The Milky Way was once thought to be "murky" or "miu a1pt)bs 7sf*lky" but is now considered to be mada )1 sspfut*b7e up of point sources. Explain.

A star is in equilibrium when it radiates at its surface all the energy generan6ai dxvvag0- hds5 *9rs .q;mted at its core. What happens when it begins to generate more energy thar.*5gqs0v;ivn d9 h6sdm ax-an it radiates? Less energy? Explain.

Describe a red giant star. List some of its propekg)qz3:w o kw7qw0fn+m)abijvr6b v1 1h 2v8crties.

Select a point on the H-R diagram. Mark several directions away f* h9o1kou,1cvhh56q6i+ 8ctvwva m gbrom this point. Now describe the changes that wouldvba6m+ctvhqw1u oh6 i5,c9 k*1gov8 h take place in a star moving in each of these directions.

Does the H-R diagram reveal anything afc6 5l)y;ofcuc4pop -bout the core of a star?

Why do some stars end up as white dwarfs, and othersftju+p d zu 7uv2zn(,( as neutron stars or black hu( ,dp27uu+fz(v j tnzoles?

  Can we tell, by looking at the population on t x p0ddxn,3oaf.zbkmn n4ipq0vv ).32he H-R diagram, that hotter main-sequence st ddkm xpb.v2304 .zp,n)o3qv0x fninaars have shorter lives? Explain.  ----待选择----yesno 

If you were measuring star parallaxes from the Moon instead of Earth, what cy k/3as5e-pv morrections would you have to make? What esm5v-p k3/aychanges would occur if you were measuring parallaxes from Mars?

Cepheid variable stars chan4 m*ea 7a ytng77z6rvsge in luminosity with a typical period of several days. The period has been found to have a definite relationship with the ab4nseyt 6zgv77aa*r7m solute luminosity of the star. How could these stars be used to measure the distance to galaxies?

What is a geodesic? svg 48gewkv qd*-5 :eeWhat is its role in General Relativity?

If it were discovered that the redshift of spectral lines of galaxies was d3ld a6acv bnz7get+gc. l2*.w ue to somethi .lg+ 6vwa 7zn. *delbt32gaccng other than expansion, how might our view of the universe change? Would there be conflicting evidence? Discuss.

  All galaxies appear to be moving away from us. Are we therefore at the79*kygvd* t vn center of the univerdvgnk*ty97v * se? Explain.  ----待选择----yesno 

If you were located in a galaxy near the boundary of our observable univusebd ).chb/px5h*t6 4nk.mvb6 pi+ z erse, would galaxies in the direction of the Milky bsb5u*p pc+)bh d.tmh6 xnez/. i4v k6Way appear to be approaching you or receding from you? Explain.

Compare an explosion on Earth to the Big Bang. Consi i7 f(*qqpi5yider such questions as: Would the debris spread at a higher speed for more distant particles, f*(qyiq5 ii7pas 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 fromt:mz3f .9 seuf a black hole, then how can we tell if one is there?3u z: mtef.fs9

  What mass will give a Schwarzschild radiuo)e m(qv9p iibll1g e2;..xvys equal to that of the hydrogen atom in its gr 2b;l9(o.gmv .v1iq pelxiy)eound state? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion years. Find ,owbogk .d.779mr zjkxy :5gpthat time on (Fig. Below). People have lived on Earth on x p5oog.k jb:gm,yd z7kw79r.the order of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic microwave background radiation is. Where2r4n :sf0ih 3wndo)fk does it come from? Why is its th:i0 4dnkswf rf2 o3n)emperature now so low?

Why were atoms, as opposed to bare nuclei, unabl:/0d)w6 6x -y0nmy+yzub i(imzy blnpe to exist until hundreds of thousands of years a6mwpymzi0 y/)y:bu zib -(+l dnyx0 6nfter the Big Bang?

Under what circumstances would the universe eve3sm q2/ sdgjt6ntually collapse in on itself?

  Using the definitions of the parsec and thj.nquo rs;qx,3 qh8go mai+j 4qe7gh1):t)w se 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 is it? dxoz /ouw(gt5):ej zu lv:-5g y =    ly

  The parallax angle of a star is mfaj.2ef l5., h4heqz $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What wja mc7/2 t7w, bhhn2a9pgk.ur 4y8msis 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 fr03 blnnf +:k,ag7lyis 55 ly away? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away 4q:v+mzo u3mcg s6vy6 from us as a second star, will the parallax angle of the farther star be greater or less than that of the nearer star? By what fvc:zq 6+3 g4yv6smomuactor?

  A star is 35 pc awaysw r w-6 zblq-6k5o0a,.zjvfg. How long does it take for its light to reach us?    years

  We saw earlier (Chapter 14) that the rate energy reacui+;ja 5)m9 d wz.g6 mx-tk y,zhc5mdyhes the Earth from the Sun (the "solar conszm +6u)zyd.5m 5d,y jc;k9 -gi xathwmtant") 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 Jupieur - .0+ c, :lqlwahkre1bct5ter as compared to its brightness from Earth? (Jupiter is 5.2 times farther from the Sun the -:r+twbul1e0hlcr ,5.ckaq an the Earth.) $\dfrac{l_{\text{Jupiter}}}{l_{\text{Earth}}}$    $ \times 10^{-2}$

  Estimate the angular width that our Galaxy would subtend if observed f cl6212x 36fp*q,qcehcpqs6wd ofj/ rrom the nearest galaxy to us (Table 33-1). Compa 6 o, *c fqr62epdccqhlps6j/1qfx3 w2re to the angular width of the Moon from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, what will bermrwijqt q)g . -h,;,e its average density if it expands ouetqhg .i )w ;mrqr,-,jt 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 d/ i-:x+f7m yvcjv/yma nq 7kug9eumsp;4b.0 wwarf, it is expected to be about the size of the Moon. What angular width will it subtend from the present dis mj:;uf/n-qgk + 4ei7v7 x9s yc/v0umbamw.yp tance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwdz .ihqk wr7d;d qkom5. 4e3.) ujn+mnarf whose mass is equal to the Sun's and whose radius is equal +.r ;)3k4dwh j.umoe5nqq mdk7nd. izto 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 has a radius of about 11 km. Cau-t izzx-61kuw l f,t/lculate its average density and compare to that for a white dwarf (Problem 13) a-tu/ z kt,i1lxuf -zw6nd 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. 3 uhwmxv rg7l)b4am, 343-2. (The mass of the very glm7mub4wx 3h rv)a4 ,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 brightness uq;y mimp-zx .xc/) n4$l$ 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 clustpx4 -tze e9khms 40q ,dlw.5t-p,uhgmer are assumed to be about the same distance from us. Two such stars have spectra that peaketz ,m h4xpk m,9dw.0sh g--45pteuql 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 ,r d x4yvep.cvm7i 9k/o:db+hstar with mass equal to that (a) of ourr:,9 p+ xceb4m/ vh.vidyo7kd Sun is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius f *ki1 s ,joo3adg:nu)h9 adxz6or a typical galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn.h+ek -u ekv-fasdgdqcouc) 8e(, .u- on the surface of a sphere, for which the sum of the angles is (a) 359º, and (-q, gsu8 h.cdvufek cu-ead)( o -+ek.b) 180°.

  What is the maximum sum-of-the-angles for a triangle on a sphere?*httms :v2 y+k    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the speed of light, roughly smvz4.o29 d4/rermmk how far away is itm kmv4srr 4.m/ed z29o? v =    Mly

  The redshift of a galaxy indicates a vel)r6e 9)8 d* sl4)vndkoc qahzwocity 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 observzsd-bnei-q5yq hrg)ep6 .u*t( l3 giaf:z12e able "edge" of the universe, say 12 billion light-years away. v n* bd ez.ag: -r quis h21(q)t65eyzgep fil3-=    c

  Estimate the observed wavelenowzl 5,,z,tr bgth for the 656-nm line in the Balmer series of hydrogen in the spectrum of,zro b ,5wl,zt 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 galv w5fqcgi4efs ,0 dd0;6fe;qa axy, and its distance from us, if the wavelength for the hydrogen line at 434 nm is measured on Earth as being 61050fwvs , dqei4q ec;dg06f; af 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 galajfdc99df2 am 6*qkp* cxy with $z = 0.60$? v =    c

  What would be the redshift f*m s.pi:l6ddn*u8lpq0x*lhparameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Doppler nyc2ih7tgu6a.rd - j e2tz /a(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 (:tt w dr4nr;fpeak of the blackbody radiation distribution at 2.7 K using Wien’s ldw ntr(t;rf :4aw. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of the universe is mpc 2z3 t blhn-yq4+p,we8kh/$\rho_c \approx 10^{-26}\ \text{kg/m}^3$. 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 an*7y4k as4 socwy one moment is believed to have been inversely proportional to the absolute temperatosw7sy4*kca4 ure. 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 cktt5td s2t4**2reirc ooled below the threshold temperature foitt d*t c45etr 2skr2*r 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 )l+gutb ;;mbwq st37bthree changes represented by the three arrows, A, B, and C, in the H-R diagram of Fig. 33-28. For each case, descri gbq37;ttsm+lw );bubbe the changes in temperature, luminosity, and size.

  Assume that the nearest kk+ye( eogi8+stars to us have an absolute luminosity about the same as the Sun's. Their apparent brightness, however, is ab++ky(eieo 8kg out $10^{-11}$ 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 er vwdrc3 zqb09m3z4: velocity of a neutron star which has3qwzb 9r r04c:zmdv3e collapsed 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 kinetic eneroa (9mi ilv0/;da1ufvkv d; m1gy change when the star in Problem 56 collapses i;a9;ko1 a/d(udlivf1 vm v0 mto a neutron star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believed to be a neum(aq84b( si +acxjh1xni6.pbtron star of mass 1.5 times that of the Sun, with diameter 20 km, is observed to have a 4xjip is6 1(cabahn.q 8+ bx(mrotation 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 o 3qam/;5 9k)dqv n;cn7kpr zraur Galaxy 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 ep, 8abv3rwwxccj(-i6a) ty*vV) would provide the critical density to close thetwrvxccya,jib w-(p3 *v8)6a universe. Assume 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 peak at 600 nm and 400 nm, respectiv,r)jr(rhhv oa4tw8*8yw z ch(ely, both lie on the main sequence. Use Wien's law, the Stefan-Boltzmann equation, and the H-R diagram (Fig. Below) to estimate the ratv8 h)ryr( a*rotzh jwwch4(8,io of their diameters. [Hint: see Examples 33-4 and 33-5.] $\dfrac{d_{400}}{d_{600}}$ =   

  Suppose we can measure distances wm9xend(vims,ot+a 1)e6ag( p ).d breith parallax at 100 parsecs. What is our minimum angular resolution (in degrees), based on t.saneed()gvbx +1empomi a)( ,tdr9 6his information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from singly ionized heliubxx19(t ,fc bvm in a distant star happen to overlap with the Balmer lines from hydrogen (Fig. 27-22) in the Sun. How fast is th1(tbx,9xv cbfe star receding from us? v =    C

  What is the temperature that corresponds to 1.8-TeV collisions at the Fermilab 7ng:: a26bbon vjd;r pcoll:pb6n; b27g:jarvd noider? To what era in cosmological history does this correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotat(o wbnsp4wq/9 ion of gas around what might be a supermassive black hole of about 2 billion solar masses at the center of a galbw9 4/so(pq wnaxy. 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" hydrogeupj.mtd/a)v 0ss9b lhpf f18 3n line at 434 nm emitted from the galaxy is measuj91u0 fstbl. a8p/ vdphfs)m3red 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 massivesk0iuo *r.fq ev0/c7r enough) will begin fusing carbon nuclei to form, for examplecer 0 .sufq7 vri/ok*0, 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 reactioni3h9yc1op.g2 vao q0 hr4mz g*
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 dens /ugt: 3f5dkvk;z de2bity equaled the critical density of the universeektd dgf;k: v/z b52u3, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$