The Milky Way was oncer/p y)2m, pqr lp)gzd) thought to be "murky" or "milky" but is now considered tor2 d ,)myq)p rppzgl/) be made up of point sources. Explain.

A star is in equilibrium when it radiates at its surface ajcz 5orl; 0s2tud*+ed ll the energy generated at its core. Whatzcujde20+dto r ;l*s5 happens when it begins to generate more energy than it radiates? Less energy? Explain.

Describe a red giant star. List someow3 1 59h skjgel3z4tw of its properties.

Select a point on the H-R diagram. Mark several directiu76lezf (n+3 lb1c sazons away from this point. Now describe the changes that would take place in a star moving in each of these direct bn az671e3zl(+c slfuions.

Does the H-R diagram reveal anything abou kf.lv;fj,v3msat2futl1 3 4ut the core of a star?

Why do some stars end up as white dwa;y+(kft0*kvlrq( uuoso m.x (rfs, and others as neutron stars or black h o(; v(f0lx+mku(*y usqrko. toles?

  Can we tell, by looking at the population on the1b(sfy 9cj 65wynism: H-R diagram, that hotter main-sequ1s9 jy 5 (6siwcfm:ybnence stars have shorter lives? Explain.  ----待选择----yesno 

If you were measuring star my:em;1geqj + ns4l t;1apk.iparallaxes from the Moon instead of Earth, what corrections wol gmm.t ak;j4y nse qei1:1;+puld you have to make? What changes would occur if you were measuring parallaxes from Mars?

Cepheid variable stars change in luminosity with a fqm iejx2*9-0d)nm f htypical period of several days. Them*hdffe n2 0mjxi9-q ) 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 distance to galaxies?

What is a geodesic? What isdq; qtr, a3qy,p;tbr)k6 bi7c its role in General Relativity?

If it were discovered that the re 9sih6thd)r3wy/3n cqdshift of spectral lines of galaxies was due to something other than eh/ynsrc)i 6t9qh3 dw 3xpansion, 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 therefg kwxc)ha-i(p/1q65s3oupz v5c - op sore at the center of the universe? Expla51p/ vsqo w3 -a(s kiuog )p5xz6chc-pin.  ----待选择----yesno 

If you were located in a galaxy near the boundary of our observable universescqa3 qab7 n+0, would galaxies in the direction of thes 3cnqb+7 aqa0 Milky Way appear to be approaching you or receding from you? Explain.

Compare an explosion on Earth to thby:e gtq9 u;+4r)cyrsx 5nb) ie Big Bang. Consider such questions as: Would the debris spread at a higher speed for more distant par);ty:u+qbrr 9s b)negic5xy 4ticles, 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 caa:il2sss9lug j -z5 h14 xv.qun we tell if one ivlljsau gh9-uizsxs .5:2 q41s there?

  What mass will give a Schwarzschild radius equal to that;(n1 lp8m9uu3hji gxg of the hydrogen atom in its ground;( jn9muu8ix3hg 1 gpl state? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion years. Find that time on (Figvjbp )fx5a/s +. Below). Pv x5b+ jpa)f/seople have lived on Earth on the order of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic microwave backgroundb e:g osr-(ja,ekf/d * radiation is. Where does it come frb( :re/foj -dseg* a,kom? Why is its temperature now so low?

Why were atoms, as opposejm -2jnb1f4k.ujbocb)i /*;.g/nijy tr9t gid to bare nuclei, unable to exist until hundreds of thousands of years after the Big jmi/jtigf4b .to2*gcjkrn-/bn .b yi 9 u1;j)Bang?

Under what circumstances would the universe eventually collaph17 xx7 jx 0z;1kyeqr;hsh2x pse in on itself?

  Using the definition4 c65(.f zfc clxvl,tw,esnh0s of the 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 far away is 4g:gi/y4n/b i8 brtoa it? d =    ly

  The parallax angle of a star i heoge ,c-w2*,s h-p3bg ng:rzs $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its parallax anglhfe1po+nl60gkaak 77e?
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 r;b3m8r xw5ug 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, wh/:e+ 4vxyons ill the parallax angle of the farther star be greater or less than that of ns/:+vxeho 4ythe nearer star? By what factor?

  A star is 35 pc away. How long does it take for its light to reaeh gmh2 22yac6p-j rl-ch us?    years

  We saw earlier (Chapter 14) that the rate energy reaches the Eart7 ogb 5.*kmwnxh from the Sun (thmk* o5wxb .7gne "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 from 512jlqg9d mh7k gq-zw;j bhd6Jupiter as compared to its brightness from Earth? (Jupil527;9gdh1 zbh q -mdjqwjkg6ter 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 ooqqsm:/4mz k)r8 u;6igwtp.9yxldn . (e df7bbserved from the nearest galaxy to us (Table 33-1). Compare to the angular width of the Moon f9m x;/6ntsm q.:frzbydk4wo. igeq7up(l)8 d rom Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant,wbt*i2 *fki90-3jhd swiz sb + what will be its average density if it expands out to the o9ji0sziwhs -bd**+b3w 2 itkfrbit 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 5xbpsu/0emyj8.l j 4l be about the size of the Moon. What angular width will it subtend from the present distance to Earthbjj/80yu sx5el4.l pm ? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whose mass is equal to the )v/0;py:n ss-l,n9,eoi9gmcgjh salSun's and whose radius is equal to the Earth's. How mavaeghny/j i 90llm)nso pss-:, c;g9,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 s eb7g*z) y(-pn-lqwf9 g(lergolar masses has a radius of about 11 km. Calculate its average density and compare to that for a l z9gegp(lb e-rg7y*w)-q nf(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 burning reacqc)kmij9 d2.5 fe, ed45tytcytions of Eq. 33-2. (The mass of the very unsemi5fdtjy. 5c,qe)t9c 2 4 kdytable $^8\text{Be}$ 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 sa u6g cf 0g;bd2;zhw/itme 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 assumed to be about the same di5h37fnyz.po.d, s /kvn9y6td qj1zm zk s09rzstance from us. Two such stars have spectra that peak 3d./y0m1qh z,kkjf zpdozy r 5n6vzt9nss.79 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 toc)gu0 p7 i6v1 piyu4f6ol sxu; that (a) of our Spi)gx 0l; o761sivu6f4y upuc un is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typical galaxy (-7amku fhp :r+like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle,742*)m ct9prz vtzkf 6s -ygni drawn on the surface of a sphere, for which the sum of the angles is (a) 359cv9)tz4ik p2m76r gftnz*sy -º, and (b) 180°.

  What is the maximum sum-of-the-angles for a triangle on a sphere? : wmi,khp-y.a   $^\circ$

  If a galaxy is traveling away from us at 1.0% of slt 6j t1ds -5nn*e-n s;b1mynthe speed of light, roughly how far awan5m-yn6sj1*sb-tel n dt1ns ;y is it? v =    Mly

  The redshift of a galaxy indy y*t u:tk u(:8kakdsi 1ox;+jwy9 5tiicates a velocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (relative to us) that bo/j/a nragy-34b bq9 e2-o zsis near the observable "edge" of the universe, say 12 billiq4j /na zb -syaobe/g9b-ro23on light-years away. v =    c

  Estimate the observed wavelength for the 656m pd*+mot +e(r-nm line in the Balmer series of hydrogen in the spectrum of a galaxy wt+(dm+ rpeo* mhose 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 f 2or+6o6dusu 5 bod:1 bti-yi buj8h6vrom us, if the wavelength for the hydrogen line at 4b :obitd 2ub+ v6o-jud yu5os 186rh6i34 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 wit6lou )moke.tqk0 6, sth $z = 0.60$? v =    c

  What would be the redshif+gci p uz09n.rav a/d*t parameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3mbuf1 +ieex). , show 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 wavelengtyk5y2bec p 1m2h at the peak of the blackbody radiation distribution at 2.7 K usby ymc2e51 p2king Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of the unive)ll7n*1u ad0zgfhpv-o hzz:5 rse 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 galaxies) at l 4pcpcsnl6e)w b** :afi2kg*any one moment is believed to e*)c2l:ika*bg6npwlfc* 4 sp have been inversely proportional 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 univ3z zv 64 az.u*relvft.erse cooled below the threshold temperature for produciva .tu.vze4fz rl*3z 6ng
(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 three c;/jds l)tavtz-b h* mstlgskkz61(,, hanges represented by the three arrows, A, B, and C, in the H-R diagram of Fig. 33-28. For eas/s (6t*atbhz; m1, gk,lk-tz)ds lvjch case, describe the changes in temperature, luminosity, and size.

  Assume that the nearest stqrl3 27 4 xx)ft.zu*7zrv jxop0o)tblars to us have an absolute luminosity about the same as the Sun's. Their apparent brightness, however, i oxq* zrx3072l.7 utbxrpv tfzo)l)j4s 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 momf w+ j9)gm fobf1ke65oqv6b4eentum to estimate the angular velocity of a neutron star which has collapsed to a diameter of 20 km, from a star whose radius wab)gj f46kmeoowv bq6f+ 1 e5f9s 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 kine3uae r/fcs -u ihd8e .-uns-l-tic energy change when the star in Problem 56 collapse--elu d /eauu3ss-8 c-h.i nfrs 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 times that ogtc-k :wpl2cw :trd +0f the Sun, with diameter 20 km :dr k0lc2ct+:-tgwwp , 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 Galaxy07kftwz k0kz cf(833bll o8oh 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) would 19w b8pmua1hiprovide the critical density to close the universe. Assume the neutrino density is, like photons, abo9 phuwbm8i a11ut $10^9$ 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 z nm,(0etvu+ps6ebdt(hj51 h nm, respectively, both lie on the main sequence. Use Wien's law, the Stefan-Boltzmann equation, and the H-R diagram (Fig. Below) p, +tetz(6h0 vh(n1 msb udj5eto estimate the ratio of their diameters. [Hint: see Examples 33-4 and 33-5.] $\dfrac{d_{400}}{d_{600}}$ =   

  Suppose we can measure d(gx)4ucmp(ve ato*h5 istances with parallax at 100 parsecs. What is our minimum4c(ga*xte5v) hpu o (m angular resolution (in degrees), based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from singly ionizey:mvz9wxi8p ;p xqkeu8 k-d3)d helium in a distant star happen to overlap with the Balmer lines from hydrogen (Fig. 27-22) d)mk8xp : 8xqzwyu;ei93p v -kin the Sun. How fast is the star receding from us? v =    C

  What is the temperature that corresponds to 1.8-TeV collisions at the Fermilab:+n01it.( 4tsdtgsszx ux//dm ro d0l collider? To what era in cosmological history doer uxog/dm xti01ls.n /dst+ t0(d:4sz s this correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation of gas around what might bemdz1oy 4 d gl1c*x;7l upb(b1g7q k,qx a supermassive black hole of about 2 billion solar masses 1oym,l4gq 7* zbu7(1gcdxql1 ;dbpxkat the center of 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" hydrogel-volcyszb ;/:-v-x on line at 434 nm emitted from the galaxy is mea;v-l x-zsocb -:lo yv/sured 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 evolution, a star (if massive enough) will be l4th v*hrjgagt-c9l ahrb;evj(, 0:.gin fusing carbolthg0bchjrgtv;,*- : (a e.h4a9jlvrn nuclei 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 reactiol0v 3bemq2u6 un
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 5bdu topkf; 81o0jmj5b-k 1wqequaled the critical density of the univbk10 tu1dowpok8 m; b55jjqf-erse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$