The Milky Way was once thougi-+ ueh-87ybe: u ofxkht to be "murky" or "milky" but is now considered to be made up of point suye-:ikh+8 -oxe7 fu bources. Explain.

A star is in equilibrium when it radiates at its surface all the energyeblk)rxz43rz)x* -mi 8ft:zx; bb3j n generated at its core. What happens when it begins to generate more energ e4zk 3bmx i)f*z )xrzrtn-8b; j:3lxby than it radiates? Less energy? Explain.

Describe a red giant star. List soz)rnc ,n .h+ b-,al:sk/:sjaqfz ml8r me of its properties.

Select a point on the H-R diagram. Mark sevel fmy8gtahg(e8)w/ nv 8j 1q0rral directions away from this point. Now describe the changes that would take 8tmh (e18jyrv lagw 8f/q)0gnplace in a star moving in each of these directions.

Does the H-R diagram reveal anzh,a za;u.9ls4 y k(ovything about the core of a star?

Why do some stars end up as white dwarfs, and others as neutron stars orpr wc1. 0jf4bd;pmnx6ky6hv9 black hol m1bh vpwcdr p60njfy4x9.;k6es?

  Can we tell, by looking at the population on the H-R diagram, that hotter mainqxb .fp+mt6 sr/o rj.3-sequence stars have shorter lives? E jq+sbo/p3m .x r.6trfxplain.  ----待选择----yesno 

If you were measuring star parallaxes from the Moon instead of Ear bjyp ik5dv x;- wk(9y9*xouw1ioa68uth, what corrections would you have to make? What changes would o1v dw 9( i i;xpya -obkj*yo8u56w9ukxccur if you were measuring parallaxes from Mars?

Cepheid variable stars change in luminosity with a typical * d*xwquiie)(period of several days. The period has been found to have a defi*i* )wd(xeuqinite 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 Rela1*r+mmuiuua l2ilm o5 ;2ge5 otivity?

If it were discovered that the redshift of spectral lines of gmshabu:ie;b8dw/x8rq 9 ;-oq alaxies was due to something other than expansion, how might our sh9:axudo8b/q8eq i; m;br- wview of the universe change? Would there be conflicting evidence? Discuss.

  All galaxies appear to be moving away from uo28fn y .wvm1is. Are we therefore at the center of the universe? Expla8w i1vf y.nm2oin.  ----待选择----yesno 

If you were located in a galy g6/rf gr3l2naxy near the boundary of our observable universe, would galaxies in the direction of the Milky Way appear to be approachingrg 63ylr/2nf g you or receding from you? Explain.

Compare an explosion on Earth to the Big Bang. Consider ab 4oyzz*7:mcbkl) 8xsuch questions as: Would the debris spread at a higher speed for more distant particles, as in the Big Bang? Would the debris come t8ac)zo:kz*b 7mxy l4bo rest? What type of universe would this correspond to, open or closed?

If nothing, not even light, escape;us4n.mpk7f l s from a black hole, then how can we tell if onf 7mun;kl sp4.e is there?

  What mass will give a Schwarzschild radi8ceug0.u*pu m rph3(l us equal to that of the hydrogen atom in it0um (r3pgcuuhpe.*l8s ground state? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4wlg8 oteqio/d74, dx, billion years. Find that time on (Fig. Below d,od84xg/q l,e7t iwo). People 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 background radiation is. Where dol*vrc4 c b;obi8 wntutgy+3.t6u1 a6qes it come from? Why is its te g 8 c3yb;r 6q+c4tt.1nlu6* bauivowtmperature now so low?

Why were atoms, as opposed to bare nuclei, unable to exist until hu s 2,h fulss/0u09ryerndreds of thousands of years af se92y/uur0lsshr 0,f ter the Big Bang?

Under what circumstances f c8;un+htgc4ol4ubc ;6 leuz*8t+g twould the universe eventually collapse in on itself?

  Using the definitions of the parcvk7l6h3yl ai x 47hl q+tx6(osec and the light-year, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.38 secondug z71a qzr69di:u6e ds of arc. How far away is it? d =    ly

  The parallax angle of a starhx ams-1sc9s9 j6 8tlr is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its parallax anglo9o*w hnr+wg j.(xz 2v1 uno)se?
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 i q5src1q/9d) :-o9 xle9zfb wpyvd b1bptq0*o s 55 ly away? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away from vms9;ch5)d w ooc( 8vsus as a second star, will the parallax angle of the fa(;8 c)9cs5vwdoo vsm hrther star be greater or less than that of the nearer star? By what factor?

  A star is 35 pc away. H-7ohn oj au/q(rwm6d .ow long does it take for its light to reach us?    years

  We saw earlier (Chapter 14) thasak3 ygm15c2 6 v,wsstt the rate energy reaches the Earth from the Sun (the "solar constant")yskmc s t153 a62w,svg 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 brightnlyib*3(ii8 goess of the Sun as seen from Jupiter as compared to its brightness froio8l (ygi* b3im 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 our6kez*xu/ 6zq m Galaxy would subtend if observed from the nearest galaxy to us (Table 33-1). Compare to the angular width of the Moon from Earthuze6mk * 6z/qx. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, t91 a qg f;u0(kqqo5.zwpd)dh what will be its average density if it expands qg0)9 tq dwf.ohqu ka;(dzp1 5out 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 be about the size of th /xkqqtvd.3:+s fc+jrw1 w*tqe Moon. What angular width will it subtend from the present distance to Eark+v /x+wq tsjr3wtq*q1d cf:.th? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a wh tvb5;-l nly*vite dwarf whose mass is equal to the Sun's and whose radius is equal to the Earth's. How many times larger than Earth'st* -vl bnvy;l5 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 solarn+l7i;q -mf,vsfig(6x67s1l*msa 5b s bcow q masses has a radius of about 11 km. Calculate its average density and compare to that for a white dwarf (Problem +6;lnssw 5msmbq -i(bff,q lcsi vo16*7ag7 x13) 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 E dzop+v97zjr1m.6dkfuqp*: .n0v ahvk4brf.q. 33-2. (The mass of the ver z9:op.7bdj0 .vz+dvfk4. fuma1nv rqh*p6kry 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 a(fme-+4)omgn7 g: fo2me iplc ).zpvmpparent 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 cli p2wu ;oh)mk,guktbt)0+c-t9ob 1yy uster are assumed to be about the same distance from us. Two such stars have spe;b2 oo y)0-wmtuukyh+ pti19 k),tgbcctra 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 (a) of6l39)bxlapvzi(1t j5yek b-v our Sun jvp ) lail53ybb9e txkzv6-1(is    km, and (b) of Earth is    mm.

  What is the Schwarzschild gu8r1nblf k//fbr 5 fjinj4,qh od4cje *-)w:radius for a typical galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a sphere, for which8vm s,(i *k, s+luc2ga4z0w etd xa-zi the sum of the ang la,uks4zswd,x tai(*0 -eg2iv + mzc8les is (a) 359º, and (b) 180°.

  What is the maximum sum-of-the-angles for a triangle on a sphe 8yt+ e,;wovnk nlzvb en7o8oq1(-0jfre?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the speed of light, roughl9 v0jjue -zndpaz;7 v;y how fjvaj0 ;pun;7-de9zv z ar away is it? v =    Mly

  The redshift of a galaxy indicates a velocito63wt(p /ut liy of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (relative to us) that il(q p 9v2mxfr7s near the observable "edge" of the universe, say 12 billion light-yeap rqxf 2mv(9l7rs away. v =    c

  Estimate the observed wavelength for (*/* plo*z*wnufdlhtnx2 i*u the 656-nm line in the Balmer series of hydrogen in *ounfp*( / *z lw2t*d n*iuxhlthe 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 itsovs 1jq8 ao 4a(m8l1la;6dpz c distance from us, if the wavelength for the hydrogen line at 434 nm is a8lm1j qapa vz4od68(c 1;los 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 :;8v ( xrt:po)jgnu m ;bjswjvul defv 7)6-.tgalaxy with $z = 0.60$? v =    c

  What would be the redshift parametk8o k;cv f dcv7e2.a6s g3)/szvj moc9er $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, shd,yr61 fduc6841dh 0iluj(m+ x ag terow 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 distribution a4mwt d2. pg u avjur:6h9w*em8 b),bm(a umh7jt 2.7 K using Wien’s law. 8. 7,m u*g2aba)4vu(erm pt6 jbwhm9wuhm:jd$\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure i(*ja-atj1 rc 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 galaxies4h+*rvd gnwk5) at any one moment is believed to have been inversely g4 nk5whd+vr* 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 ths0vnw pl1h; dip,.ja8,8xy rwreshold temperature for producx 0,8, d.wh v8wp;arynijspl1 ing
(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 t bpfslu *i.dpq9+*hu,hree changes represented by the three arrows, A, *h*d+uip9lpu, bfqs. B, and C, in the H-R diagram of Fig. 33-28. For each case, describe the changes in temperature, luminosity, and size.

  Assume that the nearest sfsxamfd-h u -(x ia,17tars to us have an absolute luminosity about the same as the Sun's. Their apparent brighfhxxm -, s-u 17(afaditness, 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 velocity 3jok;5cyckdys de)er mo:062j l+*zl of a neutron star which has collapsed to a diameter of 20 km, from a star whose radius was equal to that oljm23krj 6c ;0dky*oz )lo es5+cd :eyf 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 ro7jc(ed kl3b2xtational kinetic energy change when the star in Problem 56 collapses tb72jck(d3l x eo a neutron star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, besquepl xza :: jy44, otg86ze2lieved to be a neutron star of mass 1.5 times that of the Sun, with diameter 20 km, s,o6jz2teep:4:lxyau8z gq4 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 Galaxy is lap+rvd, v ,;3ot tk,mabout $2 \times 10^6\ \text{ly}$ 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 rh3pz:2 cb1vp (cemn3r est mass (in eV) would provide the critical density to close the universe. Assume the neutrino density is, like photons, about vpz(cmnb1r323cp h: e$10^9$ 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, respec1; 1do)u g4)v3o4osibtrr/rrg+n mu vtively, both lie on the main sequence. Use Wien's law, the Stefan-Boltzmann equation, and the H-R diagram (Fig. Below) to estimate the i bv;/4r rrtuv mgo)od1 n43ruos+)1gratio 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. What is oy *7dbew*hb l:ur minimum angularl: d y**whb7be resolution (in degrees), based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer li 8uhceg2kw93: 2 ln,-nfy)2vmg dmgn oj-k+nones from singly ionized helium in a distant star happen to overlap with the Balmer lines from hydrogen (Fig. 27-22) i dkk c),wlfne2monn 2ggyh9+o g v-8:2m3u-njn the Sun. How fast is the star receding from us? v =    C

  What is the temperature that corresponds to 1.8-TeV collisions at tpm r4:+3;zforoftg p1 he Fermilab collider? To what era in cosmological history rt+oop4 pfm31 rz:fg;does this correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotatiyn 9u-2py1 n*m8 i)hkvei,z gkon of gas around what might be a supermassive black hole of about 2 billion so kiy y inp8vmhk-e9g2n,*1zu )lar 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 line at 434 vp2 1x4yihcb05w acwt/ +uzi1 nm emitted from the galaxy is measured ui2bt41cvw5h ciw +y/1 0zxpaon 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 evolutio hzwxc;,4qzqn2 )m+s 56pkvson, a star (if massive enough) will begin fusing carbon nuclei to form, for exho,vqzs5npxmsz k4) 6 ;qc2 +wample, 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 ogoks(8( a)27mo f5 jr e:rens
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 the1r4*: sssh/ dcbk)iahwft3h3j i/ ws- univers4a3)f/-:kdchs3/hbsr siwjswt h 1i* e, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$