The Milky Way was once thought to be "murky" or "milk8a i69u fih;ydy" but is now considered to be made yd6a9h i8ui f;up of point sources. Explain.

A star is in equilibrium4 g*hnhdggr-.ric( z(srs 1u 3 when it radiates at its surface all the energy generated at its core. What happens when it behc (rsn34.ggzr*ghi ur1sd-( gins to generate more energy than it radiates? Less energy? Explain.

Describe a red giant star. List someim(pc)b a 8q*f of its properties.

Select a point on the H-R diagram. Mark severi;mce +sz3a 1c)u w8clal directions away from this point. Now describe the changes that would take place in a star i 8ec1c) c ua;+3zlmswmoving in each of these directions.

Does the H-R diagram reveal anything about the core of a5e rxzitw(*y +bo */9ko)c++ma bezc u star?

Why do some stars end up as white dwarfs, and +t-.k++3bwm6th8ptshb ifm wothers as neutron stars or black holes+tskw-3h8bt i+tfhm6m bpw .+?

  Can we tell, by looking at the population on the H-R diagram, that hotter main-sx r g+;(up3ivdequence stars have shortuxi(pd+ r; 3vger lives? Explain.  ----待选择----yesno 

If you were measuring star parallaxes from the Moon instead of Earth,r qcla 1g ys suy9af6w22y)zgnf386 b( what corrections would you have to make? What changes would occur if you were 6fblzf)6ws 21g s g ru3y9yqny8a( ac2measuring parallaxes from Mars?

Cepheid variable stars change in luminosity with a typical period of ag2b6c9bd4 giu.w 6zm several days. The pec 6 6mugaib9 g2b4.dwzriod has been 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? ,url. 0 6 rqujp7z6t iawutp0:What is its role in General Relativity?

If it were discovered that the redshift of spectral lines of galaxies wad2+x/p 5xc qokuff 29ys due to something other than expansion, how mighykx+xo9f2/ p qc2ufd5t our view of the universe change? Would there be conflicting evidence? Discuss.

  All galaxies appear to be moving awayd 3-hogqo8e / gcstg..l:y0mr from us. Are we therefore at the center of d.so gtg0y3re .go8cml /q:h-the universe? Explain.  ----待选择----yesno 

If you were located in a galaxy near the bou tft- cd4ce3qd; +,7ek 9vfypandary of our observable universe, would galaxies in the direction of the Milky Way appear to be approaching y a9k,cv7d3e+c-f y4f ttq;edpou or receding from you? Explain.

Compare an explosion on Earth to the Big Bangjv9f.,f ,tcpu. Consider such questions as: Would the debris spread atuf pc. ,j9,tfv 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, w;+.bxb g3 s0iwk4qh hpz1zl 5dj06u ythen how can we tell if one.hz0ji153 wuw6s hqbg0+y bkx4d lp;z is there?

  What mass will give a Schwarzschild radius equal to thf2i b(s45 yengat of the hydrogen atom in its grfe bysg5n2(4i ound state? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion year6g jz9j)1mbm f0 iwd0ks. Find that time on (Fig. Below). People have lived on Earth on the order of a million years. Where is that on (Fig. Below0) 1i b0km zgj6jfmw9d)?

Explain what the 2.7-K cosmic micr ka d,drhzxn6h) 5r+(kowave background radiation is. Where does it come from? Why is its 6 nh,5 )hkr(ddza+rkxtemperature now so low?

Why were atoms, as oppt:)h+5wc*qy w pwelt 9osed to bare nuclei, unable to exist until hundreds of thousands of years after t:qethlcw w w )ytp*9+5he Big Bang?

Under what circumstances would the universe eventually collapse in ozy6j2erdin230*v7b so4t aqh n itself?

  Using the definitions of the parsecuh j p(6jlk*(aupqns y) 2j9t( 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? ;/yds hbtu *xv yft68/d =    ly

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  A star is 36 pc away.uipx ;-pvy2 5om5w/cfl/,z gl h.vym7 What 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 that is 55 ly bxwl2. hq mrbc:s1u av/ 2ok):away? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away from us as a second star, will the parallax ang6e8m):o2u/ vjmy xw6a(xfemxle of the farther star be greater or less than that of the nearer star? By what facto66 (yj):oa2efwu mve x mxxm8/r?

  A star is 35 pc away. How long does it take for its light to reach 61xh -eom*s (0/yzfi3yusl7o :uomw sus?    years

  We saw earlier (Chapter 14) that the rate energy reaches the Ehmoa c j1.ptd518b/faarth from the Sun (the "solar 5otd /pmj8a1c.f 1ha bconstant") 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 Jupiterlu,q:vyhhm2b1 zj 0var +p+ a2 as compared to its brightness from Earth? (Jupiter is 5.2 times farthh jabyv:a1+uv2l,h 0mpz+q2 rer from the Sun than the Earth.) $\dfrac{l_{\text{Jupiter}}}{l_{\text{Earth}}}$    $ \times 10^{-2}$

  Estimate the angular width that d*2vlbc*ld ; nour Galaxy would subtend if observed from the nearest galaxy to us (Table 33-1). Compare tolb l;*2vnd*dc 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 densi.ibt0 kif9q o+ty if it expands outo0+ fb qiti9.k to 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 expected to be about the sizysq)zmpe+d 3ung 0e6, e of the Moon. What angular widtu3dmg q6y0s)e z +pen,h 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 equal to the Sun's and6 l9y+3c) fe eq(celci whos6l9fccle)+yi e(ec 3qe radius 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 mas6 kaa91iv( u bo,ijya7ses has a radius of about 11 km. Calculate its aver7a(9vkja6 aub1yiio, age 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. 33-2/ 6dhscms))sij*coq 7 . (The mass of the ve7h) csciojm6d)s/s * qry 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 thppkupr: *hxtzx + f75jvxby5afz- 42)e 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 dzph7a(8 fk8t same distance from us. Two such stars have spectrad(7tz8pfk a8 h 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 radix/ j jw wzfj*ewngw3i5q+e*n 16i4f;pc ,f wg0us for a star with mass equal to that (a) of our i,+zcw*w4* wefj0xj/6jfggqe 5n 3infw 1p;w Sun is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a 0wu;yfh1*y7yzz hl4a typical galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a sp2g n /0g.rhqgfhere, for which the sum of the angles is (a) 359º, a2gqr g0nfh/.gnd (b) 180°.

  What is the maximum sum-of-the-angles for d/o3myu/qh)0v bn,lo a triangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the speed of light, rouezus op ;c:bb3f 9mg9v r74:mfghly how far away is 4 ;3bv:rm:b zfop99mufc7g se it? v =    Mly

  The redshift of a galaxy indicates a vetejmur8 pd2/5 locity 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 observable )*adx vd5zmih7xha/8 "edge" of the universe, say 12 billion light-yeai*v8 ma ah) dx7/hdz5xrs away. v =    c

  Estimate the observed wavelength for the 656-nm line in the Balmer series .met-) aud :tfsl-c* odb*t5yof hydrogent- 5cb l-duay:eo)t** t.s dmf in 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, aj1hm,, j(( m f)-rmuidpng z8znd its distance from us, if the wavelength for the hydrogen line at 434 nm is mea( ,z-gm)mfh1 di,(p j8rzmnujsured 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 galaxyy4t-p3 qbiv8g with $z = 0.60$? v =    c

  What would be the redshift paljz7/ o,xfs0yrameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Doppler shift in wavelenujp5324po umc tr:gx, b92je ngth is $\Delta\lambda/\lambda \approx v/c$ (Eq. 33-5b) for $v \ll c$. [Hint: use the binomial expansion.]

  Calculate the wavelength at the peaa, wr-6dw2 :gij.vwdlk of the blackbody radiation distribution at 2w,lvr6iwg dd:. a2-wj.7 K using Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure ozlj, g vag nbri/0;/f0f 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 universe (the average e:* s04d 5ylpdw++z4mswywzl distance between galaxies) at any one moment is believed to have been inversely proportional to the absolute temperature. Estimay4 p*wssdzlzm4y+ 0:de+ l w5wte 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 thres7-jke+ oz1xvd37km q ihold temperature fqo1ikdv-3k 7x7em +zjor 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-sequenjd+ ;5wrzql0c8m-qwem 4lz )cbx9 /wbce stars could undergo the three changes represented by them xbj wqrl;c-c lqz9z+/)mwbe45 80dw three 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 absolute l gbqunx6+ cif.p;:o,vuminosity about the same as the Sun's. Their apparent brightness, however, is aboqncxbgu f.v 6 o:+,;piut $10^{-11}$ 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 the angular velocity of am.u6m hfwx5: c neutron star which has collapsed to a diameter of 20 km, from a c.: h5mxm6wuf 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 rotati s.xwom1 ky39avg2y,qhx d a+)onal kinetic energy change when the star in Problem 56 collapses to a q +)gdh asxw 9.okvyxy2m31,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 6l)div: t 2how1.5 times that of the Sun, wil6w2: thvod i)th 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 galaxy to our G 7,z1 knu)trexk.0c sc6jzf g0alaxy 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 4mi6fn2j+b ak (in eV) would provide the critical density to close the universe. Assume the neutrino density is, like phoaj 2n mkbf46i+tons, 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 peafi.mqd -ip8 (j cnt*a9k at 600 nm and 400 nm, respectively, both lie on the main sequence. Use Wien's law, the Stefan-Boltmtf*nd8(q c -p.iaij9zmann 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 paraljkk/ 85igp:4yb-e wu vlax at 100 parsecs. What is our minimum angular resolution (in degrees), based on this infor4k5kbyp8:-uwg /ijv emation? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from singly ionized helium moxl kj +,;m7-zo(jvi in a distant star happen to overlap with the Balmer lines from hydrogen (Fig. 27-22) in the Sun. How fast is the star receding from us? v( ox,mzil jv ;jk+7m-o =    C

  What is the temperature that corresponlu mrh 5o vh401 mcb2oji*ld.-ds to 1.8-TeV collisions at the Fermilab collider? To what era in cosmological history does this mo-2u*hlrc.hom0 1l v i45jbdcorrespond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation of gaqn86qvke :)bk uk2 5ojb 38xggs around what might be a supermassive black hole of about 2 billion 6k8geo:8qgk nqub5jkv)x 23bsolar 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 awayn77gu +nq+ ypr from Earth. The "blue" hydrogen line at 434 nm emitted from the galaxy is measured on Earth to be 650 y7 nu+7nr pqg+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 ex5h 3mh1e*bqevolution, a star (if massive enough) will begin fusing carbon nuclei to form, for exa1e*5qhxb e3hmmple, 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 reactioa1p;.c ijtc,n n
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 densipo)xux04egu+xi s: ox2w: ilsc-w r+1ty of the univero + s:uixww+c:2psil1 o)uxr- xx eg04se, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$