The Milky Way was once thought to be "murky" or "miepe a704bs zo7lky" but is now considered to be made pee074 ozsab7 up of point sources. Explain.

A star is in equilibrium when it radiai+ d cgnnxpttbknq0/ i1j5 9,1tes at its surface all the energy generated at its core. What happens when it begins to generate mordn1 05kig/xj tn9q1b+tpinc, e energy than it radiates? Less energy? Explain.

Describe a red giant sta 8defyr+*vj e3fumwbha0..0xu s::dw r. List some of its properties.

Select a point on thex jot9p9qrm. 1- hg g/tu+pa+w H-R diagram. Mark several directions away from this point. Now describe the changes that would take place in a star moving in each of these dirmp/9p a-xqgu hgrt+ + otw9.j1ections.

Does the H-R diagram reveal anything about the 3wi ) kcl 7:p8 6ggh0os/pbnqtcore of a star?

Why do some stars end up as white dwarfsbhh l mhld 8nav:v3:zk313rt+, and others as neutron stars or black hol::dhv mah8l+hv3z1l 3n3 krtbes?

  Can we tell, by looking at the population on the H-R diagram, tha7ivf7(hr sdn4m 9ag7b wys.n 3t hotter main-ses(d.n 39 w7yn r4i 7a7ghmfvsbquence stars have shorter lives? Explain.  ----待选择----yesno 

If you were measuring star paral )cneb3/ 7y2wz -lwhizlaxes from the Moon instead of Earth, what correction/ ncz7 2w ibzewy-lh)3s would you have to make? What changes would occur if you were measuring parallaxes from Mars?

Cepheid variable stars change,h 7zw l2lr4spqf-.rc in luminosity with a typical period of several days. The period has been found to7 pf,. qw2rscl4rhlz- have a definite relationship with the absolute 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 Generzpf9embltps )17 j3j*03 buai al Relativity?

If it were discovered that the redshift ofme3 : 2(nc5ua*chfs ob spectral lines of galaxies was due to something other than expansion, how might our view of the universe change? Would there u nacm3:ecf( 52*osb hbe conflicting evidence? Discuss.

  All galaxies appear to be moving away from us. Are we therefore at the ce 9l txdwqy/ ml4r5bi :b1z0f3ynter of the universezl5qirfbd y mlxw:yb0413 /t9 ? Explain.  ----待选择----yesno 

If you were located in a galaxy11-/wih wqzdpr54 dhr near the boundary of our observable universe, would galaxies in the direction of thwqd1zrp h h4ird5- w/1e Milky Way appear to be approaching you or receding from you? Explain.

Compare an explosion on Earn:8( y9zf.bymsq qyl8th to the Big Bang. Consider such questions as: Would the debris spread at a higher speed for more distant particles, as in the Big Bang? Would the debris zlnmyy s q8b y:9.(qf8come 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 tw9;9 vc5fwo aybtfc2yyrv9(tm4 0:un ell if one is tha99w0ub cv9(cw:v; fn frmty24ty5oy ere?

  What mass will give a Schwarzschild radius equal to that of the rk6i1vkcrwnmy.f1/ );gar0fjf*j9 rhydrogen atom in itsv* r0yjnfk) fr.fijar /6kcrw1g ;91m ground state? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion years. Find that timd2bvy80k . o(j0gph yke on (Fig. Below)..80okbjhkdyyv (p20 g People have lived on Earth on the order of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cg a:wmsizpft45wh 85 7osmic microwave background radiation is. Where does it come from? Why i7 is zwt5p5h4w8am: fgs its temperature now so low?

Why were atoms, as oppos r*d:ywz3,iiab83 p fhed to bare nuclei, unable to exist until hundreds of thod38f3bz yaihpi r,w*:usands of years after the Big Bang?

Under what circumstan +h;ztmiu2v +vces would the universe eventually collapse in on itself?

  Using the definitions of tltzdieob0)x, k 21re*he parsec and the light-year, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.38 seconds of arc. How mt ui6nw3 w+9sfar away is it? d =    ly

  The parallax angle of a sta 8( b(*go,c)tva riv5dxyns; br is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its parallax angle 6745ldwic yk 6kpdn4qu-n)dkm. nf o2 77rure?
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 awinfom/cln im65 1/hf2 ay? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away from us as a second star, will tpnfhx * 1jfhw25s:ho(nh 9 ;ih5l0 bwdhe parallax angle of the farther star be greater or less than that of the nearer star? By what factor29i *(l w5bf5ohjs; 1fhn:h0hnhwpxd?

  A star is 35 pc away. Hmm x./8gm/w99ziy fusl ce) .qow long does it take for its light to reach us?    years

  We saw earlier (Chapter 14) that the rate energy reaches the Earth fr(y-/: xhnmk1: pms,j68glceg czbh5 uom the Sun (the "solar constant" (g ,:6cp5l-xumb8z/js 1gh :mcenyhk) 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 o weya tw(jr4gm5 3 0jg.rtr0wd,yz4-bf the Sun as seen from Jupiter as compared to its brightness from Earth? (Jupiter is 5.2 times farther from the Sun than the Eawyzw,dm( 43 .gw4yt -rrj0gr bj5et a0rth.) $\dfrac{l_{\text{Jupiter}}}{l_{\text{Earth}}}$    $ \times 10^{-2}$

  Estimate the angular width that our Galaxy would subtend if observed f04iiy+s sdef5d;r ) gurom the nearest galaxy to us (Table 33-1). Compare to the angula ds4+gr ify); e0sdui5r width of the Moon from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, what will be i3ns t8zmgx8 *nts average density if it expands out to tz 8sngnx8 3tm*he orbit of Earth ($1.5 \times 10^{11}\ \text{m}$ from the Sun)? $\rho = $    $ \times 10^{-4}\ \text{kg/m}^3$

  When our Sun becomesg0w7smun5 p*i a white dwarf, it is expected to be about the size of the Moon. What angular width will it subtend from the pg5i0swupm n7*resent distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whose mass is equal to the Sun's and ww y1zh;hhfvfv5 b*f9n2w xvbe):h.f7hose radius is equal to the Earth's. How many times larger than Ear7vb5):e xhv 2z;v9f wf* h1 .wyhfhbnfth'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 has a radiu) p+)fcnz qcv( k(w1moonl38as of about 11 km. Calculate its a1o)w vm8a3 + )coqpk((lnfczn verage 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 burpxdnc-: 7jd( u6t+hhtning reactions of Eq. 33-2. (The mass of the 6h(nuhxcdt 7+:djtp- 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 the same apparef( 3do j4aqbo1z,o f,pnt 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 clu;o0jjbd7 p3. n5ccardsfq f/ 6ster are assumed to be about the same distance from0dj;df36crnpbf s q oc .5a7j/ us. Two 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 our2dk0-2 8f .rs h ,1wbf2 bure6aqlwhou Su s f,fbwe 8k2l uoa2- u1h2drh6wrbq0.n is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a xhjnl3grn q1 0.oob (5typical galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of5gze*dx8 1tkl a sphere, for which the sum of the angles is (a) 359º, and (b) 11 8xezt 5gdlk*80°.

  What is the maximum sum-of-the-angles fo*z*vt+d a-o fvr a triangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the speeda6xh awep:45c(0 v pa6fh 2bjk of light, roughly how far away is itaa pvp h 4bwkj66 :05hxc(fa2e? v =    Mly

  The redshift of a galaxy indicaocs.0qg u4j4 nwb2*r ctes a velocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (relative to us) that is near the observabl : ddp-s1+db-( tkpncqe "edge n1qpdk:-bdpcd +ts-( " of the universe, say 12 billion light-years away. v =    c

  Estimate the observed wavelength for t;p9 pvb sama-*lem8/ahe 656-nm line in the Balmer series of hydrogen in the spectrum of a galaxy whose disb pa/v89e*aam lm;-pstance 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, y0 e6dsew 0+xrand its distance from us, if the wavelength for the hydrogen line at 434 nm is 0y ew 6+0exrsdmeasured 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 +h:4f7m)xveuxsri . oa galaxy with $z = 0.60$? v =    c

  What would be the redshift parabj7 3tg; 7kt-eh. wetkmeter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Doppler shift in wavelenh(-w lb8 siqc1:gi x:rgth is $\Delta\lambda/\lambda \approx v/c$ (Eq. 33-5b) for $v \ll c$. [Hint: use the binomial expansion.]

  Calculate the wavelenc 9v) mxm(57iyh0uhpogth at the peak of the blackbody radiation distribution at 2.7 K using Wien’chmioup v7 590y(h)mx s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of the9dr6tokqr27gr5bc )o 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 galaxiealp:t ,(r) pee 6:pyxzluev.0s) at any one moment is believed to have been inversely proltrl(ee0y:x p6:,)zp u ev.apportional 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 time had the universe cooled below ltka)+y-m nau * ynf3,z*.mq ythe threshold temperature for produci m,**ml3.) a-ta+yyyqn zun fkng
(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 th h) jz)( /szqc:n7tr w*cr)ouux;*jc hree changes represented by the three arrows, A, B, and C, in the H-R duxj cnu)**hjw:oz r s7)t /c )c;(qhrziagram 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 luminosity abs e/ (6sn(8rd5e7s acgr sce3dout the same as the Sun's. Thenr (s8se35ea6(resdcd 7/ sc gir 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 veloci9w: m wir,c:/cfbebtz gz+dl2v7 1c2oty of a neutron star which has collapsed to a diameter of 20 km, from a star whose radius :wrdctc mi+9cv ,2/ egf 1z z:2lbbwo7was 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 th9e +zxsn oy;y.e rotational kinetic energy change when the star in Problem 56 collapses to a neutrony;nz9os+yx .e star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believed to be a neutron stark -;*;s ru-5hcdykavg of mass 1.5 times that of the Sun, with diameter 20 km, is observed to have a rotation spee sv;k5-;chudg-a *ykr d 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 Gala .fkz5 t:fs/grxy 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 uw y0yih-. t)or-z+fr .gftj2 eV) would provide the critical density to close tutrf--+rhzj.wg i2 0 .fytoy)he universe. Assume 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 2ihc6 gt0fkc)u bpf), 0rp ua+peak at 600 nm and 400 nm, respectively, 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 33-4aifbuk )2cr0th6c0)gp +uf, p and 33-5.] $\dfrac{d_{400}}{d_{600}}$ =   

  Suppose we can measure distances with paralla 6pr+xvx +mskj i 42y+lz6qc;yx at 100 parsecs. What is our minimum angular resolution (in degree6p + yqicvl+sx +;4m zxjk26yrs), based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines fro rx36t8xrr x d65qp.nom singly ionized helium in a distant star happen to overlap with the Balmer lines from hydrogen (Fig. 27-22) in the Sun. How fast is the sn6 xptd x5xo38.q6 rrrtar receding from us? v =    C

  What is the temperature that c8-xua.ea5 t/ eimm*0 vo.hfytorresponds to 1.8-TeV collisions at the Fermilab collider? To what era in cosmological history does thisu a.*hm e0-efa m .itvt8y/5xo correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently m5aff9p//cqw ceasured 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 to the gas cfwc / 9cqa/pf5louds 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. T9.9rra5j mrv zhe "blue" hydrogen line at 434 nm emitted from the galaxy is measured on Earth tm9zvrrr aj. 95o 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 ykmz 1k54c3opn, a star (if massive enough) will begin fusing carbon n4z okcmyp31 5kuclei 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 ;skfxkh/jv vr5 iz0 na-0;u: w
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 Sv+q,m;t(ks /ilvb (dzun be if its density equaled the critical density of the universed+v /,ti( bmv ;z(kslq, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$