The Milky Way was once thought to be "mury,r8 x2czd2d78s7 cvsh6yb z lky" or "milky" but is now considered to be madeyrxc 7 dsvb,yzsz c276d2lh88 up of point sources. Explain.

A star is in equilibrium when it radiates at its surface all the enerj68, ;wdevob+gxr/icxmc/ l 7gy generated at its core. W dcv ;//e,c67rw x jixoml8+bghat happens when it begins to generate more energy than it radiates? Less energy? Explain.

Describe a red giant star. Lijzv+q8w0m -gcst some of its properties.

Select a point on the H-R diagram. Mark several directions away from 00 0gbf: xj)y za/2zdn hb*rz4 virav6this point. Now describe the changes that would take place i: bb 6hr 4v z)xr2n0yjfv/azg0a0 zd*in a star moving in each of these directions.

Does the H-R diagram reveal anything about the core of a s g,e73 z0we0aaa3j ifltar?

Why do some stars end up as white dwarfs, and othersz:zz8 (wx 7lxp6dz.lk as neutron stars or black holesld w(6x8.pzxk:z7 lzz ?

  Can we tell, by looking at the population on the H-R diagram, thu *h0qnz;k-ghat hotter main-sequence sthk; qnz* -u0hgars have shorter lives? Explain.  ----待选择----yesno 

If you were measuring star parallaxes from the Moon instead of Eartv2 ua0m jzey cw:n9v90h, what corrections would you have to make? What changes would occur if you were measuring parallawnze009ya:vj2c v9 umxes from Mars?

Cepheid variable stars change in lugvi cjjw 2*)k+minosity 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 used to measure the distance to gal)c 2+*iwvkgjj axies?

What is a geodesic? What is its role in General Rel ui1/d.gu+kqkilgr;8 28k+ q qk(mps sativity?

If it were discovered that the redshift of lg wp21p*in7vi np6,, /rbcsyspectral lines of galaxies was due to something othe2bl1 cn,yp/n pi*g7 svp,wi6 rr than expansion, how might our view of the universe change? Would there be conflicting evidence? Discuss.

  All galaxies appear to be moving away from us. Are we therefore at the cen 65 4+n) vvp ih)ggyswgi7c*dlter of the universehp)7dcyg v lvi 4g* 5gn)s6+wi? Explain.  ----待选择----yesno 

If you were located in a galaxy near the boundary of our observabl2oz7gi17 vl,y) z7h-fl esaqfe universe, would galaxies in the direction of the Milkvegi l71a)zso-yq h fz7,f27ly Way appear to be approaching you or receding from you? Explain.

Compare an explosion on Earth to the Big Bang. Cikez1rani mf c8qwv 0/om 8ax+7g/ 0l-onsider such questions as: Would the debris spread at a higher speed for more distant particles, as in the i 0ofc1qe vng80/ x8-r/a+w7a mzmki lBig Bang? Would the debris come to rest? What type of universe would this correspond to, open or closed?

If nothing, not even light, es9 qb1vwgvpg1w8w rcrg6s 7r87capes from a black hole, then how can we tell if os6pv1g98 wrv78rc 7 g1wrw bqgne is there?

  What mass will give a Schwarzschild radius equal to that of the t 2z3wov fok)7hydrogen atom in its ground state? M vtf23owk7) oz =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion years wjj85aifm:.q . Find that time on (Fig. Below). People have lived on Ef.5jw8j:m qai arth on the order of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic microwave qscp,07ov.au; za3nq4t) xynbackground radiation is. Where does it come from? Why is its temperature now so low?aau3 oq yqv s.tc;0xnn,7zp) 4

Why were atoms, as opposed to bare nuclei, unable to exist until hundreds of thoo+)dh kggnneqo3 h)m(z6 qd, 7usands of yea (dezg+ 7)h ,kmgn6ohqoqdn3 )rs after the Big Bang?

Under what circumstances would the universe eventually colla eyg*pos 8hzsl;s:p5 0pse in on itself?

  Using the definitions of the parsec and lwffiwhi6d r ((9.zwpm - 2;ttthe light-year, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.38 seconds by eg px*iobv5:x33(o, gl/k8et,j uuof arc. How far away is it? d =    ly

  The parallax angle of a5z,r8m/9rev.**en ii+qlxyd9 f jon a star is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away.krg0/ 62jvzvtd..wwf e7/ /hil mkm:t 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 ..do-t: gs:4r d vtelathat is 55 ly away? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away fromigtiqh5w)e0rf)dl1 7,wwo( f us as a second star, will the parallax angle of the farther star be greater or less t) gdfl(7 hi0r1f ,qww ow)i5tehan that of the nearer star? By what factor?

  A star is 35 pc away. How long does it take for its ligh0rpqtg;uiup)nd8 (q2wf:s w8lik -*h t to reach us?    years

  We saw earlier (Chapter 14) that t/;m j.gtn7lcc j dbg//he rate energy reaches the Earth from the Sun (the "solar constant") is abodj7. m/ bg/ j/;clngctut $1.3 \times 10^3\ \text{W/m}^2$. 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 brightnessnyh c8r/t-5 278aofb 6p2wfz u5bogxm of the Sun as seen from Jupiter as compared to its brightness from Earth? (Jupiter is 5.2 times farther from the Sun than tofr 8a2o76hfcpgw -ybz 25 u nbtm85x/he Earth.) $\dfrac{l_{\text{Jupiter}}}{l_{\text{Earth}}}$    $ \times 10^{-2}$

  Estimate the angular width that our Galaxy would subtend if observed from thb,j0m8meoz,fgg t ..te nearest galaxy to us (Table 33-1). Cogf,mt.,mo8j.te0zb g mpare to the angular width of the Moon from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, what will be its average6qth1ac3f (vx density if it expands out to the q36fv 1cx(tahorbit 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 si1v6v)w- ricq l cp*c;tz:u-gaze of the Moon. What angular width will it subtend from the prgv*lc): ; aq6u -1rvcipztc-wesent distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density :ogkg 3q 6i7yhof a white dwarf whose mass is equal to the Sun's and whose radius is equal to the Earth's. How many times larger than Earth's density is this? y6hk :gqoi 73g
$\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 s*x4e rz1-7w wwelkg*g olar masses has a radius of about 11 km. Calculate its average density and compare to that for a white dwarf (Problem 13) and g -rz wk4le*w* e17wxgto 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 6giqx6y;rb .zthe He burning reactions of Eq. 33-2. (The mass of the very uns q xz;.ri6yg6btable $^8\text{Be}$ 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 apparent brighhldj: -w9c-br2sx1y pj q6b7ntness $l$ 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 assum)yees :l-* d4 em; hxfdy;f3sb:y+dzwed to be about the same distance fromwe-)z: xldbfs yym ded *h;ye+3:4 s;f us. Two such stars 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 Schwarzschild radius for a tgzjr g1l+ 5h.star with mass equal to that (a) of our Sun i5jl.gg 1h tr+zs    km, and (b) of Earth is    mm.

  What is the Schwarzschild radiu+klfjos1ut6q4 x0ntd6 e 1xo+s for a typical galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn qalz(p 0i-i k7on the surface of a sphere, for which the sum of the angles is (a) 359k 7(z0qi ipal-º, and (b) 180°.

  What is the maximum sum-of-the-a6pmfpqfx ;k++ g0caq*y lko:3naxq :a41 5ub rngles for a triangle on a sphere?    $^\circ$

  If a galaxy is travelingoxajex 6:sm ;-a 91fk/m4fkj1 az4x xy away from us at 1.0% of the speed of light, roughly how far away j oxf 94mzx aax:mfya s14x1jk6/e;k-is it? v =    Mly

  The redshift of a galaxy indicates a vel*ljti*9 ,h f(ia jat)gocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (relative to us) x(dnb-d)5 axwla v;v.that is near the observable "edge" of tx;v aalwx-v(b)n 5.dd he universe, say 12 billion light-years away. v =    c

  Estimate the observed waveeldi;e(j 0r 8slength for the 656-nm line in the Balmer series of hydrogen in the spectrum of a galaxy whose disldi8 ej;0e( rstance 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 lqph 9,s08hth --wuab distance from us, if the wavelength for the hydrogen line at 434 nm is measured on Earth as being 610 nm.lhw p9 ,a--hsqt bh08u
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 galax phiru.u qv9zw09y(, qy with $z = 0.60$? v =    c

  What would be the redshi)j(k;jc dn, ceft 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 wav:w3* nefj(n37xtaj zr /f.ems elength 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 m z.* j1p-bpceph6hp6 of the blackbody radiation distribution at 2.7 K using Wien’.6mb-pepc* h1zpjh p6s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical densityks.)( . mzxyl(vb ovlmr69a5u for 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 between galaxies) at any onv n854)zq zmmbe moment is believed to have been inversely p5nm4mq v 8zz)broportional 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 tn 7pt+w*srt*w2rc )uzx:6 cefj;,bl py 97yhmhe threshold temperature , mzw7w+ pbrc6;yjl2nrh*e )9t:f7y p*t ucsxfor 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-sequej-g2sh * xwfa0nce stars could undergo the three changes represented by the three arrows, A, B, and C, fwa2hj0x * sg-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 l5 l4 jq8xok6.b.(c p*uwpk bhnuminosity about the same as the Sun's. Their apparent brightness, however4k5*xchp nlbbu.(w. po86 k jq, 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 eudgc.5v.zi2h - ,ofdangular momentum to estimate the 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 ourvddo u .5fh-gc e.,z2i 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 rops tf/2f jw9+ttational kinetic energy change when the star in Problem 56 collapses 2p+ s/tf9jw ftto a neutron star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believed to be a neut)4zp co n5u.knron star of mass 1.5 times that of the Sun, with diameter 20 km, is observed t .ouznck4)5n po 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 our5ihjytn,c0 *w+;nwgsuajgj7 94mraw; -(jen 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 neutrinh4 rnfywu8yv5pa3 v,+o rest mass (in eV) would provide the critical density to close the universe. Assume the neutrino density is, like photons, about 8 u4ywvv +rhpy5f ,3na$10^9$ 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 spect0,1b7t m1 / fl0rhei:qtedrzora 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 ratierl,o 1tmr7b hz01 /tedqi:f 0o 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. Whaf1tk,qej8u a9x l:1 ght is our minimum angular resolution (in degrjg9u8a, :kxh f1qlte1ees), based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from singly ionized helium in/a ma.5o(gow g3, c(bhmtw,dw a distant star happen to overlap with the Balmer lines5,.m o( bcod3 mggwaa,tw w/h( from hydrogen (Fig. 27-22) in the Sun. How fast is the star receding from us? v =    C

  What is the temperature that corres-9hqsb7lu g 7(l;fgpaponds to 1.8-TeV collisions at the Fermilab collide l;f lqbagug79- h7ps(r? To what era in cosmological history does this correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotat5tr c:b t0iy3sion 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 to the gas tcy305sib:tr 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 from5gd / ug 8c:g4hti-xkq88 plhq Earth. The "blue" hydrogen line at 434 nm emitted from the galaxy is measured onpd/uqh - i8lct58hgxgqgk4: 8 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 evolutiokwpnoqx/0 sqd g*8.w1 n, a star (if massive enough) will begin fusing carbon nuclex1nsg*8wp0q .qo k/dwi to form, 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 s8 v/glirxll9q42p 5*elns 9 v
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 of th t*i9ugg) -b wd,jj1pne universe, *t-pjgbndw,u) i9gj1 $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$