The Milky Way was once thought to be "murky" or "milky" but z jx6+e3eptl/y.xa:1cu 2 ozu is now considered to be aepo/6z1t y+jc u x:2ulzx.3e made up of point sources. Explain.

A star is in equilibrium when it radiates at its sn5 y:k7t icb5fgo(d)g dr6 jn0urface all the energy generated at its core. What happens when it begins to generate more energy than it radiates? Led(k nrn0o)g6 :byftc7jdi 55gss energy? Explain.

Describe a red giant star. ij8f-ha xm30mch/ z6gList some of its properties.

Select a point on the H-vz6 ki k+oh(x;e gp05*3asl80pwize eR diagram. Mark several directions away from this point. Now describe the changes that would take place in a e 3 z+p;gikwv hk(s*8 aiel50xozpe 60star moving in each of these directions.

Does the H-R diagram reveal anything about thetnr*w7( iycq2 0 8px:puviyq((he :mg core of a star?

Why do some stars end e9 s3t6hvzsib1t+ rrnx:v++7nq9 rkuup as white dwarfs, and others as neutron stars or black hh+i9rv+ 3:ttzs7nkv6r1x q9n u+ sberoles?

  Can we tell, by looking at the populatio9qdouriptu5gif am( 199+ : f2wl(tm c+tpnu.n on the H-R diagram, that hotter main-sequenc(1c29ufmlwi9ou5p+.ptf(q udin tm tr+ 9ga:e stars have shorter lives? Explain.  ----待选择----yesno 

If you were measuring star parallaxes from the Moon ij t8 l+ek b6xe8(y*ifonstead of Earth, what corrections would you have to make? What changes would occur if you were meo8 tfb6(y* 8l jxke+eiasuring parallaxes from Mars?

Cepheid variable stars change in luminosity with a typical period of sevg8qv.v-r.ww1rvx4 tseral days. The period has been found to have a definite relationship with the absolute luminosity of the stas vvt v x-8gwr.1r4wq.r. How could these stars be used to measure the distance to galaxies?

What is a geodesic? What is its ro0 g+jgfrnhm c5ps5d+7le in General Relativity?

If it were discovered that the redshift of spectrxs b.r/y w*wj.x3+lby)w ntjnne 4),i al lines of galaxies was due to something other than expansion, how might our view of the universe change? Wouldistr3 nnnj wxj bb.x4e.) /ly+w*), yw there be conflicting evidence? Discuss.

  All galaxies appear to be moving away from us. Are we therefore at the center odt0+vtu27asfr m6 yi7f the+y7tsvm0iu fdar t627 universe? Explain.  ----待选择----yesno 

If you were located in a galaxy near the boundary of our observable universe, wk-. 8c mxdzlaruo14ht oi(7*sould galaxies in the direction of the Milky Way appear to kih*7tooz-(lc a8uxrm d.s14 be approaching you or receding from you? Explain.

Compare an explosion on Earth to the Big Bang. Consider such quen xheuz.qr73.oape) )stions 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 uniqa.nep .))73 ouhzerxverse would this correspond to, open or closed?

If nothing, not even light, escapes from a black hole, then how can we tell idl hlj) 8z)x:9 5dvtt2af2 ecqf one 8f )d)vllqcxet a:jt9h2 d25zis there?

  What mass will give a Schwarzschild radius equal to that of the hydrogeoqd4i):j0 gdtn atom in itsi4t 0dgqd:oj ) ground state? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion years. Find that time on (F47uazj7 fy7*ruk6fz xig. Below). Peopz fau*7774 rkfz xu6jyle have lived on Earth on the order of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic mi663-c idparhc-br lc 6crowave background radiation is. Where does it come from? Why is its lap -bc663i c6-cdrhr temperature now so low?

Why were atoms, as opposed to bare nuclei, unabdal 3j p-r(2iqle to exist until hundreds of thousands2 -3qrlaj(ip d of years after the Big Bang?

Under what circumstances would the universe eventually collapse in qtp-wm )(mzc3 on itself?

  Using the definitions oqdt bp5e,//r+ uwphn220c(lpz 1y r gif the parsec and the light-year, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of +7 yy0z+cns)m 7rlt dq0.38 seconds of arc. How far away is it? d =    ly

  The parallax angle of ib ii-b6di0icx 9 g2s 1nisq :m02kxe4a star is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its parallax anglz:d ( grp1f1iyxeoctx08 e+b*e?
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 star t4.qhkl ,(v yyqhat is 55 ly away? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away from us a0 +;8qo mvxe ijztxa8woi*5 at)8 .nifs a second star, will the parallax angle of the farther star be greater or less than that of the nearer star?vefnaxi ttz88;o+x ma)oi.*j 5i08wq By what factor?

  A star is 35 pc away. How long does it t ufda.sczji)c )8)r:s3ii2u,x l etx9f7gvk6 ake for its light to reach us?    years

  We saw earlier (Chapter 14) that the re.o*ip;wg/ hrate energy reaches the Earth from the Sun (the ";/ oihwegp.*r 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 to ct79h kbpwn71 its brightness from Earth? (Jupiter is 5.2 times farther from thebtcw1 ph77n9k Sun than the Earth.) $\dfrac{l_{\text{Jupiter}}}{l_{\text{Earth}}}$    $ \times 10^{-2}$

  Estimate the angular width that our Gao0mwzx/ -l+d olaxy would subtend if observed from the nearest galam o/wl-dxoz0+ xy 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 expg:l/p)v0 vr -3yj r9pslc2mfqands out to the orbit oflr:p 93 gsrf2lm0qvvp y-)j c/ 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 +kb-b 0+)b mpiqq/js b5scw/p dwarf, it is expected to be about the size of the Moon. 0s)pbq/ bi mbq-jpb5c ++ws/kWhat angular width will it subtend from the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whol h2fuf)f120 rp o2ykny 36s7zlsp4wwse mass is equal to the Sun's and whose radius is equal to the Earthlno3 ppf2wwrf 0yf 712sh4 suk)z y62l'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 masses hp - 6sam/u5obo a* imfh.7ael7as a radius of about 11 km. Calculate its average density and compare to that for 5muo /h*o7ap 6ea7im ls af-.ba 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 reactionsfiu v/e (lpc5: of Eq. 33-2. (The mass of the ve:u ef5 vlipc(/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 appa)d+d0pvhdif c;8x v)m rent 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 certawo j 2wt,d0 hm4je8bz;in cluster are assumed to be about the same distance from us. Tw ewhb2o4t0w,j8mjz ;d o such 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 radiurz zrwo: .6*ils for a star with mass equal to that (a) of our orz6iw *z.:lr Sun is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typical galaxy (l84yygf c0 sf6ibn 5fj,ike ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a sphere, for which th67 ehvqb;rxi .ph3jkxnj 4p02e sum of the angles is (a) 359º, and (b) n7v2hk;hr0x.xq 4p3jijebp6 180°.

  What is the maximum sum-of-the-angles for a triangle 9uv+gle qnecvy 344n ,w yal*8on a sphere?    $^\circ$

  If a galaxy is traveling away from us at, 2c ( /lwtg3jmgttq*t 1.0% of the speed of light, roughly how 3jt,/m q*tc(2ltt wggfar away is it? v =    Mly

  The redshift of a galaxy indic6isz8axhj (ah h y:a; 0/s-azxates a velocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (relativeoib7 5j3+xl ofslr )8r to us) that is near the observable "edge" of the universe, saloijs lrr)3f bo+5x87y 12 billion light-years away. v =    c

  Estimate the observed wavelength for the 656-n tgd eu80i;3d orvz4vtv.u+w,m line in the Balmer series of hydrogv urvduw;o.gv8 z,tt04e+3 id en in the 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 the wavele-g/iek+,-ds ;6 lmh5l kpvtvbngth for the hydrogen line at 434 nm is m kv 5ildb-p/v;gklh-m6,s e +teasured 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 gala -4kftaqev(-yxy with $z = 0.60$? v =    c

  What would be the reds)- tou,0 akpdcy;l25zd ep ,feph,ix)hift parameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show tdo1foxb9n9b n14mg z3hat 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 the blackbody radiation distribution - h y+wyu8y0l06 jglzbat 2.7 K using Wil6 uy0b0ygy-l w+zhj8 en’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for .lo:clgg jc8( 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 galaxies) at any 7o8b:5wjhmm x one moment is believed to have been inversely proportional to the absolute temperature. Estimate the size of the universe, com5 7m: b8oxjwhmpared 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 tempkfl,66f my5lzm cb)t8 8 sphz(erature for producing ,56mks ) tf p6 zy(hmbcfl8l8z
(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 tvjwai w,k ;oue)s,/cz(c4o,-sequence stars could undergo the three changes represented by the three arrows, A, B, and C, w)so/k v;ecju(,,twz,iac4o 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 luminosity about the sakl ;w-g6jg+8ms7 gdqome as the Suso ;8qk +gd-m gwj7lg6n's. Their apparent 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 angul c/ccct(4ujr: :-t tvear momentum to estimate the angular velocity of a neutron star whicht-cvc(:tu r /tc: ej4c has collapsed to a diameter of 20 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 th cp2-enkc, z7ge rotational kinetic energy change when the star in Problem 56 collapsesk72,zc gp c-ne to a neutron star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believed to be a neutron staysxx9s m9za,, +ygkl h7d.s:cr of mass 1.5 times that of the Sun, with diameter 20 km, l h ,ysxscadkz9sy79:gm, .+x 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 Gw4os-tu pf( 4ns.rpx(alaxy 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 (in eV) would provide the crixv;8vknsn )fh.0 jdd;tical density to close the universe. Assume the neutrino density is, like photons, vnhnfdsd; ;80k.jv) xabout $10^9$ 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, respeqj7kn lrf4 a6tkh6-0h9 7s ,ggh+ pore;v;e xqctively, both lie on the main sequence. Use Wien's law, the Stefan-Boltzmann equation, and the H-R ke,6g6p-j l r o ;ah0 hgf4s7x7q;hevk9+trqndiagram (Fig. Below) 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 7 5wqsg)kn8*z( kjzszat 100 parsecs. What is our minimum angular resolution (in degrees), based on thj (78kqn*5z)s kz zswgis information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer linj-w92kbug- uaes from singly ionized helium in a distant star happen to overlap with the Balmer lines from -kbwajg- u29u 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-TeV 5t,c jq9:b tifcollisions at the Fermilab collider? To what era in cosmological history doe cb5:iq,t j9tfs this correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the r0n( +v y/ /dtxpam-n1l2qtoraotation of gas around what might be a supermassive black hole of about 2 billion solar masses at the center of / a0nlo t(-vr/aqyd+mpt x2n1a 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 "bl2.aatqfy s oh3q4vhr4p .v+a c m;3o*zue" hydrogen line at 434 nm emitted from the galaxy is measured on Earth to be 650;q z.v+ ora2*y3vch t3a4hm.p4asfo q 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 massiveg.tq wyc7vet7y)* -wm enough) will begin fusing carbon nu*-t)cm7vqwe wty7.ygclei 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 cc+w)bnv1 f;e
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 ofap4d f/k wroo:(v0s+h* +zk wu the universe, s/:+wpv4+ h(dwf*k0ar okozu$\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$