The Milky Way was once thought z(hwaoxk z-y - p*o9o/to be "murky" or "milky" but is now considered to be made up of px- (kpwa*zho/zoo9 -yoint sources. Explain.

A star is in equilibrium when it radiates atqd(e . )oav(up its surface all the energy generated at its core. What happens when it begins to ge(.p (duo evq)anerate more energy than it radiates? Less energy? Explain.

Describe a red giant star. List some 3vq)gz s8me 8estz:*aof its properties.

Select a point on the H-R diagram. Mark several directions awa)ks z3-kxo kw1y from this point. Now describe the)z1kxokk-ws 3 changes that would take place in a star moving in each of these directions.

Does the H-R diagram revue0j g-) m/vzaeal anything about the core of a star?

Why do some stars end up as white dwarf ,f,3-d,ri2vql cpzdiz(jr s+s, and others as neutron stars or black hol(i -,qpdirs rlj+dz,3f vc2, zes?

  Can we tell, by looking at the populati07pj qx m:v+baon on the H-R diagram, that hotter main-sequen:+x0p7 qabjvm ce stars have shorter lives? Explain.  ----待选择----yesno 

If you were measuring star pamr q u8-q amluga/0x92rallaxes from the Moon instead of Earth, what corrections would you have to make? What changes would om q axuaqr9 -82l0/gumccur if you were measuring parallaxes from Mars?

Cepheid variable stars change in luminosity with a typi1/9vbdwmrc : :-lwt;1jn zisucal period of several days. The period has been found to have a definite relationship with the absolute luminosity of the star. How could these s wljwvm:s9zi1c- 1 ;d/tr:nbutars be used to measure the distance to galaxies?

What is a geodesic? What is its role in Genxv(8bbub m5gaxu4v c x0.2g9bwda:f(eral Relativity?

If it were discovered that the redshift of spectral lines of gal j5q3-rn,egi xvzk);jaxies was due to something other than expansion, how might our3x,) qjivegkjn 5-rz; view of the universe change? Would there be conflicting evidence? Discuss.

  All galaxies appear to be moving away from us.5po*4ne my. uke9 bf3ob+. itt9aev ;u Are we therefore at the center of the univ 9um*t; ft.n+eoe.k5a 9yiu3pb evb 4oerse? Explain.  ----待选择----yesno 

If you were located in a galaxy near )gdd -n;m lci+the boundary of our observable universe, would galaxies in the direction of the Milky Way appear to be approaching you or receding; nmg-dil +c)d from you? Explain.

Compare an explosion on Earth toyt 6d / ,)1)h;:ia-ufxa9axl dck ruxm the Big Bang. Consider such questions as: Would thx)x adumy 1ha)t,:x96-lf /;ckriaude 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 would this correspond to, open or closed?

If nothing, not even light, escapes from a black hole, then how can we tell if ho,ig-d d5+7vv eki0kg3xe3m one is 5ekxm+iev0v3hog 7d3 - dk,igthere?

  What mass will give a Schwarzschild radius equjvm l. - +y4hbb wz*ry(r3v(rval to that of the hydrogen atom in its ground state vzwvmb3r bj4l+( yhry.-v*(r? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as adgw)fb /k:m4about 4 billion years. Find that time on (Fig. Below). Peopl)fw bakd4m:g/e have lived on Earth on the order of a million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic microwave backe99b nsawchb l: l6u 0ox5y41tground radiation is. Where does it come from? Why is its temperature now s yw bull 0a:xnt4eso16c995hb o low?

Why were atoms, as opposb 4pfkh(t a5/fed to bare nuclei, unable to exist until hundreds of thousands of years after the B fbhkt/fpa4 5(ig Bang?

Under what circumstances would the universe evz 17 q.6dd/tnp swhb/bentually collapse in on itself?

  Using the definitions q1xop xb-7sc1of the 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 awahtr5zn z x-3 i;bmfb59y is it? d =    ly

  The parallax angle of a star is6giwh t 0u.ihb8cyq4* $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its parallax angle8jtu*zwf lnbs d4g.o)/i-vp+?
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 - 4wp,(dtcnep 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 star, will the parallax 1z6 f 9 vm d5w asiw.t*-kajzdwrq33g-angle of the farther star be greater or less than tha.fz dmzwt-g 3-5a9 3dr6wk iv1s*wajqt of the nearer star? By what factor?

  A star is 35 pc away. How long does it take for its lig6+ 2*vbpp ;h cvn)mqiqht to reach us?    years

  We saw earlier (Chapter 14) that tht7zc3 re 5akyr h2)no6y- qo-ge rate energy reaches the Earth from the Sun (the "solar constant") is about qeta7 rko3-gz2yno5ch y) 6r-$1.3 \times 10^3\ \text{W/m}^2$. 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 wpmwwq+15 ikv2h;p w;seen from Jupiter as compared to its brightn+ipp1;w2ww;vk qh w5mess 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 Galhrr(qvh*)hr*e2,h2t.wwtptu 87 vd/ poa*y eaxy would subtend if observed from the nearest galaxy to us (Table 33-1). Compare to the angula 2a*t hhvttp*(*2re,/ 8. wp7uwrvoqyer h )dhr 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 exusacqp38 l,s 68x: ozsisb. i:pands out to ths :z63.s:u pl,b qscsoi8 8iaxe 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 be about th bf(2pmzn;vuj vrh7,,e size of the Moon. What angular width will it subtend from the prh b7rf;pz v,,2nj mv(uesent distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a ban7bl wh6w+ *deub5 1sha2)xwhite dwarf whose mass is equal to the Sun's and whose hxl a nsb7*b 1u w+bde2hw65a)radius 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 is 1.5 solar masses has a radius of about 11 km.enool lb b2+4, Calculate its average density and compare to that for a white nb obl 4o2,+ledwarf (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 Eq. 33-2. (The mass of tft xp:4xqx/om-l7 g2 y i,y ded5r+:59fswviz he very :i2,gx 5yms+ tzid ov7:y 4-/9df xpexwr5fq lunstable $^8\text{Be}$ 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 brightw)binv )k/ b.bness $l$ 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 kh 8lose;2iq 31 vc4dvto be about the same distance from us. Two such stars have spectra thacloqs i 8hk;2e1v3v4 dt 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-rns9rnqd4t / equal to that (a) of our Snrq-ntd 4/9srun is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typical galaxy (like bt1r4.nji)db ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surfp1t(eu.v3 22zbsdc bo ace of a sphere, for which the sum of the angles is ( ebub.2ptzvcdo( s 312a) 359º, and (b) 180°.

  What is the maximum sum-of-the-angles for a triangleneh*ti:hl-t 1uh ve8(3z hi 2q on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% odm **lfr-0did xob00. pc1ok kf the speed of light, roughly how far away is it? v = i**lx -rp o 0kc0 fm10bkdddo.   Mly

  The redshift of a galaxy inzhgc i*j*v p1s +knr) l3()f8otm icc4dicates a velocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (relative to us) that is near the observable "edgk kdx (kyi3:b+e" of thi d3k+ykx: (bke universe, say 12 billion light-years away. v =    c

  Estimate the observed wavelength for the 656-nl3)(g. 8 mgxw+nypg unm line in the Balmer series of hydrogen8g)xw nglgnp.+u(y 3m 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 gl7xw 1jsp99s /k2tzngalaxy, and its distance from us, if the wavelength for the hydrogen line at 434 nm istskngp9/x7 9jl 1w 2zs 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 galax +:.(0tpcbuxc -r iprdy with $z = 0.60$? v =    c

  What would be the redshift parame ,. im1o6fnifhter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-q/yg9 5p-tp0gy v tn/r3, 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 radiation distributio4 ku1zdejih24yiwg-gs5v b0, n at 2.7 K using Wuv 40ig5jwbis2zey h, -4kg 1dien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for c4. lhq(jokljd7tno0/ losure 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 4rd0x-j1a5 gntir;b5awy j00zzl 4.a q w u;cdaverage distance between galaxies) at any one moment is believed to have been inversely proportional t0d15d;4z5t aqzaw-l xn g rijr40c0.uwayj;bo 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 eu cih9kh9i0:threshold temperature for prod i:e ui9c0hh9kucing
(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 undergo the three cu;7(py0 v o x3vde,xwnhanges represented by the three arrows, A, B, and C, in the H-R diagram of Fig. 33-28. For each case, describe the changes in temperavyu w3v op,0d7(xn ex;ture, luminosity, and size.

  Assume that the nearest r u6ko*j(m, austars to us have an absolute luminosity about the same as the Sun's. Their apparent brightness, however, is oj*ua, r(6km uabout $10^{-11}$ 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 estpnvvj,,)l: fy imate the angular velocity of a neutron star which has,,:pl) vvynfj 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 rota am;qu 9bk itwvf3+5h,tional kinetic energy change when the star in Problem 56 collapses to a neutr aqbk vm5f+itw,9u 3h;on star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believed to be a neutron star of kb)e0l kl5b7c mass 1.5 times that of the Sun, with diameter 20 km, 5lk7l0e b)c bkis 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 px5;f y6t,r6-akh tk q s*t2ywGalaxy 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 (ia:qz89 kuhoy5 n eV) would provide the critical density to close the universe. Assume the ykq9:ohzu 58 aneutrino 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 and 40;5f2rm 9dz qwxbi cg5,0 nm, respectively, both lie on the main sequence. Use Wien's law, the Stefan-Boltzmann equation, and the Hci5;5mzxf wgdr9 2q,b -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 parallax at 100 parsede.m,hcqph-x p r7i7 0 dr)2sucs. What is our minimum angular resolutu7sp2 r rimheh7)d.cq p,xd- 0ion (in degrees), based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from singly i2pngr0 1 4 ,f1 hvkwvfh*1jturonized 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 recej h1*4uh n g210ktrvfr v1pfw,ding from us? v =    C

  What is the temperature that corresponds tot2 w4 7akpoi28-ailag)7- - foravi ew 1.8-TeV collisions at the Fermilab collider? To what era in cosmological histor ila-ar a8)7g2ia2owv--kwt4ofp7 i ey does this correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation :s d) )l/s0ozwf+/ev4maujsv 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 evu/o dwz s)a04sv+s )fjlm:/ 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. s 5y pyrpm:4l)4 ppnygv)a9d bs*e+7qThe "blue" hydrogen line at 434 nm emitted from thsppb l)4eydr :7m+p59q ays ypn4v *g)e galaxy 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 stelb0fpj,ap.oin3j yp (mzr74 ,llar evolution, a star (if massive enough) will begin fusing carbon nuc.bfi ,p,3l (j0pz ypmr4a jon7lei 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 y)4u kncic3g/
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 theqd/lr bc: fwvh*f,0:kxg u 88y critical density of the universe, ky gwhvf::,ur/8xl8*cfb q d0 $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$