The Milky Way was once thought to be "murky" or "milky" but is now csnn l 93(cs7jx1m2v wlonsidered to be made up of point sources. Explas1n73j9(2 nc llsw xvmin.

A star is in equilibrium when it,xd1rav4tgyw3qn c4 ) radiates at its surface all the energy generated at its core. What happens when it begins to generate more energy than it radiates? Less energy? Enqt3vx,r4y1agw d)c4 xplain.

Describe a red giant star. (3ohrsgaq +lp.tp tu k6+j 2(sList some of its properties.

Select a point on the H-R diawumr/oow zo 2p) ap*lt4nm7 +.gram. Mark several directions away from this point. op two7 lm ra4/m)w+.o2z*upnNow describe the changes that would take place in a star moving in each of these directions.

Does the H-R diagram reveal anything about the 7 bo2 mxt6 ,t9uj9d1i fpi5icxcore of a star?

Why do some stars end up as wxaemc2i- +v,v hite dwarfs, and others as neutron stars or black holes2- x+v,vaeicm?

  Can we tell, by looking at the population on the wh9n *y 9/bvbuH-R diagram, that hotter main-se9yu h *bv/n9bwquence stars have shorter lives? Explain.  ----待选择----yesno 

If you were measuring star parallaxes from the Moon instead of Earth, what c 1:dbia-1bbgv, 1qkejspzo 2,orrections would you have to make? What changes would occur if you were measuring parallaxes fr2jqvk 1b is,-bzd,pag:11oe b om Mars?

Cepheid variable stars c /0zcs)05yo whix rop+hange in luminosity with a typical period of several days. The period has been found to have a definite relationship with the absolute luminosity of the star. How could these star0/)yo5 pzsxi c 0+howrs be used to measure the distance to galaxies?

What is a geodesic? What is its role in Genec ryf,kw*3 u6uxtl46.ks z ;qvral Relativity?

If it were discovered that the redshift of spectral lines of4 f67f ck/g 8gh*tjunj/6szxb galaxies was due to something other than expansion, how might our v/g648 fsjc*jxfn ub7tg /hkz6iew of the universe change? Would there be conflicting evidence? Discuss.

  All galaxies appear to be moving away from us. Are we thc5s*xfn0uw ,fudjk 4/erefore at the center of the universe? Explafj5*du 0/cuwk s,n4fx in.  ----待选择----yesno 

If you were located in ad)i wie/ntnzdd/ *i9 0xg6gx 2 galaxy near the boundary of our observable universe, would galaxies in the direction of the M 6i9i2znd0) n/xde xwt /iggd*ilky Way appear to be approaching you or receding from you? Explain.

Compare an explosion on Earth to the Big Bang. Considehjbu2 j;29bx1t 3h*szn 2*ou*skuhgx2acgp +r 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 correspond tx *ju2t1n23 k 2hag zh2cbup*sxg9 h ;+busoj*o, open or closed?

If nothing, not even light, mykdc ,gw/.qb0o ;fh( escapes from a black hole, then how can we tell if o.qm bdc/(y,who ;f0gk ne is there?

  What mass will give a Schwarzschild radius equal 2, mgs.iphl-z to that of the hydrogen atom in its ground state?.m pzislg- h2, M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billionu t a9e)uiby+) years. Find that time on (Fig. Below). People have lived on 9+aeubi )ytu) Earth on the order of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic microwave background radiation is. Where does mat f yyvm9ocv8*;4vswz x7w 1ad3*g ,it come from? Why is its temperature now somzy *w3 7*d vom9aa, yt w8fg41sxvcv; low?

Why were atoms, as opposed7zjmem9o5d l7 to bare nuclei, unable to exist until hundreds of thousands of years after the Big Ba5m7zm do 7le9jng?

Under what circumstances would the universe x yt7ut cun8688g0e22 oav.ce.agffe eventually collapse in on itself?

  Using the definitions of the parsec and the light-year, show th 9ye1(t(42rp pqi3knc f;prcgat $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.38 secorcb *. bzv9;g ;q(8kb czy,lqrnds of arc. How far away is it? d =    ly

  The parallax angle of a s-x *7up qmb-.mtzm:kltar is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its p6w.htw r fv9/xarallax 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 iudam .. h2;cjk*phqz i9y l2)qs 55 ly away? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away from us asfq1f(ixu .,7xd0bxb, c 6deik a second star, will the parallax angle of the farthxkx17xif d6c(fueb. q bid 0,,er star be greater or less than that of the nearer star? By what factor?

  A star is 35 pc away. How n9lr w3y .a15nezguw sn5.ip7long does it take for its light to reach us?    years

  We saw earlier (Chapter 14) that thah- ozcv7u/*w k4b3kk e rate energy reaches the Earth from the Sun (the "solar cov4 kak h/*k3zcb7uw -onstant") 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 br aerpn(* y:- 59pbdtkbightness of the Sun as seen from Jupiter as compared to its brightness from Earth? (Jupiter is 5.2 times farther from the Sun than t prb- dae9pb:tynk*5( he Earth.) $\dfrac{l_{\text{Jupiter}}}{l_{\text{Earth}}}$    $ \times 10^{-2}$

  Estimate the angular width that our Galaxy would subteno9gv,t a(lq*+doa8 xa oug-j,d if observed from the nearest galaxy to us (Table 33-1). Compare to the ag*g,8a(ooq +u-tdvj9ax l,oangular width of the Moon from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, what will b3cjim7,; q qcfe its average density if it expands out to the omq3f,qi 7;ccjrbit 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 dwhaw fh4ce32(k arf, it is expected to be about the size of the Moohkaf c2e(h3w4n. What angular width will it subtend from the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dr9 gd .wez6+yjwarf whose mass is equal to the Sun's and whose radius is equal to the Earth's. How many times larger than Earth's densiw6 j+.ezr9ydgty 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 m1*mj-ep7i cfx/x0(vx(i9avqyy x0isolar masses has a radius of about 11 km. Calculate its average density and compare to that for a white/(yx c i(0ef7pav0vqj *1- ii m9xxymx 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 re 048ufw njcec3actions of Eq. 33-2. (The mass of the very unstableewnu80 c3cf j4 $^8\text{Be}$ 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 apparen0 c czr(qu:/tnt 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 kj) hukojh/jnd i0l:.p-m3 ,w are assumed to be about the same distance from us. Two su uj/0n.,hj)l 3k w:-pijdhokmch stars 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 rdh7dj6aa8j). h uguc ps, ;/p5+lcxqt adius for a star with mass equal to that (a) of our Sh +)j7j.c;/ sla5,hqpgxdupcadu t6 8 un is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typical galaxy (like oursjl0il-b ud2fb/zi 5qmwf*7r qi -cek8 lwy3*1)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a sphere, for which the sumt0xh 4-gwulq6w1je dc(-amc/ of the angles is (a) 3tw4-u/xa-c1e c6j(g w hdlqm059º, and (b) 180°.

  What is the maximum sum-of-the-anglesy x6x*m0dch8x2k do 4h for a triangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the speed of light, q m,yzx l)2*8k i9slhdroughly how far away is it? v = k8z)x9ql, y *dmi2hsl   Mly

  The redshift of a galaxy indicates a velocity uxrboe c6 lqw qy) 1y+6 ne-8q1io4 u/i9ej+zoof $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (relative to us) that is+shq b*g4pz.v near the observable "edge" of the universe, say 12 bipz.sh+* b4qvg llion light-years away. v =    c

  Estimate the observed wavelength fo,5 qeeh y:dk-er the 656-nm line in the Balmer series of hydrogen in the spectrum of a galaxy :ey -q,ehe5dkwhose 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 gal,8 rruaky6im xq6,g*/cc1txqaxy, and its distance from us, if the wavelength for the hyduqac1kg,qx8 /rc, x6im* try6rogen 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 witpph 6gcs g.nyf,ti54+s72n5wdt :bq b h $z = 0.60$? v =    c

  What would be the redshiftb r,n))lu8 4ptj 9ekv:gvn9ri parameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Doppler shift in i6nxd7rznn/h*b/3 x8 ll2g t cwavelength is $\Delta\lambda/\lambda \approx v/c$ (Eq. 33-5b) for $v \ll c$. [Hint: use the binomial expansion.]

  Calculate the wavelength ato;g).otz*rnqj yti+ 2 the peak of the blackbody radiation distribution at 2.7 K using Wien’s law. yjq*;ttgio.n r2) +zo $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of+ l n9smem5l7a/qq(e m 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 dista9pq3i+b wa yx):cy,z3 2f/g .us unlponce between galaxies) at any one moment is believed toyax.)3piyc uq: nl3 +sg op/ ,z2bw9uf have been inversely 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 cooled below the thr0v0o-oj og*pn eshold temperature forg*0ooo0 v-np j 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 three chang)0 uy7oz e:asqes represented by the three arrows, A, B, and C, in the H-R diagram of Fig. 33-28. For each case, describe the chansezy0)q:u7 o ages in temperature, luminosity, and size.

  Assume that the nearest stars to us have,kyk/sz)9 b vj an absolute luminosity about the same as the Sj ,vkzbs9y)/k un's. Their 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 estimate the angular velocityp*9bd2t vp beb/dz w+ 8:wgzh7s/s6n0w,xum s of a neutron star which has collapsed to a diameter of 20 km, from a star whose radius was equal to that of our 8sw szh vu6w m0s7wbgdpz +n9,ex2/ dt:/pb*b 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 kine9 3x .lz*ahnof b,z0jntic energy change when the star in Proble, oznhf0bj*n9a 3.z lxm 56 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 mass 1.5 times that of t*wr bmq md;c*9xb.67uazy3k77 ikk hjhe Sun, with diameter 20 km, is observed to have a rotation speed ofqhz yb ad kr 73k7uw. ;xm69kb**jicm7 $1.0\ \text{rev/s}$. 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 am+1kv 4ge)ts bbout $2 \times 10^6\ \text{ly}$ 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 densityzi l77uerfeg, st7ev v 9n.*q5 to close the unive97l*7een,zgq5u si rvev.7 ftrse. 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, respectively, both lie on thi-y (x tw)is/je main sequence. Use Wien's law, the Stefan-Boltzmann equation, and the H-R diagram (Fig. Below) to estimate the ratio of thy/i) t-wjxs (ieir diameters. [Hint: see Examples 33-4 and 33-5.] $\dfrac{d_{400}}{d_{600}}$ =   

  Suppose we can measukl9pdwi(w9-ib i, +c 3s;hcpdre distances with parallax at 100 parsecs. What is our minimum angular resolution (inwwi; i- p3d9 l9(dk,hpb+ccsi degrees), based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, tvxi; y+v+ u60 hv )ik5dpv*lughe Balmer lines 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 receding from us? v = p v5y u iug0h)ixk+l*6+;v dvv   C

  What is the temperature that correspojc sh w:d* 93i7up gtaiq:(cc,nds to 1.8-TeV collisions at the Fermilab collider? To what e(jcdpgacc ti3 * isw9u7:q:h,ra in 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 mighz3 .w3t-:)mfuu:r pgm lmw*pocpm 3b4t be a supermassive black hole of about 2 billion solar masst 4ou)3rbpm l:3gf 3p:pm * zw-m.umcwes at the center 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 "blue" hydrogen line at 434 nm emittekufvc,agyxk)bmf- )4q j x16,6l (lz8 nywm3dd from thekz6kx)f,avycu bml(w61l,8nq) jmf 3-gdy x4 galaxy is 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 b:8sb5 xx3d7/hcmol nevolution, a star (if massive enough) will begin fusing carm3bxcb5sx87dh l:o/ n bon 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 v*l bxsdl5 ;dcw5p ra:4zs 8 .teqv3 tv;6g.xe
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 deo /u/; lks6yqbnsity of the univu s /bkq;6l/yoerse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$