The Milky Way was once thc:kl9l7u n gs qe;s+7gought to be "murky" or "milky" but is now considered to be made up of point soucgsl9nu e+l s ;7qk7:grces. Explain.

A star is in equilibrium when it radiates xe/ a0o7odx4xqt m(q8at its surface all the energy generated at its core. What happens when it begins (m/xa4q0d7ox oe 8tqxto generate more energy than it radiates? Less energy? Explain.

Describe a red giant star. List some of its prolfhii+s6v b02ujqq4(yw lp/+ perties.

Select a point on the Hi4/*:1 v;hscrlzo nht-R diagram. Mark several directions away from this point. Now describe the changes that would take place in a star moving in each of th*or ;/ :nzvc1l4htsi hese directions.

Does the H-R diagram revea1rux:0mc t+kll anything about the core of a star?

Why do some stars end up as white dwarfs, and others as neyh iu:ay, f30p)2rq ybutron stars or black hole:2yp )qh03,au i yfyrbs?

  Can we tell, by lookin g2rw, f ab ml74)z*sncd-i6fug at the population on the H-R diagram, that hotter main-sequence stars have shorter a w4sb-mlr 6f2d *ng if)7cz,ulives? Explain.  ----待选择----yesno 

If you were measuring star parallaxes from the Moon insteadq*k k *pdi6k2e of Earth, what correcti6p d* 2i*kkqekons would you have to make? What changes would occur if you were measuring parallaxes from Mars?

Cepheid variable stars changpfs +d1 ad6 3,kshxgj5- ts;1kzf d+ffe in luminosity with a typical period of several days. The period has been found to have a definite relationship with the absolute luminohsdk1+fxf+-s1a5f6f;pz tkd g d s3j ,sity 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 z-,(qvz(jz u+ri8aw u Relativity?

If it were discovered that the redshift of spectral lines of galaxies watkul8i - 752qxjs,nm1xtx+ sts due to something other than expansion, how might our view of the universe change? Would the8 ,2+il x tsjqstkx175x mut-nre be conflicting evidence? Discuss.

  All galaxies appear to be moving away from us. Are we thereforei2ct1ew -nu/j at the center of the universe? Ei 1uw- ne2jtc/xplain.  ----待选择----yesno 

If you were located in a galaxy near the boundary of our observable unroxuwr+ 7w/8 civerse, would galaxies in /cxow8 rr+wu 7the direction of the Milky Way appear to be approaching you or receding from you? Explain.

Compare an explosion on Earth to the Big Bang. Cuv0t tc4 vs6 bm3enox- +;,zcfonsider such questions as: Would the debris spread at a higher speed for more distant particles, as in the Big Bang? - cnf t vc;vube0os4xt,z+63 mWould the debris come to rest? What type of universe would this correspond to, open or closed?

If nothing, not even light, escapes from a bl8 g:ygsju64hin;uwd 7 ack hole, then how can we tell if onsu7: y g8hu4;jiwd6g ne is there?

  What mass will give a Schwarzschild radius equal to that lqo(hra6 *0tj of the hydrogen atom in its ground st0*(to larqj6h ate? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billionga.o(i(hs3 ev- pbikt)c6 o dj4op h+* years. Find that time on (Fig. Below). )a(tp6 +g kcs*ph eidbv3(o.o-4iojhPeople have lived on Earth on the order of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic microwar/npf /t,d:b03i*tns e+aexjve background radiation is. Where does it come from? Why is its teeit0sfj :at+/xnnbp 3r, d*/emperature now so low?

Why were atoms, as opposed torvybz p , bm0a.4s gq45*wnm;f bare nuclei, unable to exist until hundreds of thoumb.saq,r*05 zv 4 pnb4ymwfg;sands of years after the Big Bang?

Under what circumstance8q*n ar 7 2y f/ 0q6g5bzy+xi0ang ivyevqo3q8s would the universe eventually collapse in on itself?

  Using the definitions of tqb uakgu 49.nbrvl 683he 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 awaw/qyvm i7bha 2 gkr.)6y is it? d =    ly

  The parallax angle of a star isw4lrs /j pj;b1s3us(tz*aq j7 $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its parallax ac:il,v)u sajvpz3 r-m6/+ td 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 stahvq :)cq b(xx.r that is 55 ly away? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away from us as a second*e /.zyksgs3zp4*t 3ypg4s t j star, will the parallax angle of the farther star be greater or less than that of the .*tyg 3t4s3y/pz 4ekpgj z* ssnearer star? By what factor?

  A star is 35 pc away. How long does it take for its light to ps)di 1r7 fp;dhin*uc9b/agw7/8gf n5: q hri reach us?    years

  We saw earlier (Chapter 14) that the rate energyg :c9dqwxq08 dxvyu )* reaches the Earth from the Sun (the 8)cgqx duyd0w:xv *9q "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 Sun as seen from Jupiter as xuxulm ,q2,ywa;3oeu,,:m wlcompared to its brighw, ow:mqm,uula , ,;2u3exl yxtness 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 would subtend if observed from the nel3sobf9y7 t mk2l;fnos48ri tpc00 f 4arest galaxy to us (Table 33-1). Compare to the angular width of y ob8t 9f;i02l4l4kc0osn7s fr3tp fmthe Moon from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, ehbpt4i o.b4( a+f4g iwhat will be its average density if it expands out to the ore hbi( ob4i .gap4t4+fbit 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 aboutbc1w lk 6ibin p.a*/+ub*my5 o the size of the Moon. What angular width will it subtend from the pres/+ukbobm .cyn5p6* ia*wlb 1ient distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white d; )dvvoimxi g/y b1;p kx)r24xwarf whose mass is equal to the Sun's and whose radius is equal to the Earth's. How many times larger thanb vvx1))r px;ky2oig di4;m/ x 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 14 2 lks6ktde5g1 km. Calculate its average densikegk 5d l2s46tty 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-valuwxb 9s9ksj*i- z;4doox/tp 8oes for the He burning reactions of Eq. 33-2. (The mass of thx/8oi bpos;k9swjdo x z4t*9-e very 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 the same y2o6 6k9oouy6cf ;8w)cthl lgapparent 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 same di 5 pvi.04onbolu(de)y97huhlstance from us. Two such stars have spectra that p.l)54(do ibvphu9u o e7ynlh0eak 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.r)tu n(j273m ea/f(rhdm1:vp q mrgj mass equal to that (a) of our r t/j31erf 2m 7vhmp)d(maquj(g. :nr Sun is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typical g,pj9vnx q;lh+82r j fgalaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface ld; n4kxtf*t4of a sphere, for which the sum of the af; *nx4tl4 dktngles is (a) 359º, and (b) 180°.

  What is the maximum sum-of-the-angl4h 2i v9y 8e7d1hzbt:da q+ikpes for a triangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the z6 w er31stje,uah+0d speed of light, roughly how far away d j+ze6h twra01e3su ,is it? v =    Mly

  The redshift of a galaxy6rk * a5 i;0chmowlp,k indicates a velocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (relatd1 8:oqv4raotcm.xwt0 :fke: ive to us) that is near the observable "edge" of the universe, say 12 billion light ad:m qxt :f84 twrv:.1kceoo0-years away. v =    c

  Estimate the observed wavelength fo 1sz8-rr7vody r the 656-nm line in the Balmer series of hydrogen in the spectru71y vzrdors-8m 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 galax 7dq)j0x9vbb zry(zv) f3be*dq fwr3(y, and its distance from us, if the wavelength for the hydrogen line at 434 nm is measured onwx9 zb(rqz73f*) f)0(q vd y e3dbbjrv 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 galab.mdy+e5 fb; lxy with $z = 0.60$? v =    c

  What would be the redshift cm;v77 ht5ste parameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Doppler shift in wavelength isoo3d vjn;/ccx3+mlx b 6wh0c( $\Delta\lambda/\lambda \approx v/c$ (Eq. 33-5b) for $v \ll c$. [Hint: use the binomial expansion.]

  Calculate the wavelength at the peak of the blackbody radiation dctc6l6v mw+ +m7 :ndpqistribution at 2.7 K using Wien’s law. 6 w6vq mdcc +7nmplt:+$\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closurv .*- d0f47 c6 mbwv0 pn9sz2fdfzuduce 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 avern +lqil 7j 9vj.1*xeweage distance between galaxies) at any one moment is believed to have been inversely proportional to the absolute temperaturw e qlijv9 .enl+x7j*1e. 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 belo(h - yji/l8uprw the threshold temperaturijluh-r8 / y(pe for 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-sequencr6h)f;, ptc+us ouv(ae stars could undergo the three changes represented by the three arrows, A, B, and s+ u6 h)o(v pt;fuca,rC, 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 luminosi/j :xv,t*uskdyzt 3c6ty about the same as the Sun's. Their apparent brightness, however, 3tzj: yxvcdk s6tu,/ *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 angularnwxfy) b9glj* 4cw5;z momentum to estimate the angular velocity of a neutron star which has collapsed to a diameter on9*fxlgb;j5 4wyc )wzf 20 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 rotation1j:n+9oqryow+w 1cbqyh; 6qhal kinetic energy change when the star in Problem 56 collapses to a neutro qh+w1c6 1yr qj+yw:nqo9;bhon star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believed to be a neutro15uv2 z0d towkn star of mass 1.5 times that of the Sun, with diameter 20 km, is observed to have a rotation spe1 5w0kov2tdz ued 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 buf-7qx3c q 9gour Galaxy 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 -mp ;3vmt*o vfee o66(nzr0 3rbeena: provide the critical density to close the universe. Assume the neutrino density is, 6*o e3mr n-be:poa ve0z3(ertmfnv 6;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,w ;7ok g857itswy1 r (bksnz)a both lie on the main sequence. Use Wien's law, the Stefan-Boltzmann equation, and the H-R diagram (Fig. Belo)8yo7sta;k (1g 7z rikbsn5ww w) 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 parsecx; q-bnbd lv- +7ueu5es. What is our minimum angular resolution (in degr+xbq 7-;5bde ue-unl vees), based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lic9iw*5a 5p n ,yovbk*nq(wy7qur3 i1xnes from singly ionized helium 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 fi55o9w1*icuyxbnpw rv na k3*y( q7,qrom us? v =    C

  What is the temperature that corresponds to 1.8-TeV collisions at the Fermm6)oi twla8;; q2qa:pfbde 95y/iqti ilab collider? To what era in cosm q i5:; bt2amo aqt)depqw/f68y i;9liological 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 -j8o;-zg)pxbb ffm s z xx73 9jmor++pbe a supermassive black hole of about 2 billion solar masses at the c- ) zpj-xbx7j8f3sog+b orx9pfm;m+ zenter 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 ap,0f gk-p o nsitj+l6.way from Earth. The "blue" hydrogen line at 434 nm emitted from the gafnp-6 kjl p,.i0so +tglaxy 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)v.fezhbkc z 3o )b4m69 will begin fusing carbon nuclei to form, forvkb ) 93e4 6mfozhc.bz 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 4jfd ejfl z(n+c1*m(g
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 critica o)*hjx1 o5jwnl density of the universj1* h w)5noojxe, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$