The Milky Way was once thought to be "murky sg 6i6qzdw2rc/,tb+w" or "milky" but is now considered to be made up of point sources. Expl2zw 6dwgtc /+qr b,is6ain.

A star is in equilibrium when it radiate3c fntxrx;0 y4v*sw2es at its surface all the energy generated at its core. What hacwenxvst4 3r *yf;x20ppens when it begins to generate more energy than it radiates? Less energy? Explain.

Describe a red giant star. List some rmmat2fx9ni yy 1d)36j h c7:tof its properties.

Select a point on the H-R diagram. Mark several directions away from this poj9*ge2+(c sfzl bjec,sk) hi+ int. Now describe the changes that would take place in a star moving in each of thes,l*ih 2bksg9ejf +e+jc cz)s( e directions.

Does the H-R diagram reveal any47nkg imj rj/8thing about the core of a star?

Why do some stars end up as white dwarfs, and others ae(g* op v;gn5gs neutron stars or black hole e;(gnog5 vpg*s?

  Can we tell, by looking at the population on the H-R diagram, that hotter maiwnb3sso q:s d:s(rnhv,3f t 97n-sequence stars have shorter lives? Explain. s ob dsh3(wns,nr9v73: q fs:t ----待选择----yesno 

If you were measuring star parallaxes from the Moon instead of Earth, 621zr ukzyxh) what corrections would you have to make? What changes would occur if you were measuu) 61xhzykrz2 ring parallaxes from Mars?

Cepheid variable stars change in lumh.9rlvhfg7 f wb.e+u (inosity with a typical period of several days. The period has been foundf+ r h(ebgulf.7w.9 hv 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? W13x 7ggm* gqnksng9:ahat is its role in General Relativity?

If it were discovered that the redshift of spectral lines of galaxies was due m c/,tg3tjy 1ato something other than expansion, how might our view of the universe change? Would there b3jc /a1gty,tme conflicting evidence? Discuss.

  All galaxies appear to be moving away frokd2/cn-i ; 7x(whgydg:a mi9m m us. Are we therefore at the center of the universe? a9dkg c2 im7/;:m-(dgw yihx nExplain.  ----待选择----yesno 

If you were located in a galaxy near the boundary of our observablew: qx6: a qmuoyt9og1* universe, would galaxies in the direction of *:oauo6w:1ty qq m 9xgthe Milky Way appear to be approaching you or receding from you? Explain.

Compare an explosion on Earth to the Big Bang. Consider such questi)d ) m3sdm6bzdons as: Would the debris spread at a higher speed for more distant particles, as in the Big Bang? Would the debris come to rest? Wh6d)smzd)md3 b at type of universe would this correspond to, open or closed?

If nothing, not even light, escapes from a black hole, then how can bi,madz+h.pie8u w u85 d56igwe tell if odeu68miw .idubhg 5zp + a,i58ne is there?

  What mass will give a Schwarzschild radius equal to that of the hydrogend8f,z;(oqfr z atom in its ground state?of;qf, r z8zd( M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion years. Find that time on 7 yj9rp1o8pisxe+my , (Fig. o8ixp ,jr7 py+1sme9y Below). People 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 background radiation is. Where xouuvc brj +d17au06w7.xe 9odoes it come from? Why is itsjuw xoo797 +6e bvca ux01udr. temperature now so low?

Why were atoms, as opposed to bare nuclei, unable to exist until hundr js2d1hxq fcm 2i(/wigl9l)f. eds of thousands of years after.ld9 /21q cgfmixw()j2fslhi the Big Bang?

Under what circumstances would the univers--o;qkd oktb)e eventually collapse in on itself?

  Using the definitions of t2ipns 3sn90 pri n/ koaz+umt*/ ;,rfohe parsec and the light-year, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.38 spxxkok/.pt64 l3*ny-k g e: n:h cd;foeconds of arc. How far away is it? d =    ly

  The parallax angle of a sta 9 n;nn zs ou-grsuz6hu+w*44pzu7f)pr is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc awayt2i:z :*+nx1ycj+u rjwoh pz 9. What 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 angle for a sta 0+31 yshkx,2xrphyspgco )1g r that is 55 ly away? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice afr9q6+k 1l9; . kyieh-wncq ggs far away from 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 fackfq gi9+-kl;9 w rq.ng16ehcy tor?

  A star is 35 pc away. How long does i:mj 4v 0d bm -ayi+8emud0bjf8f0wy5wt take for its light to reach us?    years

  We saw earlier (Chapter 14) iaq0 n;mu;s/q *04ufdr)i adkthat the rate energy reaches the Earth from the Sun (the "sol *;u kur;aadnm00qiif4q/)ds ar 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 oey8ge h gj,5xb e2q c6+1pn9gas compared to its brightness from Earth? (Jupiter is 5.2 times fax6h ege+9 q1g,ce52 py8bgonj rther 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 ob r9nm:a13 reuzserved from the nearest galaxy to us (Tazr:3r9n 1uemable 33-1). Compare to the angular width of the Moon from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, what will be its average denpd.8,o z vyj jo1fcfy: 1x(kra1h9pg3sity if it expands out to the orbit of Ear ado1cjj9py(181kpfx 3 hyf g.zovr ,:th ($1.5 \times 10^{11}\ \text{m}$ from the Sun)? $\rho = $    $ \times 10^{-4}\ \text{kg/m}^3$

  When our Sun becomes a white dwarf, it is expected to be about the jks) dwptp1 9t2taw86 size of the Moon. What angular width will it subtend from the present distance to Earth? w1t9 tjatpp62ds8 )kw $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a whitebrzqcrd ,/ ;z; 9anzmn-l4- qe dwarf whose mass is equal to the Sun's and whose radius is equal to;;d zeqaz4n rb- r n9,cq/lzm- the Earth's. How many 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:s36ltqb ;w xhqn6 g8b solar masses has a radius of about 11 km. Calculate its average density and compare to that for a white dwarf (Problem:l8s;xqbnw63g t qbh 6 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. 33-2. (The masscsqptx0k15 w xrrk bw1.y 01+q of the very un+k .1pyr0tqqk1 s1 0wx5 xrcwbstable $^8\text{Be}$ 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 apparencrk5oe9s4v/lt 3(nntpc 4s e+t 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 tr*/sh 620o) qcrdgnogyq ik 2(he same distance from us. Two *hgr2i)qogc0k 2 6qndy(ro/ssuch 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 Schwarzschil91tedhsk 29dh d radius for a star with mass equal to that (a) of ourhhd 9 2dk9t1es Sun is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typical fhvv, nx),bhg/t k73kgalaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a sphere, for whizjzj-. i5.tay ch the sum of the angles is (a) 3j zzt.y. -5aji59º, and (b) 180°.

  What is the maximum sum-of-the-+ tm yy x:1)a;/3j8yl;g xnktx2pngiz angles for a triangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the speed of light, rof (y d-0ey+0ay y x2r5nm0xkgoughly how far away ix05 yen+ m2( dg0y0kyyrfaxo- s it? v =    Mly

  The redshift of a galaxy indicates a 0849vml2xxsd5dks c avelocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (relative to us) that is -j5ww 1tfk:rc near the observable "edge" of the universe, sa-kwwjr:f1c5 ty 12 billion light-years away. v =    c

  Estimate the observed wavelength for the 656-nm line in the Balmer series of hy icg6:fnbi nz2cn(i8 :drogen in the s2cnn(zib8ng i f:6 c:ipectrum 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 distancet9u 7s)kflhp4 from us, if the wavelength for the hydrogen line at 434 nm is measured onlp7us h4 9f)kt 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 a0psiq( bwe4h, rm- at2 9ao8zm galaxy with $z = 0.60$? v =    c

  What would be the redshift parameter8;p,2w:q emtfublpd 5 $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Do (xt(gd v(c9 2+c.xqhwij ska,z t6bd4ppler shift in wavelength 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 ofs5fmznp,0asa8zdj1 0 the blackbody radiation distribution at 2.7 K using Wien’s n,sp1azsd05j mfz0a8 law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of the universe is g ia3-y hx4igr1 2 99dfp1pxqb$\rho_c \approx 10^{-26}\ \text{kg/m}^3$. State $\rho_c$ in terms of the average number of nucleons per cubic meter.    $\ \text{nucleons/m}^3$

  The scale of the univers., um p.mr+)c-j- u1m glnxbaoe (the average distance between galaxies) at any one moment is believed to have been inversely proportional to the absolute temperature. Estimate theb ,ol.mg-.m +rx)njcp-mu 1ua 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 timehs syl,tri i8kl-; 74t had the universe cooled below the threshold temperature f tk84 itlyihsr-;l,7sor 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 main9 6a8dsmtw0n n-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 temperature, luminosity,9m n08tdsw6na and size.

  Assume that the nearest stars topg06ac06qx 0jmjz36r h9olw 4o :mrz i us have an absolute luminosity about the same as the Sun's. Their ap:xgqwopocjmjm46l 6h6 0r9zz 0r3 ai0parent 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 velocity of a neutrt uq13:4hgi.2scnvb f jve m;3/uk:qron star which has collapsed to a diameterrv /v1h.s :j 3k;4umq ctfuqi3 en2:gb 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 P x58:e,mocz x(toxty4roblem (ot t8z5c,: o 4xxyxem56 collapses 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 ofkt 6g).8wp 0ui i-e 9bgh*kxwh mass 1.5 times that of the Sun, with diameter 20 km, is observed to have a rotation speed gw680*eb9t- .uihwkg)kp i xh 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 );ni;4o vw6bous; qn:0kjul i our Galaxy 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 cr o*;n-di1 e 0amem9zdwitical density to close the universe. Assume the neutri dd9mnezae1*;m0ow i -no 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 peak at 600 nm and 400 nm, respectim9o(xei cmdbb) u4pf4)83tp u9een 0ively, both lie on the main sequence. Use Wien's law, the Stefan-Boltzmann equation, and the Hi3eub p)em40f nuxpe)9 c4td mi(b89o-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 10 rt /yqg.i-7q2,i e r ,tbu69qacoyw1f0 parsecs. What is our minimum angular resolution (in deo,fuar,e7 -rwbqc 1gqy6i/29 .tiyt qgrees), based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmerwa -q-kf5f:xgx 2 y(bwx*b;av lines from 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 star wa aqy5x2( fb wkf*v;x-bxg- :receding from us? v =    C

  What is the temperature that corresponds to 1.8-TeV collisions at the Fe py0(ezaqd zv-3dna;qz 0)q,irmilab collider? To what era in cosmological history does this correspond? [Hint: see 0z0-anid;p(qye3zvaq z ,d )q(Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation of gas around wh 0 rg,rr7/m gwk*jk,vtat 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 clouds is 60 light-years, wha*jg,m rr7vgkr/, tk0wt Doppler shift $\Delta\lambda/\lambda_0$ do you estimate they saw? z$\approx $    $ \times 10^{-3}$

  A galaxy is moving away from Earth. The "bluo1:zs1h zi jnac-0ha5 e" hydrogen line at 434 nm emitted from the galaxy is measure ajh10h1icn5s -azoz:d 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 kuav;k3q(6 y5 yl z-ccmassive enough) will begin fusing carbon nuclei to form, for example, magnesiu yq36c( lckz5;uky-v am:
$^12\text{C} + ^12\text{C} \to ^{24}\text{Mg} + \gamma$.
(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 ha-* q rvg) ,bwkhur81
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 t6gdutfx3 *.rwhe critical density of the un.6gu*3 frtxdw iverse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$