The Milky Way was once thojn gp8 toi3d75iwi9/hught to be "murky" or "milky" but is now considered to be made up of point sources. Expw gpd 9ji8i75ioh t/n3lain.

A star is in equilibrium when it radiates at its surface all the energy gener-x,kie x,,.z6qwki xo ated at its core. What happens when it beginsx ,-zio6.xexq,i,kwk to generate more energy than it radiates? Less energy? Explain.

Describe a red giant0p4deqja; 7gitd( z7 h star. List some of its properties.

Select a point on the H-R diagram. Mar.w mx)i/jdoi6k several directions away from this point. Now desx.mi/ iwo)j6 dcribe the changes that would take place in a star moving in each of these directions.

Does the H-R diagram reveal anything ai5 c:j1iz8 edgbout the core of a star?

Why do some stars end up as white dwtpq)cex 2pz*be8) v /iarfs, and others as neutron stars or black holesbx8/c z )pit)2qvep e*?

  Can we tell, by looking at the population on yk+k2 ft+l cu18rp9k ithe H-R diagram, that hotter main-sequence sk21l+t k+ pr kfc89uiytars have shorter lives? Explain.  ----待选择----yesno 

If you were measuring star parallaxes from the Moon instead of Eaz)tb 4:cyiecug*u5*hztx2 . 9 n( .v6sb vompkrth, what corrections would you have to make? What changes would occur if you were measuring p)4ubuz po:(h. kc n. sxz9 ytvv e*cm2ibg*56tarallaxes from Mars?

Cepheid variable stars change in luminosity with a typical period of severdiw:a (z s6s3(mhml 0c4wwcr6al days. The period has been found to have a defini6im(rmc4s:0ch6al w(wz s d3w te 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 is its role in Generalo+cozqitt/8 p aax 6kyz gou7+,;vv;) Relativity?

If it were discovered that the redshift of spectral lines of gpgd/l ;swmd +2g,4lm balaxies was due to something other than expansion, how might our view of the univew4llp,; dgg d/m2bm+srse change? Would there be conflicting evidence? Discuss.

  All galaxies appear to be moving away from us. Are we therefore at thm ;o*qdspzc9:z :frxj erc-8le(v jxh5;6la:e center of the universe? Explai p hf;:qclj(ms9 5;v :zr*coxel z6ad-x 8er:jn.  ----待选择----yesno 

If you were located in a galaxy near the boundary of x:0z8j8j l 6l fjx(vzd(8xlacour observable universe, would galaxies in the direction of the Milky Way appear to be appl0(8ldx8j x l (c8jz:jz6xavfroaching you or receding from you? Explain.

Compare an explosion on Earth toqv-0 (n qb+qy/5pt cmlk ;)egm the Big Bang. Consider such questions as: Would the debris spread at a higher speed for more distant particles, as in the Big Bang? Wol5+c-b(e 0mm/;ktg)qy vqp n quld 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 tfbl* (xz,q) hl// 6i/hz)yw2 pwhq2 dc1mflhkell if one is 2bzhhky)hmf l* wq lc2zqiw /l, )h6fd//x(1p there?

  What mass will give a Schwarzschild radius equal to th iw0dw6lh5d ta( gh-5rb)k(u uat of the hydrogen atom in its ground std0d t6rkl-wwg(u 55hab( hiu )ate? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often giv b s5l-th/jt-gen as about 4 billion years. Find that time on (Fig. Below). People have lived on Earth on the order t 5j -bsgl-h/tof a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic microwa8j10r xzma,eh ve background radiation is. Where does it come from? Why is its temperature nowahe1,r0 jx mz8 so low?

Why were atoms, as opd 9.pecmfo;h br+v1(xposed to bare nuclei, unable to exist until hundreds of thousanovfp 9b (.x;cm1dhe+r ds of years after the Big Bang?

Under what circumstances would the universe eventni u 0 zgak.6*wt fn7)ix;uxu,ually collapse in on itself?

  Using the definitions of the parsecg1t8; pb zzit eech434 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 if dm qi-:7:zaqs it? d =    ly

  The parallax angle of a star is 5lrz/5ha q;vk a)g y,m$0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What isnmwns7t55o 5xozq :awd 0k0c8e8n -fj 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 ay +:;t: *ycgz/kpx1tx3vtug 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 secondqepmh6x1l,*rc f 5h-r star, will the parallax angle of the farther star be greater or less thh6lhfp-rrm5xq ce 1*,an that of the nearer star? By what factor?

  A star is 35 pc away. How long does it take for its light to:v3 5( 37g w/njsrqpgpnjqc.d reach us?    years

  We saw earlier (Chapter 14) that the ratesh +(.xbnva 1w energy reaches the Earth from the Sun (the "solar cowxa+n1vb .s (hnstant") 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 +w gpds ,qrk 3,)2q/atyhxy 4gzc:g4t to its brightness from Earth? (Jupiter is 5.2 times far:)xc 4pyyz h kr/ 3gd2aqq+tg, t4swg,ther 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 ower94ggkx9u + bserved from the nearest galaxy to us (Table 33-1). Compare to the angular width of the Moon from Earth x w9krgug+9e4. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant l+ e3xqc50zxw/)we:evjt2 kh , what will be its average density if it expands out to the orbit of Earth e2/5ke:wx)we h c tvjz0+x 3lq($1.5 \times 10^{11}\ \text{m}$ from the Sun)? $\rho = $    $ \times 10^{-4}\ \text{kg/m}^3$

  When our Sun becomes a white dw /5k e6af+hdzjarf, it is expected to be about the size of the Moon. What angular width will it subtend 6+/jak5d f hzefrom the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a z-sey8c, )v dzn 4ezdg.ct:f9white dwarf whose mass is equal to the Sun's and whose radius is equal to the Earth's. How many times larger than Earth's density isyne4 8 dgs:c )z,d-9e.zzcvt f 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 io0cqm8 w5/do a radius of about 11 km. Calculate its average density and compare to that for a white dwarf (Problem 13) and wi m/o5 0qdco8to 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 H 5k wwtm *b,bz9/1 um3lvnq,rte burning reactions of Eq. 33-2. (The mass of the very unstablmn3 t ubqmlwwt,vz19r kb,5/ *e $^8\text{Be}$ 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 app kf uw+ jo8;v,6l (.yg.tzt 7eh es4jzp;lbmm9arent 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 samen,t2 :+eu lmpb distance from us. ,un+ et lb:2pmTwo 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 star with mass eg 9g7o /lkm*li ,z )janep2a-bqual to that (a) of our Sun )z-k* ngm ab, a7gilej /po2l9is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typical galaxy (like ours)? Rp9gnl w ydk,4mvw/ /f1 =    $ \times 10^{14}\ \text{m}$

Describe a triangle, dr5,i9ke eba.d z(q1eh gmmt7o( awn on the surface of a sphere, for which the sum of the angles is (a).z(k t(d a h, 5qm7eomi9egeb1 359º, and (b) 180°.

  What is the maximum sum-of-the-anglex sb(-+s b edvi4 ,p;jks2k3nvs for a triangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the speed 6*k5*lg9 ti cjyzd 4nbof light, roughly how f9tz6c* 5yj nl4g*bi kdar away is it? v =    Mly

  The redshift of a galaxy indicates a velow;t yl7taj/ u4city of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (relative eify 4u4p2 sqe*ajs7;to us) that is near the observable "edge"4squi*;y7e eps4fa2 j of the universe, say 12 billion light-years away. v =    c

  Estimate the observed wavelength for the 656-1*b l/ta9jcqb nm line in the Balmer series of hydrogen in the spbb lt9*a/c 1jqectrum 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,i1i3-;wj w s62nc1rm gczn 4wfg5ic ;k and its distance from us, if the wavelength for the hydrogen line at 434 nm is measured on Earth as being 6jic1igfz4cw3 -ws;n51rwk cmg; n 62i10 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 galmxew8x*1o k zmlj 87 72aqpua:axy with $z = 0.60$? v =    c

  What would be the redshift u2cogsv-1nf :;/qxvp parameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the f y4;hminaeelfcw1ad :v ) b8n77q)b6Doppler 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 wy7p(*sr, n,:eoarnd the peak of the blackbody radiation distribution at 2.7 K u,,re nywn:(ro*adps7 sing Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical densityy 9,nl lsr-i9b/ hp3 vvdzrs-9 for closure 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 11tzgdgp/f8njn0njux - *hj/distance between galaxies) at any one moment is believed to have been inversely proportional to the absolute temperu1hxj*n0jn 1 - 8jz/tng p/dgfature. 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 timexnao z*57 3ihm had the universe cooled below the threshold temperaturimza h7o53x n*e for 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-sequer1fnwui1m+ 8cnce stars could undergo the three changes represented by the three arrows, A, B, and 8ncrimf1 w +1uC, in the H-R diagram of Fig. 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-,1 du9is v8vpexv 7m5o8t gqu the same as tguq1dm9 peu 78oivv5,x s-t8vhe Sun's. Their apparent 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 5n7f clx0luq2angular velocity of a neutron star which hxuq 5lfn72l c0as 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 change6w-xks tko8+ki*at2-s ;-w (vc5:s ixoiklzn when the star in Problem 56 v ixcz-lk2 owit xiw-kk(6 sk ;: n8o*t-a5s+scollapses 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.o- s9d ,8xmtjrh qbp(u n.jj0u*foxcjgy:90.5 times that of the Sun, with diameter 20 km, is observed to have .j:0qs9 f jgjmoo8d-0t xh9ubr (,py*c .uxnja 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 galaxyeak 2tyl327i q 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 mass (in eV) would provide the critical +1ob*vx 5j6/em0lc ip jlqe1zdensity to close the universe. Assume the neutrino density is, like 5 jqvbpi0jemec1/1l*zl + 6xophotons, 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 q2. rzloiel/s 2w+(;uko n2nlvtty30 at 600 nm and 400 nm, respectively, both lie on the main sequence. Use Wien's law, the Stefan-Boltzmann equation, and the ;(zerqt2olonu0 t2/2kv +w nlyl3si. 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 distancessm4.zz78redu. m p 8zs with parallax at 100 parsecs. What is our minimum angular resolution (in degrees), based on this information?szr mupd8ez.z 78.ms4 $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from singly ios:- w bu.az .6iyn.b/ wyzzrzfvwz6mg8v 4(n4nized 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 receding fr(wiv 4a/.s. wmvn6nwyr g-zz8zfy6 4:bzb .zuom us? v =    C

  What is the temperature that corresponds to 1.8-TeV collisions at theac( nxb1/mb w0x 5z29kbhvd*o Fermilab collider? To what era in cosmological history does this correspond? dzhm(ax/bx w2vb90*nk 15 ocb[Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recuv.* pwzk v4y)ently measured the rotation of gas around what might be a supermassive black hole of about 2 billion solar masses at the center of a galak4zvpw ) y.u*vxy. 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 emitfhk eeaf8ug x o-soa2/26l lyg5j9z41ted from the galaxy is measured on Eafs52a y 8auf ogjlh/6 9exgezl124ko-rth 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 g mr;/s iy-l,omol(m: *((kvr / ughdamassive enough) will begin fusing lghm;o(-(s a v dlumgk/*m i(:r,ry/ocarbon 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 z+i+/n /wejyk
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 equale/ vop d/ajoa,mvf,wa+ v30y* ed the critical density of the universew0vay3jfa p omd,+ oa, evv*//, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$