The Milky Way was once thoul*bqiq;0 to5lfca/) ught to be "murky" or "milky" but is now considered to be ; *0to/il5fq lc)baq umade up of point sources. Explain.

A star is in equilibrium when it radiates i ,nutkksw+ 38at its surface all the energy generated at its core. What happens when nwk8+u,k3ts i it begins to generate more energy than it radiates? Less energy? Explain.

Describe a red giant star. List some of iteb7voy+tr)3u 9 *e9lrq w7yyfs properties.

Select a point on the H-R diagram. Mark several directiq:5bj a t/qgjko; va3,el5n( nons away from this point. Now describe the changes that would take place in a star oekjqq :gn (/n5 ,a tlv5jba3;moving in each of these directions.

Does the H-R diagram reveal anything about the core of a ucay,6mmm.9e star?

Why do some stars end up ;.z:9nq+ludwjvm pj- as white dwarfs, and others as neutron stars or black holed .mlwvj ;+-9qzu n:pjs?

  Can we tell, by looking at the population on the H-R diagram, that hot x1ei4mao-q+s ter main-sequence stao+s xeq4i-1amrs have shorter lives? Explain.  ----待选择----yesno 

If you were measuring star parall d849r8u ylfuyh0pcl.axes from the Moon instead of Earth, what corrections would you have to make? What changes would occ 8ul dl8r0.9y4fpuhy cur if you were measuring parallaxes from Mars?

Cepheid variable stars ch bxp-4ep4f o,pange in luminosity with a typical period of several days. The period has been found to h4epo p,fxbp4-ave a definite relationship with the absolute luminosity of the star. How could these stars be used to measure the distance to galaxies?

What is a geodesic? W a7z3 fa98eaighat is its role in General Relativity?

If it were discovered that the redshift of spectral lines of galaxies was dueq:vn yb4t,ai* to something other th va*n4:tiyq ,ban 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 t 3icdf)/gkay/u 9f: ylhe center of the universe? Expladc9 /)l f /kayu:gfi3yin.  ----待选择----yesno 

If you were located in a icr xdopbc (l0f3m90qblh:)2 galaxy near the boundary of our observable universe, would galaxies in the direction of the Milky Way appear tc0(2m9) qbrh fx3d clli o0bp:o be approaching you or receding from you? Explain.

Compare an explosion 9b+s8eemjwi ) on Earth 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? Wh em )iwj9b8es+at type of universe would this correspond to, open or closed?

If nothing, not even light, escapes from a black hole, then how sj2nht brx8c n7/6fsdhts w+ ;/1tje 2can we tell if one wxh+dr2h 16f8b;ej t sj/2st nc7 st/nis there?

  What mass will give a Schwarzschild radius equal to that of the hydrogen wn;qub o kgppm7*z;m 8bzlg- u92as6;atom in itwlm;*97q z;opup8nma -b z2 usgg 6b;ks ground state? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 bill *r6ms kj7z(qfke0/rhion years. Find that time on (Fig. Below). People *0es 67jqmzh(/k kfrrhave lived on Earth on the order of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic microwave background radiationeg55 3-f g;jm* gmkgjy 0irpwo3x6mk/ is. Where does it come from? Why is its tempw g6mj -3*kme 5gf;ik 35yg/jrmo0p gxerature now so low?

Why were atoms, as opposedhd/+am2,qzb 4uz7 lcu to bare nuclei, unable to exist until hundreds of thousal z,muadz/ 7c+4bq2uh nds of years after the Big Bang?

Under what circumstances would the univey iu2emms -1t7xzw+: rv8pg6 urse eventually collapse in on itself?

  Using the definitions of the parsec and the 3 )7 ecq(5jyakxxhhmvr-7kbw 5b:1qi light-year, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.38 seconds of arc. How fa wd cf(;+6ruiqr away is it? d =    ly

  The parallax angle of a star ibc4a);6ku keu s $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its t5n1x9 -favk+s:(lm se 4ozqa)fr 3z sparallax 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 starl7t3ou meg2 4r that is 55 ly away? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away from rw 588ak0gvir us as a second star, will the parallax angle of the farther star be greater or less than that rvag 8irwk8 05of the nearer star? By what factor?

  A star is 35 pc away. How long does it take for its light to r-f 9d 91m0ykihqkzt9 reach us?    years

  We saw earlier (Chapter 14) that thebc 27bnnn* kzx)0 :enl rate energy reaches the Earth from the Sun (the "solar co2n:knbcn )le*7zx0 nbnstant") 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 i)ox(8bbx lf c w..xkm(8b:mbto its brightness from Earth? (Jupiter is 5.2 times farther from the Sun than the8 cli fm8 wx.)m .b(xb:(bxokb Earth.) $\dfrac{l_{\text{Jupiter}}}{l_{\text{Earth}}}$    $ \times 10^{-2}$

  Estimate the angular width that our Gan,1ouys g1 z(tlaxy would subtend if observed from the nearest galaxy to us (Table 33-1).,y ng su1ot1z( 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-lfo uo acp0az ci;/.4s+ i(re if it expands out to the orbit / o+czas0-i(eua cl;ifpo4r . 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 dwarf, it is expectedr z;5f0gk bl.l to be about the size of the Moon. What angulb 0 kg.lzr;l5far 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 equalangnu v**gjb3 k+t4 r+ to the Sun's and whose radius is equal to the Earth's. *ak*4njbgr t++ n uv3gHow 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 massepce0v0; iz3 wgs has a radius of about 11 km. Calculate its averagig v0w;zpe 30ce density and compare to that for a 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 reactions of Eq. 33-q 16ef y8fw*r2qaz8ju2. (The mass of the very unstablezu rf21qj qy 6ae88w*f $^8\text{Be}$ 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-ete jmko/4 7se hnk:il)f9 8vrent 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 bol my+.42a qkabout the same distance from us. Two such starsqa.y 4+komlb 2 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 radius for a star with mass equal to that (a) of ouq dgwp9 bl/s5., hf/de,qd)yx r Su.df9d q,5g peq)b//h ,wlyxsd n is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a*qft+gr(q z12abm*g x typical galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the stm y 4ih+-3pmcurface of a sphere, for which the sum of the ang3 pic+y4mh mt-les is (a) 359º, and (b) 180°.

  What is the maximum sum-of-thevhv 4 i jqh/5llfcl(f8x2 :f*q-angles for a triangle on a sphere?    $^\circ$

  If a galaxy is traveling :4 p3 *yxqc tq.)fkop y)n4pc/(vxlexaway from us at 1.0% of the speed of light, roughly how far away isp4qf)cxp key* :l 3npv. x/c o(qt4)xy it? v =    Mly

  The redshift of a galaxy bz.hti .x5oq58u0ld pl eu.;oindicates 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 near the observableki )-fxxhn9 )x "edge" oxk9)x hi-n) xff the universe, say 12 billion light-years away. v =    c

  Estimate the observed wavelength for the 656-nm li/wq -kidlpml40 tu:v9ne in the Balmer series of hydrogen in the spectrum of/ldtw4:mq p0 -ku i9lv 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, an2kif w4brx ( j (2fgxpdncz;,5q1 p,sk6q stm)d its distance from us, if the wavelength for the hydrw,)x6k1nt2qzg4m(ijc qs (x,s p ;b5pf2rdk f ogen 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 a galaxy jc8/6v tn3z avwith $z = 0.60$? v =    c

  What would be the redshift p4*asu7, fx yzcarameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that /hcc 0pj0voh8 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 blackbody3o h78wjrrz96 0hh3c k lfgzrh6 ime3) radiation distribution at 2zflrm ih9hg63r)jch7krzwhe0 833 6o.7 K using Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of the uncgc;q(z6ez-z. ipdtp7 n n8d 7iverse 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 betweengww-1j/54mwg l kr d-j galaxies) at any one moment is believed to have been inversely proportional to the absolute temperature. Estimate the size of the universe, compared to today4 m w1rgdjl jww5g--/k, 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 bnf p8 suddev2)-g, +ygbrux,+elow the threshold temperature for proudfp)e2, v8gxrbsgd+uyn-+ ,ducing
(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 tb eb o;d) 4jmyz.g.9zlhree changes represented by the three arrows, A, B, and C, in the H-R diagram of Fig. 33-28. For ea; yz.jbbe m4 gz9d.lo)ch case, describe the changes in temperature, luminosity, and size.

  Assume that the nearest stars to us have an absolute luminosity a*9cq0 9iciv *x nrxp;tbout the same as the Sun's 9nv x;*ii9*c0p tcxrq. 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 angular momentum to1br ry5pwyl97 estimate the angular velocity of a neutron star which has collapsed to a9wyrlpb 7r5 1y 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 change whigf(b6 o420g+g (ffhuesex1 cen the star in Problem 56 collapses to a neutron starfug isfexg f4(1e hcb(o206g+? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believed to be a neutron star of mp,oy wf 2ncv-n j:0dm *j0xl+rass 1.5 times that of the Sun, with diameter 20 km, is observed to have a r,: ypoxdwr00c j n2*jnlm+vf-otation 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 Gal3k37hc*xl8 q lsgd7tyt 5 )ublaxy 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 critical density togzl;eg1m,gdp5s3 f*;h qaxt3 close the universe. Assume the neutrino densqtz3gh 5,;3ml esfpagx* ;gd1ity 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 gcj6, phgs z/( bxix6 l9mj(k/nm and 400 nm, respectively, both lie on the main sequence. Use Wien's law, the Stefan-Boltzmann equation, and the H-R diagrahx xb( g//6jcg jl(,zpk9s i6mm (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 10qi4. ayfmw-dhz6u2,k fv .jc:0 parsecs. What is our minimum angular resolution (in degrees), based on this informatfqy,dm4zw.-h i6vf:u2ca.k jion? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Bal. m 0 cz.4uuc9glovk1dmer lines from singly ionized helium in a distant star happen to ove0.c.zcgo u lmvu4k91drlap 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 that corresponds to 1.8-Teufq g(p)k-;6oq g4rw;fsiro/ V collisions at the Fermilab collider? To what era in cosmological history does this correspou oiqo kq/r( 64f-wr;;gfpgs)nd? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation of gas around what might be a sbg )k9tl:an u zh-(p(eupermassive black hole of about 2 billion solar masses at the center of a galaxy. If the rad:nt k(pb u)lezag9 (-hius 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 line21uhr zl yk(2b at 434 nm emitted fromh2y(b u1kr zl2 the galaxy 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 massive enough) will beginva el p*f(0sev8uc1 r q7b.;mq fusing carbon nuclei to form, for example, magnesium: e;v * . u8bqlv70fr (scmaq1pe
$^12\text{C} + ^12\text{C} \to ^{24}\text{Mg} + \gamma$.
(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 reactio98ymkbps r-0//wqnmriy/41lwa9 a dln
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 mnn r6dx:f8mqlr7 5lg79aj 3s if its density equaled the critical density of the un6853 qnda: mglfsxn rlj9mr77iverse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$