The Milky Way was once thought to bj/-hmrf1; tu*v2u hmm (p.v,uwuf-oee "murky" or "milky" but is now considered to be made up ofh1m* ,uuo. jhpwerv (uff/t 2--vmmu; point sources. Explain.

A star is in equilibrium when it radiates at its surface all the 2nt3gd43aimj energy generated aga td2mji33n 4t its core. What happens when it begins to generate more energy than it radiates? Less energy? Explain.

Describe a red giantqyneu6t-ptxo)4/f5 u star. List some of its properties.

Select a point on the H-R diagram. Mark several directions away from thibh-fcn.7q3k os point. Now . f nb7hqck3o-describe the changes that would take place in a star moving in each of these directions.

Does the H-R diagram reveal wwzk*pxj 7d 78anything about the core of a star?

Why do some stars end up as wyc(;fsor)r5 ,4d(tku c: e bkbhite dwarfs, and others as neutron stars or black ho,o; ftuyckb(5ed)r krc :s b(4les?

  Can we tell, by looking at the population on the H-R diagram, that hotter main- 9uyr,,mj- v stfw,j,usequence ,yjmfvwr9,tju - ,u,sstars have shorter lives? Explain.  ----待选择----yesno 

If you were measuring star parallaxes from the Moon instead of Earth, what correh ehvakdtx69; +m0*xo ctions would you hmo 6eax hx9kt+vh 0d*;ave to make? What changes would occur if you were measuring parallaxes from Mars?

Cepheid variable stars change in luminosity with a typical period of severj 5hf3l fob61pal days. The 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 gala pl1hf6ofb j35xies?

What is a geodesic? What is its role in General k3j l-)r*ljy3 p jigs6Relativity?

If it were discovered theft 6nxpxr(5f,e qt -,at the redshift of spectral lines of galaxies was due to something other than expansion, how might our view of the universe change? Wrtnx(56qtf f p,e-,ex ould there be conflicting evidence? Discuss.

  All galaxies appear to be moving away from us. Are we therefore at l81 y3lmax.un* y3r htthe center of tn xlhyl y3r.au*m t831he universe? Explain.  ----待选择----yesno 

If you were located in a galaxy near the boundary d krs:9/43ly h+viyggof our observable universe, would galaxies in the direction of the Milkyy+srk:4i /y dhv93 lgg Way appear to be approaching you or receding from you? Explain.

Compare an explosion on Earth to the Big Bang. Consider such questions as: Would/+b6/oro qc rb 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 universe would this corrbq/r or/c 6o+bespond to, open or closed?

If nothing, not even light, escapes from a8kmmb+ gu( (7 slxr+moje21ev black hole, then how can we tell if one ibsmm+ v(l28 e1(ox ejgrmk u+7s there?

  What mass will give a Schwarzschild radius equal to t+pq gfuy(3z5j48 uysohat of the hydrogen atom inj 5 4yyo8q u(ugfsp+3z its ground state? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion years. Find th-n1 6vnle ux1y9mc0ikat time on (Fig. Below). People have lived on Earth on the order of a million years. Where is that on (Fielvck90 i -6mynx1n1ug. Below)?

Explain what the 2.7-K cosmic microwave backgrjl4oy lm: pbpqux9w;l2t25v- 2 k9 ddqound radiation is. Where does it come from? Why is its tempdql l2o pux5-t9v24w2 9jdb:p; qmylk erature now so low?

Why were atoms, as opposed to)qyts70 s peyk:q 6a3rl;0xab bare nuclei, unable to exist until hundreds of thousands of yr :;xyybatss l6 )k30a 7eqp0qears after the Big Bang?

Under what circumstances would the universe eventuallcs wc:-ml j37f3:vwb5menej :u w4l w-y collapse in on itself?

  Using the definitions of the parsec and the light-year,j0xs:e tih*7kbwz4 did; a)nj;+p1g y show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax vn9vv*j te 57bof 0.38 seconds of arc. How far away is it? d =    ly

  The parallax angle of a c9(gg k0u*xb)z1m 6 ;gkrjsmf star is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its parallax angle? y sz6x+94:arihe9 th e
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 yd ;zj.ms . 1nd*mjvii.hv q/: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 secondym2u-abr e--;16.yqjhgoc8:ngxqy x star, will the parallax angle of thxuy1 :yxg;e. n6c j- 82 bq-h-oyarmqge farther star be greater or less than that of the nearer star? By what factor?

  A star is 35 pc away. How lof.:1ohh vth f6ng does it take for its light to reach us?    years

  We saw earlier (Chapter 14) that tj13: oka .z6xv j2j6zist, nuthe rate energy reaches the Earth from the Sun (the "solar conxiz3t6 avk.j,o uj:tj n612szstant") 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 themnp.(awl:x6 .tyu.nb Sun as seen from Jupiter as compared to its brightness from Earth? (Jnxwn.. tl 6u(p.ba:ymupiter 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 observed fromox9 x*s fflka3*q2 oh0 the nearest galaxy to us (Table 33-1). Compare to the angular width of 3f f9h0ks xoxl2 *oaq*the Moon from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, what will be itsdx eqcfrim(31 nlog.8h- x 67*lg+iwd average density if it expands out to theh6o7x .ln -g1ld *w3x iq(eig fc8r+dm 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, i,coqr*df u3y -t is expected to be about the size of the Moon. What angular wi-f *r ou,dqyc3dth will it subtend from the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whose mass 5ds tkqh 2t0f)dpmv(0pu)jc *is equal to the Sun's and whose radius is equal to the Earth's. How many times larger than Earthcm)v dp q fup0)sd20h*jtt 5(k'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 abo0m zf *)zf:rzkut 11 km. Calculate its average density and compz*) zfrzmf: 0kare 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 for the He burning reactions of Eq. 33-2. (The mass 2zsns(1e,kb r m,4msrof the vers,,sskr2m e1m rz4nb( y unstable $^8\text{Be}$ 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 brigktoxxp;/90 v2m u//pfy sh7qt 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 the same dists(b0o- ;bwu-f mfsx+-7wq.r,qp 1zjav b9hob ance from us. Twobfj;o ab70 -upqb(s fw+wxm,.1bs- -hzq9r vo 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 Schwarzfpeiw;,9)nz *xlv *dyschild radius for a star with mass equal to that (a) of our S vy)ld; n9*izf*wep ,xun is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radiu,0:t ie 9ikkpps for a typical galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a sphere, for which the sum of -p b8gc6xqdz;7zuw x 1the angles is (a) 359º, bguz xx-q71 6p;8w zcdand (b) 180°.

  What is the maximum sum-of-the-angles for a triangle on pg1r q *n86t-k;bpfk da sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% ofscy+du a51 j.q 8gsow+ the speed of light, roughly how far away is it? 1sgjoacqyw5d8s+ +u .v =    Mly

  The redshift of a gal/ng 3lv0mykgc ( i2)xfaxy 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 zf *a il5(q*pt"edge" of the universe, say 12 billion (fta *5*zlip qlight-years away. v =    c

  Estimate the observed wavelength for thea0yzu66 jlkl0x+io/u 656-nm line in the Balmer series of hydrogen in the spectrum of a galaxy whose distank jloa6/i 0zxul0u+6 yce 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 from us, if the wavumvbpmnp/ *u xx3. +t*elength for th x upt./+ um*mnp*xbv3e hydrogen line at 434 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 with ki ms* cj8nucq.46u5ttj5 d8;lixws 3$z = 0.60$? v =    c

  What would be the redshift parameter:kcxs rz 7;t um8ucz.8 $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that theceok4w22ip) in*0pb :cetz)q 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 wavelength at the peak of the blacx/b0 rt,uxtc 2;it(h ikbody radiation distribution at 2.7 K using Wien’t; ic,tuh(i2 xtxr/0bs law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of th0bok*j3wp8yomgh (+ be 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 distand yk-*o.r:0b vye o u670ua/r, obuixgce between galaxies) at any one moment is believed to have been inversu a-*0:yey,6o / bxv.biog ro0urdku7 ely 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 h: xleaefp0 rx(6qh+mu ez5r1w9v)e /had the universe cooled below the threshold temperature fvhwhe0uze5l:rp(mereqx x/+ a6) 9 f 1or 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 star/ tb.02;gqx3kg5fcz2 c b 2d+cvhhpfds 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 chv/ 2zcfbfqkx+;.t bg c g2h0dh5 dp3c2anges in temperature, luminosity, and size.

  Assume that the nearest stars to us have an absolute luminosity about theun j8o;nw- e5g same as the Sun's. Their apparent brightnog5n 8wjnu-e;ess, 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 vel+pdkmwmyg 7yj g)z6 05sq0.dpocity of a neutron star which has collapsed to a diameter of 20 km, from a star whose radius0qmj wyk pzd50g7) +g.s6pydm 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 r+ h* xwoy,;+cj q ngw*d3mvfu:otational kinetic energy change when the star in Problem 56 collapses to ug+ yw3m:x+fqh,vj;*no c* dwa 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 r -+:wf/ivluu1.5 times that of the Sun, with diameter 20 km, is observed to have a rotat-w:u/ r u+ivflion 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 G6peg(;jf-q5p txq+u s g4o :pgalaxy 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 densitxn83f z1urwum6us v 5*y to close the universe. Assume the neutrino density is, like phot 5vx6uu* 3 frnsuzw81mons, 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 4o9cig: g:g 7.bqjrq r600 nm and 400 nm, respectively, both lie on the main sequence. Use Wien'ir:gg 7.r q4g9jqco:bs law, the Stefan-Boltzmann 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 100 parsecs. What i90g3twdhqgij -: auv; s our minimi-;jqg03u9g ad w:tvhum angular resolution (in degrees), based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidencej05a+ c bs0lkp, the Balmer lines from singly ionized helium in a distant star bap0k s+5 cj0lhappen to overlap with the Balmer lines from hydrogen (Fig. 27-22) in the Sun. How fast is the star receding from us? v =    C

  What is the temperature that corresponds toyv 6s6byp,e h6kw;1dc 1.8-TeV collisions at the Fermilab collider? To what era in cosmological history does this cor6k61 ,bscpyv yhw6e;drespond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured t1gwtgq5czu;p b2(haxx7vs ;: he rotation of gas around what might be a supermassive black hole of about 2 billion solar masses at the center of a gala xbqzu 7(;p2;w1x:vtsg5acgh xy. 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 ftn c:idkikq)2- kz (gdae5) q)rom Earth. The "blue" hydrogen line at 434 nm emitted from the galaxy isia z it5-(kcd):qe )) 2gdknqk 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 u5dxhs86a( ub3vhr8 g) will begin fusing carbon nuclei to form, 85uh 3xb8 suh6g(r advfor 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 reactioyir 7u87smh(x 3e fbc,n
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 critical 1b7v+;il +ln4fhjr0ly3vu imdensity of the univer4h3lvjbfur+iy+; 7l10 nvml ise, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$