The Milky Way was once thought tobk5xgam1 .0u :cowad 4 be "murky" or "milky" but is now considered to be made up 1bamdw u 4xgoc0ka. 5:of point sources. Explain.

A star is in equilibrium when it radiates at its t,fkre)our 4l( n7 5mtsurface all the energy generated at its core. What happens when it begins to generate more energy than it radiates? Les4n5r)(m r7uttle,okf s energy? Explain.

Describe a red giant star. List some of *,ct/vh;owc3bg smq8h2y ai-its properties.

Select a point on the H-R diagram. Mark severalj5n g.fr* j*rpeunp-;f- vgr9 directions away from this point. Now describe the changes that would take place in a star movi;g9jp f j nfgru*p-*rn5 re-v.ng in each of these directions.

Does the H-R diagram rev0a: wo97b angweal anything about the core of a star?

Why do some stars end up as white dwarfs, and others as neutron stars or blackiu6:pi g/ kn3i holes?k /u pi3gini:6

  Can we tell, by looking at the mqch5+y jnyf7zq ;p4; population on the H-R diagram, that hotter main-sequence stars have shorter yqn4 f7; cqz;p5 h+yjmlives? Explain.  ----待选择----yesno 

If you were measuring star parallaxes fromg9wudx 5 6m4-i)uzvc kfh)4zs the Moon instead of Earth, what corrections would you have to make? Whag mfukv-9x hzz) i64uw4 s)5dct changes would occur if you were measuring parallaxes from Mars?

Cepheid variable stars change in luminosity with a typical period of sev*e k0or*ut 17tlp6 bvn/ 1iomheral days. The period has been found to have a definite relationship with the absolute luminosity of the stonmt*lh vb1i p6 0or1e7 t*/kuar. How could these stars be used to measure the distance to galaxies?

What is a geodesic? What is : dr- ( 6m+7(q ou5fxdctodkxaits role in General Relativity?

If it were discovered that the redshift of spectral lines of galaxies was due)muvzu /w *daq)-wf8o to something other than expansion, how might our view of the universe change? Would there be conflicting evidence? Discuss.zm)qvoudw/- fa* w8 u)

  All galaxies appear to b-o7u - 5w/w0qjdib ajye moving away from us. Are we therefore at the center of the universe? Exu jdy 5ww/a 7q0-bi-ojplain.  ----待选择----yesno 

If you were located in a galaxy near the boundary of our observable univer*ich 4,8tkdr g atej;8se, would galaxies in the direction of the Milky Way appear tokrech 8t; j8t, dia*g4 be approaching you or receding from you? Explain.

Compare an explosion on Earth to the Big Bang. Consider7f2k7oolc q hd3c:pc1 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 univercpo 7q7dc:21hco f3k lse would this correspond to, open or closed?

If nothing, not even light, escapes from a blackbrr ) 2juq.6qs hole, then how can we tell if one i )6rrqsq2bju .s there?

  What mass will give a Schwarzschild radius equal to that of the hydrogekx izwvp4;b*e/p 2 p)wn atom in its ground statpkew4i/ w;ppbx *v2)ze? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion yearshu,stgu) mdl10,( h q2w zc4du. Find that time on (Fig. Below). People have lived on Earth on the order of a million years. Where is c(muh q1lt )su24h z0,gddu,wthat on (Fig. Below)?

Explain what the 2.7-K cosmic microwave background radiation izps1d hah )u)*s. Where does it come from? Why is its t) s 1h)*pauhdzemperature now so low?

Why were atoms, as opxbwm+;-s y:rg posed to bare nuclei, unable to exist until hundreds of thousw-mg y+ ;r:bsxands of years after the Big Bang?

Under what circumstances would thegks .; p4/bv uo(-dhry universe eventually collapse in on itself?

  Using the definitions of the parsec and jeqfpy3) 8sc/b35miy the light-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 2s:m j2wp tai9is it? d =    ly

  The parallax angle of *yf;i th1bs2nj 5i-o ya star is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its parallax an5vpcm)9 :j x -0ags2com2giqugle?
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 qx zq*0 .8e tq)htuq/dly away? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away from us as a second star, wq nd f6/ep;4 7g dyh1)rlq/ozqill the parallax angle f)/6 zhdn;q4o l py/qrdegq71 of the farther star be greater or less than that of the nearer star? By what factor?

  A star is 35 pc away. How long does it take hmt)-jykf61quoz 9xw;q 3 wp 0for its light to reach us?    years

  We saw earlier (Chapter 14) that the rati3*w*ob-awneeb b a(zeghz le74 y8;,e energy reaches the Earth from the Sun (the "solar constant")z og* ley baebawehwn,e;83-bi7(z * 4 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 thel-y .ty4fsmro h6k .(y Sun as seen from Jupiter as compared to its brightness from Earth? (Jupiter is 5.2 times farther from the Sun than th-yyskm..ft h6(4 oryl e Earth.) $\dfrac{l_{\text{Jupiter}}}{l_{\text{Earth}}}$    $ \times 10^{-2}$

  Estimate the angular width that our Galaxy would subtend if observed fc0g7 x,0jw r2xhv)ilc rom the nearest galaxy to us (Table 33-1). Compare to the angular width of the Moo2j,l0wvxr7x0 hi )cc gn from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, what will be its averagey95-vuuogc 8 u density if it expands ygu8cvu-5 9 ouout to 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 expected to (muypeleu 9)jp40/nd be about the size of the Moon. What angular width will it subtend frome )uy4upnje(l/90d p m the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whose mass is equal to the Sun's anhp2bcpf22, c bd whose radius is equal to the Earth's. How man bp22cfb,2phc y 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 radius of about 11 km. qse ; 9v*8lplmCalculate its average density and compare tevl ;m*ql8s9p o 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 th,jsy-uf z8wr: -6k:qcu3 bb zie He burning reactions of Eq. 33-2. (The mass of the very unstable kusj,fy3b:zcu r8i-w 6 -q: bz$^8\text{Be}$ 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 sa21ystxaz8)ipx e*8 2pljt;i n me 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 distj+m 3a6y0 d0 j;7jtrc:gs hncbance from us. Two such hcjrt0cabg ;jy:dm3 n70+6jsstars 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 withm . jta+pna km5s+ao/6 mass equal to that (a) of our Sun is tk naso+jp6/5amm. a+   km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typical galbxu nk) m(f:/ aiiu degg(l)(,axy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a sphere,zj v v:lsx22 ls)5w (9sdrf 5yib2r1vw for which the sum of the angle( wv)rdwb2lv r252s lv j1 yzx5si9s:fs is (a) 359º, and (b) 180°.

  What is the maximum sum-of-the-angles for a triangle on a sphermv hdfvk+s *3:e?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the speed of light, roughly1oqy.z uv mg89j 3rv l/y87exc how far away is it? v xj3qyg1ro8z8myc7u e.v9 lv /=    Mly

  The redshift of a galaxyv(/./acnfr3d:zro. f mhj as; indicates a velocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (relative to us) that is near the observ n : p8csrle1p+xvg byqyu. ff;(z5kc;s .yr8*able "edge" of the universe, y5fs+gp 8 zyyc n8pvk;.e ;cf1s uxqr*(: rlb.say 12 billion light-years away. v =    c

  Estimate the observed wavelength for the 656-p d kr hgs-v 4+1xw*2hehx.yxud3q4(rnm line in the Balmer series of hydrogen in the spectrum of a galaxy whose distq d2hw dhx xx44er vugyhp+k- sr.1*(3ance 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 distad essrs6c2tj45vw4 u5nce from us, if the wavelength for the hydrogen line at 434 nm is me4seswuj6ts5d r2 5v 4casured 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 ump;cj-4xzd* w l*sxf z27 i1aa galaxy with $z = 0.60$? v =    c

  What would be the redshift parametergf8lm oe8x. xshpmy;b/+/t d. $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show thatz jt9 beq*i .;t*pku+q 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 peak of the blackbody radiation distribut.2z erglo+3wtj7dnc9-6mik0 l 5pfj c ion at 2.7 K using Wiji ezd6clfm5 9ok203cw- grnj lt+7.pen’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of the universe ilo 0u1wubol- (s $\rho_c \approx 10^{-26}\ \text{kg/m}^3$. 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 distani rkx;/kt9;8 ;eje hwlce between galaxies) at any one moment is believed to have been inversely proportional to the absolute temlt ie8;9kxkj/;e w;r hperature. 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 th j na6 1qmlr1;xktj-7nreshold temperature fora71 qmntjjr n;x-16lk 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 th,w*8j0tuq ( ly sk,mgbe three changes represented by the three arrows, A, B, and C, in the H-R 0*lg kusbywqm,,j(8t 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 absolute luminosity about the same a(v-dcmfcz8g zr-vobs/-nv z-cul, (9 s the Sun's. Their apparent brightness, howevz(,s vzlc/9--8(-z n-d bfro ccmgvu ver, 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 velocity of a neu//n nfxc qx9:ddo ,/6z(8j t) krpywbptron star which has collapsed to a diameter of 20 km, from a star whos6 q/ pczbr:k jdd x8w p9(/fot,)y/xnne 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 in Probl96f no ru.1rixxh j6: op65byiem 56 colla 6.oh6f y9op6bi:jxr x5nr1uipses to a neutron star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believed to be z9fw i7xtd(uv34 phzt /+co2zd7 a0kja neutron star of mass 1.5 times that of the Sun, with diam7j z tz cw/3kt a0f2izpd+74(9 uhxvodeter 20 km, is observed 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 f02ntb r0z9p) hxul5 gGalaxy 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 e9iu66ct zd kg,V) would provide the critical density to close the universe. Assu9c d,guki66tz me the 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 j 2j y18r cj6g/ds qg uljj+ili,w1 9ui:swt27peak at 600 nm and 400 nm, respectively, both lie on the main sequence. Use Wien1l2jj,7tq s: uijd/yi jrw+ls gwjci891 u2g 6'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 distancu dvcci 62r 9hxje301kes with parallax at 100 parsecs. What is our minimum anjiudcrc ek 02631h9xvgular resolution (in degrees), based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from singly ionized helium inmgnue xbjkce7 j4(7/z 2-r;df a distant star 7bn7c/ f-z j xejdmg4u2re(;khappen 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 *ut541m( vd*efrbhzd1.8-TeV collisions at the Fermilab collider? To what era in cosmological history does this correspond? (*ud1ftv*ezm 5hr4 bd[Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation of gas around wha xc91kg3tzuwy, 7s 8xu6wval7 t might be a supermassive black hole of about 2 billion solar masses at the c x86lswg9atku71, u7z3vywc xenter 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 wuhg)s7s,gm r0+x *ez"blue" hydrogen line at 434 nm emitted from the galaxy is me,gshu*x 7 zwges+rm 0)asured 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 star (if massive enough) will be(4 o0cj:jd9f*ipx t rygin fusing carbon nuclei toxydr940i: fo(j jt pc* 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 ht g1 s7anw6wjni8(a:l4 (vfl
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 dx9bmds g8 pqm2 ui)ta9*+4 fsvensity equaled the critical density of the univemfx)tv ub4d*ias s2p99g q+m8rse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$