The Milky Way was once thought +gla .+9pxr bdy e fim;.fm00fto be "murky" or "milky" but is now considered to .f ; p0.a eb0dffrgli9y++xmmbe made up of point sources. Explain.

A star is in equilibrium when it radiates at its surfy5 k2zy-sbd.7 vt daz+ace all the energy generated at its core. What happens when +zb2kz ay dyv t7d5s.-it begins to generate more energy than it radiates? Less energy? Explain.

Describe a red giant star. List some of its4swazhu v*s4pbwx e cet+ )-;* properties.

Select a point on the H-R diagram. Mark several direc-z1 3ffrhdo0 mtions away from this point. Now describe the changes that would take place in a star moving in each of these directmz of-f h3rd01ions.

Does the H-R diagram reveal anything about the core of a star?ld*;mf kq: -ql

Why do some stars end up as white dwarfs, and others as neutron st ybyj.z-1v0b3 ejsad- ars or black hoje--z.a 10bysj b3dyvles?

  Can we tell, by looking at the population on the H-R diagram, o)h6dgta5e ;l that hotter main-sequence stars have shorter lives? Explain. l)ed 5g ;oat6h ----待选择----yesno 

If you were measuring star parallaxes from the Moon instead of Earth k22m944bl ftx6grdf r, what corrections would you have to make? What changes would occur if t49r mgx42fl6r 2kdb fyou were measuring parallaxes from Mars?

Cepheid variable stars change in luminosity with a typical perio; ; 3uhvv4y zy:1je fez45ihazd 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 distance to galaxiesjfe 3;44e u vhv1 zz:;yhayiz5?

What is a geodesic? Whatlv e:vscjb261 is its role in General Relativity?

If it were discovered that the redshift of spectral lines of gadkx);r 8m c- ;lma3adglaxies was due to something other than expansion, how might our view of the universe change? Would there be conflicting eviddx lak3a -mg;8r)m;d cence? Discuss.

  All galaxies appear to be moving away from us. Are;czmf 8qiwl 6+ we therefore at the center of tlqf68;zi c m+whe universe? Explain.  ----待选择----yesno 

If you were located in 5ts-qag h,xfe u19imcru*8( o,zweg; a galaxy near the boundary of our observable universe, would galaxies in the direction of the Milky Way appear to be approaching you or receding 9,hiqeew5rg f,1u sua8x *( mt- c;gzofrom you? Explain.

Compare an explosion ylro1i 2vnbyc*v 3-e-on Earth to the Big Bang. Consider such questions as: Would the debris-c rl2oy-v3i 1vbn* ey spread at a higher speed for more distant 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 hol2im-q 5bgbtn+ e, then how can we tell if one ig2bi-b5mn tq +s there?

  What mass will give a Schwarzschile 8 dnto) nfh4;cp-8hod radius equal to that of the hydrogen atom in - n8nc oe;84hphof)tdits ground state? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often givey+8yy zd6u ku5n as about 4 billion years. Find that time on (Fig. Below). People have lived on Ea6z5kuy d 8uy+yrth on the order of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-Kl )sfz)1, qh idicn./tf0xt(7;kg ycb cosmic microwave background radiation is. Where does it come from? Why is its tel71,k t.ic qnxtg (ci/f) hzsb;)y f0dmperature now so low?

Why were atoms, as opposed kr(qvz-ki0 a.y 4g5zyto bare nuclei, unable to exist until hundreds of thousands o-5v.k4(qz 0gykzriy a f years after the Big Bang?

Under what circumstances would the universe eventually collapse in on itc;y0oj(c hlv e tw(1i:self?

  Using the definitions of the parsec and the light-year, ssp:j ,xgw09u bhow that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.38 seconds of p2r fwdg1q()ojti)u( pv b*:k arc. How far away is it? d =    ly

  The parallax angle of a s ed/,ghc (rmnh3 +k9gvtar is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its parallax ang.vzi8j7ux6yqv7c dj.fc8 0 o/wggr ) dle?
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 55r9;vxl2 2rj(umn2 qcm ly away? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away fro/sad1 v:lnsx. m us as a second star, will the parallax angle of the farther stsxn1:d .v l/saar 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 its light to reaca2c3 tx4r63t6ssrco0u su kl1h us?    years

  We saw earlier (Chapter 14) that the rate energy reaches the Earq -3c .5 itq3omm8 kts t9mzjwl0,)ltvn1:ezgth from the Sun (the "solar cot jlc:3)m, zq.5mlvoq t9t1z m0kewnsi t38g-nstant") 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 k awxtw+j **golf.i 1t ;1ym07 capj0gof the Sun as seen from Jupiter as compared to its brightness from Earth?. 7g1t0l*j g wc1wy*ax fkjma+0po;it (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 th xk)62tyy9sqf at our Galaxy would subtend if observed from the nearest ga2f 9x6yq)yt sklaxy 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 will be gixpojwx,0 hi jh t4,,ie1+cjyvo/5 +its average density if it expands out to the orbit of Eg,xphei,4,o 0 xt1ijvhj ojw/yc++ 5iarth ($1.5 \times 10^{11}\ \text{m}$ from the Sun)? $\rho = $    $ \times 10^{-4}\ \text{kg/m}^3$

  When our Sun becomes a white dwarf, it is expected to be f(b 0sr6iyoj( : f7bhz8b/bem about the size of the Mojy/frs78:h(e(i bbbmb0 fz6o on. What angular width will it subtend from the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whose mass is equal to the9:zig7/ra5maxz0xi; +c8dh f 4la awg Sun's and whose radius is equal to the Earth's. How many times larger than Earth's densfzral8aa0x+ag:i ; z mx5 i w7gd/c9h4ity 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 massr(c5y+o4wa 9ho umlt18gguyy75z/bg .f -odu es has a radius of about 11 km. Calculate its average density and compare to that for a 1u7z 94 5ualgr8fty-+5oh/oyd .(mcby gwg uowhite 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.cwkn bly14hk7/e)fg 47 f rzz( 33-2. (The mass of the verk7 4ywfk nfz )47l/eg hb1c(rzy 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 apparent br5ypukg9k +3s dightness $l$ 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 asy4q(hw7,wb4q.yc 9 f* ijwhfv sumed to be about the same distance from us. Two such stars have spectra that peak at4fqyy c*q jb,. f9wh w(7i4hwv $\lambda_1 = 500\ \text{nm}$ 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 oux 9t b-gsr)-wrr Sun isst-) 9g -rbxrw    km, and (b) of Earth is    mm.

  What is the Schwarzschild radiescj5h8 w58n :tc h7ocus for a typical galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on th-w(f i 6xnsg6lmwyn:1lt. *u we surface of a sphere, for which the sum of the angles is w:(-*.nl nyw f6xwiulg1 mts6(a) 359º, and (b) 180°.

  What is the maximum sumo06m5 (g jeyuw-of-the-angles for a triangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the speed of light, roughly how4wzy.ra fam7l2lgi 7rjk4 o9y1qkf98 far away 7gr1i7f9al9f8z 4.o j kya4kwylq mr2is it? v =    Mly

  The redshift of a galaxy indicat4nhqqchf 9 2r:es a velocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (repkmbwq (xfi0v;3mp ,* lative to us) that is near the observable "edge" of the universe, say 12 kfmp0,i x;qw3mbv* p( billion light-years away. v =    c

  Estimate the observed wavelength for the 656-nm line in t e-dh, 38lhvzehe Balmer series of hydrogen in the spectrum of a ez-38l,hvh de 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 oqh/u.hej 20by :m(o ksf a galaxy, and its distance from us, if the wavelength for the hydrogen lin(: 0qkmu b/hhy sjo2.ee 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 35ezobh aw-5bd(o pop06v v:lwith $z = 0.60$? v =    c

  What would be the redshift paruszxkvp.(dw*s)sa 7mj z 6*pr/*m9 4uzsbs(bameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show vs ; +qo6z cpa6;x1xo nfs3af9that 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 distribulfqn-e9;/ (abv/ni:vmw7 hsj tion at 2.7 we vqnilfs /man:-j 9h(7 bv;/K using Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closu;efwb7od2v56wsm0 y,(wr vdcbq,rf 7re 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 distanp5zza v -1 t6symnz8(ja7k h1hce between galaxies) at any one moment is believed to have been inversely proportional to the absolute temperature. Estimate the size of the universe, compared to today, j-h 67v1tzzksa z5n8a1m yhp (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 to4ywu;g 2x-e+q d.jd lhe universe cooled below the threshold temperature for pro4 x+dlodq j-e ;gy2.wuducing
(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 t6gy6 j8w 8dv7dibe(obhree changes represented by the three arrows, A, B, and C, ydjwb8 (ve8 67o d6bigin the H-R diagram of Fig. 33-28. For each case, describe the changes in temperature, luminosity, and size.

  Assume that the near q m/isnbvlyj sscn .l8-)o5.)est stars to us have an absolute luminosity about the same as the Sun's. Their apparent bright- qvnl.cs5 is) bys8n/l). ojmness, 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 velocity of a 6l ,ro)qte i: l3pf6rvneutron star which has lv6flrirot3 ):,eq6pcollapsed to a diameter 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 kineti gyl;+pcs*m.hg+rgn 4c energy change when the star in Problem 56s.np cg lhg +4rg*y;m+ 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 mk ed-69 bo7augass 1.5 times that of the Sun, 9ue6g -ak7bdowith diameter 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 Galaxy is abouo8r n(+gzlu dn*y+7z wcq0ee,t $2 \times 10^6\ \text{ly}$ 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 eVdi llffga5 + /q;mai5qf gkc,6- +mrm9) would provide the critical density to close the universe. Assume thec5a5r /d fmqi;6k m-fg,mfl9l ai+q+g 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 7v3ou ptj,8tne zh;2r *leai 6peak at 600 nm and 400 nm, respectively, both lie on the me *e z2 uop3nv76,h rlitajt;8ain 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 distancej gizncr:x-sv5on49h (l4/ e a86 ysqts with parallax at 100 parsecs. What is our minimum angular resolution (in degrees), based on this t6 z89csvj 5oqsnghyi4e/r( xa- ln4:information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from singh;8-dqz vee *aly ionized helium in a distant star happen- hadvzeqe8 ;* 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 thaz0 zqr5rs+h 6kt corresponds to 1.8-TeV collisions at the Fermilab collider? To what era 5r6+hsr zzk q0in 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 s sr 8o3j* zk,d8(bsbzmight be a supermassive black hole of about 2 billion solar masses at the center of a galaxy. If the radius from the galac8 ,zd j8rbszobks3*s(tic 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" hydrogen line at 434 nm wn l q/-/*qavhemitted from the galaxy //nqla wqv* -his measured 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 owle y, oup2p)(f stellar evolution, a star (if massive enough) will begin fusing carbon pu,o y(wl e2)pnuclei 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 reactioxh-kr:;c nxbz 4x- 1qyn
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 rtigc6fl03 c; vr 4zf(rjq*7d critical density of the univfr*(;vd6 0 ri4zl qtr73fjccgerse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$