The Milky Way was once thought to be "murky" or "milky" but is ntv gl 5/j5cod;ow considered to be made up of poijvl;t5goc5/d nt sources. Explain.

A star is in equilibrium when it radiates at its surface all the ena1/ s)gzdxto tmh 0;t1ergy generated at its core. What happens when it begins to generate mor tg0hs1t x;t1mza)o/de energy than it radiates? Less energy? Explain.

Describe a red giant star. List some of its : x:k5ucvqwa,properties.

Select a point on the H-R diagram. Mark several directions away from this )9iz3+icnbt p point. Now describe the changes that would take place in b cpi t)n3+zi9a star moving in each of these directions.

Does the H-R diagram reveal anything about the core z7m,ejh4fy,7h/ nkr p of a star?

Why do some stars end up as white dwarfs, and ofi-q)-krg lg1thers as neutron stars or black holes?-fikl1q r)g -g

  Can we tell, by looking at the population on thpn- vkdky.4 ;ve H-R diagram, that hotter main-sequence stars havep -;vv.kn4y dk shorter lives? Explain.  ----待选择----yesno 

If you were measuring star parallaxes from the Moon instead of Eartxk 8b:c7p4akg h, what corrections would you have to make? What changes would occur if you were mep48bcak7x kg: asuring parallaxes from Mars?

Cepheid variable stars change in luminos(tzgu8cxl- rgn, i*)p/z vsn; ity with a typical period of several days. The period has been found to have a definite relationship with the absolute luminosity of i *- luctp) 8r;/znxgz (,nsvgthe star. How could these stars be used to measure the distance to galaxies?

What is a geodesic? What is its j;borgd ;-zd u3.n- hurole in General Relativity?

If it were discovered that the redshift of spec: tcm2pgun d 0*yegxpfdq7dcl:g62;:tral lines of galaxies was due to something other than expansion, how might our view of the universe change? Would there be conflicting evidence? Disc c:pn0qc etldm7gu2gp gydd:;26:fx *uss.

  All galaxies appear to be moving away from us. Are wem7(/t9ovb+fb3*s az(,fs l pcwf v /mb therefore at the center of the universe? Eo+*(camp /,mbsw7 /3stzffvb9vfbl( xplain.  ----待选择----yesno 

If you were located in 7v 9g lo8p0ekm3hjl.aa galaxy near the boundary of our observable universe, would galaxies in the div7 0hao9el8kp lj 3m.grection of the Milky Way appear to be approaching you or receding from you? Explain.

Compare an explosion on Ed1/eh0 woz ame+s.*sparth to the Big Bang. Consider such questions as: Would the debris spread at a higher speed for mop.ham*+seo e 10dzws/re distant particles, 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 can we te9bdu93) ()5uzmyn qj8 xlfzwm ll if one is thermbxzjzu9qfw8)nd3l)m9 5( u y e?

  What mass will give a Schwarzschild radius equal to that of the hydrogen3uqphf jc.hu/ - 6eu3z atom in its ground state? M = /uh-qpfez3 u.cujh3 6    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion yec4)vbf n;e mg9ars. Find that time on (Fig. Below). People have lived on Earth on the order of a million years. Where9mv g c;4fnb)e is that on (Fig. Below)?

Explain what the 2.7-K cosmic microwave background radia8s )otegt0.mltion is. Where does it come fromt8et.) sm0log? Why is its temperature now so low?

Why were atoms, as opposed to barxnq ia9.akwn2n.-5ut (ixh q8e nuclei, unable to exist until hundreds of thousands of years after the Big Ba .2k xi(8qth5na.i n9u w-anqxng?

Under what circumstances would th lac./aq zxf0m2i,a saz.mksh.c43+re universe eventually collapse in on itself?

  Using the definitions of thek8pem v nlfphadi+1.r6, g8 *b parsec and the light-year, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax1 g3h(p*rw*n bqj uw*n wnx dd2qd(h-+ of 0.38 seconds of arc. How far away is it? d =    ly

  The parallax angle of a star w 2u: ;)sm .tqgq*gmwois $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its paravt5bg3 fuy.so y7zw9h:w-a*w llax 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 st;njrpcberhu.z 3h(5 g5bd;v )ar that is 55 ly away? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away fromnd 3ldm i1d4a4 us as a second star, will the parallax angle of the farther star be greater or less than that of the nearer star? By what faadd4l1n 3m4id ctor?

  A star is 35 pc away. How long does it take for its light to q ehg8sq;i88zreach us?    years

  We saw earlier (Chapter 14) that the rate energy reaches the Earth 0.o;hyg tx9*c: yp mfbfrom the Sun (thexy9yb0;f p gh. *:mcot "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 Jupiter as compared 9j t(gty:f lgr m4p27rto its brightness from Earth? (Jupiter is 5.2 times farther from the Sun tlf (trp2m:tjrg 749gyhan the Earth.) $\dfrac{l_{\text{Jupiter}}}{l_{\text{Earth}}}$    $ \times 10^{-2}$

  Estimate the angular width that our Galaxy would subtend if observed djlhpe dopv/kuu: /q67- vi8twgb24- from the nearest galaxy to us (Table 33-1). Compare to the angular width of the Moon from Earth.qvek6w:p/h u8 v-u og4 dbpli7t-/ dj2 $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, what will be its average density if it expandb voy ).sbkg:pe w)i10s out to the vbke0 )yows: gi.)1pborbit 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 be 2n u-lr)d j+)kozng7vabout the size of the Moon. What angular width will it subten zj)d)kr+gnlvo u7-n2 d from the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whose mass is equal xqogy9 z ,) hyead4y*bq4b ftsa+6*c1 to the Sun's and whose radius is equal to the Earth's. How many times y1,*of4 hgz+t y*6y4b dsxaaq9 )qcbelarger 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 has a radius of about 11 km. c+*wplu8 wf697 p paafCalculate its average density and compare to that for a w7lfcww 8uapf *96 app+hite 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. 3oq.s,l* 8rcp0c,s 5y fh)mjyl3-2. (The mass of the very s*o qjcr,58 yf.,l c p)hls0ymunstable $^8\text{Be}$ 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 brigfzsv -56t y5baf+sex /htness $l$ 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 -2 9 nwk,q,bouim5 scmthe same distance from us. Two such stars have spectra that peako q 2m,c-km s5nwu9bi, 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 equal5d 95h3 kn wn y.a7*ax5 fa gmqmezk1m8pmv03u to that (a) of our Sn yg9m3af*ep1k muah5ax5n378z5wd v.k mqm0un is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typical galaxy (like ours)? dvzq kf,l 7p54R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the snew6 zv.2:nwa9s6pb;( ehz xhurface of a sphere, for which the sum of the angles is (a) 359º,ae(6b x. swwezpz6:hnn29 ;vh and (b) 180°.

  What is the maximum sum-of-the-angles for a triang,mx0jj6 rf :qp ,-km1xwz- vwmle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the spe0fcz y q4atw(1ed of light, roughly how far ac twz fqya01(4way is it? v =    Mly

  The redshift of a galaxy indicate g( iwcmpj6e;33ezqr( s 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 observable "edgb t 60lgn oj:a1b39i-pgpxn k1e" of the universe, say 12 billno1 itpbaklxnpjg0:6 1g 39b- ion light-years away. v =    c

  Estimate the observed wavelength for the* sblce4e7ceo qo0vv q oyb5.c3/ca-( 656-nm line in the Balmer series of hydrogen in the spectrum of a galaxy whose distance fro .q3 qv ale*yveocc bc s50o-/ceob74(m 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 f/mnn ttgl1 -g6jy lj/s:y9v+ oor the hydrogen line at 434 nm is measured on Ea +/gt6nn lsl -jtvoj m1yg9y:/rth 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 gah )t1tz)pb p4glaxy with $z = 0.60$? v =    c

  What would be the redshif/5rk6d,pp)-hp+lzi+t -k4+l3 hnwu yz mrwqvt parameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Doppler shift in wavelecy 5ont ye89c-ngth 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 dis ssk) gkuz/-t.hg/k0 utribution at 2.7 K using Wien’s /sus0.h k/gk)-zt guk law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closurmi t 17nd/xi:pe 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 galaxies) at any onxw0)-w 8h17y k rij1kowhont4uopl 0 (e moment is believed to have been inversely proportional to the absolute temperatohu4itwl ) 0-prohww1kkxy1(70 j 8onure. 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 temp.*;tw(qwutlrs;n;fthr : f qx )9/k3nyeh 7nf erature forfykw.thxu;*frn lq/)te7th9 ns q:3;;(nw rf 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 s1w52kp 1qwn w*)wb1d.e mu,:eodr egg tars 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 d pew12,1gq emwg*d1b eu)o5.kww:rn changes in temperature, luminosity, and size.

  Assume that the nearest stars to us have an absolutj/giv .t o.d*me luminosity about the same as the Sun's. Their apparev ogtm .j*id./nt 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 esti-b7cq ao 6rt:0w ktklz* *k3qxmate the angular velocity of a neutron star which has 6q zklw b:* rcx3tq0a7t*ko k-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 2x5v(w l tuxi,the rotational kinetic energy change when the star in Problem 56 collapsev2lti,(w u5xxs 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 times732;t.qa x09gcx uauhsx 1wpg that of the Sun, with diameter 20 km, is ob0g x.w quc3 t7x;upgshax29a1 served 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 Galax;1u z r3u.tv, o*3xbr e3j*cgdppf0yvy 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 provide the cri+m,v,b m0.o lv0yfvpo uxhc ))tical density to close the universe. Assume the neutrino density is, likomvy, l),x0ocmf hv0.p)u v+be 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, respectivel28c4e8pc-g ccf7+ c ahz jhz-ty, 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 diametez -+c88 h-ahpztg2jc7c4ef ccrs. [Hint: see Examples 33-4 and 33-5.] $\dfrac{d_{400}}{d_{600}}$ =   

  Suppose we can measure k13 l omw0ciz0+,dznzdistances with parallax at 100 parsecs. What is our minimum angular resolution (in dznwd m310+o0z , kczilegrees), based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, thebwq.rohfwa 70k., m36;eooqm Balmer lines from singly ionized helium in a distant star happen to overlap with the Balmer lines from hydrogen (Fig. 27-22) in the Sun. w07mk 3,.h om.;ofqqwoa6 rebHow fast is the star receding from us? v =    C

  What is the temperatucc) w3: -nyfmkv.mq +ure that corresponds to 1.8-TeV collisions at the Fermilab collider? To what era in cosmolo):3m v+qwnyc-. c mufkgical history does this correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measure -rnwuh o:j:l0d the rotation of gas around what might be a supermass:h -orl0:w nujive 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-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" hydrogevgfe6c+ 7kwoje3(p e9 n line at 434 nm emitted from t keo 96w(vgc3+e7jf pehe galaxy is measured 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 mas3 /xt2epv3yr jsive enough) will begin fusing carbon nuclei to form, fo x32rp3y et/vjr 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 o6 6ypl5kefc ;kgr1eg0 1 w9m.xufw 0j
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 criticav0xfmv,4 g0xr 39a3. qxwbbdrl density of the universe, rvwb90v,xrqa xbf0x34. d3gm $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$