The Milky Way was once thought to be "murky"isf *-ndu*v64kjp xi; or "milky" but is now considered to beun6 k* ij*p4f ds;i-vx made up of point sources. Explain.

A star is in equilibrium when it radiates at i :yusvw 3 /yq+4lkqq2its surface all the energy generated at its core. What happens when it begins to generate more energy than it radiates? si uv qkqy/w+4:2ly3 qLess energy? Explain.

Describe a red giant star. List some of its propeo lm6i+uk c22yrties.

Select a point on the H-R diagram. Mark several direction jxc29.ads7et s away from this point. Now describe the changes that would take place in a star moving itsa7 cjdx.9e2 n each of these directions.

Does the H-R diagram reveal anythnf9a hg2ik(ew9,ta :fing about the core of a star?

Why do some stars end up as white dwarfs, and others as neutron star ; l-+a0 ekfk6kxn* kgm2rib;is or black hole l*;k ;x 2ef0a6-mnigkk+krbis?

  Can we tell, by looking at the population on the H-R diagram, that hotm lpxcdk(q3;ogt 69()lim ik5k8zo t. ter main-sequence stm9go 8lpkktilz kcx(5o 6(.)d3tm; iq ars have shorter lives? Explain.  ----待选择----yesno 

If you were measuring star parallaxes from the 3 gu/bcf8r/ow):hprf Moon instead of Earth, what corrections whgwr )rf:b8 f/pou3/could you have to make? What changes would occur if you were measuring parallaxes from Mars?

Cepheid variable stars change in lu,q9splt ezqt58d.8jn+n 6q zuminosity 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 tt,. szzn ln+8p 865ejqquqd9to measure the distance to galaxies?

What is a geodesic? What is its role ikxv/c mge q3)et (/st:4dtoh2n General Relativity?

If it were discovered that the redshift of spectral lines 5 ,hsw 1ij+sn( j)5vsqojzsz2etxe41 of galaxies was due to something other than expansion, how might our view of the universe chanj5w2,( veos1zj51)eqznijs4sx+ s t hge? Would there be conflicting evidence? Discuss.

  All galaxies appear to be moving ai z0w9mw9vjz:yyd 6+o u2rnp8 way from us. Are we therefore at the center of the universe? Explain.d+9i06mz opr v92jnyzu :wwy8  ----待选择----yesno 

If you were located in a galaxy near the boun fjd0q/h2lp) edary of our observable universe, would galaxies in the direction of the Milky Way appear to be approaching you or receding from y /d)jfqe lhp20ou? Explain.

Compare an explosion obaaw4e/ 1fhq+jb6sd4h nr/7z 4n d 3nrn Earth to the Big Bang. Consider such questions as: Would the debris spread at a higher speed for more distant particles, as irqewan+b344h16n s h d7fndr4ja/ /b zn 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 fl2 *fz0)rwzu- me1rserom a black hole, then how can we tell if one is lurzr-2 w )1s0fem*ezthere?

  What mass will give a Sc( ;fn.7 g3zkdwytgb* thwarzschild radius equal to that of the hydrogen atom in its ground state? M =k(g;d3ty.tz n fw7* bg    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion years. Find that time on (Fi )wfif)(k)q4ii7vkehf, lpi 5g. Below). People have lived on Earth on the orii)(qhk kp),v5w7)e 4 ff liifder of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic microwpr0xti: 5r7t;xy n:)vpz xs1- mdtm3pave background radiation is. Where does it come from? Why is its temperature now xs; r 5p 0ip7nx)tmmzyx :1tdtpv:3- rso low?

Why were atoms, as opposed to bare nuclei, unable to e:6kzc r(t5 /5cc oufzkxist until hundreds of thousands of years after thekkzz/o5c (cu56f c:t r Big Bang?

Under what circumstances would the universe eve9g.razyc5cw n3m83 lkntually collapse in on itself?

  Using the definitions of the parsec aem4q3j mm;e3d0 u9:xi 0ogzrynd the 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 fa v;0 7(mqtsbvor away is it? d =    ly

  The parallax angle of a star is g1 6ch -, 86wy bfs sfvozjoeg)+sh/l0$0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is iy5ko 9,fuaff 7ts 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 angaoacvb+; 2 zq;6cir7 ble for a star that is 55 ly away? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away from5eqdr 0dq: hz:+vi0b z us as a second star, will the parallax angle of the farther star be greater or less than that of the nearer star? By +vz q b0dh:eq :iz05drwhat factor?

  A star is 35 pc away. How long p:9fi+q+(lj6x er koodoes it take for its light to reach us?    years

  We saw earlier (Chapter 14) that the razl)s* :u342ywfd l mm9iaeg *gte energy reaches the Earth from the Sun (the "sol gam eu9 z wf)y4*lls*g2i3:dmar 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 Suy. t hpw+0sb3c6e3 kn(i/ 99acymiha*d)psmnn as seen from Jupiter as compared to its brightness from Earth? (J+.k y6na)0p aw y*h(ecsmm 9cpd3 i/htsnbi39 upiter 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 obserfiqvo4sz, o9qe-a f0, ved from the nearest galaxy to- o q9i,4eqffszo0,a v 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 nhjh)l)d6p -uif it expands out to the orbit of ))u6 djlp-hnhEarth ($1.5 \times 10^{11}\ \text{m}$ from the Sun)? $\rho = $    $ \times 10^{-4}\ \text{kg/m}^3$

  When our Sun becomes a white dwarf, it is expe r e)5k;bac4jtcted to be about the size of the Moon. What angular width will it subtend from the c;5jakt r)be 4present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwar8 gn,ef7 6qw yg/yi3*iee1pe jf whose mass is equal to the Sun's and whose radius is equal to the Earth's. How many times larger than Earth6 i/81jg eegyee7i*,ynqfw p3 '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. Calm -uu- 67hi0guwro h3qculate its average density and compare to that for a white dwarf (Problem 13) and to that of nuclear mat -u3umhhu0-6iwgr 7o qter.
$\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-value)8h7v k*7ev 1v1of4gg6dmudm a li:avs for the He burning reactions of Eq. 33-2. (The mass of the vem1:ve 86u7 givv avdog f471mkl)ahd*ry 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 apparenij/dul s fcrgc67z) v ,s(15cwt 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 certz *u jbi.a a(h/+zk0moain cluster are assumed to be about the same distance from us. Two suc a/ku0ah + i(.ojmzzb*h 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 stanae83os)g 6l..b fmj pr with mass equal to that (a) of our Sunf3 nme8j) .sl .6agbop is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typical galaxy (* ) hmz )m*m83ycpbafylike ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the suufxwk t /t1,y.rface of a sphere, for which the sum of the angles is (a) 359º, and .yuw ,/tkfx t1(b) 180°.

  What is the maximum sum-of-the-angles for a trianglrd7v,a 6ftheqb8e 3m gx.78wee on a sphere?    $^\circ$

  If a galaxy is traveling e3m1c;/4 n/tb d lpfdkaway from us at 1.0% of the speed of light, roughly how fa 4 k;/3dfnmbe1cpl/d tr away is it? v =    Mly

  The redshift of a gaka- 6mg9 f0sdc icp3 dop2lf+8;gz*milaxy indicates a velocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (relative topfv a+ayzccy1-4 l7 ,/gv q4tu us) that is near the observable "edge" of the universe, say 12 billion lighgzl14av-+ y7a4vu q/ytcpf c,t-years away. v =    c

  Estimate the observed wavelength for the 656-nm liymt +9 z7 ynvon:k)aq,ne in the Balmer series of hydrogen in qa t : nyzvn,)myko+97the 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 galaxy, and its distance from us, if :6-bnva rr i1j2cy nw)the wavelength for the hydrogen line at 434 nm is measured on Earth as being 61irv612-n:arw )b njcy0 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 ancel q9(roa p7( ptt* 6o:(xab galaxy with $z = 0.60$? v =    c

  What would be the redshift parame/pvecdm 4g8o *oyn/ r;jos36iter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, shod4 m2l 6, c6tez,9*2svsez vs5gtmidew that 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 wavelength at the peak of tb 5qtvb zkyz64 :9;kar +qan/xhe blackbody radiation distribution at bq trqz; bvk+54 / an9kyza6:x2.7 K using Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of the unzdltmoi wi:n8, 0z258g- eqr niverse 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 dis mtb5 x4runji*+rq4 n8tance between galaxies) at any one moment is believed to have been inversely proportional to the a*xniqjmrn 5+ 8t ub4r4bsolute 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 cs 7uwf v9jde0gqcf+s,/xy4 1rgs28 mthe threshold temperature sjr2v4c,/gy s9ffms ux78ge1q0c+w d 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-sequence stars could undergo the lpu 5:/t0cncjthree changes represented by the: c5uc/0 tpjnl three arrows, 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 absolb6waor83fng- 5l t3j )uqx3jgute luminosity about the same as the Sun's. Their apparent brightness, however,j3ol gx5n at f3)6bj8ug -qwr3 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 velocity offkg9q uw1(jgy ;2z, nt a neutron star which has collapsed to a diameter of 20 km, from a star whose radius was equal tt(k2fuj, zy qn9w;1ggo 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 energy change whenv5bd7h)*3h; cho f dlf the star in Problem 56 collapses to a neutron star? fhdfo lvhc 7*)5;b3 dh$\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 the b2seq+nozw :ws)z.qhnz/- 8w Sun, with diamete oh ss+)qw zn-bz8/:q2ez.wn wr 20 km, 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 is abph lpz(23o:xxa78s fiout $2 \times 10^6\ \text{ly}$ 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 p4+fr2uk,f dz arovide the critical density to close the universe. Assume,+a drz fu2k4f 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 lq 7aikn178-0wpf*mb n na y5uh a9rs2vie 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. f7y 5hbn9kr*sn -ap0umva wqian 7812[Hint: see Examples 33-4 and 33-5.] $\dfrac{d_{400}}{d_{600}}$ =   

  Suppose we can measure distances wh6.dz)z.hkcm4y6,pkqb wch(ith parallax at 100 parsecs. What is our minimum angular resolution (in degrees), based on this informati(k 6,qbz 6z.hdh mhwkcy4p)c. on? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from singly ionized heli9xf a i,u;*xykum in a distant star happen to overlap with the Balmerkyi fu 9ax;,x* lines from hydrogen (Fig. 27-22) in the Sun. How fast is the star receding from us? v =    C

  What is the temperature that corresponds toc joq+p:pjq09odlh /. 1.8-TeV collisions at the Fermilab collider? To what era in c. poo:j dh l/+cq9jqp0osmological history does this correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recenxpla5gq /l /neez60x;tly measured 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 galacti0 x 5p6a/zel;q/ln gxec 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 vi-v;wntdl);z3 be )oq ,4pmnfrom Earth. The "blue" hydrogen line at 434 nm emitted from the galaxy ism;z;dep ov,ni3-4q bvwnl )t ) 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 evolution, a star (if massive enough) h ts*sv ;s(1vywill begin fusing carbon nuclei 1h*s;vts(ysvto 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 reactioj*ufu n4j:-t vn
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 densityo 8uj,xy 1i-z f fmuh/rt)2q:e9,rqvj equaled the critical density of the univ, x q,zejr9jfi8y uoft2)r vhu/:1-mq erse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$