The Milky Way was once thought to be "mup.nflq* jb 6 ;ylcy*0trky" or "milky" but is now considered to be made up of point sources. Explcyf.* nl0 * ;jpblty6qain.

A star is in equilibrium whencobg yyy, y*w0; orc89 it radiates at its surface all the energy generated at its core. What happens when it begins to generate more eyw9ocg;y b0o ycy ,r*8nergy than it radiates? Less energy? Explain.

Describe a red giant soc7 l1vsz r( a i7bt3.k0cbex;tar. List some of its properties.

Select a point on theef7 :)rf dkh9ep/r tl6 H-R diagram. Mark several directions away from this point. Now describe the changes that would t/7tkpfr:6hde elrf 9) ake place in a star moving in each of these directions.

Does the H-R diagram reveal anything about the core ofofc3+tj,r ;o n;xp.dz a star?

Why do some stars end up as white dwarfs, and others as neucb8f-tm3i m hhw1 b89ftron stars or black hof f tc9-hwimb31bhm88les?

  Can we tell, by looking at the popubo;.ivlc+0sb v7 d3kllation on the H-R diagram, that hotter main-sequence stars have shorter lives? Explaini3b ;dc7l. blov+k0sv.  ----待选择----yesno 

If you were measuring star parallaxes from the Moon instead of Eart6s/ r zu54bcjqh, what corrections would you have to make? What changes would occur if you were measurin/zuqs6rc45j bg parallaxes from Mars?

Cepheid variable stars change in luminosity with a typ(f ;fl(occ*h;zj ,tdpical period of several days. The period has been found to have a definite relationship with the absolute luminosity of the star. How couldholdp(, tzjf;f( c*c; these stars be used to measure the distance to galaxies?

What is a geodesic? What is its role in General Relatdfb) (ua7 ip5n5yh6ce ivity?

If it were discovered that the redshift of spectral lines of galaxies wa9q1w+k:v)sqlv o g fs7i,- zfrs due to something other than expansion, how might our view of the universe change? Would th7f9q+1zrg v -sfw:,qkli ovs )ere be conflicting evidence? Discuss.

  All galaxies appear to be moving away from us. Are we thyg 4f/z ipym7l+gz3 r5erefore at the center of the universy47zgp r i35zgyf +/lme? Explain.  ----待选择----yesno 

If you were located in a galaxy near the boundary of our observable univers 3/s ob:d*qhzle, would *z 3lqsbdo:/h galaxies in the direction of the Milky Way appear to be approaching you or receding from you? Explain.

Compare an explosion on Earth to the Big Bang. Consider such questions as: Wov1o8kby1h x 12j,,k/uicadgxuld the debris spread at a higher speed for more distant particles, as in the Big Bang? Would the debris come to rest? What type of universovk d1bhy k 1x/82gjx ai,,c1ue would this correspond to, open or closed?

If nothing, not even light, escapes from a black hole, then how cano:.18 xbe (jc6vfexo c we tell if one is x1c.ec:j8xeb( vf6oo there?

  What mass will give a Schwarzschild radius equal to that of the hydrogen ato99p4epmz n8t vm in itp89 4ev mt9nzps ground state? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion years. Find that time on (Fi*zzxr jjy+/o 4g. Below). People have lived on Earth on y*j/4 rzx jz+othe order of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cf,5p sao,cqg22hfy 4mosmic microwave background radiation is. Where does it come from? Why is its teo,4 y,5gfhq 2cfsapm 2mperature now so low?

Why were atoms, as opposed to bare9fbih/h0 ja2 8 fov.ai nuclei, unable to exist until hundreds of thousands of years after the Big Bhbjai h.290of vf/a8iang?

Under what circumstances would the universe exrnik-odu k y44dqvm-z h3+3*ventually collapse in on itself?

  Using the definitions of the parsec and the light-year,ueaspw4 e0b0(b55 2sfh5b f bs show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.38 seconds of arc. How far awa; ,kb vpvy84nwy is it? d =    ly

  The parallax angle of a ex:tctc 7 eft z92a,zynds7*)star is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its parallax angle? ppn)jusjgco3(6 b+yf3-(hu j
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 w2m *r)-v ldg.9h9a9ebhg ycfly away? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away from us -s81hwr80qo2rnx /oehglxm3as a second star, will the parallax angle of the farther star be greater or less than that of the nearer star? Bo3hm1s2gehnxr l0wo8q-r /x8y what factor?

  A star is 35 pc away. How long does it take fqm;nf7fo j y /wv2,ea4,)twuu or its light to reach us?    years

  We saw earlier (Chapter 14) that the rate energy reaches the Earth v /qbzhj t e75-;)admrfrom the Sun (the "solar constant") is aq- d/v7)atrb ;j ze5mhbout $1.3 \times 10^3\ \text{W/m}^2$. 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 seo:jov 9 */ut* t+onjbxen from Jupiter as compared to its brightness fromtxo+9b/ ov njt*uj:* o 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 that our Galaxy would subtend if observed1o2)d iw3f qrn from the nearest galaxy to us (Table 33-1). Compare to the angular w)dw q123fnor iidth of the Moon from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a jfnd/e fup-i 5;m4w9 yred giant, what will be its average density if it expands out to iyf -9p;d mej5f4 /unwthe 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 expected to be about the size of t;e:4gt .up:ix:b ztsw he Moon. What angular width will it subtend from the present distance to p:. :bie stt:4 xuz;gwEarth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwszn-67mwk )an arf whose mass is equal to the Sun's and whose radius is equal to the Earth's. How many times larger than Earth's dksz7n-an )wm6 ensity 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.e6* 7:clo.gr ka. l-fias.bn m Calculate its average density an 6.l:.7 gbre.fa-lcks man*i od 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 t7 ecg3/uuqbl-a .;cm for the He burning reactions of Eq. 33-2. (The mass of the very unstabl7ml/eq c ua-3.tuc;bge $^8\text{Be}$ 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 apparekf eytvei+tjt-h l8v+(o-9a: nt 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 cer8(deld0; oq6ii iums, r8(fqf tain cluster are assumed to be about the same distance from us. Two such stars have spectra that peak ru8s ; iidl6(f,ef im8qq(do0 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 ou3 rk xqz6tiv*9r S9*kxi 6vqz3rtun is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a (e n,4j 7pchhutypical galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on thai h:j f(9 1lxb;maqx1e surface of a sphere, for which the sum of the angles is q9ijm;xalfh:( b1x1 a(a) 359º, and (b) 180°.

  What is the maximum sum-of-the-angles fdtez/p1 u) q3s(a9od3129coe yd hi kfor a triangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the speed of light, roughly h9v m( ng 0ni3kwmzrd)8ow far away is it?8i gnvkwdm (z)3rm9 0n v =    Mly

  The redshift of a galaxr5vb 85 jntj. uf rtiu5*/kefs7, f2qry indicates 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 "edl ; 4s,zc7cvwuq,oo :uge" of the universe, say 12 billion light-years ovuz;ocw:q ,4c7 su,laway. v =    c

  Estimate the observed wavelength for the 656-nm line in the B1wtbb:7x1*tq kfi5tnalmer series of hydrogen in the spectrum of a galaxy whose dis*fi1 ttq75t1 n:k wbxbtance 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** wuljju*g: c 00tu;znd6s f.44kxllbkocs. its distance from us, if the wavelength for the hydrogen line at 434 nm is measured on Earth as being 610 nm. fls.*sc4 00uobc4dn *z* jg. tlj:wk;x uk6ul
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 galaxylpv52v)e6yx6 xf,f+-wli u i g with $z = 0.60$? v =    c

  What would be the redshifw me 9/jtvfh/;:r yo(qt 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 -o f/v(4oy:u8 yw qefowavelength 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 blacle4mde g;ie,su,r y/y/;k i9k9 d w1lskbody radiation distribution at 2.1re,/il9e, ;isy/y lm;dkw9sedug k47 K using Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of the unive3:7d* cw wxnrerse 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 dis-qq2kl-s a )abtance between galaxies) at any one moment is believed to have been inversely proportional to the abso lk bqs-q2a)-alute 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 bela-n9wweh9 ;air/u0j qow the threshold temperature for prod9u/jwwqeanr;h 9a0i -ucing
(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-seqfb: 5 qia2qgo-uence stars could undergo the three changes represented by the three arrows, A, B, and C, in the H-R diagram of Figg :2foqq i5ba-. 33-28. For each case, describe the changes in temperature, luminosity, and size.

  Assume that the nearest stars to us have an absolute luminosity about the s6o i73j+j)7 )nn4deqg qyd8vlsu+ m rrame as the Sun's. Their apn6)s37d you4nm q8)e +rgd7jqr v+jliparent 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 estimatedwwc18ib 7i;w trau6-xn-;ujf m)y c/ the angular velocity of a neutron star which has c u;wnrtwdw 1; )cy7f --ui/6ic8xajmbollapsed 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 chqh3(x0o vynd. s7ncm tt93v7 nange when the star in Problem 56 collapses to a neutron star? q thvn933ox 7mn(7sv nct d0y. $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believed to be a neutron staepm 3*-q -wkrrr of mass 1.5 times that of the Sun, with diameter 20 km, is observed tq -mwr*ke3p-r o 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 galax:du i5* 5dqewwo6p9qly to 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 massfgmdj ,a ir4zl*j +2q7 (in eV) would provide the critical density to close the universe. Asm4qf+jaz il7 jdgr *,2sume 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 peak at 600 nm and 400 nm, respectivelylgpjsl6e*,/j uzzr6 z)a2 p 2vx9uh 3v, both lie on the main sequence. Use Wien's law, the Stefan-Boltzmann6ajuz sgup,6j)z*vxeh/rlz p2 v2l9 3 equation, and the H-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 ;,h8mlrmd3xyy6u2dssbdm +/0 parsecs. What is our minimum angular resolution (in degrees)hd3yls +myru/d2 6 dx;b,8msm, based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidh;;v w: x1l2;zqb5*blu*ah xxrvl y7nence, the Balmer lines from singly ionized helium in a distant star happen to overlap with the Balmer lines from yb :;*;2 xbn7hlv1lu; hwav*xxqr5lzhydrogen (Fig. 27-22) in 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 (0fg0 h oqhma8collidh mh a(o0g0f8qer? To what era in cosmological history does this correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the 2wekwf ;e -i/p d(-hvv1f.qd jox(hj2rotation of gas around what might be a supermassf-e/jik.hx;q de wvfod1(hv (w-2jp2 ive 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" hydrogen line at 434 nm emitted wlw 380a/dslt from the gaws/adw l30l8 tlaxy 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 massive enough) will vhi*,- 1:0dwt j c k u:6tgsi0fx:jpjlbegin fusing carbonk vju istc 16i:j0g:pftdl*jx w0,-h: 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 reaction t:j;ekq/s;e x.wx *tm
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 e. g*dq uf83kvxqualed the critical density of the universeg *3kqdu 8f.xv, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$