The Milky Way was on53l,;myeudhmf6zdu/ xk--t p ce thought to be "murky" or "milky" but is now considered to be made up of point sources 5dhpd-;3 m,ytule-/f 6muxz k. Explain.

A star is in equilibrium wh9,ggi no 2s-ypen it radiates at its surface all the energy generated at its core. What happens when it begins to generate more energy than it radiagy 92 sgno,i-ptes? Less energy? Explain.

Describe a red giant swc.mj lqb4a9/)rmuyygf; n 63 te(i4v tar. List some of its properties.

Select a point on the H-R diagram. M eqerrltd+*9j;u-ja 9ark several directions away from this point. Now describe the changes that would take place in a star moving in 9aerqj-j+ud9t* re;l each of these directions.

Does the H-R diagram reveal anything about the cor9qhla;kemh: 8 r53lrygajxfhl/ h+ +.e of a star?

Why do some stars end up as white dwarfs, and others as neutron star:w jlxhn u9.6es or black holejl n 6e:x9wh.us?

  Can we tell, by looking at the populgpw6 4r47yugcm( v2ffj/l i7mation on the H-R diagram, that hotter main-sequpjv(7 lmmui g 4fc/yw42 7grf6ence stars have shorter lives? Explain.  ----待选择----yesno 

If you were measuring star parallaxes from the Moonlaf39 adt 7lj; instead of Earth, what corrections would you have to make? What changes would occura3;7lflt9dja if you were measuring parallaxes from Mars?

Cepheid variable stars change2onnud 6)z)q 6+4mkuth bj9 ae in luminosity with a typical period of several days. The period has been found to have a definite relationship with the absolute luminosity of the star.+anb4))2mztoq6 6du 9u hjekn How could these stars be used to measure the distance to galaxies?

What is a geodesic? What is its role in General Relativity/ x 8 .g*8 z4rn9idc:9zpaea:imhox kp?

If it were discovered that the redshift of spectral lines of galaxies was duc(f /)ha 1+gfi k2 war:l4pvice to something other f:2wv1rgi+ci)c h4l apka(f/than expansion, how might our view of the universe change? Would there be conflicting evidence? Discuss.

  All galaxies appear to be moving away from us. Are1 mkdo: :)a;e lmrb.tag)d; mn we therefore at the center of the universe? Exp 1adbmtoemmr)n:k; la . g)d;:lain.  ----待选择----yesno 

If you were located in a galaxy near the boundary of3 sedgqeq8 b- oi8v1w, our observable universe, would galaxies in the direction of the Milky Way 8ve1d, 8e igoqs -wb3qappear to be approaching you or receding from you? Explain.

Compare an explosion on Earth to the Big Bang. Consider such questionifz(/q0 to peip vd/fh.f7v6,s as: Would 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 corresp p./v,(7edvffq/6 hf oi0tipz ond to, open or closed?

If nothing, not even light, escapeglyc9b5:5nyloze / r; s from a black hole, then how can we tell if ogcl5b 5zl noyey/;:9rne is there?

  What mass will give a Schwarzschild radius equal to that of the sez l+ 5snw4fb ds064bhydrogen atom in its ground state? M = we+n45 bsssf640lbd z   $ \times 10^{16}\ \text{kg}$

The Earth's age is often gcac4a(yr*(0tv+ .ng4m pbu v riven as about 4 billion years. Find that time on (Fig. 4cg *.0p(r+vuatmrnc(y4b avBelow). 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 +yd) xaj3 1(e6a c,dc/i9xes hper 0mfbackground radiation is. Where does it come from? Why e9h 1 3 dd+rp a0m)eijsa6cx,xf( y/ecis its temperature now so low?

Why were atoms, as opposed ekfrw8 - r8zw:to bare nuclei, unable to exist until hundreds of thousands of yea8erfw-:8 kwrzrs after the Big Bang?

Under what circumstances would the universe eventually collapse in on i tp . d.vta.u(*jix0 hlybj1b+tself?

  Using the definitions of the parsec and the light-yevf / ,m/ie0cz3 m:q -,stlq.fip2xafdar, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0c 29eg8 c;zwqh.38 seconds of arc. How far away is it? d =    ly

  The parallax angle of a star lddmk 2k5/mk3*vdb.m is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its parallaxk*k 98abi qozv o.s)/x 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 stco8b6 ;xnry2 nv,px 3bar 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 second star, will the 9: m dn.sh2,kvorrs8rparallax angle of the farther star be greater or less than that of the nearer sta8 2.s9r,h s:kromdvnrr? By what factor?

  A star is 35 pc away. How long does it take for ibr8kn 5c)qb01y 7axg b;te*vhts light to reach us?    years

  We saw earlier (Chapter 14)v6deblauc)7a;1 (xt h wqq9b e93jmq ( that the rate energy reaches the Earth from the Sun (the "solar constant";mqvq 7a(qxt uw)eah39jlbd91 e( 6cb) 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 togy 7d p;31(,h++r mwg dgmvalw its brightness from Earth? (Jupiter is 5.2 timesy7 l,+d(dh ;vgmgwam g+w 3rp1 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 obser*w: 9*6fwhychn (5)lll wbivzb 5-zn bved from the nearest galaxy to us (Table 33-1). Compare to the angular width of the Moon fnbcwl6 5*5l *hvfz:)hy (wziwn9-bl brom Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, what will be its average density if it qh46- +az 3xxn i0qoptexpands out to the orbit of 603qh+ zqt4nxix p -aoEarth ($1.5 \times 10^{11}\ \text{m}$ from the Sun)? $\rho = $    $ \times 10^{-4}\ \text{kg/m}^3$

  When our Sun becomes a white dwarf, it is e)pjla+ty5 v4 (m9ofcpxpected to be about the size of the Moon. What angular width will it subtend from the present distance tovo+c4l ja5( )ym pt9pf Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whose mass is equal to,g tzujqdkc( u: z fp)ra0(y5- the Sun's and whose radius is equal to the Eart fzr ky:tud5-)za0u((q,g cjph'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 solar masses*+zmbra7+ nnh has a radius of about 11 km. Calculate its average density and compare to that for a wrb hann++ 7m*zhite 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 dc( :lzny+,e vof theel+:(ycnd, zv very 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 sameq4b70skvni 67:+2wjt.ew an ud4v jmc apparent 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 same dic7t6 x-bs t2 nt0wnlk)g6dzo2stance from us. Two such sta n-c gwttb0 n6) 72tdzlx62oskrs 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 equal to tha*(;f tfk a0few5z yn6pt (a) of our Sun in*6 pa(0;zwetk 5yfffs    km, and (b) of Earth is    mm.

  What is the Schwarzschild radiuuka3 7 ujzc-n/s for a typical galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a sphere, for which 5- (s4y cdo/5uj vw8wbvzlv0jthe sum of the angy4/ vcjz(w8v55l-usb ojdv 0w les is (a) 359º, and (b) 180°.

  What is the maximum sum-of-the-angles for a tria(2e6qr ybpv4 jngle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the speed of light, roughly hlr9uwoatsvf -9 l2- 3crind;1ow far away9lncoa-ir wd;f ts 9urv1-3 l2 is it? v =    Mly

  The redshift of a galaxy indicates a)o 2p8fqvblm )1qz*oa velocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (relative to us) that is neofdgw 4qk 5;o- ih cyfq-(zh68jpb1 6lar the observable "edge" of the universe, say 12 billion light-years away. v =d;whfcb4p6loij -6 1(ghyofqzk q8-5    c

  Estimate the observed wavelength for ,( 9s2ah olflkthe 656-nm line in the Balmer series of hydrogen in ,la9k sf 2hl(othe spectrum 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 distance s*n gwu;otj1ii(c 3-l from us, if the wavelength for the hydrogen line at 434 nm is measured oc*3loj ns;i( wuigt 1-n 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 wit,h - k68w ssxztv0uh4gh $z = 0.60$? v =    c

  What would be the redshift y-dm7 r7v,( lx;q0xiz9vqujgparameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Doppler shift in wavelength is i: (lat1i itg+$\Delta\lambda/\lambda \approx v/c$ (Eq. 33-5b) for $v \ll c$. [Hint: use the binomial expansion.]

  Calculate the wavelength at the peak of the blackbody ra )ntr3po/ 2ao0lmvs2ldiation distribution at 2.7 K using Wien’s lm p0vta/o22n)ls3rloaw. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of the univegmc;dio0 i,ke 8p5h. zrse 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 (th+hc63qnny,h j e average distance between galaxies) at any one moment is believed to have been inversely proportional to the absolut 3nq6h jy+hnc,e 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 pd o7:hdjb.: pcooled below the threshold temperature for producing o7:bhj: p.d dp
(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 stars could undergo the three changes rx* d,sutt5zm u7m;zy8hpf0 8aepresented by the three arrows, A, B, and C, in the H-R diagram m;dh upu8zx*a8,sfm0 tt57 yzof 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 abo rncmt.vt11z9j h)0.tsfgq u, ut the same as the Sun's. Their apparent brivcgjqusr n tmz)1f 0t91..,t hghtness, 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 ve f *nb.7n 4ewzizdy qup,1(nh/locity of a neutron star which has collapsed to a diameter of 20 km, f.nh q1,ui7e* df/p(b4zwynz nrom 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 3ha5ou 5v)-w+xq +zobbp df5nstar in Problem 56 collapses to a neutron snofau5oxqd5p wz+)v b +5h-b3 tar? $\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 t/*ukpufn6 vr1 rz j75soyum))imes that of the Sun, with diameter 20 km, is observe rum*7 nvr)u)ju/pzsok1 6 f5yd 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 Galaxy i +w42 vl-iquvatg- ;yas 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 res v/gp6y)j+mqi (qez3 ft mass (in eV) would provide the critical density to close the universe. Assume the ne)qg(+/ p zfi6vm3jyqeutrino 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 i.omjv ig/ ,3ij,4xkjnm, respectively, 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 diametero,gjiivjkm x./ 43,i js. [Hint: see Examples 33-4 and 33-5.] $\dfrac{d_{400}}{d_{600}}$ =   

  Suppose we can measure distances with parallabc (.yg rc ro0-sna9.ji*ny/jm7 s q*ex at 100 parsecs. What is our minimum angular resolution (in degrees), based on this in-ng.0s*omq9cas b.y r(ji7j/r yn* ec formation? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines7kg no-h b3g2y from singly ionized helium in a distant star happen to overlap with the Balmer lines from hydrogen (Fig. 27-22)y23g-7hk on bg 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 Fermmy2)s :j3(pg vi: mfimilab collider? To what era in cosmological history does this correspond? [Hint: see (Fig. Below).] j)(3fiyp v mgs:2mim:T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation of gas around what might .mh ime8d scc 0iy8g;.be a supermassive black hole of about 2 billion sol;c0.cm m8dih y esi.g8ar 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 fro6s;lem6 l3zu lm Earth. The "blue" hydrogen line at 434 nm emitted from the galaxy is measured on Earth to be 650 n6 meullsz3;6 lm.
(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 y 9v;nxd m*dwm08d p/tbk6f50.v t quwbegin fusing carbon nucn/ 00kpd 8 ;w59bmdut 6w .vxvyqfmt*dlei 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 reactioytb85e1j ba+c6-xeke 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 equale2f ;;*snfvdz mqiq7y: d the critical density of the unf2; *i:qv7 zqmdfs;yniverse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$