The Milky Way was once thought to be "murky" or "mikb4md d/i1e:dlky" but is now considered to be made up of point sources. Explain.em/:4d d dbik1

A star is in equilibrium when it radiates at its surface all the ener a8w8h7x g9zswgy generated at its core. What happens when it begins to generate mas8gw7x 8h9w zore energy than it radiates? Less energy? Explain.

Describe a red giant star. List some of its pr0s8vq78.twcp0s9kwme obej * operties.

Select a point on the H-R diagram. Mark several directions away froz/ * bnl (zcf:37oisqgm this point. Now describe the changesb/7izlzn of:c (g3q*s that would take place in a star moving in each of these directions.

Does the H-R diagram reveal anything about the cors2f 2f2(ey:upem:obe8 r xti7e of a star?

Why do some stars end up as white dwarfs, zl11oe6cbguv6y0 j p *and others as neutron stars or black hol e6b6vg1jc*p z y1u0loes?

  Can we tell, by looking at the population on the H-R diag dza y1 e5)h-v+zj6t,fjuud (xram, that hotter main-seque 16azde+(u -fvzx y5u),jjdh tnce stars have shorter lives? Explain.  ----待选择----yesno 

If you were measuring star parallaxes from the Moon instead of Earth, what correwuk0,6c g dq,zctions would you have to make? What changes would occur if you were measuring parall,kqw0cg d,6uz axes from Mars?

Cepheid variable stars change in luminosity with a typical period of several daynrgdo)hygm( he+322p mvn2 z8 s. The period has been found to have a definite relationship with the a om3zy(p m+rhd2e nhv )g822ngbsolute luminosity of the star. How could these stars be used to measure the distance to galaxies?

What is a geodesic? What is its role in Genero4n/rqhe ly., al Relativity?

If it were discovered that the rer)anbhfgos,9,c33w6tr 7 is 3pj 9pj hdshift of spectral lines of galaxies was due to something other than expansion, how 3fppw h,hai3g )s 6j93 nsjtrobc79,r might our view of the universe change? Would there be conflicting evidence? Discuss.

  All galaxies appear to be moving away from us. A2;mg0 bwf uhq t8i*;33xhgd 4um3vmhgre we therefore at the center of the universe? Expu2vt*;f gguwm3; 4 b08 qmg3dim3hhxhlain.  ----待选择----yesno 

If you were located i);yhimb(- frs0cj8hh n a galaxy near the boundary of our observable universe, would galaxies in the direction of the Milky Way appear to be ap(hs;f8m jrc0yhib- h)proaching you or receding from you? Explain.

Compare an explosion on Earth to the Big Bang. Consider such queisg f;ib9v;dvabxh73, ts59 ustions as: Would the debris spread at a higher speed for more distant particles, as in the Big Bai;9i7v;t a gx,bfudv 395shsbng? Would the debris come to rest? What type of universe would this correspond to, open or closed?

If nothing, not even light, escapes1 flfowbjqh 5zo ,r-mhscwo:y4 3c1 26 from a black hole, then how can we tell if one is there?1- y2sh c15wr:4omhb6jf owoflzc,3q

  What mass will give a Schwarzschild radius equal to that of the hydr39r8sg2+la pn ll7dtwyl 4yo6 ogen atom in wyy7ol3lsl dtg+ 8r2lnp6 a49 its ground state? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billi:h 4 rd5gf2a0p kg9dfpon years. Find that time on (Fig. Below). People have lived on Earth on the order of a million years. Where is that on (r kp20pgdhf4g:9 a f5dFig. Below)?

Explain what the 2.7-K cosmzn s/d6eot*++aedq0lli + wcotfb(/5ic microwave background radiation is. Where does it come from? Why is its te/ *+wnq0ct+(soaf oeldb+/ lt de56izmperature now so low?

Why were atoms, as opposed to bare nvlsqj5 bd ux84e+m04o*u-fu t6hg rf ,uclei, unable to exist until hundreds of thousands of years after the Big Baner -+ 4 lf 4u*6hmdut0vf,xgbu85sq jog?

Under what circumstances would the universe eventually collapse in on itself?n )2ms+ ovh3xn6+qs *lwy7xoc

  Using the definitions of the parsec and the light-year (s85)8 fzfzb7m t m9ymzf*nay, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.38 seconds c+o7/zo zne*xg0;vzd+ ov0ex of arc. How far away is it? d =    ly

  The parallax angle of zc+/y- zt +udua star is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its par huoov uhk/)2.allax angle?
State (a) in seconds of arc,$\phi''' \approx $    ($\times 10^{-2}$)''
(b) in degrees. $\approx $(    $\times 10^{-6})^{\circ}$

  What is the parallax ang /6fkpz 9.pbo(rjo (pple for a star that is 55 ly away? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as :bp8jjs83yt 4tpq9zs far away from us as a second star, will the parallax angle of the farther star be greater oyqj jtbzs893 8sp 4pt:r less than that of the nearer star? By what factor?

  A star is 35 pc away. How long does it take for its light tot eewkjzn/d7 e51 ;*ek reach us?    years

  We saw earlier (Chapterz95 rkwu v7ue p5p1tl2 14) that the rate energy reaches the Earth from the Sun (the " lp r5e2w5putz7k1vu9solar 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 cqyo 5u.1yi+nhompared to its brightness from Earth? (Jupiter is 5.2 times farther from the Sun tha qiyu5oh1ny +.n the Earth.) $\dfrac{l_{\text{Jupiter}}}{l_{\text{Earth}}}$    $ \times 10^{-2}$

  Estimate the angular width that our Galaxy would subtendrta h+zjg q xno1l+ vjs:*h-86 if observed from the neare h *jr:ol sxv1-hzatqnj++g68st galaxy 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 if it expa3y) s9:5t 3np bpr wwi)hll2ndnds out to the orbit of Ea r359h l 3sp)n )wpl2:indtwybrth ($1.5 \times 10^{11}\ \text{m}$ from the Sun)? $\rho = $    $ \times 10^{-4}\ \text{kg/m}^3$

  When our Sun becomes a white dwarf, it is exlyq7:d vx h6to yxl, )y-n8/cv6u1qdwpected to be about the size of the Moon. What angular) 7y/x v,w-ocx16lq hd tyny8uqv:d6 l width will it subtend from the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whose mass is(mhdq(m -x o6 l-dm(5tl:ju gx equal to the Sun's and whose radius is equal to the Ealt (:mudxh(-o 5q xmdm6j(-lgrth'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 masse(/p( * rae r0md4yysnps has a radius of about 11 km. Calculate its average density and compare to that for a white dwarf (Probdy(m 0y4sn( ra *rpep/lem 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 b*fs 4. 09a1vnph wnrkburning reactions of Eq. 33-2. (The mass of the very unstabl1pv hafr w0 kbnsn49.*e $^8\text{Be}$ 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 apd, q/s+-jjppm parent 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 assua)y.c9v41z f 9j/qoz p um) cuvpz--sjmed to be about the same distance from us. Two such stars have spectra that peak ) ou9amqju-)/zfzy pz p.v 1cv -jcs49at $\lambda_1 = 500\ \text{nm}$ 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 radssow vuzg.z.p .5*5,z7mzuyqius for a star with mass equal to that (a) of our Su.quz.*zs z.wz u opm,yg7vs 55n is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typical galaxy (like i7r1 mz w(h2idkb8r1*dh kp0fours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on tu)iff-b sy ,: 8 (vfqlee,5xirhe surface of a sphere, for which the sum of the angles is (a) e(5isfq,,u-lyef r )xbifv8: 359º, and (b) 180°.

  What is the maximum sum-of-theq;f 3 2o .m(wrdicpoqmj4a(ea(t8h5 g-angles for a triangle on a sphere?    $^\circ$

  If a galaxy is travelioy( vt+weni )7wdt+,c 8 hved3ng away from us at 1.0% of the speed of light, roughly how far awaevyn(o8dw7dhe3v)t, c+wi +ty is it? v =    Mly

  The redshift of a gal c/.d8j-2ueya:goxn83a.f ud-uv(mg,ag jmhaxy indicates a velocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed o.ox w cv./oev0f5nez tt4as82f a galaxy (relative to us) that is near the observable "edgec ozatf./5vt.n4ew v e82so0x" of the universe, say 12 billion light-years away. v =    c

  Estimate the observe6 /wxl0;6yi 9r -1 ig(5opq4dwxxrrqfgqhef6d wavelength for the 656-nm line in the Balmer series of hydrogen in the spectrum of a galaxy whose distance fromhq fi (6gw4lrrgfqdx6- 510op9y r6xe;iq/wx 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 the kff4w-w7tu3eytjq;kd )k 5j7 wavelength for the hydrogen line at 434 nm is mek-eyk w kfjt3w7j 45;fqut7 )dasured 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 +mn5 gvwc isljmn,lh2y740 p( galaxy with $z = 0.60$? v =    c

  What would be the redshift paro6n5 ufrsxte0c145nmameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that thexz5 nhop0jho lno.(nb8;c86r 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 the blackbody ra12g 4zowvc 4widiation distribution at 2.7 K using Wiezvgwowic1 4 24n’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for l q 6o p*cyzt7lz+zz3-closure 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 universe (the average distance between brom:,a r 0ob*iy kc0 8nfr2d+galaxies) at any one moment is believed to have been inversely proportional to the absolute temperature. Estimate the size of the universe, compared to today,c, o2fbmb ykd+rria0o *08rn: 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 below4 tn :g z.gdtyh/dqt8/ the threshold temperature for proz8g4qd:.htyg /t /tndducing
(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 threi f8qpe) m;r0d jm7/zoe changes represented by trfi 80zj o)e;q/7mmd phe 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 absolute loer8t5:oy u6hoct30cuminosity about the same as the Sun's. Their apparent brightness, ortce086tc5h o3oy: uhowever, 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 modzc3ly4h9vn 6imlul6* y)4 zsmentum to estimate the angular velocity of a neutron star which has collapsed to a diameter of 20 km, from a star whose radius was yh v9y)nizlzdlu4l 4c*63m s6 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 change when the sta (zg d7ey)gavo/;a8 ekr in Problem 56ekd)gzo/;8( 7gvy ea a collapses to a neutron star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believowuhw 2not6,g -73mmved to be a neutron star of mass 1.5 times that of the Sun, with diameter 20 km, ioo6vwhtn7wg m23 m- u,s 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 abmym*+pwo ptt/) . (iemout $2 \times 10^6\ \text{ly}$ 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 ffvi 5+8 9ae(j+7bug/pro ucpprovide the critical density to close t b7+i9f5/ua( + vopurjp8g feche 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 peak at 600 nm aojjwq4:c2 dyig 3/o 2xnd 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 Exawc 2j24oi: gjd3 /qxoymples 33-4 and 33-5.] $\dfrac{d_{400}}{d_{600}}$ =   

  Suppose we can measure distances with parallax at 100 parsecs. What isr18g56xqr os r our minimum angular resolution (in degrees), sxrgoq 6518r rbased on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lrkfh )c)vqcbo lj7973 z:+ oia chd-w:ines from singly ionized helium in a distant star happen to overlaphc) h+3b7oc)ijdkr79qf: vca -z l:ow 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 temperatuv fqf2rz3.yz6 :e0b8ph3 lerere that corresponds to 1.8-TeV collisions at the Fermilab collider? To what era in cosmological history does this czl8b6rqe .: fpyr3z 0eevf3h 2orrespond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation of gastbht52r f(h twl 7q+6b around what might be a supermassive black hole of about 2 billion solartb5 (ht rqfhw 6+t27lb 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 "bpvoh8s l.4o.n 022c1w shynrrlue" hydrogen line at 434 nm emitted from the galax.v snlcr.20 2sphhr o14yn w8oy is 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 evolut)4 8 kcrpsvdthv i2;y8ion, a star (if massive enough) will begin fusing carbon nuclei to form, for example, mag vr4y2d88h;)ktsvpci nesium:
$^12\text{C} + ^12\text{C} \to ^{24}\text{Mg} + \gamma$.
(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 ykn-pn6mp+n96 * jihe
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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,8 ynein/4 gci density equaled the critical density of the univern ,/ngyiei8 c4se, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$