The Milky Way was once thought to be "murky" or "milky" but is now considered a /m.* gzjjcbd*v- e*gto be made up of poinzm gceva*** g bj.d-j/t sources. Explain.

A star is in equilibg cd6ws 2zs9.j34 oqs+tco4ldrium when it radiates at its surface all the energy generated at its core. What happens when it begins to gensldc94+cod4s .g wqs6j 2z3 toerate more energy than it radiates? Less energy? Explain.

Describe a red giant star. List some of its properties.v5 f.e4ty y2:jyo(wo 9tplw z-

Select a point on the H-R diagramp(4 le ;ccvjah.*j+n b. Mark several directions away from this point. Now describe the changes that would take place in a star moving in each of these directio* +;4c( aeh. jblpjncvns.

Does the H-R diagram reveal anythin)p 2bvmwh 4l5bg about the core of a star?

Why do some stars end up as whit5u,gau3nnjm : e dwarfs, and others as neutron stars or black ho5 ,a3nu u:gmjnles?

  Can we tell, by looking at the population on the H-R diagram, thaty+5yxx:qrm v7m.f -z j hotter main-sequence stamyx rxy.5mv-qzfj 7 +:rs have shorter lives? Explain.  ----待选择----yesno 

If you were measuring star parallaxes from the Moon in:kv rw 22a* (chk(nsajstead of Earth, what corrections would you have to make? What changes would occur if you vracnh s* 2kwja2(:k(were measuring parallaxes from Mars?

Cepheid variable stars change in luminosity with a typical pemf2 a5fmb*q t(riod of several days. The(*5abfmq2f tm 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 Relativx.ui n0b9bzwos4 i1ed m-(.x rity?

If it were discovered that the redshift of spectral lines of galaxq qp4 5gjnkv13l5tdc ;ies was due to something other than expansion, how might our view of the universepnt 5v4qqck3 jd1l5;g change? Would there be conflicting evidence? Discuss.

  All galaxies appear to be moving away from us. Are we thezg )nz5l bf*l(nwr: b+refore at the center of the universe? Explaiw*z g+l 5fn)rln b:(bzn.  ----待选择----yesno 

If you were located in a galaxk6xex 3jmi br6 pi)5d3y near the boundary of our observable universe, wouldbkm)6x5 6ix 33pij red galaxies in the direction of the Milky Way appear to be approaching you or receding from you? Explain.

Compare an explosion on Earth to the Big Bang. Cm/e 57+fprhf5oqy ew -z sts)8onsider 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 universe would this correspon/moe t-ffz h 7s8)s5e+ rwypq5d to, open or closed?

If nothing, not even light, escapes from a black hole, then how c31;tc yiu-w)d lhq/lran we tell if one is; 3qtl )li1yrdw/-chu there?

  What mass will give a Schx t(.jv pkdh-hu hf5aa2/+o. nwarzschild radius equal to that of the hydrogen atom in its ground state? /k5(hp 2odjhtha vn uf-.ax.+ M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4x9q y1 b9zd3po billion years. Find that time on (Fig. Belox9odb3q 9zyp 1w). People have lived on Earth on the order of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K co8)bv vc odsa1+smic microwave background radiation is. Where does it come from? Why is c8sv)do+1 bva its temperature now so low?

Why were atoms, as opposed to bare nuclei, unable to exist uisw8qdwdi,b,tqg+u 5 nsj ) +.ntil hundreds of thou 58wq.+n, ),wgsd+qi jisu dbtsands of years after the Big Bang?

Under what circumstances would the universe eventually collapse in on ito negva)q pz,89+b ,08bh ehobself?

  Using the definitions of the*oegfa+v. 0wr parsec and the light-year, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.38 sec/:irhrd(o u0sonds of arc. How far away is it? d =    ly

  The parallax angle of a star is t .f6h3cf1ba 7vrn;p rhr5ts-$0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is on 2u3-/rvjdpu8 y*jd 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 6fhok0 tm(ier8+f(u9uyay -f b *5zomthat is 55 ly away? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away from uw+q (aq4c 4tcko74eq ws as a second star, will the parallax angle of (qq c+e7ok4q t4w4cwathe 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 tak /,-)ev vwxti.v/1+yoxp m beoe for its light to reach us?    years

  We saw earlier (Chapter 14) that the rate ener kvky/u, moe58gy reaches the Earth from the Sun (the "solar constant"/ uoy,k 5mv8ke) 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 t pxpj2 nw9bl2++ dca0 ,2mdndj er.it)he Sun as seen from Jupiter as compared to its brightness from Earta2+l td2ipbnc)xdj, j+ wm02dp9 r.enh? (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 obsbq,e0+qzn+jpp *zll0erved from the nearest galaxy to us (Table 33-1). Compare to the qe zlz0p b+jl* qn0,p+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 e9d 4zu pu(zp0kf.ef 1yxpands out to zyp.f(u01dpf9ku 4 ze 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 be about the size of the tly4l+q; lf *vMoon. What angular width will it subtend fromfl;*lyl+ 4qv t the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a whihu73mxby y*wp 3 ,oy-wte dwarf whose mass is equal to the Sun's and whose radius is equal to the Earth's. How manm-7y*yxh3bw3 owyup , 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 k;+h2s r;kqh ktm. Calculate its average de;2skk+ht;hqr nsity and compare to 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 t sbx3*fn*kku/he He burning reactions of Eq. 33-2. (The mass of the very unsta/ k**3x bfusnkble $^8\text{Be}$ 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 apparents ndhjo1 p8 e*o3h1p)p 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 asztz* n( n3j/txf7l(wosumed to be about the same distance from us. Two such stars have spectra that peak at owjtz (*zf (73/nxnlt $\lambda_1 = 500\ \text{nm}$ 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 ilj-3 9z- 2jlwkaabw7star with mass equal to that (a) of our Sun73lai -b9jklzja2 w-w is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typical galaxy (likerw-c a+m56lj 4nygg3t ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the slpbkvz) 5fzj+rs 2/:bss7zb4ng 6 ch3urface of a sphere, for which the sum of the angles is (a)r 6c z)/lsfk2j3 sn:v75bhzz4pg s+bb 359º, and (b) 180°.

  What is the maximum sum-of-the-angles for a triangle on a spherz*r u-mcv+ fm-e?    $^\circ$

  If a galaxy is traveling away from us at 10+ dc 5/qsfeh a.q+hza.0% of the speed of light, roughly how far away is it? v qaf/ +h.hasd q+e0 cz5=    Mly

  The redshift of a galaxy indicatl u/uyu0yh* p)fcfn5s, 1jqrt/*, jiges 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 observableob*aasj*cwqb 4,.fox a 8xq:tgxa) 06 "edge" of the universe, say 12 billionta,6.:aqqjag*8 x x 4ocs0oxb a*w) fb light-years away. v =    c

  Estimate the observed wavelength for the 656-nm line in the Ba y2joq+a4kuda1ic2 n (lmer series of hydrogea 42 1auk 2inj+ycd(oqn in 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 distance fromf2 w.vg4kyqy 0 us, if the wavelength for the hydrogen line at 434 nm is measured on Earth ayyk0w. vf24qgs 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 cil2p ev.ym/r+ju,c/ a galaxy with $z = 0.60$? v =    c

  What would be the redshift parameter fg32 zldqyp6.00k sbv $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Dopg0 :za6 4x3 6m hggizvi;c./jxzj+m yupler 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 a/vf4 8-be 0fxz 57h+dq bpzjwpt the peak of the blackbody radiation distribution at 2.7 K using Wb0w8zv/ f qp7 d4px+bf5- hjezien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure oiej;;rm6vzeu g 0t 3.cf 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) at any one momw1a )y::u9vatl ,bhd went is believed to have been inversely proportional to the absolute temperature. Estimate the size of)la9 d:ht 1y,v:wub wa 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 threshoe qojmk )qqi+.b4s8k: o)i n*f 3*tmxrld temperature for producing bt sq4ikkf)3qmj+*:o*nie .rx oq)8m
(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 unr*+vzmi b:.mk(ld1y5p7 o kqfdergo the three 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 lv k 1d*qz y.m7:rk+b(mio5pfin temperature, luminosity, and size.

  Assume that the nearest stars to us have an absoc x5eudr53ze :znl;u)lute luminosity about the same as the Sun's. Theieur) 5l;zx3ed z c5n:ur 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 efrd6/njzf cx t-k()5* o iim3;xhtfm+stimate the angular velocity of a neutron star which has collapsed to a diameter of 20 km, from a star whose radim- z tkf(d/+63hxi5j m);*tcnffiro x us 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 whenw:p)6 ya8vexl the star in Problem 56 collapses to a neutron svx8wl):p6 ye atar? $\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 that of the Suxi vqav/ j9;sf:e:2vdn, with diameter 20 km, is observedfsid v;xe2/q ::9a vjv 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 aborf z 6;4l8syni.+3 usytc3gkn j6z ks,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 mass (in eV) would provide the critical density up .*xl9i8x k0u 0q,vxz3fts fto close the universe. Assume the neutrino density is, lik, 8flxpzu.txfq*9v 0s3ix uk0e 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 600v*3 wsdfp ps12mnq-, o nm and 400 nm, respectively, both lie on the mssd pwv3op-m *fq ,21nain 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 ad w)vc. b) n./-djnkydistances with parallax at 100 parsecs. What is our minimum angular resolution (in degrees), based on this infor k nwav d)db-c.yj/).nmation? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer livah kt8c,2e 0*g+sylrnes 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 star rec28r s*+v,chatey0 gk leding from us? v =    C

  What is the temperature that corresponds to 1.gd fmk zv18t,78-TeV collisions at the Fermilab collider? To what m,f kd8tv 1g7zera in cosmological history does this correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation of g6qqn;)wbh3 p (5x-jvloh ihkdw*x q/*as around what might be a supermassive black hole of about 2 billion solar masses at the center of a galaxy. If the radius from the galactic centhwxxlwkqo-3hd*b) vq5q ;* pijn6( h/er 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 eb3*dnnbsolz dt:2 dcyki *z. wt)9 q2/mitted from the galaxy i/sqcd 2)tni k3w.d d:b oynbtzl* z9*2s 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 of stellar evolution, a star (if3-uk)kbbqo jrki 660r massive enough) will begin fusing carbobbri-u36kq) r0okj 6 kn nuclei 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 )zpmqn3qh y.e75dzgo .yl5*xkni ob37u : /dy
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 densx-h (d5b0 h . zwjd)tdnfnq:.wity equaled the critical density of the univdf bwddwh .hnqxz:n0.t)j5-( erse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$