The Milky Way was once thought to be "murkyqaq ui 0n.d*c;,+gy fz" or "milky" but is now considered to be made up of point sourc0ay if +c qd,.z;qg*nues. Explain.

A star is in equilibrium when it radiates at its surface all the 1ftc.0 )uk . 0w1qbheg ngg4geenergy generated at its core. What happens when it begins to generate more energy than it radiates? Less energy? Ex w fg1.g. hg4bee)u1tck g0qn0plain.

Describe a red giant star. List some ofj1h,:i61 giyj zv,utg its properties.

Select a point on the H-R diagram. Marky39 ribc8j0jv several directions away from this point. Now describe the changes that would take jb v 9j8i30cryplace in a star moving in each of these directions.

Does the H-R diagram reveal anythin;fsda r2gl s,4g about the core of a star?

Why do some stars end up as white dwarfs, and others amh7tm *-,n(r0e ,jo )bgo8xhjho uio6s neutron stars or black holes? on 7,b8ehuoh ,0ogi *(-o)6 mtrxmjhj

  Can we tell, by looking at the population on the H-R di v4/ce r:ia 37vy;gaujagram, that hotter main-sequence stars have shorter:/g3iev jv ;ay4ucr7 a lives? Explain.  ----待选择----yesno 

If you were measuring staz)*sl xevr + 37yor/*jdx*ty.6vo ebgr parallaxes from the Moon instead of Earth, what corrections would you have to make? What changes would occur if 3oevobty/.6g 7 +*s *dx r*rjvz)lyxeyou were measuring parallaxes from Mars?

Cepheid variable stars change insnt jxnd (1nm*c/u9h 6 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. Hmn9 *x6ntncj h1d /u(sow could these stars be used to measure the distance to galaxies?

What is a geodesic? What is its r3 jdujcj*4-j pole in General Relativity?

If it were discovered that the redshift of speha10 gk 1czv1uctral lines of galaxies was due to something other than expansion, how might our view of the universe change? Would there be conflichzg1u0av 1k1c ting evidence? Discuss.

  All galaxies appear to be moving away from us. Are we therefore at the center ofnm4 msw+ss- g+ the univ4+sgn-sswm+m erse? Explain.  ----待选择----yesno 

If you were located cf:.8 cup;efm67 -kjdkbipy3in a galaxy near the boundary of our observable universe, would galaxies in the direction of the Milky Way appear cjcf-pi 7.f 3ke;u pm:by6k8d to be approaching you or receding from you? Explain.

Compare an explosion on Earth to the Big Bang. Consider sucju2on dnplu/my*) n+8 h 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 of universe wounn8p udjm2y n+o*u)/ lld this correspond to, open or closed?

If nothing, not even light, escj*e,vs6 md m.yapes from a black hole, then how can we tell if one is ther*mymdevj6s., e?

  What mass will give a Schwarzschild radius equal to that of the hydrogen atom bu6sn7;b5f. 8ur pbl. w y2vhzin its ground star 2swnzv5;plb7u8ubf6 by. .hte? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given ux7o7yuvq yble4ftk1) r8.0t as about 4 billion years. Find that time on (Fig. Below). People have lit7xvyr1ku78) t.ofuq4 lybe0 ved on Earth on the order of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic microwave background radiation is. Whew(x7wk m 7piqz1ag2o 47fso* +ma3sbgre does it come from? Why io*i a2737+ogs wzm fg( mx7aw1s4bqkps its temperature now so low?

Why were atoms, as opposed to bare nuclei, unable to exist until huhi u.p ee29fvsv a/t3)ndreds of thousands of years after thev2/v)teua .93f phs ei Big Bang?

Under what circumstanv0e 8i9/ zo4o/j v 2k+rbmkrbnces would the universe eventually collapse in on itself?

  Using the definitions of the parsec and ,+ qtqml9ui-ta j3gn ;the light-year, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax 76wxsrx hjq5 i i8(w3vof 0.38 seconds of arc. How far away is it? d =    ly

  The parallax angle ofy o,8yz0ps lh* a star is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its poh,x))ct*lzwn y1 bu9arallax 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 ths:s-q;dybb+1gp;* :12k ri zi ohbiapat 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, wi7xib1 d;eim *xc hg-;bll the parallax angle of the farther star be greatix1-cb;*ghei d 7x mb;er 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 reach9 8nj, gm )edipqr6p-xw rn6h* us?    years

  We saw earlier (Chapter 14) that the rate energy reaches the Emjz1 r ,e2 /onkkpmn+te5qe7 .arth from the Sun (the "solar constant") is eqnkmm2z7o, /j.+ r kp1ete5n 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 Jupitec)70 gw 5vkkb bb+*ujir as compared to its brightness from Earth? (Jupiter is 5.2 times fartheb k5vic*0bku7b)+wjg r 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 tzp *r)l6 5mgj a79olbjhe neo9a6*rgll 7 z5)j pmbjarest galaxy to us (Table 33-1). Compare to the angular width of the Moon from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a re7fl h( 8 )ubalsue7ou9d giant, what will be its average density if it expands ous978uuf) lh( 7eblaout to the 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 dwarf, it is expected to b/xst+ joe 11bwb*pz4v2 .asy xe about the size of the Moon tjv +b s4xyzp2*xwoa11se ./b. What angular width will it subtend from the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of6z pdpln/cs5* a white dwarf whose mass is equal to the Sun's and whose radius is equal cp z5lp s6n*/dto 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 is 1.5 solar masses has a rad2algt0kml r z..c ;*.rzsrr9kius of about 11 km. Calculate its average 0r grzktkcm2. ;zs.l la*9.rrdensity 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 forkn)(*8 bbeaxlu +9q,cet vf3c the He burning reactions of Eq. 33-2. (The mass of the very unstablea3c u89bc( xef l+n)*btv ,ekq $^8\text{Be}$ 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 samem966j g3a dyezdc2zv* 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 as s:cw1 f; ) 8;di9jw*x,j0ecx sycucygsumed to be about the same distance from us. Two sj,c8cwcjd)xuf01 9; ;gcs s*w :eyxyi uch 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 Schwarzschilzr1wf;x+ woilr0y1y :d radius for a star with mass equal to that (a) of our Sun ifo;yz r:11wl w rx+yi0s    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typical galaxy (like ours)? ;,o z+seq 4q*+qebpe kR =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a sphere, for which the sum of the aa49c9sqcep/ d ag dvh,(ir hyf5h82.angles is (a) 359º, and (b) 180°.s vdc r f4e2gc9iqa h(yh 5,d8a/h9.ap

  What is the maximum sum-of-the-angles for a triangle on a s;b5ul h2f8schgtc3 6r (xpa 4vphere?    $^\circ$

  If a galaxy is travelilob3n um5 5.1bvrw6q,ama zh3ng away from us at 1.0% of the speed of light, roughly how fw a5z5lr,3vh6aum1n3bom. b qar away is it? v =    Mly

  The redshift of a galaxy indicate*fs0;. gsfoa,dvc2tus a velocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (relative to us)m b+sns: ipx(ia2n t gv*8f7;p that is near the observable "edge" of thna: is; xv8t*7+ sn igpb2(fmpe universe, say 12 billion light-years away. v =    c

  Estimate the observed wavelength for c;18 hl2q vxxtthe 656-nm line in the Balmer series of hydroge82xclx1v; qh tn in the 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 distance from us, if the wavelength for sh d i49 x*)hslwl*qb12r9zw othe hydrogen line at 434 nm is measured on Earth as being 610 nm. iw slobh1r9 9 wlxs* qz4*2)dh
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 galaxdv85q9lu 0qrxy with $z = 0.60$? v =    c

  What would be the redshift para;whc+kdu (/ hr 81qic(5kiydcmeter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Doppler shift in1ek(ok+swyw6 8 g/i ek0dnx9h 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 radi5 .ac(drmpk9 qation distribution at 2.7 K using Wrm q5 kp(a9d.cien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of the unive 1qgj6u n21rqx9jn,k5 qjxk z)rse 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 gad 4kfxw+78b idlaxies) at any one moment is belix4k f8+iw7bddeved to 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 below the b50r 4wtcu:qcs +qd( tthreshold temperature for producing dcs+0c ubt :qrq(4 t5w
(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 dtwfyqb*sxl1;: cpy op3s t* w66tj1)stars could undergo the three changes represented by the three arrows, A, B, and C, in the H-R diagram of Fig. 33-28. For eachj1cyt)6w *fq6;x :wsptp3d s1tybol* case, describe the changes in temperature, luminosity, and size.

  Assume that the nearesyt lha0m1 q.*xwkvq66z )dbhatc 6h2/ t stars to us have an absolute luminosity about the same as the Sun's. Their apparent brightness, however, lh)xby2* a0a/h16tqz6v6 .w kmch tqdis 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 1h9-wngu xdt,4/rhnbr.a ve.angular momentum to estimate the angular velocity of a neutron st .h9,.4erv ath rnwu1g/bn d-xar which has 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 rotatieu4qp6/z8ka qi/i p1n onal kinetic energy change when the star in Problem q81kp6p/i4aq ziu n/e56 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 maj*e8gtgr aahgpy, u+ a*3a*:k ss 1.5 times that of the Sun, with diameter 20 km, is observed to have a*h*raa8upag3:*,tyg + g je ak 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 gala)sl/j9noa w+g- ab. znxy 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 neutrinoa2s(h+ogch / t rest mass (in eV) would provide the critical density to close the universe. Assume the neutri hash (2+t/gocno 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 peak at 600 nm bgpxmmj , z5zc(+ rs o7i:0/grand 400 nm, respectively, both lie on the main sequence. Use Wien's law, the Stefan-B, pb5x7z0s:g(z+ jo imm/rcrgoltzmann equation, and the H-R diagram (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 distances with paralpd x/rpi8 mx5.lax at 100 parsecs. What is our minimum angular resolution (in degreesx5irx/d8pp. m ), based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from singly ioniz2 ot b-,u giov..olg*ned helium in a distant star happen to overlap with the Balmer linto o.gnl*g-ouv b, i2.es from hydrogen (Fig. 27-22) in the Sun. How fast is the star receding from us? v =    C

  What is the temperature that corresponds tsm/p xr z9+c;co 1.8-TeV collisions at the Fermilab collider? To what era in cosmological history does this correspond? [Hint: see p;cs c/m z+9xr(Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation of gas around what miqh9r zg nfqxb3l*ra1 0m3g;c2 (4as z8tvq1zwght be a supermassive black hole of about 2 billion solw8z a41 z3f19l q 2n rgczqms(rqg ;thxa*vb03ar masses at the center 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 away from Earth. The "blue" hydrogen .* (m0m rzthnxci/1 w8ch*t hbline at 434 nm emitted from the galaxy is measured on Earth to be 6crw(i08xnh**cmhb 1mtzth/ . 50 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 enouggmqqzyc t (ea-q(4ha w1 74tj6h) will begin fusing carbon nuclei to form, for example, a- j4e qcth6(a gzqwt74myq1(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 reactio66 l onoahj xe. okk/xr(8/e -xt6cl+en
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 oqu3ibjklh:1p ck/+;v a6kn n7f the univeu nb7 q6 ckli3av h1pj;kk:n/+rse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$