The Milky Way was once thought to be "murky"zfq49i-djc .z or "milky" but is now considered to be made up of pointfcjidz 9zq.-4 sources. Explain.

A star is in equilibrium when it radiat.xm8c:n( atei es at its surface all the energy generated at its core. What happ( x:i .mtnae8cens when it begins to generate more energy than it radiates? Less energy? Explain.

Describe a red giant star. List some of its r*k )bzv9oce+properties.

Select a point on the H-R diagram. Mark severa/u6h4aa 5cc kbl directions away from this point. Now describe thcabc4 k/ha65u e changes that would take place in a star moving in each of these directions.

Does the H-R diagram reveal anything about the cor0 9cnjne:vcgy 89r6fte of a star?

Why do some stars end up as white dwarfs, and others as neugrlyh.25 xfhy/d. k0fy hf2u 4tron stars or black holesf2yhgrkfdf..u yy 05x2lh4h/?

  Can we tell, by looking at the population on the H,r2t tam9 a-xx-R diagram, that hotter main-sequence stars h,rt9 x-aa2tmxave shorter lives? Explain.  ----待选择----yesno 

If you were measuring star parallaxes from the Moon instead of Earth6ugo(yc8*y p o, what corrections would you have to make? What changes woul8y o*6( ycgupod occur if you were measuring parallaxes from Mars?

Cepheid variable stars change in luminosity with a typical period of sev z8ivogf zl*dcz)d9/.eral days. The period has been found to have a definite relationship with the absolute luminosity of the star. How could these stars be used to measure the distancediz*9dvgzl)o cf/ .z8 to galaxies?

What is a geodesic? What is its rol(fuf t z8*qx+ue in General Relativity?

If it were discovered that the redshift of spectral lines of galaxies was due t s86x m8sdsa6xo something other than expansion, how might our view of the universe change? Would there be conflicting evi8sxdsxs8m6a6 dence? Discuss.

  All galaxies appear to be moving away from us. Are we therefore at the center o- clxh bt(0czk6(f nn5f the unn 0cx6z h(5k n-lc(tfbiverse? Explain.  ----待选择----yesno 

If you were located in a galaxy near the boundary of our observabn00fl x.k t-o7g 9cckhle universe, would galaxies in the direction of the Milky Way appear to be approaching you or receding from you? Explain. lc9t70kofkxn.- hcg 0

Compare an explosion on Earth to the Big Bang. Consider such question+7qwk 1mvcl2ts as: Would the debris spread at a higher speed for more distant particles, as in the Big Bang? Would the declt7 2vkwq+1mbris 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 t2 j(/t+yqxyba ell if oney+ax2 y (b/jqt is there?

  What mass will give a Schwarzschild ra1q v;jz j8f. zc+acun9dius equal to that of the hydrogen atom in its groundnj1 z8vz f.ucjaq ;c+9 state? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion years. Find that time on t 8iyd2m3m -sg))hk-37wxx*s cpiorw(Fig. Below). People have lived on Earth on the order of a million years. Wherhsc-o-3si)x wygmr mpkx 7t832w i)* de is that on (Fig. Below)?

Explain what the 2.7;a : ji r0h+q9xbbfsg,-K cosmic microwave background radiation is. Where does it come from? Why is its temper:bgjqbs, 9 xf+r0ha; iature now so low?

Why were atoms, as opposed to bare nuclei, unabl8ha8i agf**ip:0i/(lsxj4 v4;weqve did , xle to exist until hundreds of thousands of years afi x v0/d 8hivjia(s4g :l,wpx8*lfee *i;qda4 ter the Big Bang?

Under what circumstances would the universe eventually collapse in on itsel bpytx az:6)/yyj s4h;a:)fegf?

  Using the definitions of the parsec and the light-yee8rtwc.all j0. /zzb6guyk k1m+.z 6ear, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.38 seconds of arc. How fa*51 it(cx frjxr away is it? d =    ly

  The parallax angle ofon)i h+1 b howotj)0e. a star is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is l-1/:xxo*+ dedu u+8)sjguc :ivupuiits 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 ankl ;; :9b l:ykohcxe5kgle 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 th6 x w.daq,codx4w 5y)6lfgakc h7th+,e parallax angle of the farther star be greater or less than that of the near6+q lcx) fcgkt,5y7 hddh6,. 4oxawawer star? By what factor?

  A star is 35 pc away.,1jbossuw3,s * :i aw*n ehrf41tv 9mp How long does it take for its light to reach us?    years

  We saw earlier (Chapter 14) that the rate energy reaches th:7cibhnqr s2- 7 no9vde Earth from the Sun (the "solar constant") is ab2n 7-drh sq9 ocbniv7:out $1.3 \times 10^3\ \text{W/m}^2$. 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 co u8:wt6bh5tauw il p2i-dl+ k;mpared to its brightness from Earth? (Jupiter is 5.2 times fart5 -w+iu8ahut 2ib 6;tplk l:dwher from the Sun than the Earth.) $\dfrac{l_{\text{Jupiter}}}{l_{\text{Earth}}}$    $ \times 10^{-2}$

  Estimate the angular width that our Galaxy would subtenb * wgpt.ozcj,)qs5y -ma7emk4jx5: i d if observed from the nearest galaxy to us (Table 33-1). Com*4.5jgpm7 bmaj,: wt-s)5 ecyq okizxpare 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 average density iv9jd) me;x1.rqwzb 7f-yewn *f it expands out to the orbit of Earth)*q d j .nx-wrzw;emvye7f 1b9 ($1.5 \times 10^{11}\ \text{m}$ from the Sun)? $\rho = $    $ \times 10^{-4}\ \text{kg/m}^3$

  When our Sun becomes a white dwa(. jfwbf m)fovyx 24x)rf, it is expected to be about the size of the Moon. What angular width will it subtend from the pr fxb)vow(2. j) xmy4ffesent distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of e;wc0 59rss0 9jgc zkx jhs5v)a white dwarf whose mass is equal to the Sun's and whose radius is equal to the Earth's. Howewz 5g0xs ; jc)0s9 rs59ckvjh 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*tq r tg69 pl6vf17aiw.5 solar masses has a radius of about 11 km. Calculate its average density and compare to that for a 1ql*arpti w f96gvt 67white 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. 3qv4n 3aow5*a:l fs).pe ak4w0wjzttypv6m:2 3-2. (The mass of the very uns oy:sv4ke2a:pw*a45 l0qw.pwan3) vmtztj6 ftable $^8\text{Be}$ 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 apparent brighx;4n j7tunef 2tness $l$ 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 qb7 vpe9)ln5j q86cpb*8syqmto be about the same distance from us. Two such stars have spectra that peak j qp9nqq758eps)lcmy86v*bb 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*x0ttdyz)mf) ziv 15t mass equal to that (a) of our Sun is *xvz5 td)0tzt y)1imf   km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typical galaxy (like ours)? R = 0/llru r 7c-ee8gryf6    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface o bxbw4 bl x: 909;m-ltcz5nzjq6eb8 exf a sphere, for which the sum of the a69mlw9 ;x:b0e-njletx8b bbzc4z qx5ngles is (a) 359º, and (b) 180°.

  What is the maximum sum-of-the-angles for a triangle on a sphpsu6m o; r2-;o ki*smkere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the speexb-tb8 3vrl 16t3cjq sd of light, roughly how far away is tbr 6lqs1tv -j8bx33cit? v =    Mly

  The redshift of a galaxy indicates a velocity o cj9-xg4cuw(we )sm+mqv hb 6/f $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a5 gibk :o:vy,.bl,ta r galaxy (relative to us) that is near the observable "edge" of the universe, say 12 billion light-years away. ,.yi:bvg:rtl,k o ab 5 v =    c

  Estimate the observed wavelength for the 656-nm line in the Balmer series of hyzo/om y*67 r3a1xbkn n4l0idkdrogen y *7r3o4ln 61z/nmxkokdi0 ba in the spectrum 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 us, 1r(d7 h ,jzzqlif the wavelength for the hydrogen line at 434 nm is measured on h7z jl,drq1(z 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 galaxy w9ke1 b;)cevwn4ke+k iith $z = 0.60$? v =    c

  What would be the redshift parameum/0 bn ve0l-tter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Doppler shift in wavelengt s zydxwwniru68l8o:/ *fuv;0 h 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 blackbody radiation distr qsjmd bjg*j;; wdm3n h4r/+-vibution at 2.4 r/wjqbmnd+djm j;v3h*;-sg7 K using Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for clowp)*t9-wvt 0a a d qc/oscrr);sure 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 galaxi9m,d4bs ;)lf9gi.g 7o gsk 3o6lbjrkg es) at any one moment is believed to have been inversely proportional to the absolute temg 7gdgkbm ior)3b 6 ls,kogl;94j.fs 9perature. 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 threshold t)r(h9.x3kdbf o ;rzq+ yggn m,emperature fb)rg 9 kgxnfqzhrmo 3,+;. (ydor 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 tht(u t/,b+wa h ajd;xj-e three changes represented by the three arrows, A, B, and C, in t-d ujba ;thxatj,+(/ whe 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 co8pd0zwz/(fuu1tsag/9 +y z luminosity about the same as dcatz/8 /9z us1+pzowg0u( fythe Sun's. Their 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 to estimate the angular velo7;v 1 9bmkv0lgc 1gfzmhdm7)tcity of a neutron star which has collapsed to a diameter of 20 km, frok d1b f 71g70mgv;l9htcvmmz)m 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 change when the star in Pro4d8px6 vmf9fi qasiqfm f+5fgqe24+( blem 56 collapvgi8f9e5 + qdq4mffxm+fp6i( sq a4f2ses to a neutron star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believed to be afg b7a fpq3for24qk4. neutron star of mass 1.5 times that of the Sun, withf4o4r3 p.ak2gbffq 7q 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 our Galaxy is about +6.0 z:d:3a1 ftnxrh(q+pxqnkze aq r$2 \times 10^6\ \text{ly}$ 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 rsp.11w6 kybjq est mass (in eV) would provide the critical density to close the universe. Assume the neutrino density is, .kbq1ps w6yj 1like 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 onud8vg 6fy+hj5b0t b 0w 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 6v5bhw +080dufg bjyt Examples 33-4 and 33-5.] $\dfrac{d_{400}}{d_{600}}$ =   

  Suppose we can measure distances with paralla(6)s73uhlvr) m15 eiexpsg uafm6cg 2x at 100 parsecs. What is our minimum angular resolute1umhavf2iep )x)g g7 sus c6r3m5l6(ion (in degrees), based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from singly ionized 7t sz,1g/w ufrdvlf;5helium in a distant star happen to overlap with the Balmer lines from hydrogen (Fig. 27-22) in the Sun. Howfg,rl/f 7vu d1w z5st; fast is the star receding from us? v =    C

  What is the temperature that corresponds to 1.8-TeV collision ibpme rywx69 k8 *v)3ftya--cs at the Fermilab collider? To what era r 9ce3 i-yvfmt)bw*6k-8xpya in cosmological history does this correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation of gas around whai xc2d3h3)z umt might be a supermassive 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- hdz3uxm3i) 2cyears, 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 xrmtag3. x3daa1wd5z-i *o +pat 434 nm emitted from the galaxy is measd z*3w1 agxdimt+ ap a-xo5r3.ured 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 evfh 4 yb qvv+7dt fwy/1,-voh.bolution, a star (if massive enough) will begin fusing carbon nuclei to form, for example, magnesium: 1 4b/. vft,yfoqh7vvwhyb+d -
$^12\text{C} + ^12\text{C} \to ^{24}\text{Mg} + \gamma$.
(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 reactionar2ynv sce7tjva ;4 un7 iu/(/
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 den9r5w3kx :8xkzeoh ukd3lrm5 9sity of the universe,k8 5eo9hm3rk95k w z:u3 dlxrx $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$