The Milky Way was once thought tep8dp 3:f;vxza) n+ kao be "murky" or "milky" but is now considered to be mad8vaz f +pd3apk)nxe :;e up of point sources. Explain.

A star is in equilibrium when it radiates at its surf,y 0cjozif/ -race all the energy generated at its core. What happens when it begi oi,0zfc/- yjrns to generate more energy than it radiates? Less energy? Explain.

Describe a red giant star. List ghmr+g 6fw55 c4 h)y;vke+iyc some of its properties.

Select a point on the H-R diagram. Mark several(km rv*v j3c-f directions away from this point. Now describe the changes that would take place in a star moving in each of *jm( f-3vrv kcthese directions.

Does the H-R diagram reveal anything about the core of4stmsk9, q na1l wy/5x a star?

Why do some stars end up i8 5a7fvk equ4as white dwarfs, and others as neutron stars or black hok85a4v iequf7les?

  Can we tell, by looking at the population on the Hn/ic d,lv 5tdh.yl37i -R diagram, that hotter main-sequence stars have shorter lives.,dihl 7 di/nlyc3v5t? Explain.  ----待选择----yesno 

If you were measuring star parallaxes from the Moon instead of Earth, whg f 29jp3qmm.16 b;ywl jga)onat corrections would you have to make? What cj9nm 2m 6bl 3;1wp)fggoq.j yahanges would occur if you were measuring parallaxes from Mars?

Cepheid variable stars change in luminosity with a typical pe,6 /d q0r xnt4v/gdtfi03y(c+f0k-zffizudv riod of several days. zc,dgvk0i0tnq4ffd vt/6 iyf(f -r/z03+ u xdThe 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 galaxies?

What is a geodesic? What is its role in General Relat t5k)c sq9tl mxkkvjv9 9a7:ms0af6 r6ivity?

If it were discovered that the redshift of spectral lines of v ij5(mfkjf gz7h5 )t9galaxies was due to something other than expansion, how might our view of the universe change? Would h()j9zi fk5gv57 m jtfthere be conflicting evidence? Discuss.

  All galaxies appear to be moving away from us. Are we theu6fx 9f2wouf -refore at the center of the universe? Explain. ff ux-w9u26of  ----待选择----yesno 

If you were located in a gal4. z+f/hxglksaxy near the boundary of our observable universe, would galaxies in the direction of the Milky Way appear to be approachig.zh /+4sxlfk ng you or receding from you? Explain.

Compare an explosion on Earth to then+q,r,ce* ho/laoq;v Big Bang. Consider such questions as: Would the debris spread at a higher speed for more distantvh;r*oeno q+ l cq,a,/ particles, as in the Big Bang? Would 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 hoqy791 ystc wrg7:dz rz .8cf7gle, then how can we tell if one is thsq78 zygyd: rw7z7grt1.ccf9ere?

  What mass will give a Schwarzschild radius 2j/uw,sgv+ udequal to that of the hydrogen atom in i + jwud/vsu2g,ts ground state? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given p)vzd/(g9l oveqz s. /3pcz/jco9 he9as about 4 billion years. Find that time on (Fig. Below). People have lived onzo/po)9 .e39 9l/sdvjcv pzzq hge c(/ Earth on the order of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic microwmwm gn,vruhl8+7k.nf /:zz2 iave background radiation is. Where does it come from? Why is its temperature now so inm,.+l2z uk:nzrw8hv7m /gflow?

Why were atoms, as opposed to bare nuclei, u-7 + q doiiapie,agvb,9cy0o 1nable to exist until hundreds of thousands of years after th1bida q9iyo- p io ,e70avg,c+e Big Bang?

Under what circumstances would the universe eventually collapse in4/ yky5;7x*cq y tdxff on itself?

  Using the definitions of the parsec and the light-year, showlj q,ew*x- 4*;zwtxon that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a paray+6xv7 cl(ad/fwo93b z rt4j,h( t tcwllax of 0.38 seconds of arc. How far away is it? d =    ly

  The parallax angle of gvpa ;3ru1fcfx6xmh(k ,5 s4n a star is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its parallax anglecen 54:ohd ,3nx4g k/03o wbaxq+yaimoicy 7-?
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 ly j), ep9pieug.ps6dy:dm)op(c 7lv9baway? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away from uu srznusk6. y mx4g4;s+tck02s as a second star, will the parallax angle of the farther star be greater or less than that o n 0mg4kcu4kx sr;ysz u.s+t26f the nearer star? By what factor?

  A star is 35 pc away. How lonf;vbscyq+r16v- g b, l)yt t.ig does it take for its light to reach us?    years

  We saw earlier (Chapter 14) that the rate energy reaches the Earth from the S /w+ 1ws,rto5uum3thuun (the "solar constantmw tur 3twou+hus,/15 ") 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 Sak4dj+ycu(( af k,)9lqzd7bd un as seen from Jupiter as compared to its brightness from Earth? (Jupiter is 5.2 times farther from the Sun than th(clja)kf+(d q9ab4,ud d ykz 7e Earth.) $\dfrac{l_{\text{Jupiter}}}{l_{\text{Earth}}}$    $ \times 10^{-2}$

  Estimate the angular widthmp4nqa 3(p(j zj 3;his that our Galaxy would subtend if observed from the nearest galaxy to us (Table 33-1). Compare to the angular wi( zsn4j3m; (pqp3h ajidth of the Moon from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, what will be ij 6lmfpco+8r0g m*5nm;gj 7ghts average density if it expands out to the orbit of Eartj60m7mr*g jgc5; mlfng+o h8ph ($1.5 \times 10^{11}\ \text{m}$ 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 thev+ jij-x(j7zsykj (iutciq/o5*h iz b22:ba , Moon. What angular width will it subtend *(: x57ob uqvbi(jiiskzh-ji t+,/ 2 2 zjcyajfrom the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a whis);3n-b ,tajk q no- :x-btwe:7bvyoste dwarf whose mass is equal to the Sun's and whose radius is equal to the Earth's. How many times la7 o-:oxysb; knwt)v--j: 3b sanbt, eqrger 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 masszn pao/ 7k2lp9es has a radius of about 11 km. Calculate its average density and compare to that folk/o pan9 p2z7r 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 but: ne) +9)kaenb-pumt rning reactions of Eq. 33-2. (The mass of the venute)p):n k9ema +b-t ry 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 apparenbs- .(ld4csj yn( zf8 ,-8keq h6vtc+cqtpig* t 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 dnxdca;*r4 4c, allq3)ot m/z are assumed to be about the same distance from us. Two such stars have sqax cc4atmd*4dzl3on;/ ,)rl pectra 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 Schwarzsc7ws- 2/c wj l)ngyyj,ohild radius for a star with mass equal to that (a) of our gc-lwj , j2o7wyn s)/ySun is    km, and (b) of Earth is    mm.

  What is the Schwarzschild rady3oowk91: bzy t9wu5q ius for a typical galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the s.bo 1zh)(a egcurface of a sphere, for which the sum of the angles is (a) 359º, and hgo 1)b.az(ce(b) 180°.

  What is the maximum sum-of-the-angles for a tbyb8b64 v udi)riangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of thl19.m+ruyzz kk 0nvaz: ob1m,4rx9k qe speed of light, roughly how far away is it? znro1 kka0k41z.xvumzq,b9 :l rmy+9 v =    Mly

  The redshift of a galaxy indicates a velocity o4;hd6ws e ,ntzw-f8vr kdt)l(f $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (relative to us) thatypsn ,s+:*oj :ottn9s 4rv8:dd *nnqk is near the observable "edge" of the universe, say 12 bir ,* :nvdtyo :kdsjqnn :*os 9+pn4ts8llion light-years away. v =    c

  Estimate the observed wavelength for the fz.ax ed dsl l5lm (u(/2*ubt3656-nm line in the Balmer series of hydrogen 52at 3ulddsze*l.lm uxb ((/fin the 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 /fdwv k06tp +ia4x,z)9rlc zudistance from us, if the wavelength for the hu4zp ai9+6vfc tzw/l0 ,rkxd) ydrogen 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 wn;iemurcj8/ ; .pl4zt ith $z = 0.60$? v =    c

  What would be the redshift pae w g(fx012ctgh3c2ob rameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show t t,+)lbgtl9ke. r)d; eoy5pylhat the 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 pml bi2vl1;p;x/t-(byar5rnveak of the blackbody radiation distribution at 2. b/vxnbrl2;y m(vi5-;prtla17 K using Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of the universey;rz o .*ydj*o 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 distance between galaxixrp739 *rdpo;yu.lrfes) at any one moment is believed to have been inversely proportional to the absolute temperature. Estimate the size of the unive *l7yxop9p3rr.drf ;u rse, 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 universev xadx .-6n )9go9kqq6d7ch6bnexf+p cooled below the threshold temperature fo ddk p 79oqb-6 6x9nn.gx) 6ac+xvfhqer 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 stars could undergo op:f,0mga22 t :w60ft/izuev2n jrsd the three changes represented by the three arrows, A, B, and C, in the H-R diagram of Fig./0t2z0isr jv6fe2 m 2d u,o::pfnwg ta 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 sampw1(l;8 xqnrf.w7xam ),v ,jz4 bqjpme as the Sun's. Their apparent brightness, however, is aboxp;xnmw8p) jw,q4 q mb (lf.aj,1rv 7zut $10^{-11}$ 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 estimagsh(e,5apb*2a 3p hego u31j+zoz:t ite the angular velocity of a neutron star which has collapsed to a diameter of 20 km, from a star whose radius was equal t:hotaop1gpzis 3g +b(e* e25uh,zja3 o 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 rotati91au qi97mod sonal kinetic energy change when the star in Problem 56 collapses19oq isum 79ad 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 1.5 times that5)pz*xym; n dm of the Sun, with diameter 20 km, is observed to have a rotationzdpm5;n)x my* 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 is about /feee-: pg(hl)y*h rn$2 \times 10^6\ \text{ly}$ 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 cd oes4 k1e- gohtu.wmf9tapx(4n9x2 *. ,abtbritical density to close the universe. Assume the neutrino densk4teob9hm n 9x2eag. d,w*xb (1fpa s-t.ut4oity 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, respectively, 3lsq0p0ttcvd 5ku ;m- both lie on the main sequence.-qpkud300 ;lt5msvt c 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 with parallax at 100 parsecs. What is our minim/nrmepa)i p*(qi+ 0 t*uia2xjum angular resolution (in degrees), based on this infptiqa/*r ) jeauix20 m+ (i*npormation? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from singly ionized helium id,j0ou(j m .kvn a distant star happen to overlap with the Balmer lines from hydrogen (Fig. 27-22) in the Sun. How fast is the star receding from us? v = vm,.j(d k jou0   C

  What is the temperature that corresponds tpdcdew )6.p ;go 1.8-TeV collisions at the Fermilab collider? To what era 6cw; d dgpe).pin cosmological history does this correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation of gas around what might be 3f .wylivud5sker9- ) a supermassive black hole of about 2 billion solar masses at the center ofskv. if5lye)-r39uwd 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 awwdi*(4n q 5q i2qrhcb.4o zag;ay from Earth. The "blue" hydrogen line at 434 nm emitted from the galaxy is measured on.aq o 4qdn(g24 h;5ib*zqriwc 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 dph7+npp.s kps i89;k star (if massive enough) will begin fusing carbon nuclei to form, for example.n pd;kk+7p9pip ss8h , 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 reactiom67k q ue1ql q13z84tepg, qhan
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 eqv7zbt: w h1u4tualed the critical density of the univtz4thw1 b7 u:verse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$