The Milky Way was once thought to be "murky" or "milky" but is now considd 7t-ha -gh9twered to be made up of point sour - -tghh7dw9atces. Explain.

A star is in equilibrium when it radiates at its surface al-ivvl7 t+kn * ,p8fj8fjfhs:hl the energy generated at its core. What happens when it beg8 ij,:j*h -fvln fp kfv+7sh8tins to generate more energy than it radiates? Less energy? Explain.

Describe a red giant star. List some of its ur9);o:ya*wtas:d gdil4/p dproperties.

Select a point on the H-R diagram. Mark several di6o p f,n*:vsn )vrvw*arections away from this point. No)nw: *vponsavv,fr*6w describe the changes that would take place in a star moving in each of these directions.

Does the H-R diagram reveal anything about the core of a star? evw2iwco/v2+

Why do some stars end up as white dwarfs, and others as neutron stars o8kybhbg1 ygu s833n6gr black holes?gh1bb3n3 ky6 ugy8sg8

  Can we tell, by looking aaisf;twq:4;6 *r or plt the population on the H-R diagram, that hotter main-sequence stars have shorter lives? 4*la6q; oirp ts:;wf rExplain.  ----待选择----yesno 

If you were measuring star parallaxes from the Moon instead of w b4*2 5gcskljohq:9 by01s ci6pbx5 yEarth, what corrections would you have to make? What changes would occc6 2*j5byw9bp s5: ko1b4yqshcg0ilx ur if you were measuring parallaxes from Mars?

Cepheid variable stars change in luminosntt 9 uwhwr4o651vx r;ity with a typical period of several days. The period has been found to have a definite relationship with the rnwt w;h6o1trvx9 u54absolute 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 General Relak qe,7b ; 75c2vbugy vdd(iwu1tivity?

If it were discovered that the redshift of spectral lines of galaxies was due tlaw.zml y30( 0 z45wmssiam38n/ke g mo something other than expansion, how might our view of the universe change? Would there5lk.i ne3 zaw8a w/s(4s ymm 03gmmz0l be conflicting evidence? Discuss.

  All galaxies appear to be moving away from us. Are we therefore at the centectgets60 i16 xrc9e3w; rnaa; r of the universe? Explain. 6 g3r0 enx;16ctws9 teraa ;ic ----待选择----yesno 

If you were located in a galaxy near the boundary oa7. ut2lt5du ik2nyd )f our observable universe, would galaxies in the directiont2ud n).2ty 5 kilaud7 of the Milky Way appear to be approaching you or receding from you? Explain.

Compare an explosion on Eaz:tuah 6j l2p4rth to the Big Bang. Consider such questions as: Would the debris spread at a higher speed for more distant particl26 4phazlu :jtes, as in the Big 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 hole, then how can we tellwb)t .8 rv9b1rj81nhns0o c vy if one iw)rs0b8 rh89.onb vvjt1ny1c s there?

  What mass will give a Schwarzschild radius equal to that 69v)tc b12rpmuqfx )w of the hydrogen atom in its ground state? M =69vp)2 b cu wmrxtq1)f    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion years. Find that time on (( q.6m iazlvhy**+xhpFig. By (hh6*xiz+ pvqm *al.elow). People have lived on Earth on the order of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosm7gdi kg.tn 5jf/9 av)cic microwave background radiation is. Where does it come from? Why is its temperat9 /fdavin)gcjk5g7.t ure now so low?

Why were atoms, as opposed to bare nuclei, unable to exyzodwunj.0 8+ ist until hundreds of thousands of years after the Big Bang?.o u0wd jyn+8z

Under what circumstances would the universe eventua3r;mz-rph ;oec m +sudsl* 2e;lly collapse in on itself?

  Using the definitions of the parsec and the light-year, wob4: so2qrtk; 1t vrr2t+g)hshow 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? db(( bzs jxw+b. =    ly

  The parallax angle oc+7)j w94(vbj6m sl hay-lfhyf a star is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is gb6 lom5n5xs-i(lzv5qr 5mez* oi-a- 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 stdgf657xj gf5o3wt+vgd w( v-n ar 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 ytqy) dc bky8t5z,(w//h5/hjo/xcao second star, will the parallax angle of the farther star be greater or less //ot(j)y5o 8c h yh zkcd/ x5abqt/w,ythan that of the nearer star? By what factor?

  A star is 35 pc away. How long does it ta07 5wcar/ nm6bn/:+skje cznxke for its light to reach us?    years

  We saw earlier (Chapter 14) that the rate 0dzh:w5 d im*rr7 vvb+energy reaches the Earth from the Sun (the "solar*v :mw5i0dzrr bv7h +d constant") 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 k tk;zl+6d7umqm9(e s the Sun as seen from Jupiter as compared to its brightness from Earth? (Jupiter is 5.2 tiezlqs9;u(+mtk7d km6mes 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 observedo5lh gq+n381 fhftvo9zo f;+ z from the nearest galaxy to us (Table 33-1). Compare to the angular width of th;1+zftng oq5f hhl 9o+3f 8zove Moon from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, r2mg0z(j1ncmo ,60yhp ng9uc what will be its average density if it expands out to thz h9pjcgcno m,u6r0 2(mgn1y0e 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 the size yb 0z+ais8ke,of the Moon. What angular width will it subtend from the present distancz8y,iasb 0+ek e to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whose masj44mn;1j wcw xrnnrq,+r ip35s is equal to the Sun's and whose radius is equal to the Ear jm1 j4rq,nr i3+4 cnpw5x;wnrth'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 hmq*cpg;c4 g2 cas a radius of about 11 km. Calculate its aver qpcc2 *4c;mggage density and compare to that for a 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 burningj7 gy* 6m* b3v2von dwmi7 :o9ltqx/io reactions of Eq. 33-2. (The mass of the very unstablt/o vm 2 *my7vgni 7wq9j*ox:idl3o 6be $^8\text{Be}$ 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 th/w4rj i ck-6le o),,0 yiknvtle 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 clus hvxt z;w s,+60m/+ /aeuecyf5a5u nutter are assumed to be about the same distance from us. Two such stars have spectrauyh/c fxau5+ e,tun6mze+;v0sw ta5/ 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 c 0akcwc,,+uh (a) of our Sun uch+0, ckacw, is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typical galaxy (like tcsle)2/ auf8ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, draw;;n rkbvm5-j/,6dc9d d oach zn on the surface of a sphere, for which the sum of the angles is (a) 359º, j5vo m;,6dz kbrn/d;9h cacd-and (b) 180°.

  What is the maximum sum-of-the-angles for a triangle on a sphum0 h8o m-) cn9hz6:7h inuqydere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the speed of lightzgm ix1mx 72y*y9po1i , roughly how far away ismz 71o x x2ygimi*9p1y it? v =    Mly

  The redshift of a galaxmz d f40ng87bmome(fx/ck6 c3y indicates a velocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galayt b q9r,:z zgst/ as+,udr+h:xy (relative to us) that is near the observable "edge" of the universe, say 12 billion light-years away. v = sa/+r9zr gttu:sh,+bz , : dyq   c

  Estimate the observed wavelength for the 656-nm line in theaw z.ol0 u6 a, 9-5/fckvkgbls Balmer series of hydrogen in the spectrum of a galaxy whose distance from usc/-a g0zf.ul wobk9 ,56kal sv 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 us, if the ruyaseamh .ycn u 2alfm6s:cq4e ,3b93),yu9wavelength for the hydrogen ma s) enes,ybu9a 26lcf 3:3hra q,uymcu4.y 9line at 434 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 a galaxh00)t)fda re cy with $z = 0.60$? v =    c

  What would be the redshift pa/ 5q5 keo 15cjajr6cjdrameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, r xpd b3y-l4 ;l6 k1i44cjibylshow that the Doppler shift 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 peakgyye9a fbfk.wzla y wt.6c9,:w463ml of the blackbody radiation distribution at 2.7 K using Wien.693llefg:a c6.t4w,k9m yyywbza fw’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density zjp3pg2- w 3 ,z7dmplwfor 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 univers sgvo/hex3945k,a cnye (the average distance between galaxies) at any one moment is believed to have been inversely proportional to the absolute temper3xagn9o ,5hve/ 4kys cature. 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 t,l ) /uz)tp .ruc-gwb-igt5g che threshold temperature for prodwg)-cgrtu5 ,u)cig- tz/.p bl ucing
(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 thpb 17p qlow-he6 w03ckree changes represented by the three arrows, A, B, and C, in the H-R diagram of Fig. 33-28. For each case, describe thew6h7 p-kwboc 031 peql changes in temperature, luminosity, and size.

  Assume that the nearest stars to us have an absolute luminou s6*8 c9j wz/ervxg2tsity about the same as the Sun's. Their as wc j/6gx9ue*8zt vr2pparent 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 t7vgvybzet(;pazf b+;n+7o 8d he angular velocity of a neutron star which has collapsed to a ddf; e77+ybz+; bn8(vtzov pga iameter 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 kinetj teeax/dmyo2p1-l 89ic energy change when the star in Problem 19y/8ojexp-mla de2 t56 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 of mass 1.5 timt7s k6 ij6jn;tes that of the Sun, with diameter 20 km, is ;k s6i7tnjj6tobserved 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 galohlu cc c j1ra(02.-yzaxy to our 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) cr;r4hf*k9otb 2bq3 jwould provide the critical density to close the universe. Assume the neutrino density is, like photons, about c4;q *h9kbfjto r2r3b $10^9$ 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, o/ 5ji.dad l7crespectively, both lie on the 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 5/7dcila j. do33-4 and 33-5.] $\dfrac{d_{400}}{d_{600}}$ =   

  Suppose we can measure distances with parallax at 100 parsecs. What is ou )rt -jh yll8tb8pwo*ai1l+mfrh1. j2r minimum angular resolution (in d1.w f*l h2m)lri18jj +a8ht-yopt lb regrees), based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from sinmllc9 k-3o/x,k 2 /kcn fjtx9ugly ionized helium in a distant star happen to overlap with the Balmer lines from hydrogen (k 9-cu9k/kf/o,j2lnl xxtmc3Fig. 27-22) in the Sun. How fast is the star receding from us? v =    C

  What is the temperature that correspon m6cf7z r+u;r n3v*g,ur 6ukowds to 1.8-TeV collisions at the Fermilab collider? To what era in cosmological hisw6m73 ru,ro*gn+fu zuc6;vrktory does this correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the ro ld ;b;w4be8nftation of gas around what might be a supermassive black hole of about 2 billion solar masses at the center of8d4bl ; w;benf 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" hydroxs4i/)lsu 0s :yvqr )mgen line at 434 nm emitted fr0)mil:vuss4q rs x)/yom 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 evol) :1odvoqkri(ution, a star (if massive enough) will begin fusing carbon nuclei to form, fod q1 o)(koirv:r 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 reaction1aj+yo(kcncv*e i(7t
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 densit 8k3tkoas.+horp9wa eq ;zv y8wt;.y,y equaled the critical density of the universe, w+a;9.ro ysak .v3tk 8zy8;phtw q,eo$\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$