The Milky Way was once thought to be "murky" or "milky" bos.f.l+m un;h 1 ftpjrw356x cut is now considered to be made up of point sources. Expla txf of+ujm.hn 3;1rp.w sc6l5in.

A star is in equilibrium when it radiates at its surface all the ene d8t+gb tgiu(/rgy generated at its core. What hat8u+dgi gb /(tppens when it begins to generate more energy than it radiates? Less energy? Explain.

Describe a red giant star. List some of its u.g0j3dtg7 v*x(:(5ejxfzhug s9ewj properties.

Select a point on the H-R diagram. Mark sez+z6t7vw6ygbn; trf ta;aoa5fcw50 6veral directions away from this point. Now describe the changes that would take place in 7v0 6 ;fwa bf+tc5o5atngzt6rw6y za;a star moving in each of these directions.

Does the H-R diagram reveal anything abvb,war98 k z;zout the core of a star?

Why do some stars end up as white dwl*9l+*erg pcv byq34/gp nb7parfs, and others as neutron stars or black holyp4b nlg /*verl7*9 cp+gb3pqes?

  Can we tell, by looking at the population on the H-R diagram, that hotter (joo, 3(o /-m annftuemain-sequence non3(jfaoo ( mtu,/e-stars have shorter lives? Explain.  ----待选择----yesno 

If you were measuring star parallaxes from the Moon instead of Earth, whatfbl) s yebh:(1 corrections would you have to make? What changes would occur if ybl)e ( y:1shbfou were measuring parallaxes from Mars?

Cepheid variable stars change in luminoz9b z.wupqdxfpsb+* : 9. ag)isity 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 measurbgzd:zapi* q.9bw. x9f) su p+e the distance to galaxies?

What is a geodesic? What is its roljcb2 qu:ewtt d*, 1*4mjg(cjfc-j3 lde in General Relativity?

If it were discovered that the redshift of spec x5bm7p0+mte-t6 zppqtral lines of galaxies was due to something other than expansion, how might our view of the universe chang b t6zmp07x-qtep5 +mpe? Would there be conflicting evidence? Discuss.

  All galaxies appear to be moving away from us. Are wa3v.1-fk q e949zx blfjjzmv.e therefore at the center of the ua9jfv. evq-l1zj zmk3 bf49x.niverse? Explain.  ----待选择----yesno 

If you were located in a galaxy near the boundary o*h-ijg-vjml2 s8i c t3vnb(f/f our observable universe, would galaxies in the direction of the Milky Way appear to be approaching you or nb/c* -v2sv8hmj( fig3t- j ilreceding from you? Explain.

Compare an explosion on Ear(9o oqsfckt :/th to the Big Bang. Consider 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 universe wouldk9 s:oqo/ (fct this correspond to, open or closed?

If nothing, not even light, xh ff.wqo dh0b9*gb3) escapes from a black hole, then how can we tell if one is there?xqh 9h)0g.w f dfb3*bo

  What mass will give a Scvg nw8+9qu41;neb nnehwarzschild radius equal to that of the hydrogen atom in itse98eb n+;nnngvu4qw 1 ground state? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion years. Find that rgq++(81 m:j,av7l5s zv y rc tbkq:dbtime on (Fig. Below). People have live a :cg1j5v+qrmbrs d:q(8l +zt,kv7y bd on Earth on the order of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic microwave background wd5t6o+ok (lx 7r3nhsradiation is. Where does it come from? Why is its temperature now n7lo+thwskrd x35(6oso low?

Why were atoms, as opposed to bare nuclei, unable to exist until hundreds of th kkbsyqi 0b9.2w )m(vlousands of years after the Bigly0 .2v)s w9kqimb(kb Bang?

Under what circumstances would the universe eventually collapse in on itse*o38fms jgfd60 tt:p olf?

  Using the definitions of the parsec and the light-year, sq8fw p286r2 ay.ehzqnw)c h v5how that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.38 seconds of arc. How far away is it?pm;x (*8fsot 2vvv2jo d =    ly

  The parallax angle oi md1d4*(p drzf a star is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away.ghlvuh+-po3*) 0 pmv b What is 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 for7ds52q+ b4kw j*s rns,ps*lh g 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 stardpi u91i /zw0ur 0gdu4, will the parallax angle of the farther star be greater or less than that of the nearer star? By wha iudz/gwi41u 0r 0u9dpt factor?

  A star is 35 pc away. How long 9w,pa h2u w wk+nwoy:+f y:,rfdoes it take for its light to reach us?    years

  We saw earlier (Chapter 14) that the ratc 6qf(+ r;cnvbl s9p7ve energy reaches the Earth from the Sun (the "solar constap (vcc7lfvq9r6sbn+ ;nt") 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 el;zp j+t4 i.* v;afzoyd8k0kbrightness of the Sun as seen from Jupiter as compared to its brightness from Earth? (Jupiter is 5.2 timekpt+ z ka 8y;f leo4z*d;ij0.vs farther from the Sun than the Earth.) $\dfrac{l_{\text{Jupiter}}}{l_{\text{Earth}}}$    $ \times 10^{-2}$

  Estimate the angular width that our Galaxynmks 9h u5x:4p would subtend if observed from the nearest galaxh 5n4:uxm9 spky 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 average density hz ; p2wdpii/.if it expands out to the o w .z/idpi;ph2rbit 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 dwx(w 95 ledoh-4z ug(mvarf, it is expected to be about the size of the Moon. What angular width will it subtend frx5-9ghe (um zow4l( dvom the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whose mso hnf;kzz ag25:rbcy)2(na :ass is equal to the Sun's and whose radius is equal to the Earth's. How many times larger than Eart;h y5:nnca: ( kzgsfa2)o2br zh'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 radiu mkjan ;cz5,g3rj (5ims of about 11 km. Calculate its average density and compare to that for a white dwarf (Problem 13) and to tha5zmj;im(ag5k 3r,c j nt 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. (e;3vfz i. s-x9br+gmx The mass of the vrb.xs+x3iz v-g;fe 9mery 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 a1*nru 7focwfqlzkep(d 57i(0pparent 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 ton:36: 4ueeq+sd: na9wsf hmr g be about the same distance from us. Two such stars have:dag4mnw ehr9q :es :6su3+nf 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+xt3+ecldf(pog t0;j) of our Sundltg tpxo(j+;3 0+efc is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius fori1 kzt3-doar8 a typical galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a sphere, for which iz7wlynyr56zzpo8 wu*2 15mm the sum of the angles is (a) 3n8 *o7ymimy15 rlpwz w2z 5zu659º, and (b) 180°.

  What is the maximum sum-of-the-ang6ld,m: og;) bdwsey7 lles for a triangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the sp0ajsel e nj791eed of light, roughly how far019e e jaj7lsn away is it? v =    Mly

  The redshift of a galaxy inhr(z ;nb3mjv2yf:q7g 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 a.0d8lme1 pyenear the observable "edge" of the universe, say 12 billion light-years away0 ldep1 8m.yae. v =    c

  Estimate the observed wavelength fo +.:)hwungtco r the 656-nm line in the Balmer series of hydrogen in the spectrum.:nh oc+ ugw)t 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 galaxu6 k wprw-3 z0d:/gv*ce t8zroy, and its distance from us, if the wavelength for the hydrogen line at 434 nm is measured on Earpk:w036zez v-cug8wr *d r/ot th 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 ofyge;lm n)p1 e+ a galaxy with $z = 0.60$? v =    c

  What would be the redshift parav ;omf5(y 8mpqmeter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Doppler uaysug:20gxv3 q; 3rhwot( ,lshift 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 blag;s-y0qhyts -oxow;9fux -f 5/ xe k2ockbody radiation distribution at 2.7 K us95fx2 oyoxhot us- f/x- 0;;-ywkg seqing Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of the unii.yiwh-il/9kq6uik*dfm,a 27 sk1nvverse 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 avealj d* ovol02w7+h ls.ptbou q0+xm*0s5wy9g rage distance between galaxies) at any one moment is believed to have been inversely proportional to the absolute temperature. Esti5aogo*o*lv02w7 yxjdh0s +u0.wql +tb s9 plmmate 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 temperatu ct;(q -fnxiq6re f;-tq6nf i(cxqor 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 co i 08 j*oi1:qo unuyqm22hvtj( c8s2changes represented by the three arrows, A, B, and C, in the H-R diagram of Fig. 33-28. For each case, 2cqch0q iut2n8y2 *jjso( om v8 :u1iodescribe the changes in temperature, luminosity, and size.

  Assume that the nearest stars to us have an absol3 prdur(s 9d5nkn c;sw 57gfw9ute luminosity about the same as the Sun's. Their apparent brightness, howep37cngwds 9rn ru(9d w5 ;fks5ver, 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 anggb xd 0rh4g: d(gpza4;/ qu-bnfy-4qcular velocity of a neutron star which has collapsed to a diameter of yhq4a dzr-;bnc u 4g4/q( d0:fp-gb xg20 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 kinetic energy changs2-k75lr cmi re when the star in Problem lc5ikr2-msr7 56 collapses to a neutron star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believed + 2e+dau; sifzto be a neutron star of mass 1.5 times that of the Sun, with diameter 20 km, is observed to +d2s+; uafzi ehave 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 G5+j*fwhi)sud/x ht,xp8gb( q b+fl /falaxy 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 (ibejr8/e6a db 23q mt (vwfm(a4n eV) would provide the critical density to close the4d/b(b m3awqae(8e vf6 r2jtm universe. Assume 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 t :bw4u ayezvl23/lx5gs 9* vrpeak at 600 nm and 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 3 9vybwr* 3lxt4/vl5sug:2aez 3-4 and 33-5.] $\dfrac{d_{400}}{d_{600}}$ =   

  Suppose we can measure distances withz4l v c(l5 gn6gjh7p:n parallax at 100 parsecs. What is our minimum angular resolution (in degr4n lgpn v g:jc(75z6lhees), based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from singly ionizedw.l;6)dypzoh1u e7 g i helium in a distant star happen to overlap with the Balmer line7z.i p ohgl1w6y ;)udes from hydrogen (Fig. 27-22) in the Sun. How fast is the star receding from us? v =    C

  What is the temperature that corresponds to 1.8-z)6zh 4 ino7znTeV collisions at the Fermilab collider? To what era in oi47zz6)nnh z cosmological history does this correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation of gas around what mig*tzychrt7rth 2m7 d 7(ht be a supermassive black hole of72th7z (rtm d *t7rhcy 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 Earbq; (st (+hmz9drc) vp)ctx3rth. The "blue" hydrogen line at 434 nm emitted from the galaxy is measured on Earth r+s )p3;mrtd (zt hc)c(9vbqxto 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)dbv:w zin p961hkc+q2 will begin fusing carbon q2bi1dc: 9wh6npv k z+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 a8l 3uj dlor+ z /mz6s64mqm1t-vu2n v
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 un (gci . lzjo,wfg*t/,aiverse/.azc glgf i ot,*,(jw, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$