The Milky Way was once thought to be "murky"oh+,1c obs+ jo or "milky" but is now considered tobj, c+o+ohs o1 be made up of point sources. Explain.

A star is in equilibrium when it radiates at its surface all the energy generatehn;b+ hj:mc:8ht uo8cd at its core. What happens when it begins to generate more energy than it radiates? Less energuc8mt o8j+:: hh cbhn;y? Explain.

Describe a red giant star. List some ,94cjqd,dv -46 n dnvnrl: larof its properties.

Select a point on the H-R diagram. Mark several directions away from this p0e34pu/ 2bodxfj n1 tooint. Now describe the changes that would take place in a star moving in each of these direcp4xdotuf0/o nj3 2e1btions.

Does the H-R diagram revea8. porhx((xcal anything about the core of a star?

Why do some stars end up as white dwarfs, and others as neutron stars or bla*k *kgzyr0 /5idqo5 swck holes?q0g sork55kw*zi*/d y

  Can we tell, by looking at the population-r6 bg yzps-/e on the H-R diagram, that hotter main-sequence stars havr6--pbz/e ygs e shorter lives? Explain.  ----待选择----yesno 

If you were measuring star 2qc ,p.l kdzm vk7z(++.: x ii+kpkuksparallaxes from the Moon instead of Earth, what corrections would you have to make? What changes would occur if you were measurik x2d. lp+q cuzkii+ zmks.v:pkk,+(7ng parallaxes from Mars?

Cepheid variable stars chal21ex*k03hk icx-if 2z -vowqnge in luminosity with a typical period of several days. The period has b0qik2kovl*izef1x--3 2hwxc een found to 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 role in General Relativity? 4rgihy c.(e+ cb4:hxw6d0m qe

If it were discovered that the redshift of spectral lines of galaxies wa9jczv)1i +b12 py5j das1uty us due to something other than expansion, how might our view of the universe change? b1vjp1+a5y 1stjuiz 9dyu2c)Would there be conflicting evidence? Discuss.

  All galaxies appear to be moving awah:9 sj1 sgx,gsn ux:p:y from us. Are we therefore at the center of ths,x gspj:us9h:g1 x :ne universe? Explain.  ----待选择----yesno 

If you were located in a galaxy near the boundary of our observable unuw1 ; jbpk0z.sitxx51 iverse, would galaxies in the direction of the Milky Way appeax05.p;w izx1jb1 ksu tr to be approaching you or receding from you? Explain.

Compare an explosion on Earth to the Big Bang. Considerd*pg2m1lf cc9 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? What type of universe would this correspond to, open or closed 1gmcp2*f9lc d?

If nothing, not even light, escapes from a black h h-yw7ufqy8f *yfv7l5kpz8nd( wn)y9ole, then how can we tell if one is therey8y*y fnhy n f)wz578wk-(vl9du fq 7p?

  What mass will give a Schwarzschild radius equa 5db9+4 fp-ftrtnyv s6l to that of the hydrogen atom in its gps6tnfftyvr-+94b5 dround state? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion years. Find that time j4efqq 7;ua cc1o.s( don (Fig. Below). Peoplefoq. 1a udecsqc;(47 j have lived on Earth on the order of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic mip6 5vg5 zmt)xqcrowave background radiation is. Where does it come from? Why is its tempera mg z556)tpvqxture now so low?

Why were atoms, as opposed to bare nuclei, unable to exist untilaxoyh89y43e a ed-ix. hundreds of thousands of years after t -eehi.4x9 ayxa3 yo8dhe Big Bang?

Under what circumstances would ta1vm6z*ss stke. qgv46tv5 2qhe universe eventually collapse in on itself?

  Using the definitions of the parsec and the light,/nj);f hc n8ik. g.ubwkf;q g; mxm;t-year, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.38 secor xv5/9zps us*nds of arc. How far away is it? d =    ly

  The parallax angle of a star iszei0;0dux /im $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its para7lo*4 :ac1);ug a(b,bdvw fcr rui 6bxllax 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 that is 55 luqpq3yl0hd ruwkj4umc 63f 7ptp)/ 0-y away? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away from us as a seco5lenk.s 6)f- ypuztz/nd star, will the parallax angle of the farther star be gr 6sk-y5p zl/)zn .utfeeater or less than that of the nearer star? By what factor?

  A star is 35 pc away. How long does it take for its light to reach u( .r* tij)vbwvs?    years

  We saw earlier (Chapter 14) that the rate energy reaches the Earth from tf6d;vq j*2p 5ks3su omhe Sun (the "solar constant") i2s m p;u3sd6vq5f *kjos 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 toejmil/w:35 sy its brighw/mi5lye j:3stness from Earth? (Jupiter is 5.2 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 wm*03f ;luunk would subtend if observed from the nearest galaxy to us (Table 33-1). Compare to the anm3f n;wl*ku0ugular width of the Moon from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a ryd 10n ik-qxb :xqmd;bpm:jz522) daved giant, what will be its average density if it expands out to the orbit of E;52d:xd0-va 2)y 1 dpqbbmjqnmzkix :arth ($1.5 \times 10^{11}\ \text{m}$ from the Sun)? $\rho = $    $ \times 10^{-4}\ \text{kg/m}^3$

  When our Sun becomes a white dwarf, it is exw:sq)/hm:pk w pected to be about the size of the Moon. What angular width will it subtend from the present hmp:q/k):w swdistance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whose mass is equal to the Sun's and i8fb1l q6c3xtwhose radius is equal to the Earth's. How many times larger than Earth's densi3l6b8x ct1 qifty 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 soljcad4m: +bti9dh r3yj 1 4ub+war masses has a radius of about 11 km. Calculate its average density and compare to that for a white dwarf (Problem 13) and to thha1j4w4 ib+dd3u c:m tj+yrb9at 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 masshbp-ne r4rg4 s(hb/ml 2rv1+cdw q* o6 of the very unstan(gr-4 borsc+*1ph d2 mqlv/ ebw46hrble $^8\text{Be}$ 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 iu mnhc,b 9g6 6i/xa oo:mbb:1apparent 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 abo/6npnzkh z15l ut the same distance from us. Two such s 1hlp6 znzkn5/tars 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 Schwarzswwuwf pw21r+p l5 /x x.n5cs/rchild radius for a star with mass equal to that (a) of our Su5r nrlp/c2.u 5x1wps+wfww x/n is    km, and (b) of Earth is    mm.

  What is the Schwarzschbkp(c8r5mu1 p6 b)lwc ild radius for a typical galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a sphere, for which th1d 2a7md;a82m ng tlhm)8xmohe sum of the angles is (a) 359º, andahm8h )1; d72lm tmdomga8 x2n (b) 180°.

  What is the maximum sum21e:k1mp q-m8yhulu v6 p o3gw-of-the-angles for a triangle on a sphere?    $^\circ$

  If a galaxy is traveling a./( ue2vdj5mbd)o rofcf16d 30hwsruway from us at 1.0% of the speed of light, roughly how fw0o bfv5h sufd63r.dd) c21um je r/(oar away is it? v =    Mly

  The redshift of a galaxy indd-efv yqg c063icates a velocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (relative to us) h1vtc)teqpd;01 ur 3n that is near the observable "edge" of the universe, say 12 billion lip0; vt3qdce h1ut)1rnght-years away. v =    c

  Estimate the observed wavelength for tuq59bkevc m3raxqoy ( m)/(g:- 2ccdahe 656-nm line in the Balmer series of hydrogen x m /vcgc2 qb:-3y9)r mk5(cu qoea(dain the 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 t6s4pmps5nl vb. 5zeb 8he wavelength for thn e5.pb5m l4z8spsv b6e hydrogen 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 withtyhud, u 6(fc. $z = 0.60$? v =    c

  What would be the redshift parameuv.1l ekms-o ef1wgyho-t :*6ter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Doppler shift in wavelength is 1-tqez)kaj 9qy1p3 m c$\Delta\lambda/\lambda \approx v/c$ (Eq. 33-5b) for $v \ll c$. [Hint: use the binomial expansion.]

  Calculate the wavelength at the peak of the 23 0kg 6gm7mu.b. kb5gw zyfo jdw6tq3blackbody radiation distribution at 2.7g.gb 0z.o kb3tfwwdqjy5k6 mm67 ug32 K using Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of the universe xcz+:hqu p 0aff4 c:m8is $\rho_c \approx 10^{-26}\ \text{kg/m}^3$. 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 dis/nswe kfb.qoxs 4c08.e ar; 1/4gqxz vtance between galaxies) at any one moment is believed to have been inverselssn owr0/../e4c q vxb1g 8akx;z4qfey proportional to the absolute 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 univeyo*y:v+ 5c rftrse cooled below the threshold temperature for produy5t o c*v+r:yfcing
(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 766vwjugv j u0stars 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, luminosity,u6j7 6g jvwvu0 and size.

  Assume that the nearest stars to us have an absolute luminosity abojdr)zjv*npmo u-s(-)2v9qw yut the same as the Sunj2qzso(9 ) )mw-r yupd*v- jvn's. 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 to estimate t0oss yr7gu*5(ulu t .bhe angular velocity of a neutron star which has collapsed to a diameter of 20 km, from a star whose radius was equal to that of our Sun ut(u.*bug57o slys r0 ($1.4 \times 10^9\ \text{m}$) 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 star in Proble)dbiu 1 :qq(tzm 56 collapsesbdz:t)q1(i qu to a neutron star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believed to be (,f lvoz3ava* a neutron star of mass 1.5 times that of the Sun, with diameter 20 km, is observz v3fal *,(aoved 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 Gala3;9+afjk tkdnxy 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 hv:u* ;o enrw7dq) 0jxeV) would provide the critical density to close the universe. Assume the neutrino densir e)7:d; xwvu 0jqn*ohty 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, both lie ms.43 afvyml; on the main sequence. Use Wien's law, the Stefan-Boltzmann equation, and the H-R diagr.f 4mal m3;vysam (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 distan*lqe50/z ;w.tryuiko/p:y7du4v0r d lhqtg- ces with parallax at 100 parsecs. What is our minimu:0io7yqzy0 dvpe / w q;5*dl/tug4urlkh.t -rm angular resolution (in degrees), based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from singly ionized hbxhl db37v)4 oelium in a distant star happen to overlap with the Balmer lines from hydrogen (Fig. 27-22) in the Sun. How fast is dbx)l7vh 4bo3the star receding from us? v =    C

  What is the temperature that correspon+:e7 u mzpkw,nds to 1.8-TeV collisions at the Fermilab collider? To what era in cosmological history does this correspond? 7wm,:n kp +uze[Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation of gas around what migurq5 ,n:emeb;d4jw, rht be a supermassive black hole of about 2 billion solar masses at the centd4jrr5 , u,m;w e:qneber 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 Emeki. *m8+y wb usy. oj6x+-faarth. The "blue" hydrogen line at 434 nm emitted from the bi .f jk*ysyme- ox8.+6mu+awgalaxy 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 begivq/utf; 57k skn fusing carbon nuclei to form, kks vf57 qut;/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 +siph;2ynx 0l v;w*wl ft)+qz
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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+- n lls;of1 r(xw4biz of the univ w-b ;1n +4ro(szlfxilerse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$