The Milky Way was once thought to be "murky" or "milky" but is lky96e3uzk46cdi.v ;kz-iwunow considered to be made up of point sources. Expl. uyiciv ;69z-wd4l 6k3uekkz ain.

A star is in equilibrium when it radiates at its surface alljypjacz6rp ki2 ,;9 sjt-d 8k) the energy generated at its core. What happens when it begins to generate more energy than ; k9 s r26,i)jc-pkzt jjdya8pit radiates? Less energy? Explain.

Describe a red giant star. List some of its h-54,sqascw1( rkki wfyaa 49 properties.

Select a point on the H-R diagram.zu g*9ca /(: 48zys+ mjyom whq,mwz8x Mark several directions away from this point. Now describe the changes that would take place in a star moving in each of twm zzjs4z yu qya9x/oc:8wm(m*g8+h, hese directions.

Does the H-R diagram reveal anything about the core of aex.un5 (w8lw y.z z+zq star?

Why do some stars end up as white dwarfs, and othewc9whv p1:c 6x)l,nd qrs as neutron stars or black h),qhwcwpc19dx6 vn l:oles?

  Can we tell, by looking at the population on the H-R diaiwj * bzn ml50;pch p00* on+:2aryypqgram, that hotter main-sequence stars havewm 0p; hblpnnp2y o0+ ca*i *0:5jzqry shorter lives? Explain.  ----待选择----yesno 

If you were measuring star parallaxes from the Moon insteadz.55 d5 he j45kau,iw fgz85uny1ehaq of Earth, what corrections would you have to make? What changes would occur if you wered5n55ahq ,8huw5gizzu5k1jay4 e. ef measuring parallaxes from Mars?

Cepheid variable stars4hlt; gir3:z)o10h 2 qilelp d change 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 star4) r:1pl;hqe0toz2lgi3ilhd. How could these stars be used to measure the distance to galaxies?

What is a geodesic? What is its role in6cb ;a d m7irtap9(o8h General Relativity?

If it were discovered that the redshift of spectral lines of galaxies was due to3* j x mz-kfvp2jmg2.h something other than expansion, how might our vij2 2vmg*z3j h km-xpf.ew of the universe change? Would there be conflicting evidence? Discuss.

  All galaxies appear to be moving away from us5)in+lxo: tma x5bcq 2. Are we therefore at the center of the universe? Expi) c b ql5x+x:a5mto2nlain.  ----待选择----yesno 

If you were located in a galaxy near the bounawg7txrbu*,i ::e 2qhdary of our observable universe, would galaxies in the direction of the Milky Way gbi e::w,2tq7auxhr*appear to be approaching you or receding from you? Explain.

Compare an explosion on Ea/by.o b-9dqm blf4*z arth to the Big Bang. Consider such questions 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 unb*bb-q4z lo df/ mya.9iverse would this correspond to, open or closed?

If nothing, not even light, esc2uey0tm s 8e+eapes from a black hole, then how can we tell if one iut2 mesee80 y+s there?

  What mass will give a Schwarzschild radius equal to that of the hydroge zcgw72oh geft-ru510xbl8 p;n atom in its ground statez5w- xpul0 hg etf7rgb1oc; 28? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion years. Find that (dgmg0kk/e+ r9i vnt, time on (Fig. Below). People have lived on Earth on the order of a million years. Where is that odm 90 ven/ ik,grk+(gtn (Fig. Below)?

Explain what the 2.7-K cosmic microwave background radi79q) yuuhui)yp kv blf; 5swjm,pi(+) ation is. Where does it come from? Why is its temperalms+ i);wpfy) (5kvqbu9u, j7u y pi)hture now so low?

Why were atoms, as opposed to bare nuclei, -a 7*/mqn6hgy* eljzy unable to exist until hundreds of thousandzay*7 leqgm *-y/h6j ns of years after the Big Bang?

Under what circumstances woy :rt:yq9o+0fa z- ixluld the universe eventually collapse in on itself?

  Using the definitions oyu ulg8 io5arod4p10)bg5 k9i;do .xwf the parsec and the light-year, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax i.m3 bqh2;ugfgt.t4 xof 0.38 seconds of arc. How far away is it? d =    ly

  The parallax angle of a j91zy3u5 o41pmp fohestar is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is itshh*2z 4mmxb i3 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 star ksb l3mbm mzru375- p*that is 55 ly away? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away from us as h65qmlhos5.dbl49 w) (fy6p4 sbu qiua second star, will the parallax angle of the farther sta6)m( b56u.wdh o4upqiyls4hbflsq59 r be greater or less than that of the nearer star? By what factor?

  A star is 35 pc away. How long does it take for hr8 p)9ttwt 1oits light to reach us?    years

  We saw earlier (Chapter 14) that the rate energy reach;gwz ha (3wf4e x-**ra dv-b.qj3c akoes the Earth from the Sun (the "solar con- 4q- f*j aer3a;owbvdzk.(3xhwa *gc stant") 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 compa. 6,j(jg* d0 rl 9(rgjyjsadmdred to its brightness from Earth? (Jupiter is 5.2 times farthedj .das j,ydg(j*j(6 0rmgrl9r from the Sun than the Earth.) $\dfrac{l_{\text{Jupiter}}}{l_{\text{Earth}}}$    $ \times 10^{-2}$

  Estimate the angular width that our Galaxy would dx6n) ;*ehvzusubtend if observed from the nearest galaxy to us (Table 33-1). Compare to the angular width of the6n v*uz;hd)xe Moon from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, what will be its averageiep:bg9zajxz5 7 o3/a density if it expands out t73o ej/ zb z9xi5apag:o the 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, it is expecteqw5+pqf/ 2 affd to be about the size of the Moon. What angulaawf +q2qf /5fpr width will it subtend from the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a whiap 9,t w:ha +9li.y;/pgu4vgmxp don/te dwarf whose mass is equal to the Sun's and whose radius is equal to the Earth's. How many timv/; agi p9l4/y p o,dnht.xmw+:g u9apes 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.ujf 07yb/i0 aq5 solar masses has a radius of about 11 km. Calculate its average density and compare to that for a ifau bj /y7q00white 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 reactionsv croh r*ms*7: of Eq. 33-2. (The mass of the very un7*mhro*rsv:c stable $^8\text{Be}$ 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 br**)6y bzcu+g7cuf -k a+xzmcjightness $l$ 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 cert+1gf 8fmql00w fco4 orain cluster are assumed to be about the same distance from us. Two such stars have spectra tha w glf+0o1f8rqf 04ocmt 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 +i7zuz vt3 :3pvw g4rn(a) of our Sun i:i3gtr4vu+ 3vp 7znwzs    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typical galaxy (y8k8+ jx1v5c0gyyx co like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the ad9d 41 9.njp am3uvbvsurface of a sphere, for which the sum of the angles is (a) 359º, and (b) 18ndb9av1da p49 3j. vmu0°.

  What is the maximum sum-of-the-angles for a triangle on a sphere? mm5m0md0rtw t*(znx;    $^\circ$

  If a galaxy is traveling away from us at 1.0%x ox:q;/3 nozj of the speed of light, roughly how far away is oxonxjz3/ :q ;it? v =    Mly

  The redshift of a galaxy i3a1i wvpad1 -b2vjly 7ndicates a velocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (rj6 a.8 gl ecx( afyk i4i(+*lr02rlxdpnqmj8,elative to us) that is near the observable "edge" of n+ 4 q,mgxj8 i2xiy(60r( *8apafld.eclkrjl the universe, say 12 billion light-years away. v =    c

  Estimate the observed wavelength for the 656-nm line in the B, ic) 8m5bswmialmer series of hydrogen in the spectrum of a galaxy whose distance from)m5wi, s8b cmi 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, and8h,tx2jr8edalwm0ia) (znzr f *a 0o* its distance from us, if the wavelength for the hydrogen line at 434 nm iafwz(m* aiz0*)ja 0nl2e h,xdto8 rr8s 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 z xlz 6u6ww;q m+7,ww )4ppx)/nckzkda galaxy with $z = 0.60$? v =    c

  What would be the redshift qxka3)l 1 b cn1.da5trparameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, sh 1 xnle)j6 6uifm jp*3-hw/elwow that 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 wavelen1feej ex q;9u +6qxeg+gth at the peak of the blackbody radiation distribution at 2.7 K using Wien’fqxeuxg;9+6j+ 1eq ees law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of ,hfyma dp c.;no::(rmthe 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 univeg s-*3*zr1z 0zep cayfrse (the average distance between galaxies) at any one moment is believed to have been inversely proportional to the absoz 3fyz**-z ercs0pg1 alute 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 thb;enwwwyp*9 ;e o+-tee threshold temperature -+* pteeb;w yowe9wn;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-sequence stars could undergo the thre6m364 em(eekanjhd * de 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, a3em jmae4d* d66n he(knd size.

  Assume that the nearest stars to us have an absolute luminon)pfh/46y yjq sity about the same as the Sun's. Their apparent brightness, however, is aboqj6f) 4h y/pynut $10^{-11}$ 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 the1 h xvhky-00 (v(btvnf angular velocity of a neutron star which has collapsed to a diameter of 2100v( kxbh t- vvhyf(n0 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 change when the star idv c np5bh(.fhm8j(*ln Problem 56 collad(5(v.jhc8 fpl*bm hn pses to a neutron star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believe qasl4- i+pgd,d to be a neutron star of mass 1.5 times that of the Sun, with diameter 20 km, is observed to havl-qa,p dg4is +e 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 is abo40f u)iuw i85x3sallh ut $2 \times 10^6\ \text{ly}$ 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 m :pdn9 p3z urq20,yqta ve3sl3.hay,tass (in eV) would provide the critical density to close the universe. Assume the neutrino density is, like pho:ahvd zpy0ta3.s, e3 ql2 39 tnq,upyrtons, 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, both lipn(h: +fwbxsm2f3z zpphcn4 o9 5 fc0;e on the main sequence. Use hpc 45fn 0 pn9z c;+foz:3mfb2hsp(xwWien'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 distancesr+rpv,d*)l q6 cqn:ns y(bhn) with parallax at 100 parsecs. What is our minimum angular resolution (in degrees), based on this informn yv hqnpns:))br+(rqd,* c6 lation? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from singly ionized helium in a ep6x/m x m+ v.9v k.j;lxxybcble4a47distantmj;x9c kv76.belxp / 4x+axvblye. m4 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 =    C

  What is the temperature that corresponds to 1.8-TeV colo0kv)qx*;n9 dc.s i*f+ g ziyrlisions at the Fermilab collider? To what era in cosmological history does this correspond? [Hint: see (Fig. Below).] ng ). ikoyxrv df*z; ci+*sq90 T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotatv26m sq(/d0;r t omybdion of gas around what might be a supermassive black hole of about 2 billion solar masses at the center of a galaxy. If the0d tr 62moyqvsm(/d;b 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 awaw 08 m6tg b5eydrkq1c2g :c(yqy from Earth. The "blue" hydrogen line at 434 nm emitted from the galaxy is measured on Earth to be 650 nm. 2(ye8 ry 1dkqgcb5w6m 0tg c:q
(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 y9363k ic c/jlbck)nj(if massive enough) will begin fusing carbon nuclei to form, for example, magnesiu/kkbnci3jl93c j) c6ym:
$^12\text{C} + ^12\text{C} \to ^{24}\text{Mg} + \gamma$.
(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 colbqg3sl zjv1:z/3 *
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 dlk . tv0).nrbhbxiu 0ofjo x39kr 9p72ensity of the universex0l0 hr.k9.butb9 nfj3)v oir2pox7k, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$