The Milky Way was onchfr2a ;fb.f75g wk/j xe thought to be "murky" or "milky" but is now considered to be made up ffhrw7g k a;xf b/j25.of point sources. Explain.

A star is in equilibrium when it radiates at its surfaculic; :ylyx( jzbu q 6z0-33vee all the energy generated at its core. What happens when it begins to generate morveb-jy6;3xu0lyuc zizlq:3 ( e energy than it radiates? Less energy? Explain.

Describe a red giant star. List s) eqe(/ knun-xnpcho7k 9qk)-ome of its properties.

Select a point on the H-R diagram.*zsw40+tn aoy Mark several directions away from this point. Now describe the changes that would takea0t* 4 +osywzn place in a star moving in each of these directions.

Does the H-R diagram reveal anyt3p.gwch7aabpz 32yilob(7 4 rhing about the core of a star?

Why do some stars end up as white dwarfs, and others as neujp q7 1 vd*9adij*z:betron stars or black holes?* ijzea7vd*j:b1p q d9

  Can we tell, by looking at the population on the H-R diagram, tr(5w gp rj;o2shat hotter main-sequence sw pj os;2g5rr(tars have shorter lives? Explain.  ----待选择----yesno 

If you were measuring star .qq1ka0pi /w1 d8lcopoq+tm-parallaxes from the Moon instead of Earth, what corrections would you have to make? What changes would occur if youo q0/t+icqdaw8pmp1o.1k ql - were measuring parallaxes from Mars?

Cepheid variable stars change in luminosity with a typical period of wwah /56tc u;fseveral 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 to galahwacf t6w/u5; xies?

What is a geodesic? +g9o)) em l;bztwa a1gWhat is its role in General Relativity?

If it were discovered that timb2 8gyw6*hi7 n8rvwhe redshift of spectral lines of galaxies was due to soimnghibw6rw y8v2 78* mething other than 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 therefore at the 9nl,j wbxcy7o)o 06v ucenter of the universex)69vnjcowlb07 o uy ,? Explain.  ----待选择----yesno 

If you were located in a galaxx9 h9w22pifguq5 sl*r y near the boundary of our observable universe, would galaxies in the directihq g*lux9if5wrp92 2 son of the Milky Way appear to be approaching you or receding from you? Explain.

Compare an explosion on Earth to the Big Bang. Consider such questions as: Woult qr gi;-b(n9ns9k q4tv:)0 u;/niuudb f mn5vd the debris spread at a higher speed for more distant particles, as in the Big Bang? Wouv0br /-gik; 4t 9fu bsiunqdu(9n:n;qntmv5)ld the debris come to rest? What type of universe would this correspond to, open or closed?

If nothing, not even light, /y nry444qbijdm. ; ivescapes from a black hole, then how can we tell if onevry. i4ym4i;qd/n 4jb is there?

  What mass will give a Schwarzs ;k:tm)1grdan. n5 ,njihwk eg6+ qzg:child radius equal to that of the hydrogen atom in its ground state?g ;zg:dh qg+j.5:nw16rn i,t)ke kma n M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is ofteoxw*cjd uqu*o6 u0n2c+ k 7(vtn given as about 4 billion years. Find that time on (Fig. Below). People have lived on Earth o wj*+vcu7ok*6nqx(t2cd o0uun the order of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic microwave backgrorufh3,y l:j4k und radiation is. Where does it come from? Why is its temperature now so low?4klu jyh:rf, 3

Why were atoms, as opposed to bare nuclei, unable to exis.ueg7jl )q,(p bszv+ft until hundreds of thousands of years after the Big( q. fbug+se7lvp jz), Bang?

Under what circumstances w 2 h7n+2pc 5cpvblhei0ould the universe eventually collapse in on itself?

  Using the definitions of )vt v-rn 9)a8m. kcfqgthe parsec and the light-year, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a para24v g.p pdy(b0,lcdzwllax of 0.38 seconds of arc. How far away is it? d =    ly

  The parallax angle of a starnhg f9 o0pkn5: is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its paz 66xmy ,pv2burallax 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 s.tm4j zv,**xkog52o oa(lbt otar that is 55 ly away? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice a1 hoqd jgsry)lx ot;:lu: z4;9s far away from us as a second star, will the parallax angle o;91u tyzhx):j :qdso r;lg4l 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 ,gf2g. niy 6flq ec5v/its light to reach us?    years

  We saw earlier (Chapter 14) that the rate energy sr6md q(;b :q1xlsqc )reaches the Earth from the Sun (the "solar sl16qb )m: q;(d xcqrsconstant") 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 Jd v rq zd5u 9214/zygffbys 6p0,bibl(upiter as compared to its brightness from Earth? (Jupiter is 5.2 times fb1r0yd fs( pzl24fd/vq gzb9 iyb 56u,arther 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 observedx 8 sa.ak: pjrspafz.;4h* 0gr from the nearest galaxy to us (Table 33-1). Compare to the angular width of the Moon from Eart: ag8 rzhpjka4rp*s.xs; .a0fh. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, yutfpdi-y d6 15,1qang3rb e4what will be its average density if it expands out to the orbi4y npraued g1ft3qb1,diy- 6 5t 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 whi+hr8am *vo9 ycte dwarf, it is expected to be about the size of the Moon. What angular width will it sucryv9omh* 8a+btend from the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whose mass is equal to the Sun's and wd0 hu. 3yfr2.slbbm0ohose radius is equalblsh 203 odmy.0rub.f to 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 massesn6w c.l5tf 12qto8fw0 a9gfi q has a radius of about 11 km. Calculate its average density and compare to that for a white dwarf (Problem 13) and to that i6n5fcqag9wf0f 8 .t1t2l oq wof 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 reactionmpfm06 dt0s 2 op1 up9mne;led3xkv0-s of Eq. 33-2. (The mass of the very unstam0d t2x6 ;epemp1m9lfuvp0 n3 so0k-dble $^8\text{Be}$ 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 sapetw,1/ gj4gy7g+2shdt8 cz lme 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 to be about the same dista.b: + we7 otma:v(yjybnce from us. Two such stars have specbw m:etb.7+ov:( yy ajtra 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 Schwarzschil+4zbn6q.rf cq: ysrk9 d radius for a star with mass equal to that (a) of our Sun i9fs.4nyb kq+z6cq r:rs    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typical galaxy (l382kxp ne1g ayike ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn m/w:1mzjh7s dmx8k y 0on the surface of a sphere, for which the sum of the angles is (a)0mm hs7j/k:dmxy1 8 zw 359º, and (b) 180°.

  What is the maximum sum-of-the-ang+iy 0xg0:ogyz7t nf 3qles for a triangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the speed of light, r x478 gbdifk*n 6o23 gk5a3nlfr lzd4voughly how far away is it? 38 g7f456 l inobakdkvr xzl4gf2d*n3 v =    Mly

  The redshift of a galaxy in1) vg 3zzj xs32z8k4gf;or;1qttvbjzscr--a dicates a velocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (relative to us) that is nearm -36szv7nlm 4qb9zgwc::nj g the observable "edge" of q7vbn zg6mz- smn:c:4j3l9gwthe universe, say 12 billion light-years away. v =    c

  Estimate the observed dq 2 suxop),1 pxnai+*wavelength for the 656-nm line in the Balmer series of hydrogen in the spectrum of a galaxy whose dna*q+o dux2)x1ps,p iistance 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 disri lijot(z5 i ,h9h; w8hp8q3gtance from us, if the wavelength for the hydrogen line at 434 nm is measured on Earth as beingii p8t5gr9 hoihz,3l(q w8 ;hj 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.rh)wd gb *ie5 with $z = 0.60$? v =    c

  What would be the redshift parameter/g*71mij w:de5zg ,n7tyapym $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Doppler shift in n/g1dwv ,d8zc:o q nq0wavelength 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 radiation distribution2 sx47g7 ukvth at 2.7 K usinuh7kt2 gv 7sx4g Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure o 4u3khxa c(,d2c zhw.of 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 uni nwipvyq7 :1 esjsu 94j4o8rw3verse (the average distance between galaxies) at any one moment is believed to have been inversely proportional to the absolute temperaturee9sjruoy1 3w4 n74:jw i8vpq s. 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 threshold temper0o* mt) eh;5ft vi tr,hir10rbature frh1o5f r0e,) vtt; t *b0irmhior 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/5j 8 ..2gzwuhg .jamnr6bkyz changes represented by the three arrows, A, B, and C, in the H-R diagram of Fig. 33-28. For each case, describe the chang..akg b.y 25/rj6wzghjmz8 n ues in temperature, luminosity, and size.

  Assume that the nearest stars to us have an a 7 xiu5yzk+qmm:d 3uf*bsolute luminosity about the same as the Sun's. Their appauu*q x k zm3:7d5+imfyrent 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 velocity 2qm 49jcxx 6d6szu lz a3mw :)a9sw2ugof a neutron star which has collapsed to a diameter of 20 km, from a star whose radius was eq)msaw 2 mu2z: q6azgwl ux4dx963s9jc ual 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 kinetic energy change when the star in Prob 9hqi uthh ,7zhr v9bgr/x405,da9d mtlem 56 collapses to a 9 h9t,hm/09d hgr7r hi4vu5q a zt,dxbneutron 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 6eb-gug8a 5 uhwn*m,cdn;dr8times that of the Sun, with diameter 20 km,,ag8 u6-ndgh8ebdm*r5 u;wnc 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 abouh3 hjh;r9k km,t $2 \times 10^6\ \text{ly}$ 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 critich 9 vtj(m(cad pr94uz*al density to close the universe. Assume the neutrino density is, like photr4(tvp9*ch z j9u (mdaons, 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 a 2h;8llqq1 nhon the main sequence. Use Wien's law, the Stefan-Boltzmann equation, and the H-R diagram (Fig. Below) to eah q1 28lh;nqlstimate 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 parsecs. What ishe,36.yk ktm(j )7vvo +ya. ynvqtzb(dx ,hl) our minimum angular res(env7 k,)t. xhd ykv l6(zyoqb,m)jyh +3va.tolution (in degrees), based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from s0o xuksi 5bu2x- j gvmh9i74/vingly ionized helium in a distant star happen to ove g-viu s0x9mk 4/b 27juovh5xirlap with the Balmer lines from hydrogen (Fig. 27-22) in the Sun. How fast is the star receding from us? v =    C

  What is the temperature thajx; -jxm8/rby pkj;i )bf;q q.t corresponds to 1.8-TeV collisions at the Fermilab collider? To what era in cosmological history does this correspond? [Hint: see b jj8r;xjfq yp -xk;m;i )qb/.(Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recenx 4n1 idh0+xrntly measured the rotation of gas around what might be a supermassive black hole of about 2 binn 1+rdx h0x4illion 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 "blue" hydrogen line at 434 nm 9 ).m-nx gb:qiaz y c4vwq.e7oemitted from the galaxy is mezn4 ) a-iqxvcwe:7gyqomb 9..asured 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 evolutw ;pel 4dlpe+t3mkj*4ad8oh -y hn.m 6ion, a star (if massive enough) will begin fusing carbon 8n;l dkp aw6me-+jhp hed3ty.4 * mol4nuclei 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 3r ;an4 f798qpc/b4/yft / ktrrcis.yjgzt 7l
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 the uno5q4of2hwif uvn/ )b1h /iw15o) 42nofvuf qbiverse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$