The Milky Way was once thought to be "murky" or "milky" buldt6it9- 7hm:ct+p*0jihz-u l gqe c 5t is now considered to be made up of point soucui5z76lh9e m pj* t+lt:di-hgt c-q0rces. Explain.

A star is in equilibrium when it radia y -iv,54d mxn p+)g0jsjopkc3tes at its surface all the energy generated at its core. What happeg pi3 4xs, n-jkcj5ovd+mp)0yns when it begins to generate more energy than it radiates? Less energy? Explain.

Describe a red giant star. List some o50ks*hm g+*zx 9xcn o6n,mgv(k9iqlof its properties.

Select a point on the H-R diagram. Mark several directions away fro72n z)b-rg -q2 n8ft.qylaaabm this point. n- )fr7-.l zyt8bb2q gaa anq2Now 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 cor nmkqyae0 8sta-9tn*86gs c b4e of a star?

Why do some stars end up as white dwarfs, and others as neutron stars or bl0p 1mhx,4wl(2w(ucjxy rz hv7 ack hv4jrwm xz2px w01c hhy(,u 7(loles?

  Can we tell, by looki .ocmeh0l)(xg5wk-k wng at the population on the H-R diagram, that hotter main-sequence stars have shorter lives?h(.0 c5k okg)mww-elx Explain.  ----待选择----yesno 

If you were measuring d 7m++u9dp(f :/mwyjlcz zx* pih yr;9star parallaxes from the Moon instead of Earth, what corrections would you havz :zm+d;y9+r*/7dw cuy l(pxjphm9f i e to make? What changes would occur if you were measuring parallaxes from Mars?

Cepheid variable stars change in luminosity with a tyf*y+c0l o)rhq0 akcd- pical period 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 r c-yk0d+a f)0l cqho*the distance to galaxies?

What is a geodesic? Whae(ut/2 jgj;7ujv8 w f *xljt9mt is its role in General Relativity?

If it were discovered that the redshift of spectral lines of galaxikvth,0qps9w,xi8 23 gir1 z7xog ltj1es was due to something other than exp98r 2o0 klpix1t1ggq7v,hjis wx,3 tzansion, 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 thejj4q)xo4+3vygf.dc puy +wc. center of the uxcyp3)f .4.+jvw+ j yu4dcg oqniverse? Explain.  ----待选择----yesno 

If you were located in a galaxy near the boundary 6e g isnhzf+ x1f;)yw+of our observable universe, would galaxies in the direction of the Milky Way+ff;z 1g6xy ehiswn+) appear to be approaching you or receding from you? Explain.

Compare an explosion o6nu 4(32xnp6s oxsi brn Earth to the Big Bang. Consider such questions as: Would the debris spread at a higher speed for more distant parnsos 24pr3i6bxn6x( uticles, 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 hole, then how canmnqan7j yy 55p7e2z8ev b,gk 3w7u9fk we tell if one is ther9ku57m3f 7gzanb veyw857 ,2ynk ejqpe?

  What mass will give a Schwarzschild radpt 1:6g.useneius equal to that of the hydrogen atom in its ground sta.u:s t61nege pte? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as mloep+ 8i5nb f dgx/7y5x16yx about 4 billion years. Find that time on (Fig. Below). Poyfnmeg1x p8xb55dl7y / ix6+eople have lived on 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 ikn :bxkvi :jcod 3,(x0t come from? Why is its temperatur (nx3: c:djbv0o ,xikke now so low?

Why were atoms, as obs/(ndb,l- 5yfq1 eld pposed to bare nuclei, unable to exist until hundreds of thousands of years db bdq y1l-en/f,5sl (after the Big Bang?

Under what circumstances would the universe eventually collapseya)ght m sgy3ux 9i.*+ in on itself?

  Using the definitions of the parsec and the light-year, show thakukw+:u 8lf z: k64kf.wnzw(vt $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.38 secondsi+-r aqkc z56;wwf a3s of arc. How far away is it? d =    ly

  The parallax angle of v ,dp n:kl:z/wkog*k. a star is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is it sxkpi1m+6 c.z lc3o/zs 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 thapluf/fl iv c/5kd (.;kt is 55 ly away? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away from us as a second star, wiqf p/8s vyqjw )rrxg;z i*,+i.ll the parallax angle of+,* ji rxvwsqzpy/if;r8). q g the 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 take for its liuz b6 3m xo)-ntjf r-*e(unnefod2g5(ght to reach us?    years

  We saw earlier (Chapter 14) that the rate energy reaches the Earth from the Sun su:-p-ek w;dl (the "solar consku:-sw p-ed ;ltant") 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 Jupitec/)z ndqe8 2:yhu rb3r- 967pdaq jzhw;a6bcdr as compared to its brightness from Earth? (Jupite9u8 r;qa :epj2b3nd -/zcdc6hb7)dahq6ywrzr 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 obser;yrq:y;qv 3i gved from the nearest galaxy to ;igy 3:qvq;ry 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 its average density if it expands; ed*d/r7tu bhz.77k2,xb) puyd lo 8ay 8aatg out to the orbit o arue8l d t 7g8x7hd;a2)*b .7yb up/kt,yoadzf 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 ahv;;qn qw13v 2 pjyd1dbout the size of the Moon. What angular width wdqw1;ydpq3n1v2vj ;h ill 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 theg:zqm-.1mz6sr thvg 7czf 6;9a hzij ,o;(wf w Sun's and whose radius is equal to ths9iz1 v g qa ffj 7woz(-rzt h6w6m.c;z:hmg;,e 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 radiushq6 ra:5iu*i g of about 11 km. Calculate its averag*65i:air hugq e 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 burning reactions of Eq. 33-2. (Thch2 1h e8jcv1 3tj-dlbe mass of the very unst j13j2bc8vdhet lhc 1-able $^8\text{Be}$ 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 ofp )fa72eho7jhi ai*n 8 the same apparent 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 u3z168nd(ca*bovu ); mq yvcwto be about the same distance from us. Two suc vm8uc)qbz3*( 6dn1ycv oua;wh 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 radius for a star with mass equal to that (a) o xtpysb4z 8l15f our Sun 8z tb 5x41yslpis    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typ qne ho,ctu8.s3n v-q8ical galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a sphere, for which the sum o0mpws:i /kffa+ 76v gnf the igp:07w/avnf6fk +msangles is (a) 359º, and (b) 180°.

  What is the maximum sum-ofvkvd mmdou + -:7 r4/,cygthf)-the-angles for a triangle on a sphere?    $^\circ$

  If a galaxy is travelingwu(c*s4 t egc4 away from us at 1.0% of the speed of light, roughly how far awage twu4*c(cs4y is it? v =    Mly

  The redshift of a galaxy indicates a velocm3ca(nh5,j h- 3xc eee,fc8 r6pz ,pjsity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (relative to us9xvm) ag--1so/cmv og) that is near the observable "edge" of -1agv mom s9-/gxcv)othe universe, say 12 billion light-years away. v =    c

  Estimate the observed wavelength for theh0pom7 g2fhc1 656-nm line in the Balmer series of hydrogen 2hf pgo01h7c min 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 galp5aq8in(yt4syu3 l6 faxy, and its distance from us, if the wavelength for the hydrogen line at 434 nm is measured on Earth asf3(54yul6n8tq i y spa 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 withyc:2wwb3yq w*dt74n q $z = 0.60$? v =    c

  What would be the redshift bx e1fz.d+en3 )sj8chylt3j 4 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 waveleng.r ho6mep 5hj+th 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 radiationmq cyfi m,3t/k+x0t3d distribution at 2i0f x3 kmty, md+qt3/c.7 K using Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of the univer 9;9 ua4at-xexj ya;y(5pdbde se 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 (the6 rlhxzvnjm1 yx5* 0r xi,om8- average distance between galaxies) at any one moment is believed to have been x lxm0m*1rhjrnz86- ovy5,ixinversely 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 univeqd8w d,:p;xua zxkvm4 5;r+ qmrse cooled below the threshold temperature u8rmzd p;4wq a;:mx5 ,v+dx kqfor 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 undergm; ye7z+ brce 60qdokukt6,p6 o the three changes represented by the three aro6reme67p c,t;b dkuzq0yk +6 rows, A, B, and C, in the H-R diagram of Fig. 33-28. For each case, describe the changes in temperature, luminosity, and size.

  Assume that the nearest stars to us have an absolute lumi:qs:k7-qd jf x.lpd8dnosity about the same as the Sun's. Their apparent brightness, howevfk j::l8d7qdxd .pq -ser, 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 estimatez,gk)l 9; 8 rs5z utxaim:fcw9cvph*) the angular velocity of a neutron star which has collapsed to a diameter of 20 km, from a star whose radius was equal )*t;h9g89 :zpf rc 5s a)mwkcuxvzil ,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 rotatifj+e q x+ahc9;50 vag1zq mp:lonal kinetic energy change when the star in Problea+:f91p0a e+ jlc q;m5vx gzqhm 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 th -s((rhgd klzlx::*/kl hktk/at of the Sun, with diameter 20 km, is observed to xl:d-/t(k l k:hr*lh/k(kgsz 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 a1wva98oj*f :i x.rc s.9qtbzgo *apokm/ 1-ia bout $2 \times 10^6\ \text{ly}$ 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 critic 7ya,+jyip3q pal density to close the universe. Assume the neutrino density is, like photons, a 37qy+,jpp iaybout $10^9$ 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 pedy o8f2,co os.f* bh+q3dhx 2xak at 600 nm and 400 nm, respectively, both lie on the main sequence. Use Wien's law, the Stefan-Bold8df o,qf2x oh+ysx. bhco23*tzmann 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 distances with parallax at 100 parsec 58- wso. z*tyfygut+fs. What is our minimumy+t*-o s5 y 8z.wfgftu angular resolution (in degrees), based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from singly io906hh upcbg(u94k+lapt: s g/ 3elaffnized helium in a distant star happen to overlap with the Balmer lines from hydrogen (Fig. 27-22) in t/( hl b904p+tk6l gsehuga3ufp cf:a9he Sun. How fast is the star receding from us? v =    C

  What is the temperature that corres n76ourw( q;ut 49jvniponds to 1.8-TeV collisions at the Fermilab collider? To what era in cosmological history does this correspond? [Hioi6 7q r;u4nw tvu9(njnt: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation . viu *2e/cx0jxlsrb *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 galactic center to the gas clouds is 60 light-yv*j*xr. /e 2csux l0biears, 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" hydroge2c a5/c dehe+rn line at 434 nm emitted from the galaxy is measured o2+c5eae rdh /cn 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 massive enough)zcxe7 e,0uwp: will begin fusing carbon ee07,w xczu:p 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 nylu(*4 a 2 -k-lyyy:am7wswv
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 equaledlniz kz7*nh12 the critical density of the univ*k1hi l72z znnerse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$