The Milky Way was once thought to be "murky" or "milky" but is9fhox t fq) h o531adbe25uo*d now considered to be made up of point soura*3 bqt)ou9ef 21dfoh xodh55ces. Explain.

A star is in equilibrium when it radiates at its suq( g .ge5*dqtnrface all the energy generated at its core. What happens when it begins to generate more energy than it radiate .*dgq( geq5nts? Less energy? Explain.

Describe a red giant star. List some of its propert tm1)vhr5h1nn ies.

Select a point on the H-R diagram. Manel27xf0 spg *rk several directions away from this point. Now describe the chan2lg*s0 x7enpf ges that would take place in a star moving in each of these directions.

Does the H-R diagram reveal anything about the core of emvtw+ yt .q)l/4dg)m a star?

Why do some stars end up as white dwarfs, and others as neutron stars or blacpqrc 7v)*d fl3ayuk o fu0i:+8k holesioy *df3fvq7 0ul8ra+p):uck?

  Can we tell, by looking at the population on the H-R dia epe9opnq+/ /hgram, that hotter main-sequence stars have shorter lnph /qp/9ee o+ives? Explain.  ----待选择----yesno 

If you were measuring s 8a/83omq;jdz4p aku star parallaxes from the Moon instead of Earth, what corrections would you have to make? What changes would occur3u 8jq48a;dpz /moaks if you were measuring parallaxes from Mars?

Cepheid variable stars change in luminosity with a typical period o)9j8a8q wmhntf several days. The period has been found tnj9)q 8htma8w o have 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? What is its b . za3lmzx9p(t6si,f role in General Relativity?

If it were discovered that the redshifb1h7/ -(tptjma3 amap c5h+ xdt of spectral lines of galaxies was due to something other than expansion, how might our view of the universe ct- d3ht+cmab ( 7p1a/axm phj5hange? Would there be conflicting evidence? Discuss.

  All galaxies appear to be moving away from us. Are we therw-)xur *bydtf 07s)rm efore at the center of t*)yf0 tu d7-rswrbmx)he universe? Explain.  ----待选择----yesno 

If you were located in a galaxy near ) 4s*:+abz ufqf5iqgh6dsg 6zthe boundary of our observable universe, would galaxies in the direction of the M4 +q)6df6sbzfqs*z ia u5:h ggilky Way appear to be approaching you or receding from you? Explain.

Compare an explosion orblp 3 ot8cg:(2(r11y hdtbffn Earth to the Big Bang. Consider such questions as: Would the dht rb1(ytpbor2f l d 1(3cg:f8ebris 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, escapes from a black hole, t(bislz ko270 ahen how can we tell if one is th iksz02bao7l (ere?

  What mass will give a Schwarzschild radius equal to that of the hydrogk7/9nef roqfi )70h+g5wx ixtijp2n- en atom in its ground s)o9xifr 5f0ne htkix7n /2wpqg+ j i7-tate? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion years. Fi,f+izlc)*cb- hvpb 1+aos/f ind that time on (Fig. Below). People have lived on Earth on the order of a million years. Where is that on (Fig. Below)? f ,i) olic+/-vzcsa hp*fb1b+

Explain what the 2.7-K cosmic microwave background radiation isboy6)+adv e q 73nxj i7mk66li. Where does it come qboii)3+6d eknv 6jm 76ya lx7from? Why is its temperature now so low?

Why were atoms, as opposed to ba z0et3qfg-*sn re nuclei, unable to exist until hundreds of thousands of years after tht -s*q0gfnze3 e Big Bang?

Under what circumstances would the universe eventually collkop)we6dx 1p 4t/api4f 5ay.capse in on itself?

  Using the definitions of the paat d,i.ckw24 : io8tgwrsec and the light-year, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.38 seconds opb3)qg4th2 m,z nx2oof arc. How far away is it? d =    ly

  The parallax angle of a star fqvc- y)i/6d/ )xv lwr6vlo/r is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its parallax angl rmrd7c21g 4i hv.:eble?
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 thtjzl4/ 0tv g,3f /gw0 klw.nnwat is 55 ly away? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away from 6o- (wayzsp*dus as a second star, will the parallax angle of the farther star be greater or less than that of the neards-op( 6ayw*zer star? By what factor?

  A star is 35 pc away. How long does it ta3g 2(-b iqhrw4q6ovxeuzsb 5 98dr fy0ke for its light to reach us?    years

  We saw earlier (Chapter 14) that the rate energy reaches brb2fv qi k)n b2;2u9lthe Earth from the Sun (the "solar con2;b9ibqr2l n vku2f)bstant") 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 ycp eufnc,9 *:f,mar ;Sun as seen from Jupiter as compared to its brightness from Earth? (Jupiter is 5.2 times fartp;ec cma,y u9* f:nf,rher 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 ifx 6:wtywv -oo6 ..ump5xqj ;gb observed from the nearest galaxy to us (Table 33-1). 6poy6bq.ovx:w;. -g 5xw umjt 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 idu:ue-d 8 h+uxt expands out to thuex :uud -8dh+e orbit 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 whithopv 2 eyweag)j p,nrwh4vt*98g7 , u/e dwarf, it is expected to be about the size of the Mgu,4h*7rp/yw8othw9 ,)v g ve2 apne joon. What angular width will it subtend from the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarov7djly2e n:7 f whose mass is equal to the Sun's and whose radius is equal to the Earth's. How many t7ej:ovdn7 2lyimes 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 has a radius of abou-+ngqu8ttvt 8w .oq 5h v/c1lht 11 km. Calculate its average density and compare to that for a white dwarf (Problem 13) and to that of nuclear mahtw5ucnl/8h8 t1.vvo q-+q g ttter.
$\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 1*mre)nqp;wi8)nrch :8 dxlb He burning reactions of Eq. 33-2. (The mass of the ver8 *8xrmhw1lncned)i:; )p rq by 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 t9uz py qo1o,kt4zy lr2.4 no5ohe same apparent 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 about the same dist6gqef1 ysr. c,(j2wf onym;,xance from us. Two such stars have spectra that peaw(gqfoejs.n6; yy , fcx 2rm1,k 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 k9: oqk0rkk,c6pzy, tradius for a star with mass equal to that (a) of our Sunky,k ,z9k6 0:cptqrko is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radiuskwd56 hq1gt/vg0kis : for a typical galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a sph3ez,-h1zcm+ jwdef,xere, for which the sum of the angles is (a) 359º,3edwjh1+m,, cxfze- z and (b) 180°.

  What is the maximum sum-of-the-angles for a t41tynqz+d)jk -1 ch7pd1md t hr3) mukriangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0%l2;1ejd9tw9x d2 vg(d)w im eb of the speed of light, roughly how far awa t(2x d)le9wi jd;1wbmg2v9de y is it? v =    Mly

  The redshift of a galaxy indicates a velocity of / 8 5kdeuwb(+dtyy0h+a 1dd7p lujs*nvi 5)xi$3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galbxne +4uesj3b 09y: ouaxy (relative to us) that is near the observable "edge" of the universe, say 12 billis:3eo0 byuj94bu +e xnon light-years away. v =    c

  Estimate the observed wavelength for the 656-nm line in thk ni.l (r0t-fhe Balmer series of hydrogen in the spectr0fh.lrnk (- itum 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 galax. )42fgsk zdcsumi;2xy, and its distance from us, if the wavelength for the hydrogen line at 434 nm is measured on Earth as being 612)czsm2kgdx s ;4.fu i0 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 gaqrhj ;o5 m6yj.laxy with $z = 0.60$? v =    c

  What would be the redshift padk r3dg 7hup12rameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the q+sew/:9x2zir/e pap /sq j+dDoppler 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 p85j ny-n vygf:eak of the blackbody radiation distribution at 2.7 K usingjy5vnf8-y gn: Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for ckgbhn :: kg5 kttsgh2.sh /-7ylosure 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 unive+* f+et8p;hb,m hpmrt0 qu 5ghrse (the average distance between galaxies) at any one moment is believed to have been inversely proportional to the absolute temperature. Estimate the size of the universe, compared to todt+r qmbp *hg0f u,h;8m5t+e phay, 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 universe0xu e nvb0)4hy cooled below the threshold temperature 0y0x unvehb4)for 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 sdg(i6rt4*7pa9zl 11+x(d bohc qtllytars could undergo the three changes represented by the throq l(ig(1c l1ha 7t*9ytrz6bd 4dlxp+ee 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 abi,-tgjsqs jg3v5/f- psp 2m-dsolute luminosity about the same as the Sun's. Thes s -m/j-t5dvgsg ,3p2j-qifpir 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 anjoo6h,;r7p4bb ,kbar momentum to estimate the angular velocity of a neutrobba6k ,n;hbr,pjo 7o4n 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 ener)-f1f 1hdzoivgy change when the star in Problemfivh1 ozd-1)f 56 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 of mass 1.5 timn-0gk+gj1x18jy2g1pkydps r es that of the Sun,-ygjs81rgy1 0 x j+1 dpp2gnkk with diameter 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 galad 8t,5n eyp,u(-0d3 ejesekvpy0*g vaxy to our Galaxy 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 providevc p5 z10 a)ttob5e*xqk t5n0t the critical density to close the universe. A a010zb*vt 5epotk5nq )cttx5ssume 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 and 400 nm, respectively, bc2f t nboq6+ljtkkq9 .k 532bloth lie on the main sequence. Use Wietnjb2bk 9o3qtcl+2.lk5k f q 6n's law, the Stefan-Boltzmann 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 paraljro( oit 18vhulqo2a 5..m5dkw pt apb; t.1s)lax at 100 parsecs. What is our minimum angular rhsjlpv;5 kt8.t b 1ioqawor(d) oap.2t 1. 5muesolution (in degrees), based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines frwd*2mfty-d-.j e mifwy 9z,n:p vn 0+rom singly ionized helium in a distant star happen to overlap with the Balmer lines from hydrogen (Fig. 27-22) in2tm*ny wy-+zd0df wi.:r, pemf v-jn9 the Sun. How fast is the star receding from us? v =    C

  What is the temperature that corresponds to 1.8-TeV collisiykjnok3zm 1;8uwdu) *98ug rd ons at the Fermilab collider? To what era in cosmological history does this correspond?u1)k*n;koud z d889rwyu 3g mj [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation of gas around what might be a se-3n g t-:ijk.c fid/rupermassive black hole of about d:i. 3c irgn-fkj/t e-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 Earth. T q6dte2f i7ul5he "blue" hydrogen line at 434 nm emitted from the galaxy is measure fel572uiqd6 td 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 d; 5p94r+ ffztq hyz)ozxx g7/(if massive enough) will begin fusing cfrd ;t zz hx 5ofgzq4)x9/p7y+arbon 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 /fkj76zao fq3g i/-f i
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 equaleu6 tb2gcgie255d h 3dmd the critical density of the universe,i dmt 23h u6edbgc25g5 $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$