The Milky Way was once thought to be "murky" or "milky" but is now considur5od v7 q9 ego3pyb75 rtdq7-ered to be made up of point sources. v7 gq35 5pourr7yqddtb 79e -oExplain.

A star is in equilibrium when it radiagi6bia (9kfs0a5i xp,tes at its surface all the energy generated at its core. What happens when it begins to generate more energy than it radiates? Lessf, 0(65ikp9gasaxiib energy? Explain.

Describe a red giant star. List some o0w 3gx8 hv0)hpyx 7hftf its properties.

Select a point on the H-R diagram. Mark several directions away f7x4bs9w7u uv/ra dgovc +as61rom this point. Now describe the changes that would take place iur7 w /o 1sa4gu6+vx97sb davcn a star moving in each of these directions.

Does the H-R diagram reveal anything about the core of ld*+zd 3e:jnd a star?

Why do some stars end up as white dwarfs, and others as neutron stars or blais:ddi tie /jg.;n6 +bck holdiisd j:gb+/e6.; itn es?

  Can we tell, by looking at the population on the Hsm54x--ojlp 5ud90vklg/o t i-R diagram, that hotter main-sequence stars have shorter lives? Ev lku9o o 55-0js/md4tg-lixpxplain.  ----待选择----yesno 

If you were measuring star parallaxes frt.w*;ikh. ihqom the Moon instead of Earth, what corrections would you have to make? What changes would occur if yoih; wi.k*ht .qu were measuring parallaxes from Mars?

Cepheid variable stars change in luf+6cl y jto*gxfjx1cpa58/r6minosity with a typical period of several days. The period has been found to have a definite relationship with the absolutrylj f6/1o6*cj +t85ac xfxpge 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 Relatic;(i i8ubsa:if-mxtu m )p1c+yi 0mi *vity?

If it were discovered that 3ds e:*twhkl xfc5a5 ,x6*dwpthe redshift of spectral lines of galaxies was due to something other than expansion, how might our view of t* *,a: d6wxh5xwspt 5d 3kceflhe universe change? Would there be conflicting evidence? Discuss.

  All galaxies appear to be moving away from hbpv*1a,*uxq us. Are we therefore at the center of the xu*h1pva b* q,universe? Explain.  ----待选择----yesno 

If you were located in a galaxy 12w0wei:keo2mp j kj, near the boundary of our observable universe, would galaxies in the direction e:k2o,kw 2pwjm0j ie 1of the Milky Way appear to be approaching you or receding from you? Explain.

Compare an explosion on Earth to the Big Bang. Consider such quey3xfa:rnsr65r oix+z 3. /wkestions as: Would the debris spread at a higher speed for more distant particles, as in the Big Bang? Would the debris come to rest?+ re5f.rnir x / 6:wszx33kaoy What type of universe would this correspond to, open or closed?

If nothing, not even light, escapes from a black hole, then hok/m ket4ce- j*(4h+9 albtipjv9h7f ew can we tell if one is th 4i9t 9 -pceemb/+7fka(j* h4 ejtlhkvere?

  What mass will give a Schwarzschild radius equal to that of the hydrogej9l3usyu dau0x(7 0jan atom in its ground state? Ma7j yuu (d0a3l0ujs9x =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4n, gohx1ql4;m billion years. Find that time on (Fig. Below). People have lived on Earth on the order of a million years. Where is that on (Fig. Beo 1x;qmng,l h4low)?

Explain what the 2.7-K cosmic microwave background radiation is. Where doe/zc/s /k:lhe / i4b:xwdq qyq,2v7ar ws it come frxhe2bdliw, :q/v7az kr/sq4wc q /:/yom? Why is its temperature now so low?

Why were atoms, as opposed to bawj: h dr3j/3kure nuclei, unable to exist until hundreds of thousands ofu wk 3jr/3dhj: years after the Big Bang?

Under what circumstances would the universe eg,q6ilcn ,x8 ou)5ynom13rgrventually collapse in on itself?

  Using the definitions of the poz, 05p emv ervaa4(.qarsec and the light-year, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.38 seconds o(l.m6bjoh.iuk) urc3 f arc. How far away is it? d =    ly

  The parallax angle of a ydo/- hzhv2 w6star is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. Wha c*c0h)/kl gnxt is 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 star that is 55 ly (rp0eab)qd 2cho vg (4y8l)oa *g,yrtaway? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away from ue+mz(xb1ej+ 1 t dmbcp(3y-oi*2czd os as a second star, will the parallax angle of t-cmiz+ *cepbdjz1t x e o(3 +m2doy(b1he farther star be greater or less than that of the nearer star? By what factor?

  A star is 35 pc away. How long doesk:lg7 h u5 z3str/( ipja36fvq it take for its light to reach us?    years

  We saw earlier (Chapter 14)3 ( e+1)o iqexd o,v4x.dzlci v+vwdm1 that the rate energy reaches the Earth from the Sun (theo d c e+4 zqmxxd31,d(iv.+)ivvol1we "solar constant") 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 ta/-a3o :g 1o7;os sks 9ogxm uof(r6ezo its brightnessx;go6ks-(our :ogso1/a3fz7e9m osa 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 our Galaxy would subtend if observed frorm0 s l( bkxo5a )(jzidej3x,2m the nearest galaxy to us (Table 33-1). Compare to b2k5 0)lmxero (3j(xdjzsi ,athe angular width of the Moon from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, what will be its average density if it expa-us v3 rr,v*5(kubt/b-g ndfsnds out tobvu /g5r dvsfsn*3 b-tk(- ru, 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 expecte5yz 8kg)o *; i)ychzdad to be about the size of the Moon. What angular width will it subtend from the present distance to Eyg8;*5ky )ahico zzd )arth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whose mass is equal totx u)5,dd6 vza cfk4l) the Sun's and whose radius is equal to the Earth's. How many tilu 6kcfxt, 5)zda v4)dmes 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 radius of about 11 w ;/1wcg*m nkmkm. Calculate its average density and compare wwg/1n;c* kmmto 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-zv ua15(1 r) lolju:nu2. (The mass of the very unstable rv ulzl1onju u():5a1 $^8\text{Be}$ 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 dl y9ym..o e 2(9fg(b 7hcruqabrightness $l$ 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 ngkh die 8s+f km8lk((:e/a u+zm+a- gbe about the same distance from us. Two such stars /a mku+eg+e (-l8hnsz k:i(agd k8+m fhave 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 witht:l*k (e zyk4h mass equal to that (a) of our Sk(:lze tkyh4*un is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typica zy/w)ky9sw7w l galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surfa nik-(.gx n r5l (lnd+.3glvfnce of a sphere, for which the sum of the angles is (a) 35n. (5ngfgx n. d+ki(-l3lvrln 9º, and (b) 180°.

  What is the maximum sum-of-the-angl. v ltjoc2g0,des for a triangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of uzi:4 7lqhw1 dwvk.imww:,j/ 5)dmththe speed of light, roughly howwtj v7 h4wh.1/d):du :5mi w q,lzwmki far away is it? v =    Mly

  The redshift of a galaxy indicates a velocity oovx mufw:4 )q4f $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (relativ)lex0: /d .fjwh7:qyn ufb(fle to us) that is near the observable "edge" of the universe, say 12 billion light-years lhf(qjyl xf :)7fd/:e. nw0buaway. v =    c

  Estimate the observed wavelength fod/2rg5p h oxc)r the 656-nm line in the Balmer series of hydrogen in the spectrum of a galaxy whose distance from 5 ocdxp)h r2g/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 waveleh* nrml0 4bs1pngth for the hydrogen line at 434 nm is measured on s*rnl hm1b04 pEarth 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 iw0 dru 9 zfyfgjjpf ;f,-/8:ha galaxy with $z = 0.60$? v =    c

  What would be the re kyp7iry:.+xbx +gzasg3m4/sk, j( i ndshift parameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Dopple - gw66yi0zt *upbpj0qr 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 blackbody radiatp wxp6)rxl i76ion distribution at lipp) w6xx6r7 2.7 K using Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for o3okhejy )j/5h z n(ls0rht)2 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 (the average distance between galaxies)+9* jv6a80m+op +ih zyknuob o at any one moment is believed to havevnz h+uy+m o*p 80a9o+ okb6ij been inversely 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 had the universe cooled below the threshold tempe75e *6hde6 t2vlmssft rature fof 5mel*t t6de7s 6vsh2r 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 three chh7b1y; g( c sd ;dvd0qagzl8h9anges represented by the three arrows, A, B, and C, y7 (al;bd1shg9zdg;0cdq8 vhin the H-R diagram of Fig. 33-28. For each case, describe the changes in temperature, luminosity, and size.

  Assume that the nearest stars to us have an absolutm0s+ 5 jvkx onqadv-+:e luminosity about the same as the Sun's. Theirmv05:ojq d++vks-x na apparent brightness, 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 vy :ypalsp(cak 3l,f* +elocity of a neutron star which has collapsed to a diameter of 20 km,fpcly s3lpk *+aa:y (, 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 rotatione ,uwq+/bcp2val kinetic energy change when the star in Problem 56 collapses to a neutroc 2eb+ v/uqp,wn star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believed to be a neutronm ipd3ox63jbi4 ) 5jgt star of mass 1.5 times that of the Sun, with diameter 20 km, is observed 53t6 jmg3xi4 ijpo bd)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)l5.8uah3lkrb q g;dd 6 jy; b+q4*b fhi0dixe 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 critichvk7i8 k6 dv0kal density to close the universe. Assume the dv608kk ivk7h 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 u5gk rs s2d0q2*1g su bakj bopc2/:-unm, respectively, both lie on the main sequence. Use Wien's law, the Stefan-Boltzmann equation, and2buu2*rjs/ 0spg2a d1:c -ou5b gkkqs 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 dista.jyjmgah*q kp4 b.pt )bj2v3)/qng 9ances with parallax at 100 parsecs. What is our minimum angular resolution (in degrees), based on this infoj4t))gnkvyp2qh j* jg/.b9.m3 qpb aa rmation? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincid/s+h5(d2ms ,db:vokwld z-yoence, the Balmer lines from singly ionized helium in a distant star happen to overlap with the Balmer lines from hydrogen (Fig. 27-22) in the Sun. How fast is the sta5som-w/sdkd zoylv 2,hb(: +d r receding from us? v =    C

  What is the temperature that corresponds to 1.8-TeV collisy0u j)r8qp1nb ions at the Fermilab collider? To what era in cosmologic1)rqu pjb ny08al history does this correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotati qp 9l 4a-fx-*ots0tku+ eqt-w inu6q;on of gas around what might be a supermassive black hole of about 2 billion solar masses at the center oa0fquns-qwopt 4k* ulet- + 6 9;tix-qf 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" hydrogdyawc 5vuer7.6mtna;*i 31ksen line at 434 nm emitted from the galaxy is measurerdy5u1ecn 37si6kw m;t ava *.d 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 7+skvmhbhj+*s+d;va+zn/y 6msp- m r star (if massive enough) will begin fusing carbon nucleiv ap ++7 m/;kvmrs d6sj y+h+bhsm*zn- 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 reaction rj:g5 nlx6o p(
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 density oeaj 1 k/l u9o 22vr-wth;qfjd4f the universe,traehj1lq9;f2o4-d2k w j /vu $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$