The Milky Way was once thought to beuu; z 2a(2fnsj "murky" or "milky" but is now considered to be made up of point sources. Eszfaujn ( 22;uxplain.

A star is in equilibrium when it rano+wy 0 g x.ol-:dqw7ldiates at its surface all the energy generated at its core. What happens when it begins to generate more energy than it radiates? Less energy? o wyl-o7 lwdq .:x0ng+Explain.

Describe a red giant star. List some of its propedpno4qz7u k 68 ydi8o/rties.

Select a point on the H-R dia-s .xi*d41oz +jl 8 nhlm5jv*jh8bhnggram. Mark several directions away from this point. Now describ ng8nv i.d8hm*+j sjbh4zoj* ll-x5h1e the changes that would take place in a star moving in each of these directions.

Does the H-R diagram reveal anything about the core of a nkfclc2x+;j )cqf uw,1 jo;:f star?

Why do some stars end up as white dwarfs, and others as neutron stars or blax+38m bxf;xyr ot.f v8ck holes3 8.x8tvxfxfm + o;ryb?

  Can we tell, by lookiny/tq+r739c cnay8fkmg at the population on the H-R diagram, that hotter main-sequence stars have shorter li839fc+/mar tnycy kq7ves? Explain.  ----待选择----yesno 

If you were measuring star parallaxes from the M6v 7cvtfpknf5) z+ 2w:/wdnk z5ikmb5 oon instead of Earth, what corrections would you have to ki):k5d7zwn5tkfwvpzmf2 6c b/ +n v5make? What changes would occur if you were measuring parallaxes from Mars?

Cepheid variable stars change in luminosity with a 1,b2xnlp au 6 e7u(sxs nsva*swda-+jz .h08x typical period of several days. The period has been f+ du- n, wjs(72.s xvalezs p1usx ahn0ab6*x8ound 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? What is its role in General Relativity2m 3+c0 3wwofyh a0vhf?

If it were discovered that the redshift of spectral lines of gal5iyoycb 8la/ 4)k(f gdaxies was due to something other than expgkla/oif c5yy( d4b)8 ansion, how might our view of the universe change? Would there be conflicting evidence? Discuss.

  All galaxies appear to be moving away from us. Aft d9coa*af 50re we therefore at the center of the univ5a 9*oc ffd0aterse? Explain.  ----待选择----yesno 

If you were located in a galaxy near the boundary of our observable uj9*f nsa0m 5tsniverse, would galaxies in th0*jts5ams n9fe direction of the Milky Way appear to be approaching you or receding from you? Explain.

Compare an explosion ona*g 8.ifvdd: y0jh*vh Earth to the Big Bang. Consider such questions as: Would the debris spread at a higher speed for more distant particles, as in the Bighd* d.fjy0vig h*v:a8 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 y3a)lh ckn.p g*5l 3xzmow9 )ci 7omm7black hole, then how can we tell if one is 77o img9m*pmc 53). nakl)3xowylchz there?

  What mass will give a Schwarzschild radius equal to that o,n/ g)(/vwag ev cqf18ii(kpi f the hydrogen atom in its qinw,i/eai(gv kc8 g(1vp/f) ground state? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion years. Find that time/ t.zck9taa 4sl5ots 7 on (Fig. oa.czsta 4/l 75ktst 9Below). People have lived on Earth on the order of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmidt+ 3wlb4q xn(acz*2fc microwave background radiation is. Where does it come from? Why is its temperature now so loxbt*a z+ lfc2d(n4w3q w?

Why were atoms, as opposed to bare nuclei, unable to exist unsy3jkl,cf2 nnasu/se-. 07 pptil hundreds of thousands of years aftesclu7sfy2ann k.p j, / 30e-spr the Big Bang?

Under what circumstances would th 2yc2retmitgtb5g: wrb l/(1 4e universe eventually collapse in on itself?

  Using the definitions of the pbu ** 3ls)h ),yff ,smrjugt+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 away is v+*hv 1 oty:g ;k-frplit? d =    ly

  The parallax angle of a star *e:01 kflu wacl:qk+ yis $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its parallax angle? e9yedkf ez(8-
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 fdm( x6o.fn* bis 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, will t22l21 za y7ysi fx9 qv+mfgzj7he parallax angle of the farther star be greater or less than that of the nearer star? By what factorf7jy21 s z9 y g2lxqv+mi2af7z?

  A star is 35 pc away. Hx2vsvp0 i16a eow long does it take for its light to reach us?    years

  We saw earlier (Chapter 14) that the rate energy reaches them9c vgdk t74y: Earth from the Sun (th4tymdc: 7gk 9ve "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 asvos(kl14 c49kxyb-kv +-c kq r/(pyx x seen from Jupiter as compared to it -y9vk(/b+xrxqk(c144 kscy- kv lpoxs brightness 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 5q cxw vw :co;fy94oh;if observed from the nearest galaxy to us (Table 33-1)4 ohc; 9yfwvq o5;xwc:. Compare 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 average density if it expadgall8 bb)jwk -b+y(9nds out to theg bab) +-wd yl8kb(lj9 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 dwa2 )q lr*hxbgl5rf, it is expected to be about the size of the Moon. What angular width will it subtend from the present distance to E*hlr5 qb)l g2xarth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwar h-t2x r40tgn ctfeb6ob:kf.6f whose mass is equal to the Sun's and whose radius is equal to the Earth's. How many times bne trxtfg.2h f o466c:btk0- 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 sot0 sji6vo7ts 3zl0s t:lar masses has a radius of about 11 km. Calculate its7o vt6tsjsi00s: zt3 l average 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 fmyau q4v*ib a3i)*07no:qvxEq. 33-2. (The mass of the very unstable4yvf3 *aqinoquabvm0*i7: 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 apparent brightde +l,c k0co2gness $l$ 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 twfd l.s)s 3j8floj8ghh*0 w v:he same distance from us. l8h)jlhd g 8f0.wfo3vj s:ws *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(*an)qv-zp ya radius for a star with mass equal to that (a) of our Sun is anvy-z)q a(* p   km, and (b) of Earth is    mm.

  What is the Schwarzschild r-)5f a6vt8ws nk5- qhc djvlo1adius for a typical galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a sphere, for which tx, n.uu o4m+rfxb2p+f he sum of the angles is (a) 359º, andfb +.2pr xufno+,u 4xm (b) 180°.

  What is the maximum sum-of-the-angles for a triangle on a spher. ;cly (fph(p )ei9izre?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the speed of light, roughl3;q qao*u2fg p(hs b+yqf,p6sy how ay(uf phs+s23g 6q; op*qb,fqfar away is it? v =    Mly

  The redshift of a galaxdq lu7b gmth7b0mi r2*9;*6bl np /sewy indicates a velocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (relative to us) th phnd.+etpk33ro5u u8at is near the observable "edge" of the universe, say 12 billion light-yeo5 eutukr 3+3hnpd8 .pars away. v =    c

  Estimate the observed wavelength for the 656-nm line in the Balmerv- moab. (+ ty(r u(xq1ahpsq0,t0uyv series of hydrogen in tm100+tqbu (r,p.uh v-yav (aq yos(xthe 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, and its 1uz)tkwqog. e1jopc8 4f-kr 0distance from us, if the wavelength for the hydewoqk1c- 8)1rftp.kzj0u 4 g orogen line at 434 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 a galaxy withkho owej/60+t $z = 0.60$? v =    c

  What would be the redshift para*ch g62qtc*b dgqptq*o 9 zlkp,* -kq*meter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, p :c(fq9bd+xlct;,lu show that 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 the peak of the blackbody radiati3vu:2+aznb j7gok* jpbc; v4won distribution at 2.7 K using Wiw2zvj3 4+k;7pvj*bbng:oacu en’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closksl;/mztuq-4ul 20 (wgwr7dpure 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 7qvr4 o7ihx2 vjoe 8ldmm/l-n4 -z4fcany one moment is believed tom7e2xi448m r 4-oovnq 7l fvdhz-/jlc have been inversely proportional 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 bo+i v7+z0lyxr9ld;n m cm z;(b9qi1rwelow the threshold temperature for prod1m79ryw9zbmxq+inr0il l( vocd; z+;ucing
(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 could un-ss o 64 m*n,o s01d9xeezhmm 6*qfubguvt1a2dergo the three changes represented by the three arrows, A, B, and C, in the H-R diagram of Fig. 33-2hsv tmuofsn1 e*ma* gbm4s01,6eo6 u29zq-d x8. For each case, describe the changes in temperature, luminosity, and size.

  Assume that the nearest stars to us have an absolute luminosity about the sa)q tjicnt:hne242tt*ox + kj* me as the Sun's. Their apparent brightness, however, ic)kt *qtoj 4:x 2nt2+ejnht*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 ve1c icul.dwe8b i)olj c9 *tw9fbzh5* (locity of a neutron star which hdicth uc19blc)* w 9e8.fi*(ob zjw5las collapsed to a diameter of 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 rotationa:zmp(w /ucg mdg ir8;j2 hxx2.0o2ko+jhw j6gl kinetic energy change when the star in Problem 56 collapses6hxox22jwuj0;mp . gr/k2i oh8g : mdw(g+jcz to a neutron star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believ9u5 i 3yjl 1ur*;.nhsqkp4 kqsed to be a neutron star of mass 1.5 times that of the Sun, with diameter 20 km, is observed to have a rotation spus1;3nk9sjrphq5.i u yq k*l 4eed 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 galaxgw+3(codb*qe c ,lv l)y to our 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 provide the critical density to lrz r)t pagca up)1f;.20dp*f close the universe. Assume the neutrino density pzrd c*ulpra0 pf).;af2 tg)1 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 speca i;)2pxf wn.mtra 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 diagraw i2;ap)nx.f mm (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 di9w9is i6kqopvy 7+ /sg5w8btcstances with parallax at 100 parsecs. What is our minimum angular resolution (in degrees), based on thisbo9tkisgsywv+8 i/p c5w7 69q information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from singly ionized heli )9bomjs6iw c fa*:sm5r y:*jeum in a distant star * omaeric6*ybwmsjs f5::) 9jhappen to overlap with the Balmer lines from hydrogen (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 collisions at the Fehm0sd:a, s) uib2gi ;hrmilab collider? To what era in cosmological history does this correspond? [Hintgdm):bu i ihah;2,s s0: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measu qr4g2fqp p1 ca43f.cmred the rotation of gas around what might be a supermassive black hole of about 2 billion solar masses at the center of a galaxy.q r44 c1pm 3cf2qfa.gp 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 away from Earth.1bfcv t )3rqd:c (xrb. The "blue" hydrogen line at 434 nm emitted from the galaxy is measured31cbrtbx .f(d:v rqc) 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) w z-ooyl1ihj ql2u.0/4unz t;pha ; o,till begin fusing c. i1nz lo2u pu,o/lo-;zhty4jha0tq ;arbon nuclei 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 *rs(p:8cv,-yz fh-j injm i*d
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 t6d,bm u6(nyrm he critical density of the undymbnmu,( 6 r6iverse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$