The Milky Way was once thought to be "murky" or "milky" but is now consideredzcjt2.u -cb *v to be made up of point sourcesv2 *. ccuzbjt-. Explain.

A star is in equilibrium when it radiates at its surface all the energy gh/my*xrsxod(bbcfc f*)wx0+f1 / kl0 enerated at its core. What happens when it begins to genk bfs /(rmdxx0x+yl 1wbfhccf o)/**0erate more energy than it radiates? Less energy? Explain.

Describe a red giant star. (wywq 8kk x*:mList some of its properties.

Select a point on the H-R diagram. Mark sevt )r u 4q8owsqal*3sb1q d;qk:eral directions away from this point. Now describe the changes that would take place in a star moving in each of these directi8qwd;s ro ts qk3b:*uqlq41) aons.

Does the H-R diagram reveal anything ah y2q4:g 9y(fiik7wwwbout the core of a star?

Why do some stars end up as white dwarfs, and oh w;ykvzne,5 ;*iuab si6u e6ovv 792xr/fs5fthers as neutron stars or black holev5hb,9 e k r2o s*;n56yivuv7;fzaxiw ef6/us s?

  Can we tell, by looking at the pu; l uhi8f05yoopulation on the H-R diagram, that hotter main-sequence stars have shorter lives?huufo8i ; 0yl5 Explain.  ----待选择----yesno 

If you were measuring star parallaxes from the Moon instea9)ff0uk k0vp x v/nduib(g6 p8j3*wpvd of Earth, what corrections would you have to make? What changes would occur if you were measuringn k9(puxj) gp3 68k vwf dbv/pfu0*0iv parallaxes from Mars?

Cepheid variable stars x,vo db,6p8eh*6mzgr:yi(j vchange in luminosity with a typical period of several days. The period has been found to have a definite relationship with the absolute luminosity of the star. How could these stars be dprz 8:i,xo,m6h j yg6v *vbe(used to measure the distance to galaxies?

What is a geodesic? What is itsoo+ v:f;4olhe9udt 2f role in General Relativity?

If it were discovered that the redshift of spectral lines of galaxies t7qa/ti3*bmllk+ol 9xlpkr,6nz e73: jhly4 was due to something other than expansion, how might our view of the universe change?lly:+mb r,ilne7k 6 x3hq9tlj *z3atp 74o/l k Would there be conflicting evidence? Discuss.

  All galaxies appear to be moving away from us. Are we therefopg9h7j n5:5n d sykyy)re at the center of tk7)ygjpnh9n:ysy 55dhe universe? Explain.  ----待选择----yesno 

If you were located in a galaxy near the b+h76twzoi4uk-k4 v ymoundary of our observable universe, wout-h vwo7i6ukk4z m y+4ld galaxies in the direction of the Milky Way appear to be approaching you or receding from you? Explain.

Compare an explosion on Earth to the Big Bang. Cf 96j/tlscnst y 2cd.;.g/mbq onsider 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? Whcf .6gy//dl9scm n t;j q.t2bsat type of universe would this correspond to, open or closed?

If nothing, not even light, escap,,v4 p1xm4tkkxek*n z es from a black hole, then how can we tell if one ik41mt p,4xe v kk*,znxs there?

  What mass will give a Schwa) v66akz8a zg q+3.bnyd)ods crzschild radius equal to that of the hydrogen atom in its ground statez8bdon sc6z.)d+kq6v aga)3y ? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often give2 wonz0pr:ye:r*gh :hn as about 4 billion years. Find that time on (Fig. Below). People have lived on Earth on the order of a million years. Where is that on (Fig. Berweh:yz n0 rop ::gh2*low)?

Explain what the 2.7-K cosmic microwave background radiation ijer/ /i;ma+-v0)absv fv rm;o a*n6mp s. Where does it come from? Why is its temperature now jv vomim+)armf r/*b naspae-;/v;60so low?

Why were atoms, as opposed to bare nuclei, unable to exist until hundredz+8j l /k oj*,+xqrocfn2 (wdns of thousands of years after the Big Bang? *o n+ zrkq/djxonlfc,2jw8(+

Under what circumstances would tdlp oi8c2 42lqhe universe eventually collapse in on itself?

  Using the definitions of the c hv:2:ivn4 br )zq/dvparsec and the light-year, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.38 3o5 tzipeo8;k1uy y6 qsmy:,rseconds of arc. How far away is it? d =    ly

  The parallax angle of a sq w5 fogwz0;.fa4eb /utar is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is itshn ce2c73aarrbx+ ) f. 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 thai5 tylit1y8xw;/9j yvecp2u0 t 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 star, wi2, ;y ,u) 5o/z3otra/eyhcjmllu qw6fll the parallax angle of the farther star be greater or less than 5cujmt)6/lzoy3 /o ; l2f ,yw,erqhauthat of the nearer star? By what factor?

  A star is 35 pc away. How long does it take for d ,zog -ljqquexc0-4(its light to reach us?    years

  We saw earlier (Chapter 14) that th6ylsecniiql0 .cnux,3.1)b zsp o8-ye rate energy reaches the Earth from the Sun (the "solar constant") is abou, l 3ci8lyp).0nqs c-xni1 osyb6euz.t $1.3 \times 10^3\ \text{W/m}^2$. 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 brightnl+mynnhnt 0 0gc0r-(xess of the Sun as seen from Jupiter as compared to its b(g+hl0nx 0nt-m rny0crightness 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 Galae40gm-o (e qimt52rq axy would subtend if observed from the nearest galaxy to us (Table 33-1). Compare to the angular width of the Moon from a e-5i0oq 2g(mm qte4rEarth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes dmqa11 wwh)v2nd(el 8 a red giant, what will be its average density if it expands out to the h8(mn dlw2)11w davq eorbit 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 kb 4xy 8s 3pq4oc3k2jxwhite dwarf, it is expected to be about the size of the Moon. Whj4qx34b x2ysk3pk 8oc at angular width will it subtend from the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whose mam +rf w)fs/ca((yryip3 vgr:+ss is equal to the Sun's and whose radius s++f)(r vay3/wf ig ryr:mc(p 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 gqqh-07:;1ah8qugw ik;u skh is 1.5 solar masses has a radius of about 11 km. Calculate its average density and compare to that for a white dwarf (Problem 13) and to that of nuclear matter 7;ghq kisugh:w- 0aqqk 1u;8h.
$\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 1wul* nxv1ki g/:y; qjof Eq. 33-2. (The mass of the very unstable yvul; *igw :n1jq1k/x$^8\text{Be}$ 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 ap1xs9j 3-hwd xjwo0 0 65kgl*2nsnwdc oparent 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 sam nnkehg9l;; w8e distance from us. Two such stars he;kg ;hwl9 8nnave 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 Schwarzschild radius for a star with mass equal to -tcn rds6t rcy.**g8jthat (a) of our Sun is *.rry c-86* g dtjtnsc   km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typbm ra+o r8k. yw6b.r-cical galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a spher nw)2tsp)4o(8a u+*kal dux jbne iqd(73sy 7re, for which the sum of the angles is (a) 359º, and (b) 1xpoy)8ab jr ks7i 3aq+wu)(ndts 4(2*l7 unde80°.

  What is the maximum sum-of-the-angles for a triangle on a symi9 (ayx* qh4vrz*8p phere?    $^\circ$

  If a galaxy is traveling away from us at 1.0awy:r oklq r7c-). r;5z 7egun% of the speed of light, roughly how fakr.uqr oa:c ) g-y7e5 nl;7zrwr away is it? v =    Mly

  The redshift of a galaxy indicates a velocsj + g/jd 6ssf+yza0gw b3y.h+ity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a g*n7u,6 tnyxdl vb)f25wdm;sir w:o)galaxy (relative to us) that is near the observable "edge" of the universe, say 12 billion lightywo7nilv m)6 2 wxg*dtf;bsdru5,): n-years away. v =    c

  Estimate the observed wavelength for the 65 ( bwz8i dj:)(w4yexcklw)8f,vm 5ovh6-nm line in the Balmer series of hydrogen in the sl() m : y8vo5b f(,xhvww8k4jc)wdiez pectrum 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 the waveleng4z(+5wx+q bne l9 cnxlth for the hydrogen line at 434 nm is measured oe lz+5n l4( qnwxx+9cbn 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 win- ah 41e yi6n6.) lhhyuv: er)r0oryfth $z = 0.60$? v =    c

  What would be the redshift parameter t 3 5;hen2rvap$z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the D2irr97 ls sh/bm4mrd ;)xghr0oppler 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 blacc n12:*2ql:,mv bshcdcm/if u bedj8 ,kbody radiation distribution at 2.7 K using Wien’s law.,*sd id:bemc2cm8v2jhlnc 1u, bf/:q $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of tgdr86 3zn6k xohe 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 between galaxies) at any one )tmot x qv (x9qdkbq hzh/ws)8: 5:r,hmoment is believed to have been inversely t/qt( ),z b o:5vdqmq8x:)whkrx sh9hproportional 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 universe cooled below the ,b/v z3k kxll00 r9w4hexz2wbthreshold temperature for b4xvwblz29h0x ke,/kzl0 wr 3producing
(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 stars couse ,cye -h+1fccfc* ,hld 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,1,ehye +f -h,c*ccfcs describe the changes in temperature, luminosity, and size.

  Assume that the nearest stars to us have an absoa2*.zi/l ujd j*5 vrpxlute luminosity about the same as the Sun's. Their apparent brightness, *i*zvrx.a pjd52/l u jhowever, 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 moment)h+:,tc 6c yczuile3 zum to estimate the angular velocity of a neutron star which has collapsed to a diameter of 20 km, from a star whose radius was equac l6c )ych:u3z tize+,l 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 rotix ph7 ;ol9(/.5 iq(*r7n -ehe hawac8rkyxyhational kinetic energy change when the star in Probleay( kex 7.*yrr hq7pih5 - lxai9ewo8hh;/(ncm 56 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 times t* /c*dw 0,4mn,hf1pmeu utoa chat of the Sun, ,tcp 1 wnou mu,dh*4ceam/f0* with 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 Galaxy jy.rmh ihr:k7 1 0m7lfis 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 c)sx6g9) .cr+ umrzhq pritical density to close the universe. Assume the neutrino density is, liuhg q.+ 6zxprrsc9))mke 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 spect/3xgwutt t:z od2tq(;ra peak 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. Below) to estimate the ratio of tdxqtt2 tu(zo w/;g3 :their diameters. [Hint: see Examples 33-4 and 33-5.] $\dfrac{d_{400}}{d_{600}}$ =   

  Suppose we can measure distances with parallax at 100i(darm t *7v. bc+nbm1 parsecs. What is our minimum angular resolution (in degrees), based+ib*( nd 7armtvcmb. 1 on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balf4 3wwg(hxb-v mer lines from singly ionized helium in a distant star happen to overlap with the Balmer lines from hhg(wbf43x -v wydrogen (Fig. 27-22) in the Sun. How fast is the star receding from us? v =    C

  What is the temperature that corresponds to 1.8-TeV cobd5:t)eflchzmm. +q o ,m71cky 2jou1llisions at the Fermilab collider? To what era in cosmological history does this correspond? [Hi 1tmy:qck um+ljo, md.h)7ef21b5cz ont: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation of gas around whate0j v- -il)gxl 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 clouds is 60 light-years, what Dopplerg - lexj)l-vi0 shift $\Delta\lambda/\lambda_0$ do you estimate they saw? z$\approx $    $ \times 10^{-3}$

  A galaxy is moving away frpmwuoc a.4- q0om Earth. The "blue" hydrogen line at 434 nm emitted from the galaxy is measuraqc p.4u-0 womed 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 evolutioti0i)/q h2,b d 4tqyeyn, a star (if massive enough) will begin fusing carbon nuclei to form, for examplet i2), qqi et/0dhyy4b, 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 ;k 6bz/y9u aepax7d+zy d9 y/)j9hu vh
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 cr 4/nioa3a1lz citical density of the univeraczl/4n3i1o ase, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$