The Milky Way was once thought b g df)c3/qrc6to be "murky" or "milky" but is now considered to be madfrc 6g/b3qc)de up of point sources. Explain.

A star is in equilibrium when it radiates at its sn1cks elx -c 8vct--k8urface all the energy generated at its core. What happens when it begins to generate mors-1kcvl-c8c t-enkx 8e energy than it radiates? Less energy? Explain.

Describe a red giant star. List some of its propertiesq76vsoo9q (kv vkkvq*c+.n: s.

Select a point on the H-R diagram. Mark severeb-bkn64chb+ al directions away from this point. Now describe the changes6 kcb+eh- 4bbn that would take place in a star moving in each of these directions.

Does the H-R diagram reveal anything aboutwx09 ssl13ty r the core of a star?

Why do some stars end up as whit(1.jx o rwwfzb4c ez1e,v7 onfb 40,fne dwarfs, and others as neutron stars or black hwfeze( j14n.b, n zwvorb1o7 f 40f,cxoles?

  Can we tell, by lookinaf he(f (:/t834o1yufz aa rky0 dhm7dg at the population on the H-R diagram, that hotter main-sequence stars have shorter lives? 1 fhd/armytzyfu ke 8( haf(a7o3 0:d4Explain.  ----待选择----yesno 

If you were measuring star parallaxes from the Moonh+ t+)m65 gbt5b.qe ofa1thmo instead of Earth, what corrections would you have to make? What changes woule +t 1bq mmth5+h65boo.f)tga d occur if you were measuring parallaxes from Mars?

Cepheid variable stars change in luminosity with a typical period of several da.y5*/j hy .9ep tzlx a45fvjknys. The period has been found to have a definite relationship with the absolute luminosity of the star. How could these stars be used to measure 4kx vlyf */ tn.5y .hjz9apej5the distance to galaxies?

What is a geodesic? What is its rolcz8+je()g)cvoorh v 590 shn je in General Relativity?

If it were discovered that the redshift of spectral lines of i2o-w2k,b(h.l do6/ odwitbr galaxies was due to something other than expl d 2/ob(k-. iotdw6 rwoih2b,ansion, how might our view of the universe change? Would there be conflicting evidence? Discuss.

  All galaxies appear to be moving away from us. Are vzq:e 964 efkkwe therefore at the center of the universe? Explf6e9 :k zqvk4eain.  ----待选择----yesno 

If you were located in a galaxy near the bob;t.wuikiq ,y6wl5u:pzu*e 3 undary of our observable universe, would galaxies in the direction of the Milky Way appear to be approaching you or receding ;u,w*ky blpeiu it3w: zq.56ufrom you? Explain.

Compare an explosion on Earth to the Big axun4gh39 ae5l)z s2u Bang. Consider 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 ofsa)a 5uu9zex gh2nl4 3 universe would this correspond to, open or closed?

If nothing, not even light, escapes from a black hol0 ,uj ;pnap;: zykuu;ze, then how can we tell if one is u a0z:kuy,;n;;ujpzpthere?

  What mass will give a Schwarzschild radiust 05u2q+mpss l equal to that of the hydrogen atom in its grou s0m+pq25 ulstnd state? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion yearssm)e6b2whf o g q:5sr4. Find that time on (Fig. Below). People have lived on Earth on the order of a million years. Where is thatmw g42fsb6hq or:)s 5e on (Fig. Below)?

Explain what the 2.7-K cosmic microuucxw/tx* e/(wave background radiation is. Where does it come from? Why is i (wu/t ecux/*xts temperature now so low?

Why were atoms, as opposed to bare nuclei, unable to exist until hv qwxv 5zv7l-2undreds of thousands of years after the Big Ba5z v-lqxwv7v2ng?

Under what circumstances would the universe eventually co y91 ,k) 3vsej-mzwj+xf+:jscu. s0a0lzfzyf llapse in on itself?

  Using the definitions of the parse:,hob+ j2x*ij yx,mtk2yc bc) c 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 i:1 tdaib6wt (us it? d =    ly

  The parallax angle ofd/tpz 7x4 gob3 a star is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its pa,0n+o cbaq9 sfrallax 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 ew:03 d8b6tdv-au9 d0p ch) hh6mfw vcstar that is 55 ly away? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away :o q7ec uhok3 u -0ut+ jb41lx tu+rxa6emr.q6from us as a second star, will the parallax angle of the farther star be greate4oh+aq: o3u m t616u k-0b7e +clqxu rjtr.euxr 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 us? k1 trq, 9-xg6e3jryds   years

  We saw earlier (Chapter 14) that the rate ener iyb( iwc9:; pxk7dg-tgy reaches the Earth from the Sun (the "solar constant") iwkp ;7xbitdyg( c 9i-:s 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 asl9pe,-sea + pu seen from Jupiter as compared to its brightness from Eart,+su- apl9p eeh? (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 would subtend if observd6qh-vdlehb4y*+w/b n(6m fded from the nearest galaxy to us (Table 33-1). Compare to the anbmlqnwe*4fd-hh 6v+y/dd b6 (gular width of the Moon from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a r3ulllln3ece ,ul r, x k2q.,0red giant, what will be its average density if it expands out to the orbit of Earthu,l quxll.3re,rck302n el, l ($1.5 \times 10^{11}\ \text{m}$ from the Sun)? $\rho = $    $ \times 10^{-4}\ \text{kg/m}^3$

  When our Sun becomes a white dwarf, it is expected to be about thny)w9k u4u ,vut 9n.nxe size of the Moon. W)uk4nu. 9 x, nuy9wvtnhat angular width will it subtend from the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a whitri. 4f y+ukjqoo+-qzc 7 xf,z7e dwarf whose mass is equal to the Sun's and whose radius is equal to the Earth's. H ozx++ j.zfuk o4-y7fqr qc7i,ow 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 so;jnth)up nrha5 v2)ke :c(z v3lar masses has a radius of about 11 km. Calculate its average density )hcu ae(k: zj)v n r253n;tvphand 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 elybehld/n ; o*)u:as v5/5*(ni oezcburning reactions of Eq. 33-2. (The mass of the very unstab ( *be5na/cl/i5e)devszhoo y;u :l*nle $^8\text{Be}$ 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 ofvw00b6rb nn )vr2+lq g the 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 -rrtf 8fi j)hik 6s l06izt 2e-8w2hgoassumed to be about the same distance from us. Two such stars have spectra that 8kgl2irs-ij6 t8 zhrtei- 2fw )hf6 0opeak 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 vnscrvnn opi93wk+* jy)y4./with mass equal to that (a) of our v.vjoy/kn c3*s)+4n py9w inr Sun is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typical galaxy (like ours)b+jik * c0mg:1 ghxhx3nf/r f;? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surfauw ylin( weo+9p8+ qv,qge7;l ce of a sphere, for which the sum of the angles p8(vn9+oeglwliq,wu ; qye+7is (a) 359º, and (b) 180°.

  What is the maximum sum-of-the-angles forz6 t ie e:p2;isk1uf(2exg+pw a triangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the li/c 0ol *e urvayql/ ba)i62+speed of light, roughly how far y 6 qaeolar/2c/l0v*b +ui)li away is it? v =    Mly

  The redshift of a galaxy indicates a ve sfn*ujv;0l;:(q4hf vpa kcd:locity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (relative to us) tha7 sewy. )ht-+tz h+f-nny trr-t is near the observable "edge" of the universe, say 12 billion light-+h+ -tnnrz-yfys) wttr-7e.h years away. v =    c

  Estimate the observed wavelength for the 656-nm line in tqw)pb6f q4 u,6 ,tf:d bm4fsuxhe Balmer series of hydrogen in the spectrum of a galaxy whoss,q6ftx,4:b q p dm)64 fufuwbe 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 the dj sqzu-0z zvwax4p :)-(g-jvwavelength for the hydrogen line at v u-:)(z xs-zza g- jdj0wpv4q434 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 cz 0 wbq3)l6qsa galaxy with $z = 0.60$? v =    c

  What would be the redshift /o/ 9cygk/ *tgqyzw7t parameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that ,h8adq:qrg+ebu2 v riv-1 r7g 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 th yio6/l6t,pi ce peak of the blackbody radiation distribution at 2.7 K using Wien’s la/tcilop, 6 6yiw. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for;zvs/d v7pje r (5vs6z closure 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 universe (the average distance betweeneeua::id:zh.,- n c mm galaxies) at any one moment is believed to have been inversely proportional to the absolute temperature. Estimate the size of the universe, compareacu-endihe:.:,mm : z d 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 thjtttt 5(wu2wd0owe 29 g s6i4be universe cooled below the threshold temperature for producing gb0to2t wtw5td9i6us4e( j2 w
(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 m ll u4fl 8ftj:,fe(pe3ain-sequence stars could undergo the three changes represented by the three arrows, A, B, and C, in the H-R diagram l (le4l, p38jefutff: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 luminosity about the sameia,cxhat a6p:l5vj *p:09v h (;vmrk r as the Sun's. Their apparent brightness, howxcvv:h,a:;ajh 6 9t(mlik*a rrv0 p5pever, 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 the angular velocity z/z m/ktx9m7j*ap1chof a neutron star which has collapsed to a diameter of 20 km, from a star whose radius was equal to that of o / 9cmk71mph*jz/ zatxur 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 st fkq0x3p)nyhz :v;yu:ar in Problem ;u:qzyykfp) 0nvxh:356 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 tv (md cm:x,mhle2 )em8gifx( s1mta0)imes that of the Sun, with di2:h))i0emmmv (,c8tfma lmsegxx d1 (ameter 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 Gala chr97j4obh(wz5 mo8fxy 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 provin8h;ee-x( g kvde the critical density to close texn8v eg(;k- hhe universe. 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 spectra peaf gsmjra)k0v,vry/ o4 l 5,f(ik at 600 nm and 400 nm, respectively, both lie on the main sequence. Use Wien's law, the Stefan-Boltzmann equation, and the H-R diagram (Fig. Belowm org0s/5v(i4,yj)fk l,avfr ) 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 parallax at 100 parsecs. What is our minivw (dj-mg -gjq a6vq76mum angular resolution (in degrees), based on this ia gv7v6dgwjqj -6(q-mnformation? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from singly ionized helium in 7qgkrdj1wfv+d(2 ; juy l52mkdp:yb6 a distant star happen to overlap with the Balmer lines from hydrogen (Fig. 27-22) in the Sun. How fast is the star recedinj f2my; w drbu(vldk6+y 5k1gd2:jpq7 g from us? v =    C

  What is the temperature that corresponds to 1.8-TeV collisions at the Ferm,y gfbkk :,lq* cx;zgh xf2g-1j/3 xksilab collider? To what era in cosmological history does this correspond? fkck:1 s-zf ;ggkb/hxl, yj x2q3*,xg[Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently q.j/j,; vi:vo 3jn:lt v sbay8measured the rotation 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 tovq.javs/nvi3j : :y;l 8,tbjo 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. The "blue" h,nu :e.d: pbj0,anzowb ek dk.c o.wk;:o(7v wydrogen line at 434 nm emitted from the galaxy is measured on Earthdzok udwoo07 bn:.v; bcp,,k k.:a:n.wj wee( 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 stavo -wg)xvchc g9 x*80wr (if massive enough) will begin fusing carbon nuclei to for 0wg*wx-ghoc) xvcv98m, 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 oa o+ npa0cwi. /mrp 7 d)on0zif44-qy
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 denseb l0*ldm:kcs8roac 42.eki9 ity of the univer4oe k mc9c0:rka.e*s 8i2blld se, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$