The Milky Way was once thought to bevl k9m d58o5/jrjrs5q "murky" or "milky" but is now considered to be made up of poin k9 lq5m58vos/djr5rjt sources. Explain.

A star is in equilibrium when it radiates at its suz1ea1e1 uigahp74 mg() a7fpzrface all the energy generated at its core. What happens when pmzga4gf1a (a1 ip7z)u71e ehit begins to generate more energy than it radiates? Less energy? Explain.

Describe a red giant starkui;y gbu/-71jp lq+uee7rg ) . List some of its properties.

Select a point on tho+ 44q8vhkhp58wwb mwe H-R diagram. Mark several directions away from this point. o4548+qvhwwk h8wpbmNow describe the changes that would take place in a star moving in each of these directions.

Does the H-R diagram reveal anything aboazr y2 l9smao5:g.i /dut the core of a star?

Why do some stars end up as white dwarfs, and others tr w- w3 9yjn:,+px6wqk, hpzpas neutron stars or black holes?t9, w,+kh:n6ywxzj w3- qrpp p

  Can we tell, by looking at the population on the H-R diagram, t9yokl:i hd co /njn-w6+9z of3zio7)s hat hotter main-sequence stars have shorter lives? Explain. h/ 96 3wy:-fn7o 9ozzoli)cikndsoj + ----待选择----yesno 

If you were measuring star parallaxes from the Moon instead of t a fmhbl,d0po0g;zji/h.3 v:(f0ecuEarth, what corrections would yof0uzmp 0,(/v bcf;lda e 03: hjtgiho.u have to make? What changes would occur if you were measuring parallaxes from Mars?

Cepheid variable stars change in luminosity with a typical per 0xu-4kyau aplvj,j3h jn; :;eiod 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 measure the distance;xnv :leh j;ukua03y-j 4,ja p to galaxies?

What is a geodesic? What is itvg (s* m7zug wt;2o/fhs role in General Relativity?

If it were discovered that the redshift of spect) 99pc ko7z1/bed eiontwv,e.ral lines of galaxies was due to something other than expansion, how migzw9 o97ed1 n)boeei,ckt /vp.ht our view of the universe change? Would there be conflicting evidence? Discuss.

  All galaxies appear to be moving away5j+72tx*tf6sk kusg j2ht1nf from us. Are we therefore at the center of the univers2t*sf2 xks jtjk ufng 1h6t5+7e? Explain.  ----待选择----yesno 

If you were located in a galaxy near the6x) y w5o,i7 rec,pi5dhd883rmr tdlk boundary of our observable universe, would galaxies in the direction of the Milky Way appear to be approaching you or r8trcpl,ed8ir5d) owyi7 63,dh5xk m receding from you? Explain.

Compare an explosion on Earth to the Big Bang. Consid:va+v4ca4crm8/hb b w er such questions as: Would thh44avb+/mcb8av :wr ce 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 would this correspond to, open or closed?

If nothing, not even light, 6,8hx ti*1h flpa5duu escapes from a black hole, then how can we tell if one isa6x li1fp,dth 8u5u*h there?

  What mass will give a Schwarzschild radius equal to that of the hydrogtlja 3u-g3:xpncth1co ,. fi: en atom in its ground state? ttng-3:puj ccxf1., ao 3l:h iM =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often gixd5wtn8ykg8m + 3ejy;ven as about 4 billion years. Find that time on (Fig. Below). People have liv3ydymj5w k+tx8ge; 8ned on Earth on the order of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic microwave background radiatei43js/p/dh85jrhae ion is. Where does it come frh3j/ jpsh/rd4 8ia 5eeom? Why is its temperature now so low?

Why were atoms, as opposed to bare nuclei, unable to exisw8z8 uz,q0+pxe 5ap dct until hundreds of thousands of years after the B8w zedc +pxq0pu8a,5zig Bang?

Under what circumstances would the universe eventually collapse7ex0d2 h35 j1i6jkcvg0 fntwy in on itself?

  Using the definitions of the parsec and theyqgsnn;h6on 1u.80o a light-year, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.38 semrk-*bap:alk,p 98dz8uhm8v conds of arc. How far away is it? d =    ly

  The parallax angle of a sta4htwcv6v -u9 ur is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its parallax angle?bxr* 4v asjk.wpw,x(wdyz1 x8 c 5o.e4
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 that is 55 wkcp60q1m l 7 +pwweg3ly away? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away from us as a second sdtiexac iws/ p470*-b.or3 gctar, will the parallax angle of the farther star be greater or less than that of the nearer star? Bera/o3t s.ibdc47* w0- xcigp y what factor?

  A star is 35 pc away. How (fx6cwa)/ c ewlong does it take for its light to reach us?    years

  We saw earlier (Chaptep0y4 9y.k thp nu42frar 14) that the rate energy reaches the Earth from the Sun (y40p2pfta yr4hnk9. uthe "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 kuig,:.ov/ * zo1fqbl as compared to its brightness from Earth? (Jupiter is 5b oo,v.*: i/gu 1zkflq.2 times farther 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 observw cmdibf7kglx. + . kz3srtz *k964g:ved from the nearest galaxy to us (Table 33-1). Compare to the i g7gs*x vm3k fbwrkt+:dz. l 4z.k69cangular width of the Moon from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, what will be its average density .ag t 5slqkzz*5rtr+d*5 h4drs)rt u) if it expands out to the orbit of Ear*a)rqt5lks+ rdtzz 4* r u5d5gts .)rhth ($1.5 \times 10^{11}\ \text{m}$ from the Sun)? $\rho = $    $ \times 10^{-4}\ \text{kg/m}^3$

  When our Sun becomes a whs5d7z;vhmq 6xpsx 3ev4qp/2 u ite dwarf, it is expected to be about the size of the Moon. What angular ;q6s4dsp/zu v3p7q x5mehvx 2width will it subtend from the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a pbtf0 tgh80u5bm 5qo,white dwarf whose mass is equal to the Sun's and whose radius is equal to tht 5,hu0fb 8mg0ob ptq5e 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 (gt-c vsm eu p)*q*u+ (cct6xiis 1.5 solar masses has a radius of about 11 km. Calculate its average density and compare to that for a white dwarf (Problem 13) and to that of nuclear matt)vx*6( qgti(ptec +ucs c*m -uer.
$\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 rk;o5 e q/iqz9(*vfkubeactions of Eq. 33-2. (The mass of the very uns 9qkvqi zo/ ;u(bek*f5table $^8\text{Be}$ 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 apparent brighf 4zyh(: 7jbf uyj;;dttness $l$ 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 distance s jl,-xx)b9nqbgzy( 7from us. Two such stars havxsbjyx,-qg)(z bn l 97e 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) of o: czuam9x q.3zi;(a2 :.rmgs5c uhnc vur Srzx3i2gsv.ahq( u c mmzcn .ac5::u9;un is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typicrogn.uo nyf-318olk4 - t 7atral galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a sphere, forwz9h xh9fvp p:8zv6r2 which the sum of the angles is (a) 359º, and (b) 18vvp z89fh p6hwr:x2z90°.

  What is the maximum sum-of-the-angles for a triangle on a dpy1 0ippb :9x/27 : soodicmisphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the speed of light, roughly zbq iu159fcv(8fgp:ohow far aq8:5bfoiufpvg1z9c ( way is it? v =    Mly

  The redshift of a galaxy indi f1 cvwagpa ;,/34ag, r(she4qarn1eycates a velocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galap.-c3bkep nb1 xy (relative to us) that is near the observable "edge" of the universe, say 12 billion light-. cpebbk-p13nyears away. v =    c

  Estimate the observed wavelength for the 656-nm line in the Balmer series of hpzw 2w +pd-7lcydrogen in the s wzl72dw pp-c+pectrum 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 distan .l.3 .bgvjdc) kej,,zhbwu*hce from us, if the wavelength for the hydroh, *,.vce.bh jgl.du)bzj 3kwgen 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 i cbseno9f2cs i36ze 3 nb:,/f9ju)bsa galaxy with $z = 0.60$? v =    c

  What would be the redshift parama ditwscsr/b1; ,v7e-o3,u wseter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Doppler s 7 lw xrb1qa2g5l p8zhxb y0m;*tfll-8hift 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 distrzd,;, t73rg f;mfzob ribution at 2.7 K using W;dtzz7mofgb,; ,3 rf rien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of thp..2nyl2ms od e 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 averageg j12o .kxv a:0 02thid32shus;tp kon distance between galaxies) at any one moment is believed to have been inversely proportional to the abso03vok.x0t to2i1 ;:nksg2 jphs ah ud2lute 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 th9p qk53)f4ty cg-lm ove universe cooled below the threshold temperature 4p o5yf93tqlv-k )gcmfor 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 stzxom9o tc5 ,(0rk5(+dn axycbars could undergo the three changes represented by the three arrows, A, B, and C, in the H-mnodczyc(o,5xx(b0r9t+5 ak 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 sag+v *(yaq z6 zik+by3ime as the Sun's. Their apparent brightness, hoiz( *b+ zqg3a6vy ky+iwever, 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 eufrp2o*z.m m-stimate the angular velocity of a neutron oz.u-mmpr*2f star which 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 the rotational kinetic energy chanx r( bx/-kwa8bc ew1t3ge when the star in Problem 56bakw x tc-/w8b1(rx 3e collapses to a neutron star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believed to be a neutron star r q9u +z+6rlrlof mass 1.5 times that of the Sun, with diul+6rr9+ rzlqameter 20 km, 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 ifsd;ap:yg;g68o p hiq,u (1z ts 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 critical density toi )8y* qd+vnnn close the universe. Assume the neutrino density is, like photons, abnnv*8yn) i qd+out $10^9$ 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 n-2 ifu0dolf;/ g/eiltm, respectively, both lie on the main sequence. Use Wien's law, the Stefan-Bolof-gi/0u2i/fdl lt;etzmann equation, and the H-R diagram (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 at 10, bo(vj;wlg.e/ apb0s 0 parsecs. What is our minimum angular resolution (in degrees), based on this0bo,lw ;.(/jegbasvp information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from singly ionized helium 7ycx*7ew*bt oin a distant star happen to overlap with the Balmer lines from hydrogen (Fig. 27-22) in the Sun. How fast is the star receding from us? v =teyow7 7cxb **    C

  What is the temperature that corresponds to 1.8-TeV collisions at the Ferm yq vd .-mxgss2q.;3cqilab collider? To what era in cosmological history does this corr3qyx- . cmq2 dg;sq.svespond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured x8ciy9 )m.y pdd3cox/the rotation of gas around what might be a supermassive black hole of about 2 billion solar masses at the center of a galaxy. If )cdmxpid3x yc .y9o 8/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 linenm-8nm8wprn g.ex ;/m at 434 nm emitted from the galax8;- n.mgx wnrp8/ mnemy 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 evolution, a star (if m jzz7,-vvvzq /assive enough) will begin fusing carbon nuclei tv/ -zvzvzj,7qo 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 jxp 09 n1yhu- 0bzsr79tjg+zh
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 itss)prc1nop-8jp)7l hx /g x pq; density equaled the critical density of the un)pr nh81o- lsxq;j/ ) gpcxp7piverse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$