The Milky Way was once thought togt ; wd0.db/vrbh3/ ke be "murky" or "milky" but is now considered to be made up of point sourcesdk/e.rb;d wbvt/3 hg0. Explain.

A star is in equilibrium when it radiates at its surfacenu7:rpm7*j:cn5s*4a;m/trki xj b/uzc bkg 9 all the energy generated at its core. What happe*7c: nujmjr9txp7nbkbi4k*r //c :a;5 ug mszns when it begins to generate more energy than it radiates? Less energy? Explain.

Describe a red giant star. List some of its propery oka/t*k p-wwf8u1uyz9i 1d0ties.

Select a point on the H-R diagram. Mark several directions away from this point*rny ktxe cd*c 8;poq-y.o3xuls 2 x5(. Now describe the changes that would take place in a star moving in each of these directions.tyc.s5*ucl dxx x;(no2 oq * rk8-yep3

Does the H-R diagram reveal anything about the core of a sm635 mvtga ri7gxchc ;.*ee+vtar?

Why do some stars end up as white dwarfs, and oth2c fkx ,e((/ugzlhelr *56q v q*rnoj4ers as neutron stars or black holes*k un*jqer6h f/v 4rq (z5xl2,leg (oc?

  Can we tell, by looking at the population on the H-R diagram, that hotter ;vft.-5suelde mn 9)mn,dxn. main-sequence stars have shorter livm.x nt9 dn-u)vl,fm;.5ene sdes? Explain.  ----待选择----yesno 

If you were measuring star paraltl2j rx5j6dwd sis,gg(+6ma .laxes from the Moon instead of Earth, what corrections would you have to make? What cht26mw+s(l .s65 ai ggjxjd,dranges would occur if you were measuring parallaxes from Mars?

Cepheid variable stars pgx*ltuq 84sy.u,fw (o mk5 d5change in luminosity with a typical period of several days. The period has been found to have a definite rg*d u yf4x5,.qokut 5wpm(s8lelationship 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 ek4o, p3*z /8qvx:; icpz alttits role in General Relativity?

If it were discovered that the redshift of specj,)9 5df i e knlabps.:po(-rmtral lines of galaxies was due to something oth s5n .kofbpl-)mia d(,e9 p:jrer than expansion, how might our view of the universe change? Would there be conflicting evidence? Discuss.

  All galaxies appear to be mowdttd6f624 ydi *rse p.u4c o9ving away from us. Are we therefore at the center of t*p oec.d is69dd2w yf4 6ut4rthe universe? Explain.  ----待选择----yesno 

If you were located in a 2gavzbi8,) h ugalaxy near the boundary of our observable universe, would galaxies in the direction of the Milky Way appear to be approaching you or receding from you? E 2bvaig),8uz hxplain.

Compare an explosion on Earth to the Big Bang. Consider such questions as: Woqe 1/ ,ls0bhixuld 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 un h0b1e/siq l,xiverse would this correspond to, open or closed?

If nothing, not even light, escapes from a blackyc56qltx z.0 s hole, then how can we tell if one0. xstlycqz 56 is there?

  What mass will give a Sh85t;8z s 7gg5 uc2(iyjjt9j4bbr rsbchwarzschild radius equal to that of the hydrogen atom in its gr(t;g2hi598b byj jr ss48trbcug57zj ound state? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion years. Find th8zc vq58 flq k,ymajd81 bvy*0at time on (Fig. Below). People have lived on Earth on the order of a million years. Where is that on (Fig. Belo v 8avq8mqy*kjz8 ld0c5fy, b1w)?

Explain what the 2.7-K cosmic microwave background radiation ir 2z,jm nj l96dq:u4t4p : /z(oykn(wi7 atirzs. Where does it come from? Why is its temni7d /mtr9,( 4nlzo(2w a6jq:ptzu jiyz :4krperature now so low?

Why were atoms, as opposed to bare nuclei, unable to exist until huimfro+c(77xg dc8 5i nndreds of thousands of years after the Big Bang?(7gdi+i58 c fx7n mcor

Under what circumstances would the universe eventually collapse in on itsel 63l;rxl6;halj e3,kbpbhnnc e;4zm9 f?

  Using the definitions of the parv xg15;y-ba 4gltd ofdyv*/hadw ;uvxp7887e sec 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 i5uf gu9s3yh6u t? d =    ly

  The parallax angle o)0( n2 ofoge4pvhn rf8f a star is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its parallax anv8xxva ba /+/wqbh;1 zgle?
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 ly away? 8p08 zowbet+z $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as fays2e*ub: z-nqk(hou.r away from us as a second star, will the parallax angle of the farther star be greater or less than that of the nearer star? By what fau(z.:h -bson 2qekuy *ctor?

  A star is 35 pc away. How long does it take for itsv o, hc/8qbp m/3c4 avt;i6zyl light to reach us?    years

  We saw earlier (Chapter p:t*: bp(bd5fw rk 37z; auupf14) that the rate energy reaches the Earth from the Sun (the "solar constant") is about d:7pk;p*tbup b r35wz: f(ufa $1.3 \times 10^3\ \text{W/m}^2$. 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 aw 0iu i 8iott,4/ iok1diyxu+1s compared to its brightness from Earth? (Jupiter is 5.2 times farther from the Sun thantii1t+oy0i 8i4uuiw/1 xko,d the Earth.) $\dfrac{l_{\text{Jupiter}}}{l_{\text{Earth}}}$    $ \times 10^{-2}$

  Estimate the angular width that our Galaxy i6u0iyo*/ect- ooj :x would subtend if observed from the nearest galaxy to us (Table 33-1). *ty-:excuj oio 06/ioCompare to the angular width of the Moon from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, what will be ;she w1zic+;qits average density if it expands out to the e;+iw1;cq hs zorbit 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 )b*u aa5 *ga rn1nwdo*white dwarf, it is expected to be about the size of the Moon. What angular width will nw***n d buga5 1o)aarit subtend from the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whose mass is c2w mtpyx3htjj 5,ko*k0.*t p equal to the Sun's and whose radius is equal to the Earth's. How many times larger tha h*w5ct 3p*,ktx0o2p tjkjy.mn 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 1 obhax l9n9-nyar- q,/1 km. Calculate its average density and compare to that for a white dwarf h- ynb -r 9,qlaaxn9/o(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. 33-2. (The mass n-w6m4+d ,sd fionvy9 of the very unstablenno-4mfsd , w+y vi9d6 $^8\text{Be}$ 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 ap ak-fvhzp5s 35parent 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 aru gc.)l.0k u ap9z5t 3cr-szbie assumed to be about the same distance from us. Two such stars have spectra that peak a9-c.us cpbz ikz al3gt.0ru)5t $\lambda_1 = 500\ \text{nm}$ 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 Schwarzscg21 nr4navfh m by8qe/jlzu/ +(q+f+bhild radius for a star with mass equal to that (a) of ourl + (q/ern qgahmn +buyv2jf4/8b+fz1 Sun is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typical galaxy (like oursew de 3r5w5gi3)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a sphere, 3tv,e m;w v st3w6*pxr.-k.6nir ocqm for which the sum of the an.r3 tnxvs 6e*mvcqp - 6k3wtro.m;wi,gles is (a) 359º, and (b) 180°.

  What is the maximum sum-of-thvk5cqh r157 noe-angles for a triangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 18q or)ojk,jd1.0% of the speed of light, roughly how far away is it? q k)jo,1 jdo8r v =    Mly

  The redshift of a galaxy indicatesr fxxh.av2k) -et.:hj a velocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of)lnwv alvutx;3 jea3zn 113- p a galaxy (relative to us) that is near the observable "edge" of the lv1ju33awelaxn) - tnp3v1z ;universe, say 12 billion light-years away. v =    c

  Estimate the observed wavelength for the 656-nm line in the Balmer serieso2 i6yafxc3 .l of hydrogen in theix f.l2y3a6o c 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 thg1:fw)y k:e yc3o3fbb2p f*fge wavelength for the hydrogen line at 434 nm is measured on Earth as being 610 nm. c1obpy 3gf b:)y2ge3ff:*f w k
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 wikklv:;/xw 20i*krh .3lek gbv th $z = 0.60$? v =    c

  What would be the redshift parameqb mlxf exomg:6zw+mpt, 467wxa, 3t+ter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, shozpttvmjco lj m.f.k 03) un:45w that 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 peok2q ./y :xmj8 ab*qradiation distribution at 2.7 K usin* qpykxm o .:a8je/bq2g Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of the univers - ns*f+wx5lov2wkf i/.1 zf5dzu/( ewj ujpg;e 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 galaxie) tdbl:hvp+(ks) at any one moment is believed to have been inversely proportional to the absolute temperature. Estimate the size of the universe, compared to today, avb(l ):pk+ htdt
(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 hadpj.sn.yz( 3ck;wm3hb1qd4 u w the universe cooled below the threshold temperature for producin.4z.c3h;(n1kp qs jwbdum w y3g
(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-sb3)mz +5nr7 ozy-ky bnequence stars could undergo the three changes represented by the three arrows, A, B, and C, in the H-R diagram of Fig. 33-28. For each case, describe the changes in temperature, )nkmr3zy-5o z+bn7yb luminosity, and size.

  Assume that the nearest stars to tm to4ok8q,6n1v3,9 ( (zhhm mwtkvay us have an absolute luminosity about the same as the Sun's. Thei, mawkvtv(q 8t46z9 o3mth( y1oh,m nkr 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 mom)ceoqqzb3 h gz65w/* qentum to estimate the angular velocity of a neutron star which has collapsed to a diameter of 20 6 b h/z3q5zqgcw)e*oq 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 when the sk9k3iuyue ne ok:l tv swp97 +7.l7tk0tar in Problem 56 collapses to a n+kiktp ws7l079n.u 9tu7 l kyekevo3:eutron star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believed to be a neutron star of mass ey,of.d0vy6 f1.5 times that of the Sun, with diameter 20 km,yy ,o0f6e .vdf 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 isk x(itg(qtgh) ha57 wll o839e 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 critm5 dczte6z5f -.9nsu hical density to close the un6c.9z5dm f-estuz nh5 iverse. Assume 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 spectr,2xijsh9yuam*mtjo(s 8e d9 - a peak at 600 nm and 400 nm, respectively, both lie on the main sequence. Use Wien's law, the Stefan-Boltzmandma -( tse,muoij2*hx8s 99y jn 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 distanc.+i 1q qxs*ugcnnpjs;3-8wz9.ylrs ces with parallax at 100 parsecs. What is our minimum angular resolution (in degrees), based on this infow j*l;c. nqp98q.s-3iyz r+s sng1cxu rmation? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from singly ionized hok,;dw 8q u6k:ww)r7xr jr.azz2*u lyelium in a distant star happen to j ;7uy8w *wwau2rxd r:zzkr. o )qlk6,overlap 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 c pyq)7np3cs+z 1st .v.oassi fic5s7.orresponds to 1.8-TeV collisions at the Fermilab collider? To what era in cosmological histp7acv7 foszn1ssc3spt.. i5s y.+i q)ory does this correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotat3fge i-xqlppqz0c u;g )xdfjm* 6a19)ion of gas around what might be a supermassive black hole of about 2 billion solar masses at the center of a galaxy. If the radius from the galactic center to the gas clou iglqp*;x zxecfg1p-qf0 a)3) 69d umjds 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 ao.j g 5kj,3vcpway from Earth. The "blue" hydrogen line at 434 nm emitted from the galaxy is measured on Earth to be 6vp ,jjgk.co53 50 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) wil+af:cdf)3: y: ,vhbx6f wjfsfxbk / m1l begin fusing carbon nucle:k f/fw) fd+:,fv:36hmysxf1bcx ba ji 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 8 onuc(4mqr c )(vq(p5 -k8f6nm lwite
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 of thekg:zvv:ib j23 univgk :jvivzb2: 3erse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$