The Milky Way was once thought to be "murky" op2u)6b; 4 wzhtnbd1i jr "milky" but is now considered to be made up of point sources. Explnui)bw j;z6b 4pd th21ain.

A star is in equilibrium when it radiates at its surfac enkji:5f jev5: ,.okhe all the energy generated at its core. Whi5.ek5: ej,j nv:k ohfat happens when it begins to generate more energy than it radiates? Less energy? Explain.

Describe a red giant star. List some of pmz.f xw+f4kaoa922 rits properties.

Select a point on the H-R diagram. Mark several directions away from this p wyzqeh9mj3b(jy)vm2(od ) 2doint. Now describe the changes that would take pl3b( )v w e(j2jm9oym)2dq hdzyace in a star moving in each of these directions.

Does the H-R diagram reveal anything about tha,, *nj)db4akpplnp;p6h g c9e core of a star?

Why do some stars end up as white dwarfs, and others as neutron stars or bltn(5(*2,d4dn q(qd, ba ggx onejm5jgack holajdq(jot5(5b ,, ngg*(dge4d2mnn x q es?

  Can we tell, by looking at the pop474mrn)a8kfxhwku pg4gb 5w7 ulation on the H-R diagram, that hotter main-sequence stars have shorter lives? Explain 4gk5 xw7ugwapn784h)kf 4rb m.  ----待选择----yesno 

If you were measuring star parallaxes from the Moon instea4/ e m, +bxhre)azrl4zd of Earth, what corrections would you have to make? What changes would occue+h e) l am4z,rb4/zxrr if you were measuring parallaxes from Mars?

Cepheid variable stars change in luminosity with a typical period of several da(4kh)fap je-ao 9q4v (u lua6xys. The period has been found to have a definite relationship with the absolute luminosityu4ha6vo-(pla) jaq(u k4x 9fe of the star. How could these stars be used to measure the distance to galaxies?

What is a geodesic? What is its role in Genera doz6(d+d nu5 50jpuinl Relativity?

If it were discovered that the redshift of spectral lines of galax6irf sq*xd l.5-rag s7ies was due to something other than expansion, how might our ls*g ir d-r.qsa x7f65view of the universe change? Would there be conflicting evidence? Discuss.

  All galaxies appear to be moving away from us. Are we therefor nvyivso.tr:a r(5*/6lq g4ize at the center of the universe(nyr*tr/gz.l 5:ivv6 sio aq4? Explain.  ----待选择----yesno 

If you were located in a galaxy near the boun/ ocdy-gv 7c:zhk5k 7ndary of our observable universe, would galaxies in the direction of the Milky Way appear to be approaching you or receding from you? E7vokcdzgn :5h7k y -/cxplain.

Compare an explosion on E ajeca, .kq b, l7ce.axx2q4 mf:i,be(arth to the Big Bang. Consider such questions as: Would the debris spread at a higher speed qj :(mqxi4 akbe,f,.7, .a e2eacx bclfor 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 howjqmyiejus2f-vl,lp652 g2-d q na v5 2 can we tell if one is ther j2dlvqnigef,-y ls2 pv526mqaj2 5 -ue?

  What mass will give a Schw6/ ryz*kzhd:nz qf;9ub6l1 c oarzschild radius equal to that of the hydrogen atom in its gn zu ql6rfb d;9z6okz*:h/c1yround state? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often gi5iwk6p umi2 v*cg+7 gcven as about 4 billion years. Find that time on (Fig. Below). People have lived on Earth on the order of m7v+ 5igg*iw cc2p6kua million years. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic microwave backg3 y;fo df() /bv ebumptro;w;1round radiation is. Where does it come from? Why is it)uy o/mf rv ;3;b;pfd e1otb(ws temperature now so low?

Why were atoms, as opposed to bare nuj4 i w+-ng8m g/bwv+lsclei, unable to exist until hundreds of thousands of ygjlw4+ vis-m8/ ng+bwears after the Big Bang?

Under what circumstances a +m 7sh0dsvuj3j1, qawould the universe eventually collapse in on itself?

  Using the definitions of the parsec and tg3pijb g 6;qh7gyq+ l)he 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 away0y( t 4f(obqnb is it? d =    ly

  The parallax angle of xyzs2 l nhm/(ykb4,gg15snv 8a star is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. Whjxh 426k*cfai at 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 sty4jqbqc)as tk6,1u u3p+ au7var that is 55 ly away? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away from us as86hsc 9rog6 l)p2au qx a second star, will the parallax angle of ther 6aclqu 8gop96xh)s2 farther star be greater or less than that of the nearer star? By what factor?

  A star is 35 pc away. How long does it t* 8u,aoey5iqb ake for its light to reach us?    years

  We saw earlier (Chapter 14) that the rate energy reaches the Eart1 thfnmk1 1ie+h from the Sun (the "solar constant") is aboue hi11f kmn1t+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 brightness of the Sun as seen from Jupir3aqq ia tg;578uxxwvg4k2 2v ter as compared to its brightness from Earth? (Jupiter is uav ;qwxi7v grq2t xk83254ag5.2 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 sub;,ag e/2e u ccocyt 2:bb)qww9tend if observed from the nearest galaxy to us (Table 33-1). Compare to the angular width of the Moon from Ec2b q,ub2/ e tcyoew;9wcg :)aarth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, what will be.u(;+ii t jukr its average density if it expands out tou +t;.ik(ji ur 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 rcv,c: 2af+jr.)ie7at h 4csuexpected to be about the size of the Moon. What angular width will it subtend from the presenu aj4e:tvrs irh7f a.2 ,c+)cct distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whose mass is equal to the Sun's anddru(ker46q2 m whose radius is equal to the Earth's. How many times larger than Earth's density is thisrue62 rdkqm4( ?
$\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 1.5p-i-v 4xpo:lg solar masses has a radius of about 11 km. Calculate its average density and compare to tv- ip ol4-:gpxhat 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.7y qxj r1dd)nbd (z6l reactions of Eq. 33-2. (The mass of then6d jx.bqy 7ddl(z1)r very unstable $^8\text{Be}$ 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 appan a9dt 432 /l;wpe2d f-uitlibrent 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 cz2bmr4+ fq8ly qji- m+luster are assumed to be about the same distance from us. Two such stars ym 8jb-im +f2qr+q4zlhave 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 that (gxyz b99,p s;s(sozd 9ao9os7)uw7 ooa) of our Sun is u9s o)7 sbsaxz(od; 9 ozp9,yw97gsoo   km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typical galaxy (like ours)? R k 8u+4jj rh,s3b 7 *loh.jzusl=    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a sphere, for which the sum o/lfk;+g x9f fz1f bq0zf the angles is (a) 359º,zbfq l;+zfk9/0xff1g and (b) 180°.

  What is the maximum sum-of-the-angles for a triangle on a sphere?etthddq21(mt 3ze0 ,84pox( ig3kw a gk(fr*z    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the speed of light, roug s-7r*b ualuwbl)2 x:zhly how far away is ru 27blw )s ba-*l:zuxit? v =    Mly

  The redshift of a galpr 83oudj/z m*axy indicates 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 "2s xuxohot0 (5edge" of the universe, say 12 billion light-yearxoh0 5u2 xos(ts away. v =    c

  Estimate the observed wavelength for m ,i4pzp-zf/fzrp2 3 f.k xzu0the 656-nm line in the Balmer series of hydrogen in the spectrum of a galaxy whose .i-f0z, kf342u f/zm zppxprzdistance 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 .0 nb a / c5t1cobswtn;fyb75odistance from us, if the wavelength for the hydrogen line at 434 nm is measured on Earth as bei 7t b0awnt/b;.f5yc5s1ocbon ng 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+ko8tph+;v(ept w( crhm59ne galaxy with $z = 0.60$? v =    c

  What would be the redshif-)5s*- ip xclnuoyhep* (w;oat parameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show y ceqa6nq,9cg4-g(za i* uu3k 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 pe28dje(o owhje6i4p xsz1*(f nak of the blackbody radiation distribution at 2.7 K using Wien*14e 2xj dj(8w (fnsh oeipo6z’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of the d+uk(479a .pdy.kl0m1 u,rrqk bg js8 -zscwi 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 distay q qlkbn(2dn:ian)w70j55yvw r0f e3nce between galaxies) at any one moment is believed to have been inversely proportional to the absolute temperature. ny5lkwwa:02 e5)v3q qr jn byi0dn7f(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 coos 39r8blz q:cf)3aqsbled below the threshold temperature 8sb3rla fqq b)3c9 z:sfor 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-sequence stars could 4z3mwns7 o) peundergo the three changes represented by the three arrows, A, B, and C, iwo)nms37z e4pn 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 luminosity about thfvm07rc9oj p91l 8 *y lnvl0mse same as the Sun's. Their al fvcrpl0mmj 9yns70*vl18o9 pparent brightness, however, 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 vel+umt.:ji* p ckocity of a neutron star which has collapsed to a diameter of 20 km, from a star whose r*+ctpi.um :k jadius 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 rotational kinetic energy change when the star/k0 a1lid*5,ph7.*fxv5 wt ;oilpvonwt+u a x in Problem 56 collapses to a neutron star? 5 x aitd1wt hkn*uipxfl*0;/p.a, lwov5ov7+ $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believed to be a neutron star of masscbf6c.. rt p ra+.fdt+m/isg- 1.5 times that of the Sun, withriacc -rt.b tfmdsg+. p./f6+ 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 Galaxt,taqs4yw7phy k8r8e yr*8 .by 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 provideu/q y; bx5m0 .vcmoe,z the critical density to close the universe. Assume the neutrino density is, like photons, aboutuc0 be, vmx/ 5y;qz.om $10^9$ 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 400 nm, respectively, both lie on 7 nzm2r+;pqfpf/r2 zt09 3 xisgxs9zvthe main sequence. Use Wien's law, the Stefan-Boltzmann equation, and the H-R diagram (9x g+0ptrz r72f;x3p2 vmsfzqnsz 9i/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 distance g 8j4pm3osy8rs with parallax at 100 parsecs. What is our minimum angularrms8ogy84 j3p resolution (in degrees), based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from sir/+*lwtl,k a mngly ionized helium in a distant star happen to overlap with the Balmer lines from hydrogen (Fig. 27-22) in the Sun. How far k/lm a+ltw*,st is the star receding from us? v =    C

  What is the temperature that correspo6 iw xehi7sqvpv4 o5 axb ,((,)bxxa1tnds to 1.8-TeV collisions at the Fermilab col1 ) ,,(7pxv4 xh( e6xxstb owi5ivbaqalider? To what era in cosmological history does this correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation of gas around what mid4z+we ,b jgj8ght 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, whj wj,8ez +gdb4at Doppler shift $\Delta\lambda/\lambda_0$ do you estimate they saw? z$\approx $    $ \times 10^{-3}$

  A galaxy is moving awayr)mc ))eil de;,3ab8eh omt(i from Earth. The "blue" hydrogen line at 434 nm emitted from the galaxy is measured on Ear) etar(o)m id,c)l eb3e8i;mh th 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 evolugygrzi4p-v) *ob y5qqt(x t1 0tion, a star (if massive enough) will begin fusing carbon nuclei to form, for example, magnesium:g5-q1* tqy r(4txob) zv0ypg i
$^12\text{C} + ^12\text{C} \to ^{24}\text{Mg} + \gamma$.
(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 reactionud n*d:zknbpw)8f:02 8 yqjsj
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 ;h+umq.y 6ry z6fjx s)of the unive6 u.m yzh+ x6rs)qfjy;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}$