The Milky Way was once thought to be "murky" or "milky" but is now consi-mmq p+w3w r,udered to bp,r+wwm u3mq -e made up of point sources. Explain.

A star is in equilibrium when it radiates at its su.m8yi2a439 sjsvgsz mrface all the energy generated at its core. What happens when it begins to generate more energy than it radiates? Less s2ygm89 34 mzs i.avsjenergy? Explain.

Describe a red giant star. List some of its.fv/ -oem59jr *fcex/hr thi, properties.

Select a point on the H-R diagram. Mark several directions ym3ny ,6s sy(faway from this point.n ,s6 mfyysy3( Now 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 .kby44isnmx ++11dbx fan: w1.cndlm: v -w tastar?

Why do some stars end up as white dwarfs, and others as neutron stars o6tz nap 0w1 y-5qp3qvrtl.ii-r black holeqzyvp1-l w0q 6 rttp35i .-anis?

  Can we tell, by looking at the population on the H-R diagram, -fzk3zqe/z8wsw3hc 7 that hotter main-sequence stars have shorter lives? /wk f73z-q sezz 83chwExplain.  ----待选择----yesno 

If you were measuring star parallaxes from the Moon instead of Earth, what c-hx39ldhp7zb -kaj* xw:s, ot. v dtw8orrections would you have to make? What changes would occur if you were measuring parallaxes frompzhkw-t ov wx -9hjx d.sl dt8*,3a:7b Mars?

Cepheid variable stars change in lumr1jc):/ 9tjqxu-ndr ;ixtx(znb j 1j (inosity with a typical period of several 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 z rxj/ni(j bc:(;) j9qntt1-r1uxdxj measure the distance to galaxies?

What is a geodesic? What is its role in General Relativit1yw fz p5q y4* -.vmgeiiix,4qy?

If it were discovered that the redshift of spmk:2:h n;a5 s/vkcwc lectral lines of galaxies was due to something other than expansion, how might our view of the universe change? Would there be confli;:5m w sk:kn/2lcc havcting evidence? Discuss.

  All galaxies appear to be moving away from us. Are we therefore at the cjmeu+y)m-8) ac dc ,jbenter of tm,ud j+cc ja -)e)ym8bhe universe? Explain.  ----待选择----yesno 

If you were located in a galaxy ne*kr( pb.i2um(azvdh(4 d 8qtlar the boundary of our observable universe, would galaxies in the direction of the Milky Way appear tu*zdq hbt.kimd(l2a4v 8p((r o be approaching you or receding from you? Explain.

Compare an explosion on Earth to the Big Bang. Consider such quesxxx36jggi9 k 2tions as: Would the debris spread at a higher speed for more distant particles, as in the Big Bang? Would the debris come to resi xjg6 xg29kx3t? What type of universe would this correspond to, open or closed?

If nothing, not even light, escapes f 7 sqk( dogvj +d)3x6g qw0guxe4pfu(;rom a black hole, then how can we tell if one is twkg73 )0+uog q f; xx6 d4qjgdsvu(p(ehere?

  What mass will give a Schwarzschild radius equal to that of the hydrogen atom g a:1 7y;ic pek3 h qhuj6*th5/5mqoapin its ground statqcpa:h* hpig7u55 h a j/6qok1 ty;m3ee? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion yeav:fxs2 m-ps-rrs. Find that time on (Fig. Below). People have lived-spmv-rfs x2: on Earth on the order of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic microwave background radiation is. Where does it3q9 /ul 3hxyye08q8ed)jrqhq com9x q3eqy3yd)r/8uhq lq80jehe from? Why is its temperature now so low?

Why were atoms, as opposed to bare nuclei, unable to exist until hle0itu( am37ef3:oj m cs-k +cundreds of thousands of years after the Biuoe+: 3e0sf - 7tck3ljaimm(c g Bang?

Under what circumstances would th/ecru6zh 7(9 cbs/cc de universe eventually collapse in on itself?

  Using the definitions of the parsec and the ligh1a sl )d;plf(tt-year, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.38 seconds of arc. Hkmx ckqd k0( pt g6-j0 (zxnz/;r+jgr:ow far away is it? d =    ly

  The parallax angle of a star isdixhl) 6w )nrxhz v y. xt(3xd+v+fg48 $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. Whaty9pvemrh9 qgy 2 yk6td5o+ r34 is 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 angbfbn 9m kr:nv)u8+f bae qcvm* -:n/)jle 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, willkpv98 8(t j15pju6b znm7xe au the parallax angle of the9 6x5tv8 k8jp(az7muue 1pbnj farther star be greater or less than that of the nearer star? By what factor?

  A star is 35 pc away. Howflcwqw:/+ 7+b x ;t3ybl)fz tx qq9;so long does it take for its light to reach us?    years

  We saw earlier (Chapter 14) that the rate energy reaches the Ear vkh0:4efb0up1i j 7bxth from the Sun (the "solar constant"xu4 bkjhv0 7b1fp0: ie) 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 abko :7y xk.3m 1yxd8pgs seen from Jupiter as compared to its b :8y.xkky3d7o gpm1xbrightness from Earth? (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 thatz/4uc+yn7cwxu4, cf r our Galaxy would subtend if observed from the nearest galxn,c+474 /cuyf cuzrwaxy to us (Table 33-1). Compare to the angular width of the Moon from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giav.z n3lgn:w8, xf)7t; cnveklnt, what will be its average density if it expandsv ,wez 8g;ln3)n7vltxnfk.: c out 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 ez88 +krbpysl.xpected to be about the size of the Moon. What angular width will it subten.ryk+p s88lzbd from the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whose mass is equd* ./wfeegink t:,;lulj2u1r al to the Sun's and whose radius is equal to the Earth's. How many times larger than Earth's d w .1fi/trk;jl*udege: n2l, uensity 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 1b+ytv88; )xtooltt5 b.5 solar masses has 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 mb;+ 8 )yx8t5tovoltb tatter.
$\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 os.bf ;uxv5oqmb3 2s+a f Eq. 33-2. (The mass of the very unstabls 2;qubfbmxas 5v+.o3e $^8\text{Be}$ 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 brightne s m2/80,pto t76kr o1oindhhbss $l$ 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 certaix2w :f j,jdvy6t ()ljan cluster are assumed to be about the same distance from d xf)la26j,v (jw:jytus. 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 s.n ux+x jf*ek4tar with mass equal to that (a) of our Sunk*f nxjux+e4 . is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typico* ,txw6+i3dc yiydy *tnk; 8oal galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a sphere, for which thec81wpka fqj /w +6:vtiadf-* v sum of the angles is (a) 359º, and (b) 180°fa *-ptfdc6iwk /1w:vj8+qa v.

  What is the maximum sum-of-the-angles for a trin4 )4ujy0ee3 tvbkf7zangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of t6 f.nixv, 7y gqu8/nkwhe speed of light, roughly how far away is ivxg.wqkn7 68 fnuy/ i,t? v =    Mly

  The redshift of a galaxy indicates a velocity/ i)6ceutejgcw-xt * 9revc.) of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (relative to us) that is near th0a;b p.h-q f-p itk2rahcpz8d ch/h *4e observable "edge" opc.aa;f-hh b pi8 hkh crd -p2zq04t*/f the universe, say 12 billion light-years away. v =    c

  Estimate the observed wavelength for the 656-oq8f ao5lmh z+fo3mm6hc-*5a7 w;fln nm line in the Balmer series of hydro -mhahl;o *8+f7w 3qf5f nlz aco5omm6gen 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, if the wavelength ybx 39xtg 9k.--prsy x6 (bqfpfor the hydrogen line at r-gf69xq xpbp-b tsy 3(9kyx.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 galaxy 2:/+rp6:gnroy ,arv, n+qh b7skxiu t with $z = 0.60$? v =    c

  What would be the redshift paramel6 x;v.urno o*ter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Doppler shift in wavelu7u)w2hcs3xtbh *7l+ii2 c toy)z i,kength is $\Delta\lambda/\lambda \approx v/c$ (Eq. 33-5b) for $v \ll c$. [Hint: use the binomial expansion.]

  Calculate the wavelengthcp 5fpx7/4gj6ass . aw4 noshwvi,1b( at the peak of the blackbody radiation distribution at 2.7 K usin hg5a 467 s/f(1bj,swwson.xvap p4cig Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of the univ2 rlxq0 p.qwp6erse 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 aver*wqny 6p6b /-wo2nl xaage distance between galaxies) at any one moment is believed to have been inversely proportional to nn 6wb wax/p6y-2o*lqthe 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 b,sw,on 5pgi xd+le(j91i l:6mz tl2a delow the threshold temperature for pr:nl az5dpj6xlt,s 2o 9 (l,gi1iw+med oducing
(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 mainx9b;klj x.:cmh 3+yzn -sequence stars could undergo the three changes represented by the three arrows, A, B, and C, in the H-R diagram of Fig. 33-28. For each case, describe the changes in temperaturkj3nc xhz:mxb yl.9+;e, luminosity, and size.

  Assume that the nearest stars to us have an absolute luminosity about thvhy x6(*7vrrpr 4d s2og2edb2;-nqm b e same as the Sun's. Their appdr4bqrgom-rdy 7hens6(;p x22v b *v2arent 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 g fodqv/9p9 p-momentum to estimate the angular velocity of a neutron star whicf-pq/9 ogvd9 ph has collapsed to a diameter 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 kinetic energy change when the star in -elampgg--) 5gxceq* 4ovj tj7 ey*e4Problem 56 collapeg*7le4-5 *gjeg-oc-e ) jx y pq4vmtases to a neutron star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believed to be a neutron xl 0 jzmumkd9r+3f :m0star of mass 1.5 times that of the Sun, with diameter 20 km, is : jmr0+k 9mlf uxz3dm0observed 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 Galaxqr; nkbr:4wg( y 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 resty mclh0j.gnred2 f9w1q90;,y 1 dcwn5k slb5 q mass (in eV) would provide the critical density to close the universe. Assume the neutrino densityhcw9 l ln0wfq1yc;2ny ms bg95,q.05j1ed rkd 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 spec-q - j9,wrwu.uf9yssha )d ;xutra 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) thu sru.wswjq 9x,fd--au;)9 y o 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 our mmh/3w z(8dsk/ugv 3flsukw 2 6inimum angular resohsws6kmzlu 2(3g3 w/kd uvf 8/lution (in degrees), based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from singly io ce;v3o20 la,ci(p alfnized helium in a distant star happen to overl3c l(o0afeci,v2; a lpap with the Balmer 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 3jm 2qlj65 mdj1.8-TeV collisions at the Fermilab collider? To what era in cosmological history does this correspond? [Himj35j6ql 2djm nt: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recentn:jtwylb(g*lp6slc7y t;; l fn7 9 a*hly measured 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 nnl 9 wl76y:; p f(ag7sll; bcjyh*tt*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 emitted s nusg*f. q7jy/,d/+ t zjteg;from the galaxy is measured on Earth to be 650 n.q,7 /tdesg yj; f/n*zjs +ugtm.
(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 stellalg6axu s(7zg x.kqe8e5 up t77r evolution, a star (if massive enough) will begin fusing carbon nupuzg 7 5g6ulqeatekx7x8. (7 sclei 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 d:bpn cyuev 94fkptv6la/7 6 *
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 density of the f na)u:kpd8eb4fd:;n kk6 k9i5e f dc-univekd:eu)fkn-d ;: fb69 ip8kcadnkf e5 4rse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$