The Milky Way was once thought to be "murky" or "milk jcl c/ 9)j4m-biird)uy" but is now considered to be made up of p c)dbj9cr/u) 4m-ilijoint sources. Explain.

A star is in equilibrium when it radiates at its surface all the energy generater6v4fm d8et 6kd at its core. What happens when it begins to generate more energy than it radiates? re4dtv6f k6 m8Less energy? Explain.

Describe a red giant star. List svn.,bl2:tq* u d6 fg;l,wthf xome of its properties.

Select a point on the H-R diagram. Mark s j a)osn6v4jz2 cdayg-e+a/4weveral directions away from this point. Now describe the changes that wougca-24z4eajdw+v/on6) jsy a ld take place in a star moving in each of these directions.

Does the H-R diagram revibz(6;qsw5 dteal anything about the core of a star?

Why do some stars end up as white dwarfs, and others as neutron stars or black1 u0zm)wi/ yc*huxse9 holezuc1)h9wes0u*my /i xs?

  Can we tell, by looking a4st1ihzikxh*du:u2w7n mf46 cp, p(ut the population on the H-R diagram, that hotter main-sequence stars have *dim4:c2hk14ixfws u(uzht7n pup, 6 shorter lives? Explain.  ----待选择----yesno 

If you were measuring star paralccs2. fd ;,0nsu2vlt3dray 6 zlaxes from the Moon instead of Earth, what corrections would you have to make? What changes would occur if you were measurinvufn2r26 0 cz; lsa.,3sdtdycg parallaxes from Mars?

Cepheid variable stars change in luminosity with a t4m8/p wrz:rmudy +f/typical period of several days. The period has been found to have a definite prf+ yu z/w/d 4r8m:mtrelationship with the absolute luminosity of the star. How could these stars be used to measure the distance to galaxies?

What is a geodesic? Whatc c13kt u 1gdymo0.1ai is its role in General Relativity?

If it were discovered that the redshift of spectral linetqm9p f38x* cvkk.1aen- iku/s of galaxies was due to something other than expansion, how mi /kv.u3 e1kq cn*pxai 8t9fkm-ght our view of the universe change? Would there be conflicting evidence? Discuss.

  All galaxies appear to be moving away from us. Are we ther,9(hfpdqkodl9f 71btefore at the center of the universe? Explaintdp ,7 1l(qdk99h ofbf.  ----待选择----yesno 

If you were located in a galaxy nab5+pl zyz+3s ear the boundary of our observable universe, would galaxies in the direction of t+p+sazb l5zy3 he Milky Way appear to be approaching you or receding from you? Explain.

Compare an explosion on Earth to the Big Bang. Consider such questions as: Wouliqfbu;iohe ph6fit(./v i ) y)b (b,(vd 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 would thisy (o6v ((f) p.bib f,;ihb/)i hvetiqu correspond to, open or closed?

If nothing, not even light, escapes from a black hole, thenyxf 8tz )20uhv how can we tell if one is t8ztux y0f)v 2hhere?

  What mass will give a Schwarzschild radius equal to that of the hydrogen atom0rqm, k wv7n1m in its ground stavrk07m q1m,nw te? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billio.rqc7 hanqco99szl j)w ,8a *nn years. Find that time on (Fig. Below). People have lived on Earthaoa,q ).s9 nrnz*ch wjl q79c8 on the order of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic microwave background radiation is. Wheriadb9m5v -7on q8sk- ue does it come from? Why is its temperature now-q7m d9bn o58-kusiva so low?

Why were atoms, as opposed to *aw-6pe pq-)e)evap f bare nuclei, unable to exist until hundreds of thousands of years a*-6a-qwae )vppf pe)efter the Big Bang?

Under what circumstances would the uk a3dhbfvhh0,0/b /gdniverse eventually collapse in on itself?

  Using the definitions of the parsec and the light-year, show that gjo( w/(i+ ph e+eg:yjcc:k/:hyyo1k$1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.38 sec3mqr3q .be .swonds of arc. How far away is it? d =    ly

  The parallax angle of a sta f g r2f-;/lds;(sub h ubb7yqgl/f:t4r is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its parallax angle? )hyl3*ejhwn, u/ 9 e ou5-uqm du,yxb5
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 ly away hlp) 7cc4je7a? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away from us as a second he4lf7+ h.scastar, will the parallax angle of the farther star be greater or less than that of the n+.aef s47hchlearer star? By what factor?

  A star is 35 pc away. How long does it take for its light tr;s: ioyax; v18k li.xo reach us?    years

  We saw earlier (Chaptvtoy ,k.eno8y c+kfk8p0 s2t;er 14) that the rate energy reaches the Earth from the Sun (the "solar constant") i.o te88v o+ky2ksf c py;nkt,0s 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 brig4 sdizi( uo5/dy-0gopl/rck:htness of the Sun as seen from Jupiter as compared to its brightness from Eky4 0s (dl5p oro i/dzciug:/-arth? (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 Galaxy would subtend if observed gy +g1lohi(3e4 zc2khfrom the nearest galaxy to us (Table 33-1). Compare to the angular width of the Moon from ghyh 12 +3lzgeo(ic4 kEarth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes;n8: bqic4m js a red giant, what will be its average density if it expands out4s c:bm 8nij;q 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 exrx da3oe68kx m3yq8 y rc d-br;:y*;kxbv */dppected to be about the size of the Moon. What angular width will it subtend from the present distance to Ea3kx:b p d*;3y;8qcyd/*akxdvb6e rxrmoy r-8rth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whose mass is eq4c ny;qgs)y +gxr;um-ual to the Sun's and whose radius is equal to the Earth's. How many times larger than Earth's d;+x uyg s;g-q4yr)mncensity 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 abou 6v-4i:.htrd7sxoa cbt 11 km. Calculate its average density and compare to that for a white dwarf (P4a6h.-tx os rvbdc:7i roblem 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 burnir,vm5 ),gl 5+hhugb)l bdzie ;ng reactions of Eq. 33-2. (The mass of the very unstzi+;rh,mg dh,5lv 5 b)ugbe) lable $^8\text{Be}$ 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 ofpc+9 dzwhn qif(v/1 d6*6srrd the 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 be about the same distance fr0m9ip 6nczd9t om us. Twozmi6cp9tn09 d 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 Schwar)r ;uz n/ur)xlg8lwq9 zschild radius for a star with mass equal to that (a) of our Sun is 8 w l9zn xr)ql);rg/uu   km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typical galaxy (like ours)? R =u/aa1 kkcj ru7)xe9p 7yz g64v    $ \times 10^{14}\ \text{m}$

Describe a triangle, dr0 i, rp/ ru(eb*hk(elrawn on the surface of a sphere, for which the sum of the angles is (a) 359º, and (b)hi( rl /e*0krub( rp,e 180°.

  What is the maximum sum-of-the-angles for a triangle on a sphere?y-*9wt(n b ptkasuzkm)w* 1c6    $^\circ$

  If a galaxy is traveling away from us at 1x.r wot0 cykr1 d*b8v1.0% of the speed of light, roughly how far awaocbyr 8 kxt01d1* rwv.y is it? v =    Mly

  The redshift of a galaxy indicates a velocity v*)d9x biox8skgc+h/yz s3/iof $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (relative to us) that is near the observable "a4,odxkkzf5b d c7*m(edge" of the universe, say 12 bibzk47d(co ,*5 m xadkfllion light-years away. v =    c

  Estimate the observed wavelength for the 656-nm line in the Balmer series ofy5ch(xo.m ss )p8sh1gyx ;*el hydrogen in the spectrum of a galaxy whose distance s*x .1cs hyy(;m 5op8h)lsgexfrom 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 distanc4 cz *lp.dbt)-s v5wy4yvi3bee from us, if the wavelength for the hydrogen line at 434 nm is measurl - zcb ye*)b5si4t.d vw4y3vped 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 -ypak2; cnif, a galaxy with $z = 0.60$? v =    c

  What would be the rems;ak;z r2 q0q ,yly.kdshift 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 wavelength iso5a *akg4z b/s $\Delta\lambda/\lambda \approx v/c$ (Eq. 33-5b) for $v \ll c$. [Hint: use the binomial expansion.]

  Calculate the wavelength at a0n( 98mqce eze/o8 6j f-pfnithe peak of the blackbody radiation distribution at 2.7 K usinz/enfna9 8-j8m(q 0i cfoeep6g Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of the (pqwliy4xn3nk /h.;jjc 5e* tuniverse 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 di.ghe-ges ;5pwc: stf- stance between galaxies) at any one moment is believed tp. g :5f sshet-gwce;-o have been inversely proportional to the 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 tblwszxzz:c / s 2s:3t.ime had the universe cooled below the threshold temperaturez3 ::sswz /. 2xsbtzcl 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-sequence stars could undergo u kf:jakh;p j( e6+t+ mdhf,0ethe three changes represented by the three arrowhukd+mj;f :6ape(j h 0e+ t,kfs, 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 tcz yq/jrzpl261u/b )mo ug9 3to us have an absolute luminosity about the same as the Sun's. Their apparent brightneso j g/9)bucrm/ y12zt6 up3lzqs, 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 angular velocit2kbq d 4jd4r2 mjy0 )6oy)hwuky of a neutron star which has collapsed to a diy4o r6byu q)d4k)kjw 220jdmhameter 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 kjv; ;z8-9tvrj 4tgdwginetic energy change when the star in Problem 56 collapse w4jtggzdj;8-;9vrt vs to a neutron star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believed to be a neutron 4k ojg 9(xmx*estar of mass 1.5 times that of the Sun, with diameter 20 km,*mk9 xogxe4j ( 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 our Galaxy is a;pimft,:5m do bout $2 \times 10^6\ \text{ly}$ 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 provide the critic+g;jjm ezrea-b)y-9o al density to close the universe. Assumejzo9 m -gj;ab-ery+ )e the 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, r m*okh 1cf/zhi: (v,krespectively, both lie on the main sequence. Use Wien's law, the Stefan-Boltzmann equation, and the H-R diagram (Fig. Below) to estimatekhh:r/mfz,(k*ov i 1c the ratio of their diameters. [Hint: see Examples 33-4 and 33-5.] $\dfrac{d_{400}}{d_{600}}$ =   

  Suppose we can measure distances wi.p*ok0094 q unjn7ji 9xn+c ji nq;gruth parallax at 100 parsecs. What is our minimum angular resolution (in degrees), bq9j; i4* njicpronqn90+7ngjuu0k.xased on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, thkgq v h1.oh001j)fsnie Balmer lines from singly ionized helium in a distant star happen to overlap with the Balmh01.oki )qf1nsjg0v her lines from hydrogen (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 coll 2r6nhty ytm.-dapd n8h-hi)9isions at the Fermilab collider? To what era in 6.yyn8tht)mrapd i nd9h-h 2-cosmological history does this correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation of gas around wh1ov dvt2.op4v at might be a supermassive black hole of about 2 billion solar masses at the cv d12 o4v.topventer 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 "blue" hydrogen line at 434 nm emittek:mwzf 9fa+i7yh4s8fd from the galaxy is measured o8z+ki a m:fhw9yff7 s4n 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 begin/u /jg k.a9il zu:d:9bmee,o p fusu9,z.o el j/ /e mkaui9bgd:p:ing carbon 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 reaction *7q,b3noi 2,no stw xo
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 criticall* y(tot:oy+k 8ri h:h density of the unive8ho :lk:*y(ti rth+yorse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$