshi.7 im5n/dy(h fqebj8 old temperature for pr8fiq7 e mni/dj b5hy.(oducing
(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 mn / ynbn k)v:+ wajggv(.y+zi8ain-sequence stars could undergo the three changes represented by the ta g .8yn/(nkbzgj+i)vy v:w +nhree arrows, A, B, and C, in the H-R diagram of Fig. 33-28. For each case, describe the changes in temperature, luminosity, and size.

  Assume that the nearest stars to us have an absolute lumyd4 s22q.8hqckz v1dpinosity about the same as the Sun's. Thzk cdq y281 qvds.2p4heir 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 tozkl(yp 7;fuftxv+ 1ybd(l( yz:g /u2i estimate the angular velocity of a neutron star which has collapsed to a diamdby /uiy+lyg xztz7vpku(2:1;(f( l f eter 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 e3 hs(iy(1pn ihi7ts y.nergy change when the star in Problem 56 collapses 7 ynyp1i is3i(h( th.sto 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 tinpz,:ow)wr)+v+ x mca mes that of the Sun, with diametzor m ,+:wx+v) )npwcaer 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 o ul wn*pcpl3f k:0sp6 ra36mj+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 neutrino rest mass (in eV) would provil m/hr+sb8;)klaw m)b de the critical density to close the universe. Assume the neutrino density is,bllab+) k/mshr)8w; m 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 tzg113l:.fnfr t fw x wl+oi:q.he main sequence. Use Wien's law, the Stefan-Boltzmann equation, and the H-R diagram (Fig. Below) to estimate the ratio of their diametr lff3ton:. xz1fw. 1gwq:+ilers. [Hint: see Examples 33-4 and 33-5.] $\dfrac{d_{400}}{d_{600}}$ =   

  Suppose we can measure j(+xsi *i/9)d-gamd/mmtb tadistances with parallax at 100 parsecs. What is our minimum angular resolution (in degrees), base*datx bj 9-mimas)ig(m/ d+t /d on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from singly ionized helium in a dnqh(gg i2m3r ,u6h ( *rfflxo3istant star happen to overlap with the Balmer lines from hydrogen (Fig. 27-22) in the Sun. f rgxqg2f,oul 3(( ih*3rn6hm How fast is the star receding from us? v =    C

  What is the temperature that corresponds to 1.8-TeV collisions at the Fermilab c.x:v q(etvln)ollider? To what era in cosmological history does vn():qevlxt .this correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation of gas around what might be a nce;ciz4ngrt 5c)* k s j65hu5supermassive 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 z5j tnk*c5g4iu;5h6 )crecsn 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" hyyw3d8p vlmo3 toy+g 62bqb32wdrogen line at 434 nm emitted from the galaxy isq3b o38+ytobl 2vw2dyp m3g6w 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 f yw-0j +xatvu(ex *f:kk/m2 g(if massive enough) will begin fusing carboy +(t/f kf2:kwjuxx*0ev - magn 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 reactionk.gi5r*r.haal t+v e 74z 4eu*,a5k x;zhok ct
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 rbkcw7wg8,wp u / ,-ldthe univgd bu- 7/w wpk,wlr8c,erse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$