The Milky Way was once thoughaft :p km3e2wih:/6nd t to be "murky" or "milky" but is now considered to be made /hen:wapi dfm 3:k26tup of point sources. Explain.

A star is in equilibrium when ivm3kccp(2g +dglx2 d1t radiates at its surface all the energy generated at its core. What happens when it begins topg3v c(2d 12kx+ldcgm generate more energy than it radiates? Less energy? Explain.

Describe a red giant star. 9/6uxf( pkn8r6a naxf 3fy3ef List some of its properties.

Select a point on the H-R diagram. Mark several directions away from a i976pczi ab2this point. Now describe the changes that would take place in a star mp aizb69 7iac2oving in each of these directions.

Does the H-R diagram reveal anything about the core oy s qxo9)ac;4sf a star?

Why do some stars end up as white dwarfs, af5hi; 1 ognvmp*ceszk; 6,jr3nd others as neutron stars or black holer z ;i1,;n 5vhc 3jepkgso*fm6s?

  Can we tell, by looking3 q+h;krs38,kunpggsvti5qt5 m 9f8f at the population on the H-R diagram, that hotter main-sequence stars have shorter lives? Expla qffgh+5sugk ;r,53ps8mn3 v98ti tq kin.  ----待选择----yesno 

If you were measuring star pv,rf1;+i- c+k6xl xlr9jrshgarallaxes from the Moon instead of Earth, what corrections would you have to make?,++lif1x96lgrj; rvk rx-s h c What changes would occur if you were measuring parallaxes from Mars?

Cepheid variable stars change in luminosity with a typical perio 7nq9 2x)lh 0/bypl*(qp1rgo xoj 4pbod of several days. The period has been found to have a definite relationship with the absolute luminosity of the star. j2gp7b/hypxob) 0qo*ql (94pl nr1 o xHow could these stars be used to measure the distance to galaxies?

What is a geodesic? What is its role in Gh4pj ktjw;h; do t4 gncs692.ceneral Relativity?

If it were discovered that the redshift of spectral lines of galaxieslxu /71jbsns*3lqu, d was due to something other than expansionqu *j u7bllsxs,1d/3 n, how might our view of the universe change? Would there be conflicting evidence? Discuss.

  All galaxies appear to be moving away from us. Are wi;5/s u7h9 et cjk.xywe therefore at the center of the universe? Explainht/w.u7kj cye9;ixs 5.  ----待选择----yesno 

If you were located in a galaxy near the boundary of our observable unif46h (wwx1hpb ;oh .kl*doeof )qeh ((verse, would galaxies in th(ho ; w.qh w6kfl( fpe1e(d)*oo4x bhhe direction of the Milky Way appear to be approaching you or receding from you? Explain.

Compare an explosion on Earth to the :st p w57t hqz*b58yqvBig Bang. Consider such questions as: Would the debris spread at a higher speed for more d*t78 wtvqb:55z yhsqp istant particles, 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, escapl7 7yqzy0zehds a inmm,.- dsld8 q2):es from a black hole, then how can we tell if onez)s,qadz 87i ne y qm2sdlh-l.y7dm0: is there?

  What mass will give a Schwarzschild radius equal to5*b w tvgd-0z2 6qcyaorg*l+n that of the hydrogen atom in its 5 yt ogn60*v+gbl*zcradw-2q ground state? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion yea si;)7zm2:h qb4w)foh x-rzlvrs. Find that time on (Fig. Below). People have lived on Earth on the or)w z;m :l7q of4hbvs -xhr)i2zder of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic microwave background radiation is. Where does ibe (wx3e3wsv .3a7 typt come fromw(t7bys w x3av3e p3.e? Why is its temperature now so low?

Why were atoms, as opposed to bare nuclei, unable to exix2gy 8 /vwe;kk *v,tzac2 gbo+st until hundreds of thousands of years agv2, oak; / gctwex8zvb2k y+*fter the Big Bang?

Under what circumstances would the universe eventually collapse in on itselj/m:; (u 3 /ji pxqhrmab;sjk(f?

  Using the definitions of the parsc7fw g ; o6xt) (9b4ng *oo86 x)zaemnzw*zlyzec and the light-year, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0 f2eo49gd6m zh.38 seconds of arc. How far away is it? d =    ly

  The parallax angle o7d zlxvk yttj ;/(d*c.-0 cielf a star is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What ip ai)-)yk;ikn; )+ *hd x8gtorpaatb0s 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* gyirt/s2-1rr0t euj cq4ec z5te0h, a star that 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 stac eje-b9a rs0 ;ujhw q7)69pmyr, will the parallax angle of 7e6qjm- ye )rwca99spjuh ; 0bthe farther star be greater or less than that of the nearer star? By what factor?

  A star is 35 pc away. How long doetno33 i;. vw25 lkwahos it take for its light to reach us?    years

  We saw earlier (Chapter 14) that the rate energy reaches the Earth from the Sunq q4 l+c9:( pce+wqoqh (thc+ 4(+c:qqh9qopqlwe e "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 Jupiter as compared nwqjf50+ .nc4yv yu/f to its brightness from uw.y5ny/ qn+f j4v0cf Earth? (Jupiter 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 odqle7 3mxpe1 6ur Galaxy would subtend if observed from the nearest gallq m ep71dx3e6axy to 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 averagyc*oi n) ,sbsz r.js *q8:an5ke density if it expands out to the orbit of:z* k*y. crs58is )sob,jqann 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 about tdh as wui1.768rwgfd ,,8metbhe size of the Moon. What angular width will it s , bwit 6d,8sd7ru.wemghf 18aubtend from the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whos 36im *upb yzv6yn+oe+e mass is equal to the Sun's and whose radius is equal to the Earth's. How many times larger than Earth's density is this? v3zm+ u6p+*ob yn y6ie
$\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 massesrub gqn7vpo th jn;6007m44 nx has a radius of about 11 km. Calculate its average densih4 7v7up4gn b oxjqm;n6n0r0tty 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 reace mp,-9rodb. cj*xe 7ptions of Eq. 33-2. (The mass of the very unstable m-co,p ex r.7 9jpeb*d$^8\text{Be}$ 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 , pwq)* 6)p9q,uaay ljz2 fg)wehtr1y 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 certaisni7ais21i,w uy f8/fn cluster are assumed to be about the same distance from us. Two such stars have spectra that pns2iiai 1suff ,78/yweak 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 ()q- ,ui-a9 qi8pmmidia) of our Sun q i uimd-8-9iqm)api,is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typical galaxy t1i+:gm-xplu )q j8gn(like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a sphere, for which the sum of 0;e k+5 orgonathe angles ik05r+e oa;nogs (a) 359º, and (b) 180°.

  What is the maximum sum-of-the knp8zttg+p5* m2)qfj rrx6 zfh8md.2-angles for a triangle on a sphere?    $^\circ$

  If a galaxy is travel a , bxpgimn/ka.;x)3l1pzr,y 4 2twkxing away from us at 1.0% of the speed of light, roughly how far awak/x4ytxr),a. a lni 3m1z,b;xp g2pkw y is it? v =    Mly

  The redshift of a galaxy indp j0 c3 (zxzt;ru:. k5otiq/guicates a velocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed oksi q gt1.8m4. bolo.yf a galaxy (relative to us) that is near the observable "edge" of the universe, say 12 billion s8b 1o yq .mt4.iokg.llight-years away. v =    c

  Estimate the observed wavelength fo2:fk hyy2lu+ wr the 656-nm line in the Balmer series of hydrogen in the spectrum of a galaxy y kh+l2f y2:uwwhose 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 uoa9ykt73o2la:s lui/ sdd hst6 97 )jhs, if the wavelength for the hydro2y9st3ua/ i s) 6hkt97:ha d llosdjo7gen 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 awwydwx4huf 9hs2.y.bhv ,/p: galaxy with $z = 0.60$? v =    c

  What would be the redszt2f w-mai sg0t8*d:ahift parameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Dlqt qx.p4 wuo7h)7sg9 oppler 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 the blackbody radiatione5yg 3 ba9qi mf:b k,yw(++nyj distribution at 2.7 K usw(+e3b fj m9ikq:y bna+, g5yying Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of the universe is*gzoi34 5fko a $\rho_c \approx 10^{-26}\ \text{kg/m}^3$. 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 distp4 5 hlutzo1v y e0wn)7*ldn*jance between galaxies) at any one moment is believed to have been inve)l vznh1 t0upjyd5 wlo *e*n74rsely 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 thresho/: :,ijea t6h:wohmntld temperaturt/ah6 i hjnwto:em: :,e 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-sequencdc+b z)3 2cncxbje/l; y;-fmh e 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 case, describe the changes in temperature, luminosh -f xy2ldz/ )cbm cne;b3+cj;ity, and size.

  Assume that the nearest stars to us have an aldivj (jrrlwr-5t ee / e9(/;jgox3/s bsolute luminosity about the same as the Sun's. Their apparent brightness, however, is iet/jj/g3r;x( ee9r/wlrojls ( v d5-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 estimat(y d3tnx+fop3e the angular velocity of a neutron star which has collapsed to a diameter of 20 km, from a star whose radi 3 pxdty(fno3+us 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 jlqaa2 v . +jz ns61q;)pj,xkwrotational kinetic energy change when the star in Problem 56 collapses to a neutron star? )a1jwz6j,jp ;qask2 + .lnq xv $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believed to be a neutron sta.ral o)1pkg*8qu /1dt)v npkyr of mass 1.5 times that of the Sun, with diameter 20 km, is observed to have a rotation spe*vuy q.k t18ngp lk)pra/od1)ed 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 a zzab -r8/x1ql9mhv3t 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 res vnjmu)*w7*aoc j a69)s d.vnet mass (in eV) would provide the critical density to close the universe. Ass*7) 6cusda mv j.*n9nve )jawoume 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, respectivelyc; lwh9jx ,-ul, both lie on the main sequence. Use Wien's law, the Stefan-Boltzmann equation, and the H-R diagram (Fig. Below- u9jlh xwlc;,) 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 parsjfb4r r;d ml7 +s0fx723zdjp zecs. What is our minimum angular resolurmj27zd l+ x;4fjrfp0 z3 bs7dtion (in degrees), based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from singy e siy;2i6xn.ly ionized helium in a distant star happen to overlap with the Balmer lines from hydrogen (Fig. 27-22) in the Sun. How fast isi ;x2i.ynsey6 the star receding from us? v =    C

  What is the temperature that correspog ycpx5tem / :flds9cl56iu 0ar 1)p,qnds to 1.8-TeV collisions at the Fermilab collider? To what era in cosmological history does this correspond? [Hint: 5:qe6lyxurg5dpl)f,p ic/s0mt c19 asee (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation ofuke4ro q-z) f jt6d-+j gas around what might be a supermassive black hor4q--djzeu +)6ftj okle 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 fr*nkwp6y *5kt s0fm- soom Earth. The "blue" hydrogen line at 434 nm emitted from the galaxy is measured on y-s5kt po*w*fk6 ms0nEarth 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 massiv3mtl; hs e*et d,bqz+8e enough) will begin fusing carbon nuclei to form, *; +,bmlqte t3 hz8sedfor 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 reactioy5cxbi4l ll ne+ c*f+qxw(( s-n
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 density of th-w jw62z)l kcne univer -2c)wzj6kwlnse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$