The Milky Way was once thought to be "murky" or "milky" but is now considered t u:ujt:bmtjlf ti)21: wnn-l9o be made up )21lbu 9lufm:tnt: jijt:wn- of point sources. Explain.

A star is in equilibrium when it radiates at its surface all thgi fpy7fo ,y.w)a0af(e energy generated at itsopyg 7y)ff,0 . awfia( 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 property+c6z-aw2q c eies.

Select a point on the H-R diagram. Mark several /9p p:kplv0xp(av vy ;directions away from this point. Now describe the changes tv;p a/lp:py9p0k xv( vhat would take place in a star moving in each of these directions.

Does the H-R diagram reveal anything about the core+,j cr; )r8scg /msveu of a star?

Why do some stars end up as;qeszm zz-q+ rg.i 3*a white dwarfs, and others as neutron stars or black hol a*g.3qsi-ez r+zq; zmes?

  Can we tell, by lookit w*s) bavqnmas40nlg2 ,4zb.ng at the population on the H-R diagram, that hotter main-sequence stars have shq,san2)sw nb 4bvtzg*m.0a 4lorter lives? Explain.  ----待选择----yesno 

If you were measuring star parallaxes from .0h-5o;yftpmzcdh d+ *zee+:a kjc 6 ethe Moon instead of Earth, what correctiod+y6z- :t mz.jdh; oce k *ac+pfhee05ns would you have to make? What changes would occur if you were measuring parallaxes from Mars?

Cepheid variable stars change in lumins8hn x3 +ilhy/osity 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 stars be used to measure the distance 8/ l hinyxs+h3to galaxies?

What is a geodesic? What is its role in Genzbvj**orh.: :wh3)bpm t4p t qeral Relativity?

If it were discovered that the redshift of spectral liw8clfmo x f w*31mt6a mc+8og8nes of galaxies was due to something other thmg fa8 38m xccofw+8m1 wol*6tan 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 thereforuasi 5oey1;c1 e at the center of the universe? Explain.a 5;e1 cs1iuoy  ----待选择----yesno 

If you were located in a galaxy near the boundary of our observable universebj,/ah r4 e-sz, would galaxies in the direction of the Milky Way appear to be approachin ,/j -zah4bresg you or receding from you? Explain.

Compare an explosion on Earth to the Big Bang. Consi tri5ej87n h;vder 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 unie;jnrv7t58ih verse would this correspond to, open or closed?

If nothing, not even light, escapes from a black hole, then /bcn h tgz9h 2(i4lna*how can we tell if one is thenct9hh a(4 l/nb2z*gire?

  What mass will give a Schwarzschild6 7p9w h 6x6wqyt:nua6so,d5drdhp 0:km(av g radius equal to that of the hydrogen atom in its g 6 06g(van6mkd5h:a oqup,hs9dw6ry7 wdtxp:round state? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 xdt3 uy)r97a gk-0e is5 l;jtnbillion years. Find that time on (Fig. Below). People have lived on Earth on the orders-e;9t gra7 t50yn)kdx3 lij u of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic microwave background radiation .mz a lmy0.* 0gul:glsis. Where does it come from? Why is its temperature now so low?0. alzmg:yl *s0.lumg

Why were atoms, as opposedckty2t3,1bl a to bare nuclei, unable to exist until hundreds of thotky,t1cl2ab3 usands of years after the Big Bang?

Under what circumstances would the universe eventually collapse in on itsedsacgb/,zs98q2n d:c7 )z nyj lf?

  Using the definitions of the parsec and the lightxtibt;b6x9p) 5k h) hy-year, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a paa+/n - w1-gn5brf tc)g )shzhdrallax of 0.38 seconds of arc. How far away is it? d =    ly

  The parallax angle of a star is xq n2vy 5tn+p,p,i,w) 52z 6saq8k7tg b vocke$0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What ;u(co*okk1ca 4nsz 2-h8f nu tis 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 is 55 ly away?w qbmsvlpsqnzs)7: v6:m . zc(5o;n,e $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away from us as 50 y-mnb1daz s9+iiqq a second star, will the parallax angle aq b+51nqz-90ym idis of 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 lif 7q0l 4f)cfbi,.wph p0sb1db ght to reach us?    years

  We saw earlier (Chapter 14) that the rate energy reaches the Eart aoj8v75:g whmo *6p3tj8udrah from the Sun (theo7r:jhgu a86j o8a35 *vmtdpw "solar constant") 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 Jupznn m)d:qs+ 5uiter as compared to its brightness from Earth? (Jupiter is 5.2 +)m qn us:5dzntimes farther from the Sun than the Earth.) $\dfrac{l_{\text{Jupiter}}}{l_{\text{Earth}}}$    $ \times 10^{-2}$

  Estimate the angular width that pi6u9h3e v16daqq.pvour Galaxy would subtend if observed from the nearest galaxy to us (Table 33-1). Compare to the angular width of the Moon from 61pqedvuq6 vah3 i p9.Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red*u0 egl xak q(w:+vqn) giant, what will be its average density if it expands out to the x+0nv klu(* )eqag: wqorbit 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 iqvma0,-4gl hk s expected to be about the size of the Moon. What angular width will vgm hal4q-k ,0it subtend from the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whose p457) )a o0srts. fp4z7 rx0lk bqivwumass is equal to the Sun's and whose radius is equal lbvr74rzs i w)p)fp7 0 x0tsua. 54oqkto 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 bfh19 p kqht::radius of about 11 km. Calculate its average density and compare to that for a white dwarf (Ph: f91phtkbq:roblem 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-value1oi -esawk +yna 6xa45s for the He burning reactions of Eq. 33-2. (The mass of the very uns 1xi+5osna 64-aywa ketable $^8\text{Be}$ 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 br2 q,u mj.:a yagrg lm/z-omm5;ightness $l$ 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 ;a , zk9 zxv(hbmi-g98mbbq0pr0ude6cluster are assumed to be about the same distance from us. Two such stars have spectra b0bqzx9z 8a,me96m;g vh(b -rdpku0i 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 a7f: 4ah)x/:lu8gdlqqzabg9 o star with mass equal to that (a) of our Sun isl:/bux8 gfzq:9hod )qag a 4l7    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typical tg sm1 4f) 5qwns3n8 3pv+spwb7l qu6sb rx41jgalaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a spher+eilz kd5g87x e, for which the sum of the angles is (a) 359º, and (b) 180° 8d zkgx7li+e5.

  What is the maximum sum-of5te-: io pp 8 vuh4ewev xztj1,8p654)bdmmgt-the-angles for a triangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the speed oa5 xc.bc(t5 sqf light, roughly how far away is it? s.ta(5qc bxc5v =    Mly

  The redshift of a galaxy indicates a veloc2w2;;sk r heaqt mk65city of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (relative to us) that mek;(xscmz + 4is near the observable "edge" of the universe, (kszcemx ;+4 msay 12 billion light-years away. v =    c

  Estimate the observed n;bs-) ,iypdu wavelength for the 656-nm line in the Balmer series of hydrogenn)s idpby,; -u 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 galaygp+e-.ot5 + im km2yn1v(s* ;bskkrjk-ak j5xy, and its distance from us, if the wavelength for the hydrogen line pjsvogj *m+5 es yr+bmit.n1 -(k2-kkk5y; kaat 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 gal ;acx1cc9uc.*g ;w /*xwjv vheaxy with $z = 0.60$? v =    c

  What would be the red orx; :zk(wxq2sp 99ffshift parameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Doppz 5 1p4-q8zzom ,spialsft-w/ler 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 5h31t:te;rvs os) lpfpeak of the blackbody radiation distribution at 2.7 Ks :oset t35f v;rhpl1) using Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of the universe isy6ye9ym h 1rs42lasd2 $\rho_c \approx 10^{-26}\ \text{kg/m}^3$. 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);b(9t vhpg0 jg at any one moment is believed to have been invers tv j(9;hb0gpgely 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 yei2*w7oi)io a 9fl,q universe cooled below the threshold temperaturi7qa) o2o,*i 9yefil we for 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-seqymktbp* bp( xw3s2 -9huence stars could undergo the three changes represented by the three arrows, A, B, and C, in the H-R diagram of Fig. 33-28. For each ca3hx*b -bpt 2 w(ymksp9se, describe the changes in temperature, luminosity, and size.

  Assume that the nearest stars to u 2ieafpzq bn -+y;8*fz.bn zg3s have an absolute luminosity about the same as the Sun's. Their apparent brightness, p2znbzif.e*qn b+ ;za 38f-yg 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 tv,xdwysu 6vwy;;gi at-d.1/k o estimate the angular velocity of a neutron star which has collapsed to a diai gk,y;vd /;dw x.6at-y1uwvsmeter 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 )-l t eq(ktd.34aqiq g6/yb qz1.wso ykinetic energy change when the star in Problem 56 collapses to a neubk61zy.- )o (glsqqeq4. ywdq tt/3i atron star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believed to be a neutron sxu c 8z8f8+dkp+i2 hvstar of mass 1.5 times that of the Sun, with diameter 20 km, is observed to have a r8ip8kuh++8 c dfs xz2votation 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 Galaxyogmqc5 4 0bou( 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 (i*;z 7uz+sr sadn eV) would provide the critical density to close the universe. Assume tzr s;a z+ud7s*he 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 anrnt + rbv ) q+8i*1vyhzlvr:m,d 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 diameters. [Hint: see Examples 33-4 and 3v t: 1 hb+mvyz,r n8rlr+i)vq*3-5.] $\dfrac{d_{400}}{d_{600}}$ =   

  Suppose we can measure distances with parallax at 100 parsecs. What o:0.qwzc g er)is our minimum anguz0w r) c.oe:qglar resolution (in degrees), based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from singly ionized helium in aq6s3kyr0 p tu*0n t2zt distant star happen to overlap with the Balmer lines from hydro r02q3u tt*ypn0kst6z gen (Fig. 27-22) in the Sun. How fast is the star receding from us? v =    C

  What is the temperature that corresponds to 124n ( v xpdhx6uewbxloy4y;,(.8-TeV collisions at the Fermilab collider? 2d (h( ;4bo,l xynvxyw6up4xeTo what era in cosmological history does this correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently meas3 x/ph3ok3wmg6 g*ijv ,izi;gured the rotation of gas around what might be a supermassive black hole/m 6hip jog 33w3gv*z,g;i ikx 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-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 "blueuc: yzr.t /, p0: u,uqr ef:tsc7un4xq" hydrogen line at 434 nm emitted from the galaxy is measufqccspz nye x::tut ,0u.7 : u/,ur4qrred 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 ma/*wx3mjv phhdhp*:h:a;1w .sffz hm*ssive enough) will begin fusingf* ma:hpw3 1fm z .hsdhv :w*/xh;jh*p carbon 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 fs,p **izjbhu+oo q0.
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 equa-t 2diovw *)xeled the critical density of the unwt*)e2- ioxd viverse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$