The Milky Way was once thought to be "murky" or "milky" but is now considered to4. i/uu+(8(o yr6t :yhlzqksrnz a;rz be made up of pointk(a;r . yrnz8yl q4hz/ i( zu:ruost6+ sources. Explain.

A star is in equilibrium when it radiates at its surface all the ennz9qlf o403djergy generatejd9 l40o nqzf3d at its core. What happens when it begins to generate more energy than it radiates? Less energy? Explain.

Describe a red giant star. List some of its prope28(zvx3k s: ydeadtf1-j od,sz2;mlmrties.

Select a point on the H-R diagram. Mark several directions away from this point i47o*hsmk z5t. Now describe the changes that would take place in a star moving in each of thes 5o4*t 7ksimzhe directions.

Does the H-R diagram reveal anyt2eq; k0y+ubqmhing about the core of a star?

Why do some stars end up as white dwarfs, and otherxg9t:x ygxl98/ bt+ przaucyu:3f 5r6s as neutron stars or black ho:fytup : +gc/xl95r8gtby6r9x z3x ua les?

  Can we tell, by looking at the populab f.dqgg) -pj-tion on the H-R diagram, that hotter main-sequence stars h-.fd-qb g)pgj ave shorter lives? Explain.  ----待选择----yesno 

If you were measuring star parallaxes from the Moon instead of Earth, whetlk 9as 5 sd;oo+tc6,at corrections would you have to make? What changes would occur if y sot,;ce as9dok6tl +5ou were measuring parallaxes from Mars?

Cepheid variable stars change in luminosity with a typical perc6a7 kg emkyt-e.5/d liod of several days. The period has been found to have a definite relationship with the absol.mka - yek/lcdt 57eg6ute luminosity of the star. How could these stars be used to measure the distance to galaxies?

What is a geodesic? What is)wj t/25wphmiv; ) sgs its role in General Relativity?

If it were discovered that the redshift of spectral linesvt, ekx/m5zf *j95;tyt8bz08hxlh v t of galaxies was due to something other than expansion, how might our view of the universe change? Woul/evly 8vt htkzft95;z5 xm*hx ,b80tjd there be conflicting evidence? Discuss.

  All galaxies appear to nk0k-ks-y(rz1 xw9nl r b(,d gbe moving away from us. Are we therefore at the center of the uni rylwkk1 --(dnzkn0x9, gs( brverse? Explain.  ----待选择----yesno 

If you were located in a galaxy near the bounda h3avyideza +zz n:-bw,f5 s33ry of our observable universe, would ay,:zzze 3hid3nfa-sw 53+bv 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. C9k rowj;p:mj d0 k7-5hz9nix wonsider such questions as: Would the debris spread at a higher speed for more distant particles, as in the Big Bang? Would the debris come d ;pk9mz-7 :k ijr50xwonhwj9 to rest? What type of universe would this correspond to, open or closed?

If nothing, not even light, ewwyw qx) 0pigsd:2;rgb. x- y)scapes from a black hole, then how can we tell if one is there xqy;)gwwi0s) r.: xwdg2b-p y?

  What mass will give a Schwarzschild radius equal to that of the hydrogen atomgm98uzpx* x m; in its ground statm;xp* 98xm guze? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often giwcru2 d5;84dqzafxfe5t l k-4,,bka wven as about 4 billion years. Find that time on (Fig. Below). People have lived on Earth on the or258z,axar ewcd4,u-f;bq4 w5t dfkkl der of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic miz* ya uq9lt:/ycrowave background radiation is. Where does it come from: 9y*/ytu zlaq? Why is its temperature now so low?

Why were atoms, as opposed to bare nuclei, unable to exist until hundreds of thlf e3cz4f, x 66bmcz,g8,abre ousxr,c 6 f3zagc 6f,8eb4 me,lzbands of years after the Big Bang?

Under what circumstances would the universe eventually collapse in ns x)jh.mc1n,k12q q son itself?

  Using the definitions of the parsec and the light-year, show too-1 hw)n oj mqt233rvhat $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.38 seconds of a*k5-m osn.oharc. How far away is it? d =    ly

  The parallax angle of a u.;xwg 2zhnmq.d cv nt0a:*k,star is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its para .lg,v jd.tj;kllax 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 bhf:h m nl)l.o40 ifw5:/km(kmiaym7is 55 ly away? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twicec/,j;kcu33k ezat y - 7ey;nki as far away from us as a second star, will the parallax angle of th ; nya7ik;k/-33c , zyjcueetke 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 takam4v)elh kzz qsof2g8 -8zk:+e for its light to reach us?    years

  We saw earlier (Chaptez15jw59:fd zpysv mu /r 14) that the rate energy reaches the Earth from the Sun (the "solar pf9zu zy5sv w:dj/m 15constant") 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 compares9:m1ak1 rt38luc b e:4w lzay0f.k hjd to its brightness from Earth? (Jupiter is 5.l ::yrl4bmsj h93e18kftk0z wa1a cu. 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 from4xco fwr sn8nt *k4s4+gke;z8 the nearest galaxy to us (Table 33-84nx +z44kfeks; otgwrc 8 sn*1). Compare to the angular width of the Moon from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, ck8i1+vm ke0 jzm(ds, what will be its average density if it expands out to the orbit ofdzk(j,0is+e c m81kmv 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 expeu :al( a:0 dnkyrkn2(bcted to be about the size of the Mookl( (2un:akr: naydb0n. 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 ismf yz-8wm3,1(tujhyd equal to the Sun's and whos mdtj1mzy ufh-8y,(w3e radius is equal to the Earth's. How many 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 hassh78 r7k2 qhj8yxyj5vx nx r)x-m(q cvqy(*y2 a radius of about 11 km. Calculatexq vnsyhy7 rqxh2q *xvc2 (k-yxj(8rm7y5 )8j its average density 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 the He burni sslj f:i1zp..ng reactions of Eq. 33-2. (The mass of the f1zi :ps.j ls.very 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 ap mbqdju805* wgparent 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 sameb)+bb4 zgus. 6pv5uef7 r.t0fq ezs .k-h x)gp distance from us. Two such stars have spectra thtp7bu6gv xz)p4 fefks)es0.+bh..burgz q5-at 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 Schwarzsczunob)mtt-2 4 v.j qy+kv h0h2hild radius for a star with mass equal to that (a) of our S qyku) jtv0vn.mz 2b4+ho2- thun is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a tqx).0 u cz-mlgypical galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a sphe86lzv.isbzu) 8,nvmnx p* x 4mre, for which the sum of the angles is (a) 359º, a,mxbvm8l*)i uz v6xpz4s n.n8 nd (b) 180°.

  What is the maximum sum-of-the-angles for a trianglbb/a ,hk ecjc 4*a;tv9-/yu rae on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the spe3t)m zi-8 1cu kooe6qqed of light, roughly how far a u-co )eqiq 61ko3z8tmway is it? v =    Mly

  The redshift of a galaxy indic.jr+ /*esu .bquwfc1;jd v2asates 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 t+ml vx in-dph (r;pprf8b6g-) he observable "edge" of the universe, say 12 billion light-years away. vpbmi+dph r6vp)r( g l-nx8f-; =    c

  Estimate the observed wavelength for the 656-nm line in the Balmer series of hp-p/:jrvq5* z*ow+ bir8 ozjxydrogen in the spectrum of a galaxy whose distance fro-+rpp/ozvw8z:bjjx i* * 5rqo m 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 gal7- s1egiod*m2) y,*wrqto iat axy, and its distance from us, if the wavelength for the h sea2-om*,71rywgtdiq*)i o tydrogen line 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 with70- ol+ntnm y-9ma, gcikk .lr $z = 0.60$? v =    c

  What would be the redshift pa mr .dxw5+9g bq4om4torameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show f)*t *cpzea+ithat 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 wavelengthzd 43 i8,ttfc, kv4cl k84ezij at the peak of the blackbody radiation distribution at 2.7 K 4t4k,ctzkv8 i38dl4ji f,zce using Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for clodl55ivb-kui 5 sure 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 dist-zww/u/ 4kvy eance between galaxies) at any one moment is believed to have been inversel-vuwwk4 ye/z/ y 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 cd:1 s a :rhv xfremd)ym9)dm61xtt;h4ooled below the threshold temperature for pr6mrm4r)1fsy 9hth : xtd1;x:)ddav meoducing
(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 changes z (7s- d;6y;adz xyqfqrepresented 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, 6qsq dd x;f;z(7z-yyaluminosity, and size.

  Assume that the nearest stars to us h//f 6ko or3:l7 zawfucave an absolute luminosity about the same as the Sun's. Their apparent brightness, however, islu/z3:roo f /7 6ckwfa 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 of81ocwym u +gw) a neutron star which has collapsed to a diameteruwy o+wg)8m c1 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 i l+(9( :+ -jb6z wbkrtevhxhk0gdf 9fthe rotational kinetic energy change when the star in Problem 56 collapses to a neutdfkx+h69(hb irev- 0lf z9bt :gjwk(+ron star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believed to be a neutron star of mass 1.58b60shl q, zp*6gmsor2 wo*sd times that of the Sun, with diameter 20 km,oz0d bsm6g2 *6q,wosl8s* hp r 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 isnz 5:dwnpxee5j /;s8 2pik9+eqqg jxm* 83ssz 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 critical dykx,rzs 6w**7mv xp dz +8y+hgensity to close the universe. Assume the*x,7v +pzdsrm*g8+ky y6xhw z 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 aln5:fxh8kr ) ynd 400 nm, respectively, both lie on the main sequence. Use Wien's law, the Stefan-Boltzmann equation, and the H-R diagram (Fig. Below) to estimate the ratio of their d:5x)n h l8kryfiameters. [Hint: see Examples 33-4 and 33-5.] $\dfrac{d_{400}}{d_{600}}$ =   

  Suppose we can measure distances with parallax at 1e p:nnvx yu*/76b,oku00 parsecs. What is our minimum angular resolution (in degrees), based oep * uxv/ynu76:,nbkon this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines 7qgi5 qfynymi 4 2lr-9from singly ionized helium in a distant star happen to overlap with the Balmer lines from hydrogen (Fig. 27-22) in thyf4q g7-n lm r9qiy52ie Sun. How fast is the star receding from us? v =    C

  What is the temperature that corresponds to 1.8-TeV collisions at the Fermilb5y8jw ov -y:mab collid: m 8ovy5yw-jber? To what era in cosmological history does this correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently mea8mmc rre r: gylfyla-.bt5(/x 6u,tl/sured the rotation of gas 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 grar rfe :tyu lcy bm/ l(5x-/.6gt,ml8alactic 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 aa 0,i8hcnzc: lvj5b 3ut 434 nm emitted from the galaxy is measured on Earth izv l0c3jca5u:8b, hn 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 k0fqzi8nhow5 7ovj, ep8p8, b massive enough) will begin fusing carbon nuclei to form, forj88 qpoekn0,b w v85 zphf,7io 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 ri1wgztjy 28) um6-/19g bcizan4cs d
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 den ij+pnlb+hp1( sity of the universe, 1hp+b(pj +lin$\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$