The Milky Way was once thought to be "murky" or "milky" but is now consideredmqpqx dxl l6t ;qi.)7u:d+j (t to be mal;. p6x7u+ q q jdltd)qx:mi(tde up of point sources. Explain.

A star is in equilibrium when it radiates at its surface afg -/qic0kuf4dj +b8-,qyim dll the energy generated at its core.f8-0 qfyd+c d -ijkbugi4/m,q What happens when it begins to generate more energy than it radiates? Less energy? Explain.

Describe a red giant st r)4rs6pdwlfr.u 8j z)ar. List some of its properties.

Select a point on the H-R di ;cn aov -kba8jtg)ew30aw4fmw 21o6r agram. Mark several directions away from this point. Now describe the changes that wo8mj1n wa0-oev6tawfc g o a3kwr4;2b)uld take place in a star moving in each of these directions.

Does the H-R diagram reveal anything about the cc r5mocv2;+wu bg2- xwore of a star?

Why do some stars end up as white dwarf3sx6iklg ng9bs ie9(kugtq5)uy -*8cs, and others as neutron stars or black hol9le qb9)(* 6g t ngxkyusu8kg- cs35iies?

  Can we tell, by looking at the population on the H-R diagram, t aq+9x5 nin0g5tik0eh hat hotter main-sequence stars have shorter lives? g05khn xqai5i90 et n+Explain.  ----待选择----yesno 

If you were measuring star parallaxes frou ik6rrsr(/s6m the Moon instead of Earth, what corrections would you have to make? What changes would occur if you were measuring parallaxes from Mrr(s 6r6u/ksi ars?

Cepheid variable stars change in luminosity with a typical period of severkyuh1h5 ljrz 1;o9m: sal days. The period has been found to have a definite rela5u1j1ls k: hz; 9rhmoytionship 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 fw7jv, 3dlg .7f2ih4ca 7 vvaorole in General Relativity?

If it were discovered that the redshift of spectrac /*.rcqd6yzjl lines of galaxies was due to something other than expansion, how might our view of the universe change? Would there be conflicc.z/qr*dcj y 6ting evidence? Discuss.

  All galaxies appear to be moving away from us. Are we therefore at the centee s6g*, 1bd sxq)x, 61f)hlpdetbi)onr of the univne6qe)*g d)1p xfh d t16bsb ,ls,i)xoerse? Explain.  ----待选择----yesno 

If you were located in a galaxy near the boundary of our observab lu0pn*1o5- lzcti+vkle universe, would galaxies in the direction of the Mil *ku+n l5-01tiploczvky Way appear to be approaching you or receding from you? Explain.

Compare an explosion on Earth to the Big Bang. Consider o2e p l)*cc:wasuch 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? What type of universe would this correspond to, open or closop)al 2*wcec :ed?

If nothing, not even light, ersp64pu /w6s zwxa(7j scapes from a black hole, then how can we tell if one is there? (x76u awpw6r pssj/z4

  What mass will give a Schwarzschild radius equal to that of thap h8-zj/8nc 6(ojsaqucl r7i( b;b;xe hydrogen atom in its ground state? M = xa(88rh7cpib;n6c jlaj-o( sz / u;qb    $ \times 10^{16}\ \text{kg}$

The Earth's age is oc7j5pp;j3c jx1z4 nsyften given as about 4 billion years. Find that time on (Fig. Below). People have lived on Earth on the 5jcxp 1csz3jyj ;7 p4norder of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K ksp2m/ytn, (6ig4wokcosmic microwave background radiation is. Where does it come from? Wmp (/,kw 4tn ygks62iohy is its temperature now so low?

Why were atoms, as opposed to bare nuclei, unable to exist until hundr r7;as5 )h/mm(ovdquppno. (keds of thousands of yed) /(nm k quh;5or .p(oasmv7pars after the Big Bang?

Under what circumstances would the nu*60kze tjm/universe eventually collapse in on itself?

  Using the definitions of thegwh bub;wc7n: r7+ 1kn parsec and the 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 far away is it? 3s;c vi (k,t- jm-b7 *mhikcbud =    ly

  The parallax angle of a stayygq ptmkf 2bb)f (;d,rs h76,l5pm 5cr is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. Whkn501m-j3 om(isxjdxzte6 9 mat is its parallax 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 star that3 jxy6 i;v8jsmwecy;- is 55 ly away? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far tw4fp -dy 4(8xle,jitaway from us as a second star, will the parallax angle of the farther star be greater t 4w -txjyf4pl,id8(eor less than that of the nearer star? By what factor?

  A star is 35 pc away. How lon0hckg -/j1ta dg does it take for its light to reach us?    years

  We saw earlier (Chapter 14) that the rate energy reaches the Earth from the Sunh, v;n6gr c:50zj,ol-szi3hj) r tgvr (the i -;jhh 06zvoj 3zg,:5 crsnrtl,) grv"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 xo xrf+4cvcd)0)5un wSun as seen from Jupiter as compared to its brightness from Earth? (Jupiter is 5.)xcovd+ u4x r c5w0)nf2 times farther from the Sun than the Earth.) $\dfrac{l_{\text{Jupiter}}}{l_{\text{Earth}}}$    $ \times 10^{-2}$

  Estimate the angular width that our kxu 463a2ika/ 2g. umsik zyp+Galaxy would subtend if observed from the neux/kpy32 .a z4ka6i2mku s+i garest 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 s azc ,*etla 89m2myhlp(z f:)if it expands out tf(:8pz,9y e2 l) tzaclm hams*o the 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 white dwarf, it is sl )uo7-bwl6v expected to be about the size of the Moon. What angular width will it subtend from the pl w 7v)sub-6olresent distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whose mass is equal to thez rdw,br4fuojqt9qr/.gv (7 z*(w zp 8 Sun's and whose r9.q b8(7 vzp(dorj fgrr *utq zz,w/4wadius is equal to the 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 is 1.5 solar masses has a radius of about 11 km. Calc1qzzbw3h,) +v 3jhparulate its average density and compare to that for a white jhq)p+w3z,bv ra1h3 zdwarf (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 burnb6* nrq gy(,oxing reactions of Eq. 33-2. (The mass of the v,n br oyqgx(6*ery 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 *8)jtn /j3duvr dbl 24 b.pfvuthe 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 clustes,m bl0i4 kq/n+76m dfgkan gq 9+g)arr are assumed to be about the same distance from us. Two such stars h+,dga+q r7mn)fks kqggbi l90n4/ a6mave 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 mas z-xf (rq52fchs equal to that (a) of ourzrf (xh25f q-c Sun is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typical galaxy 9*u( ;t0jlhjd,vaboss(pa.t v.bi0j (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on ;bkuej 5ro,,othe surface of a sphere, for which the sum of the angles is (a) 359º, and (b) 15 oj,o,rb;kue80°.

  What is the maximum su/u5ke1cvcjix; s-k)b m-of-the-angles for a triangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at qdvxc4lm 92hj ,fmz3/ 1.0% of the speed of light, roughly how far away is f 9mm2vjh34l/xqzd,cit? v =    Mly

  The redshift of a gal :)8o i+vbyaveaxy indicates a velocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (relative to us) tha-4 r*dou+vgn kt is near the observable "edge" of the universe, say 12 billion light-yeu*r+ d gk4no-vars away. v =    c

  Estimate the observed wavelength for the 656-nm lin0x )h*4lg x78n xtdgpy6a4a ywe in the Balmer series of hydrogen in the spectrum of a galaxyx6 *47px0alyahgytx)g84dwn 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 galar j (e-x0wqoarsu tdivv78+,/xy, and its distance from us, if the wavelength for the hydrog+ju-8/ (t,ov xqar7ev0iwd sr en 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 withlb1ay1t e+h6 yk9nb k,p8 mh*g $z = 0.60$? v =    c

  What would be the redsh551d hrw wu )48lb3r2 k nhiw:1icedzzift parameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Dopplg r3*fltk.96iljwrs+8-j4t0 sy d au fer 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 ott7f m+vo lp;(f the blackbody radiation distribution at 2.7 K f7+tp (mo tvl;using Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of the un/xc8cqkl1exl(vk 9 rd0kz n39iverse 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 (theu ;gg0fkrd km8rh9k,fb0/y1m average distance between galaxies) at any one moment is believed to have been inversely proportional to the absofmr8g /kgy; fbdru0 k 1hk90,mlute 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 the universe cooled below the thresho x xljh:acxz2 (6n*ff/ld temperature forxjf/*x:2l6ha fcx( n z 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 starkjti5s;bl ; z6 it04cgs could undergo the three changes represented by the three arrows, A, B, and C, in the H-R diagram ofl0z6tic5s k;j4i;t gb Fig. 33-28. For each case, describe the changes in temperature, luminosity, and size.

  Assume that the nearest stars to us have an absolute lumi 9p iz4cbyuomf*t) 52xnosity about the same as the Sun's. Their appare ot)5*pmycifb z9 4x2unt 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 mo1, 028 neub/gly t 88ys9pdgbepvk lg-mentum to estimate the angular velocity of a neutron star which has collapsed to a diameter of 20 km,gll128 9y-08s,geb/ gnt y8ebd vkpup 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 6f7 x-rumy,du*2bcsfs.sme -h9 5 puu rotational kinetic energy change when the star in Problem 5 usfehdrm57-uu*b u.9spsf, ym c x62-6 collapses to a neutron star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believeissh*r up/.2b m. ofe0d to be a neutron star of mass 1.5 times that of the Sun, with diameter 20 km, is observed to have2.mr b.ispos*u0 e/hf 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 fs+l,y z1s 1s4)+o2 mkmgrrcwis 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 mas8ser*tnenf./rbw 0 z+ s (in eV) would provide the critical density to close the universe. Assume the neutrino densifwn8e .er+*t/b r0nzsty 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 sbt3kh*:jk)jd z .2 xx600 nm and 400 nm, respectively, both lie on the main sequence. h )3*.bjkxszxk2j t:dUse Wien'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 measurev( jd -;dgy kez l7mz.70/wo,fyb2et q distances with parallax at 100 parsecs. What is our minimum angular resolution (in degrees), ba02lzdmz 7/;j(go7d- y kwfbe,.t yveqsed on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from singly ionized helium *yp (p+k l4v)s+ho0w.xvk cloin a distant star happen to overlap with(lc psk*o+p0 wv4vy+.xlhko ) 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-TeV collisions at the Foyr ap2*qbf0-fgsc o*qfk,2ft v *1 y*ermilab c y*ff*2of qt, a-sr*y*bvqo0 c1p g2fkollider? To what era in cosmological history does this correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation of gas around what might be a su1kgn fpt 5* fa--/2)vwbf 2rwlxv;p nepermassive black hole of about 2 billion sola2;n5f-p*nbp2kfxgv-wt/f )l e wr a1vr 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 1rpfrf l80x/ dfrom Earth. The "blue" hydrogen line at 434 nm emitted from the galapfrld8 f/1 0rxxy 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) wg;v6u0pode- )bqm u xd)ga8v( ill begin fusing carbon nuclei to form, for d 8 g-b) ouevv6p0u;(amx qd)gexample, 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 gty7l kb3:e s/:z w9cv
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 oofpz2v1 q*t3)q kvsa3f the una )qqkv*233tvfszpo1 iverse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$