The Milky Way was onths he8b3,s 8dce thought to be "murky" or "milky" but is now considered to be made up of point sources. Explain8d thhs8s3,eb .

A star is in equilibrium when it radiates at its surfamf)ctx 5ee62guq)u c8ce all the energy generated at its core. What happens when it begins tcf6g58 tuqx))uec2m eo generate more energy than it radiates? Less energy? Explain.

Describe a red giant star. List some of9v9e f;waggcz vff7u/7+v *na its properties.

Select a point on the H-R diagram. Mox9c;1 nht)b uark several directions away from this point. Now describe the changes thxnut;)1b c9h oat would take place in a star moving in each of these directions.

Does the H-R diagram reveal anything about the core of7 a6aqs9zp- pu a star?

Why do some stars end up as white dwarfs, and others as neutron stanwdcy7 u 63.r*lsoo h8rs or black holecl6 d wrnuoy3 7*.sho8s?

  Can we tell, by looking at the population on the H-R diagram, that hotter main-s5:wm e)dmoi1qsu z rj+ hb:l*7equence1us 7:zoqrh imjwml b:d5* )+e stars have shorter lives? Explain.  ----待选择----yesno 

If you were measuring star pa /0i):kwwqx nzhq*q 1erallaxes from the Moon instead of Earth, what corrections would you have i) /q nq*hkq: exw1w0zto make? What changes would occur if you were measuring parallaxes from Mars?

Cepheid variable star5c2 x d2tvhmj2s change in luminosity with a typical period of several days. The period has been found to have a definite relationship with d52hcv2mxt2 jthe absolute luminosity of the star. How could these stars be used to measure the distance to galaxies?

What is a geodesic? What h*8*htz8mz1 szpnda; is its role in General Relativity?

If it were discovered that the redshiftsf ja+(/nfj5v of spectral lines of galaxies was due to something ojaj+ f5v/fs(n ther than expansion, 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 the 9yh ( -t(jga7t2n1qvc6cgjsa center of tc aa2(v(qchg 7y nj6g 1t-j9sthe universe? Explain.  ----待选择----yesno 

If you were located in a galaxy near the boundary of our oo ( p54ws51ra xq(x)cd*rtnrxbservable universe, would galaxies in the direction 14w5 s(qnxx(dro5 prt)xr a* cof the Milky Way appear to be approaching you or receding from you? Explain.

Compare an explosion on Earth to the Big Bang. Consider such questions qvvo,1e( 29ktcw1i1 h kwo:thas: Would the debris spread at a higher speed for more distant particles, as ic1kw vhhtt9,e:o1w(q vk21 i on the Big Bang? Would the debris come to rest? What type of universe would this correspond to, open or closed?

If nothing, not even lightf vbv-/ :-rvu0rbyel 1, escapes from a black hole, then how can we tell if one is th-0 - 1v vbyreb:u/frvlere?

  What mass will give a Schwarzschild radius equal to that of th4tuh6v y, sd-ve hydrogen atom in its svdut, -vy6h4ground state? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given ajbmp*3w hr 7-cm;q g7rs about 4 billion years. Find that time on (Fig. Below). People have lived on Earth on the order gj-*mp rm;cbwhq377rof a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic microwave backgroun-f6n5kba c ab6h*ehwti+o ) m(d radiation is. Where does it come from? Why icfehhan 5(*bw+t o6i a)b-km 6s its temperature now so low?

Why were atoms, as opposed to bare nuc jq8 3-dvh,)dff9ku gzlei, unable to exist until hundreds of thousands of years after the Big B jf,kfz-8g vd3)9hq duang?

Under what circumstances would the universe eventually colluv)veqd f uq/*kg3/t)apse in on itself?

  Using the definitions of the parsec and the light-yeab:sso;;k-o fa9 jjtq 9f+q;d vr, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax 4.ajgi+ hnwf 5of 0.38 seconds of arc. How far away is it? d =    ly

  The parallax angle of a v zdmk8hkijkwr e6,72v, 4k ; ;azs)enstar is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its u8 uvnn gy8u2o3ta-+jparallax 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 star that is 55 ly away?si9vyd -:i a9z $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away from us as a second stadnx+y ub*(/ hogvvpi 35s,re s96lel(r, will the parallax angle of the farther star be greater or linovess* euhxl+g ((,95 / 6dyl3pb rvess than that of the nearer star? By what factor?

  A star is 35 pc away. wv8 ke7m:).eaw, pr7ze 7fapoq;m d:jd0*mjs How long does it take for its light to reach us?    years

  We saw earlier (Chapter 14) yprz94/df w f5that the rate energy reaches the Earth from the Sun (the/9pd zr5fywf4 "solar 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 the Sun as seen ffzeg 9arfr54:/(a ncmrom Jupiter as compared to its brightness from Earth? (rme(5ffcr/g4n9az:a 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 from the n2f:vpu )q(k nq.ma2h rearest galaxy to us (Table 33-1). Compare to the angular width of the Moon from 2qu (:vmnafr.)2pkq h Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, what will be its average densit) bdldi.h w3he+ 7hzu5y if it expands out to the orbit of Ealh)z.5e3w 7 hh+u biddrth ($1.5 \times 10^{11}\ \text{m}$ from the Sun)? $\rho = $    $ \times 10^{-4}\ \text{kg/m}^3$

  When our Sun becomes a white dwarf, it is expe 4 :rkcb2(0fqmue;ykw,abn . g4yz2rl cted to be about the size of the Moon. What angular width will it subtend from the present distance (m fk:2 4 wcr0bqyakg zbey;2l4,rn. uto Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whose mass u 7mm+lkru k3q6 q,kzy :j67cql5m4zois equal to the Sun's and whose radius is equal to the Earth's. How mak:+rulj uzmky5qq, 6c6z 7q7l mo4k3m ny 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 ham+ycdfk5( z 4f3p m3cis a radius of about 11 km. Calculate its average density and compare to that for a white dwarf (Problem 13) and to that of nuclear matter. ki f3c m5cpm+3d4zy(f
$\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 fo6o3vnd e+3 - fyhf7wser the He burning reactions of Eq. 33-2. (The mass of th3w7dfyv fon6 +hes e-3e very unstable $^8\text{Be}$ 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 ta4v w-rei5o 6ghe 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 ass f*c-s.zzo fq2mg 90teumed to be about the same distance from us. Two such stars have 9f-f. msoz0gq2t*c zespectra 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 l1g 64kvustw8 with mass equal to that (a) of our Sg86wt1u 4v sklun is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radiuswnw3 ads15u 7j4h9xnh for 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 the nycl+.;lk4;jqdp/24te f.vt;ds fjn angles is (a) 359º, and n/.;ljkv d f2p4dttyq 4;;cfnjs.l e+(b) 180°.

  What is the maximum sum-of-the-angl1exnci -6fwag (/ ycei))qpb7 es for a triangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1bo1d+o.d5a 6rttx5x h/uhb ax.b)n 4o.0% of the speed of light, roughly how far away is it? v =b5.t6ht5obn.hau x+4x ax1) rd /bodo    Mly

  The redshift of a galaxy ijqz uf+lwq)lhe-mm . ;49mkh, ndicates a velocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (relativ 4sdylz)16flee to us) that is near the observable "edge" of the universe, say 12 billio4ld yz)1e6sfln light-years away. v =    c

  Estimate the observed wavelength for the 656-nm ytmt--g+uj9rz (v 1fgline in the Balmer series of hydrogen in the spectrum of a galaxy whose distance +grj fu tg--mv (9tz1yfrom 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, if the wavew4dmi)yh5duekf(1 l7hct,4yi ,;u ovlength for the hduh1v wmy)o ie,y4c4d;uhf t 75kil,( ydrogen line 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 oemr b0+ d+i8bdjm ,7nzth5;ou k2lk 3galaxy with $z = 0.60$? v =    c

  What would be the redshiftp) uyb1wour2;au;w6 o j*5uevf qy g.: parameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show nmz,a rdbzkk::n;2 o6that 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 waveleur; gy:w*q q9e bjt:wtj e5..pngth at the peak of the blackbody radiation distribution at 2.7 K using Wien’s law. ue ;9.gwtq5 prjy bt.e w:*:jq$\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closur5p 8u1kfapj -kg ds:w:e 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 dista)uo 55hxj)px e1edd4q (rb5(ihmk.h ance between galaxies) at any one moment is believed to have been inversely proportional to the abso.bhee5ohpj(5 d5x 4k ad)mi)q( h1urxlute 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 cooled below thejc e4brsl(e8q-9j c7 l threshold temperature for producjber4 lcs- (9q8 clej7ing
(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-y7.46wabte exf hx -;esequence stars could undergo the three changes represented by the three arrows, A, B, and C, in the H-R diagram6e bhxexf7yea . -4w;t of Fig. 33-28. For each case, describe the changes in temperature, luminosity, and size.

  Assume that the nearest stars to us haveo ft7n,8fsoe9 an absolute luminosity about the same as the Sun's. Their apparent brightness, however, is about oe o8ff9s,n7t $10^{-11}$ 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 argc4;o: n(h-*dd hxbj ngular velocity of a neutron star which has collapsed to a diameter of 20 km, from a star whose radius was;*xdjr n(cg-d hb:4ho 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 enefu6hkhv9*+) hw0u t tprgy change when the star in Problem 56 collapses t+hp9*uu6hkt) wfh0vto 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 times that o6+yz0;cfmgr k f the Sun, with diameter 20 km, is obsr f0kmc+g ;6zyerved 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 8-x yv+yza9jnkz3 er+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 d;li plg9kv*h/a qp /n;h45vm mass (in eV) would provide the critical density to close the universe. Assume the neutrino density is, like photons, abo;vlp*a/vn;l g9q 45k hdih/m put $10^9$ 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 an(xmi u27a:ksfmzzngy7 z d2o8./ 5kqmd 400 nm, respectively, both lie on the main sequeni/mkado 7(2mf8z2:xk. zz7q 5nmu g syce. 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 33-4 and 33-5.] $\dfrac{d_{400}}{d_{600}}$ =   

  Suppose we can measure distances with parallax at 100 parsecs. What is 2bgef:/ vwmm8. thol 3dfi: q 4/ud,sjour minimum angular resolution (in degrees), based on thi:tf/mo32/vmhu .desjd 4,q:w8l gb fi s information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from singly ionized helium in a disaba 9sjl4yzpzw wh,37 2t*u4qtant star happen to overlap with the Ba w43*hq79bz lzawj a2y,pst4ulmer 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 collxrqg8 +dlaf:ittke,r:y +5/e sz5y7 kisions at the Fermilab collider? To what era in cosmo :5r qksa: + r y8tede+xl7igzty/,f5klogical history does this correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measure 8 1j3hop0gx r53maudkd the rotation of gas around what 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 top kdu8om33rg5jx1ha 0 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 nmh mx0ao565 fbip -hhc. emitted from the galaxy is meas0 5p o.mih-f5hc6xbh aured 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 evolutio,i.amioat+lel, 4 3 svn, a star (if massive enough) will begin fusing carbon nuclei to form, for examp,s+la vie4a3.tio, mlle, 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 l)) mjjinc)*r
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 equa0 h+l/js ,aao xgztbl(s m/y0-led the critical density of the universm,-ba/0ha lgxtoj /yzl s(0s+ e, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$