The Milky Way was once thought dw++;vldw-xcto be "murky" or "milky" but is now considered to be made up of poiwd;x-ld +vc+w nt sources. Explain.

A star is in equilibrium when 92yyq si28 qluit radiates at its surface all the energy generated at its core. What happens when it begins to geqis 292uly 8yqnerate more energy than it radiates? Less energy? Explain.

Describe a red giant star. List some of its properties fsy(ax/01ikq w6pp(f1w8pdq .

Select a point on the H-R diagram. Mas 3y/svu5: p2rk6llyv rk several directions away from this point. Now describe the changes that would take place in a star moving in each of the2y/6k 3uplv5lss yrv :se directions.

Does the H-R diagram reveal anything about the conxcwq+u; i)6 bw7j9uc re of a star?

Why do some stars end up as white dwarfs, and others as neutron stars or bl0lhvs3w4 k j*kack hh 4w0k3*slkj voles?

  Can we tell, by looking at the populationpndfi(jf2l mia/z4ch3 ., e0b on the H-R diagram, that hotter main-sequence stars have shorter lives? Exp,3fanpzm/deb i 0.4 cj2hfl(i lain.  ----待选择----yesno 

If you were measuring star parallaxes from t8 s8+6dnxd vbzhe Moon instead of Earth, what corrections would you have to make? What changes would occur if you were measuring parallaxesbdx88sz6+vn d from Mars?

Cepheid variable stars change in luminos e:rsxa e:am9tk*.+zeity with a typical period of several 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 di.x9:teae mr k ase+z:*stance to galaxies?

What is a geodesic? What is its role in General Rme(0 ah7 c9ulo 1pzdc9elativity?

If it were discovered that the redshift of spectraln14p( xwjfwl5 lines of galaxies was due to something other than expansion, how might our view of the universe change? Would there be conflicting evi4fp1l 5jwx(wn dence? Discuss.

  All galaxies appear to be moving away from us. Are we therefore at thei*z6l , r 0(yake.lolj center of the univerl l(k ,.jl*e0r6 yoazise? Explain.  ----待选择----yesno 

If you were located in a galaxy near the boundary of our observable universe,,kn ljv cofi v8iqq2h4z6v j8a3c)/l0 would galaxies in the direction of the Milky Way appear to be approachv q)qilc 8jhcj4,/2v8 6o0 aknvizlf3ing you or receding from you? Explain.

Compare an explosion on Earth to the Big Bang. Consider such quesn 2epwk) ctp20tions as: Would the debris spread at a higher speed for more distant particles, as in the Big Bang? Would the debris come to rest? W2ppt 2nw0)k echat type of universe would this correspond to, open or closed?

If nothing, not even light, escapes from a black holepkceqi 7hd p *;:pz8n5, then how can we tell if onnz:p;ci p78k*h qd5epe is there?

  What mass will give a Sc4ml9zvdut6 3phwarzschild radius equal to that of the hydrogen atom in itst6 dp9uvzl43m ground state? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as sb eo op.ok:tb)1:5 qfabout 4 billion years. Find that time on (Fig. Below). People have lived on Earth on the ordebk :1)epqt.oos b5o: fr of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic microwave(,fwtl2exdbr 5pq)*pya hgd0(zk7o3 background radiation is. Where does it come from? Why i0l2 dkp,3reh patb )ywdzx g 5*qf7(o(s its temperature now so low?

Why were atoms, as opposed to bare nuclei, unable to exist until hundreds o1)9dnzk / eujkk0c2ga4icrt9 f thousands of years after the Big r9 dkecnz) ik j/aukg49c2t10Bang?

Under what circumstances would the uj8m5wr bzr- 4cniverse eventually collapse in on itself?

  Using the definitions of the parsec and the limg-1 otf,ni 6e f8z0mh;i9khf ght-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 wzos*m6vhs9l3:s3g b e9r j(jvn- 0otis it? d =    ly

  The parallax angle of a,lz1 vusacxa q8m9ejnf n56; 7 star is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What tc kid4pebf/9p,gw)5*vt n9 tis 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 s+b ptsnol. 5,mtar 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 park*f95*fv wd ebs8s4 hax0 wl0rallax angle of the farther star be greater or less than tha5fl8 ra 9b0 x*ewdk0 f4h*swsvt of the nearer star? By what factor?

  A star is 35 pc away. How long does it take for its light to reachgo. nki bd-i22j y/davi( 9u/q us?    years

  We saw earlier (Chapter 14) that the rate energy reaches the Earth from the Sunsl4yu /a (lg+nr ,xfb37lhppg)cd-zl* *m 5ni (the "solar constant") is u ) l4ry 3*mcz,n-nf l dg/pahg5sl*lxp7+ib(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 aso 6o7a u+n 2pfzp3qc;g compared to its brigon3;a7qfpgz2 u+o c6phtness from 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 ourz.q w rb0+ttz( Galaxy would subtend if observed from the nearest galax(wtbz 0.qz t+ry to us (Table 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 w1 loyh/oa bq z0lo,.-uill be its average density if it expands out to the orbit of Earth (oq1l lo,zu/h.y b0 ao-$1.5 \times 10^{11}\ \text{m}$ from the Sun)? $\rho = $    $ \times 10^{-4}\ \text{kg/m}^3$

  When our Sun becomes a white dwarf, it is expected to be about+0n ga5qs5(1wek f f-skr;fnqi)/wg c the size of the Moon. What angular width wil )s(wan; f-re5g sigqw 5kf01c+/fk nql it subtend from the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a 84cmogq 6o nu+white dwarf whose mass is equal to the Sun's and whose radius is equal to the Earth' oq8+6 4gocnmus. 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 has a radiug rcye,b7yv72od3 rrhl b h984s of about 11 km. Calculate its average density and compare to that forhb8yye7h r3r4 c,vdlr ob79g 2 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-values6t inr7drz5) ske 8rk7 for the He burning reactions of Eq. 33-2. (The mass of the very unstabl57ze7drr )i8 6nsk tkre $^8\text{Be}$ 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:o d9//c:zqin nxp1gu 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 distance 0ui;.mr4qatz j5hk( k from us. Two such stars have spectra t 5uh (akjztqr 4i0.mk;hat 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 that (a) of o dt.phvg bjm .52tfx nno02f;8ur Sun is.gn .omhvj58bdx0tp f f2t;n2    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typical galapaj l*i6.uylg8 *x/hexy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the suxje,q)f;cw/xpc 6f* d tliu,jz o;*:krface of a sphere, for which the sum of the angles is (a) 359º,li) * xx jdkq,;*p: fz6 ftjuwc/e,co; and (b) 180°.

  What is the maximum sum-of-the-angles for a triangle on a spherrmtx12vwr: o,:al*p* hz rn x+e?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the speed of ligpqlda )v08oyom53qj; tp)s m 8ht, roughly how far awayl5vsy 8p)o ;qj3 0domqp)8am t is it? v =    Mly

  The redshift of a galaxc5od7 bzi3u/ sy indicates a velocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (relative toauwm1)thi 20y us) that is near the observable "edge" of the unai mtw)h1y0 2uiverse, say 12 billion light-years away. v =    c

  Estimate the observed wavelength for the 656-nm line in the Balmer 0dzdf(vu 2cnc p9y e v/q*7ti*series of hydrogen in the spectrum of a galaxyzpddf*v 7 uct*q c(v9n2y/0 ei 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 dkf68;.fq(mpdi j i 3xlistance from us, if the wavelength for the hydrogen line at 434 nm is measured on Earth as being 610 nm. pf6 lfjdikx(i3;8 .mq
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 iea:5ug ;r9j1wxj 2verp ex36$z = 0.60$? v =    c

  What would be the redshift dpcmceyf2l7olvxy-xt ia 0/5 a (f+ (7parameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Doppler shift in+vxy-)ijozn q3(d b6w 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 blackbody radiation distributi4kl9c 4i9 cmpri;x8xzon at 2.7 K usx9x4 8 mz9r ipiklc4c;ing Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical densityiows p 2zutg64a3e/dp+ h1o s+ 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 (tgy7cr d)e)o4g cszn2*-m +g bxhe average distance between galaxies) at any one moment is believed to have been inversely proportional to the absolx nc scdmrz4eg*)-ggbo ) 2y7+ute 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 below the threshold tempere,nxqre/ ,t l:ature for producingl/: rxe,qten,
(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 2pcxzs+ jbx.u8d( fd-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, ax c.(8j+d2p z- bxfsdund size.

  Assume that the nearest stars ya6fmjera)y)jx 2 ofv 0k3-j ;to us have an absolute luminosity about the same as the Sun's. Their apparent brightness, howeve6ejyf3-)2 rjxyfmokj aa ;0v)r, 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 an1l xy8+ gs3lvlgular velocity of a neutron star which has collapsed to a diameterv s 3ylxl+l8g1 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 k5sb 3aueo,xb: inetic energy change when the star in Problem s: bb ,uaexo5356 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 of magy7h)tuz51t d ss 1.5 times that of the Sun, with diameter 20 km, is observed to have a rotation speed ouzg1tt)y hd5 7f $1.0\ \text{rev/s}$. 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 Gal /ef /r 1zbu4ubhf50bwaxy 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 neutrini nur s 6wqaf7ub1r u.x.k.4 r9f.9ieeo rest mass (in eV) would provide the critical density to close the universe. Assume t rf.ur fabqeux1n.69 4ui.we.i7ksr9he 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, respectivelyttic.r.87+sw jk 7ftrz+p/: et+easf7gv 1ui, both lie on the mask7 7pzt +w81s 7.iefit ecvtf+ .+rag:u r/tjin sequence. Use Wien's 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 witnzk r8 t6:xo9bh parallax at 100 parsecs. What is our minimurb:toz6kn8x 9m angular resolution (in degrees), based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from singly ionized helium in a disul 2td plr/ x x2a6v8zaj9dve62/p9gncjp c 52tant star happen to overlap with the Balmer lines from hydrogen (Fig. 27-22) inn d pt//dlag2celrp2jx62j v5x 8czuv9 pa269 the Sun. How fast is the star receding from us? v =    C

  What is the temperature that corresponds to 1.8-TeV collisinrsxy )hwp5a8 w f-t;l9. tg*ngbw;0 pons at the Fermilab collider? To what era in cosmological history does this correspond? [Hint: see (Fig. hpg.9w8gtpr; *0b;nsyt5-fwx n w) laBelow).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation of gas ari6x)6pms ,pyr ound what might be a supermasppxyr)m ,6si 6sive 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" )*v u, di3hgwhhydrogen line at 434 nm emitted from the galaxy is measug,h*h )3dvwu ired 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 a90e- u qa a+oudwsyzzc 0(3/yr3c-xhstellar evolution, a star (if massive enough) will begin fusing carbon nuclei to form, for example,ay+cdx-qaa ry3hs- wu00/co zz39u(e 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 yu+t ov77*ta :hw xf e+/hi.cq
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 4wasrv3 ,x lk )kc;iebqj(-9t density equaled the critical density of the universe) ,3w;qxt k vj r9i4bslk-(eac, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$