The Milky Way was once thought : g* ;pn9:7dkz btiiswto be "murky" or "milky" but is now considered to be made up of dbt7kin:zpsi9 w;g:* point sources. Explain.

A star is in equilibrium when it radiates at its surface all the energy peen a2 0u2-r/w /aarzgenerated at its core. What happens when it begins to generatepr uaerawn/ e20-z 2/a more energy than it radiates? Less energy? Explain.

Describe a red giant star. List some ofog2 +ct-s:9sze u;1g ls+vjx l its properties.

Select a point on the H-R diagram. /uc/s*qin0uqmg4*o)my 4vm v Mark several directions away from this point. No gi4quv qvcm)sm/yn*u*0 m o/4w describe the changes that would take place in a star moving in each of these directions.

Does the H-R diagram reveal anything about the coreb0 /l3greg klsb4kayk6rj. 4- of a star?

Why do some stars endwp tutm;qov)*yv5(t9 up as white dwarfs, and others as neutron stars or black hole oy)t tu 5t;p(v*9wqvms?

  Can we tell, by looking at the population on the H-R dia75cot/;v ngumsvq *;mgram, that hotter main-sequence stars hnou;vm *;7qvtc5g ms/ave shorter lives? Explain.  ----待选择----yesno 

If you were measuring star parallaxes from the Moon instead of9z;oi:mv 7o3xfnrewvjma ,0 9 Earth, what corrections would you have to make? What changes would occur if you were mea:,0momv7nxj i 399ae; zvowrf suring parallaxes from Mars?

Cepheid variable stars change in lum7klp av+hg -v;inosity with a typical period of several days. Tvkv+ gl;7hp- ahe period has been found 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 f+y9x/x;iz*ru fbd; p+s l/eo role in General Relativity?

If it were discovered that the redshift of spects -o,*iuj *kmural lines of galaxies was due to something other than expansion, how might our view of the universe ch*-m ,*uiusk ojange? Would there be conflicting evidence? Discuss.

  All galaxies appear to be movingc0/fs0qz :nf d away from us. Are we therefore at the center of the universe? Exf0qsfcz /n:d0 plain.  ----待选择----yesno 

If you were located in a galaxy near the boundary of our observable univ+:stzy-m fk9 / zzlhy0erse, would galaxies im+/lyk:yf 9ztz s-z0 hn the direction of the Milky Way appear to be approaching you or receding from you? Explain.

Compare an explosion on Earth to the w1avg3aw/dg6 Big Bang. Consider such 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 would this correspond to, o dvgw1aa6gw 3/pen or closed?

If nothing, not even light, escapes from a bfzoj7sjd7t7 (4jxlt5ut ;jx7 1 ob*lflack hole, then how can we tell if one is tttj1f;u oltx 7bj 7zj*x577j4s(f dolhere?

  What mass will give a Schwarzschild radius equal toqkjk 5g* 0pglw:2 eh;o that of the hydrogen atom in its ground 20q k*lehgj: wk;5pogstate? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often giveo44 f f1rp d;/fp9 w;ma ai;:pyx*jsbsn as about 4 billion years. Find that time on (Fig. Below). People have lived on Earth on the order of a million years. Wh*p p4/ :sf;jp bfoma f;9a idwsry;x41ere is that on (Fig. Below)?

Explain what the 2.7-K cosmic microwave background radiation is. Where doe. 3qhqs(5/ tmk1vq afxs it come from? Why is its temperature .3ams5 q ftxq /qv1hk(now so low?

Why were atoms, as oppos7iwki (5cq g3-0)duodato 9kxed to bare nuclei, unable to exist until hundreds of thousands of id io5qg(u90ct)a-3dw x7 kkoyears after the Big Bang?

Under what circumstances would the universe eventually co: buwu5wz;oy+e ia;/ cllapse in on itself?

  Using the definitions of the parsec and themj)oi:6jrkgo 4e :c:g light-year, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.3ya*yn;d5w if 3x..qd5sa.m xq 8 seconds of arc. How far away is it? d =    ly

  The parallax angle of a starol(/umx1l b8a is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its parallax angle? ypm1hf )l( xy8
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 ty 6svcfc6 6i 04zgdm-uhat 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 an jhs40 pqa7rf,gle of the fartherqrh j 47f0as,p star be greater 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 o jf(nz,0gcq5 qs sv-oq4 9v zwd3n6.xto reach us?    years

  We saw earlier (Chapter 14) thp qt,x;exm+vqb 7/b0vat the rate energy reaches the Earth from the Sun (the "solar conxeb b/qtq0, m px7v;+vstant") 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 as seen from Jup.*g ml5nzf)nliter as compared to its brightness from Earth nzf5g*nml)l. ? (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 k07kdmf/x u6lxz: y:j would subtend if observed from the nearest galaxy to us (Table 33-1). Compare dkx:0 xz7/y6kfjmu :lto the angular width of the Moon from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, what will be its averakzgtd km.g8vhtd5d,z3 d) (g7ge density if it expands out to gv 3gh 8dzdt.g)d5(zkdmt, 7k 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 sis1 jas7q (p qqkx2r;a7ze of the Moon 7(1s7 qajr;pqxa2sq k. What angular width will it subtend from the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarfam zgfmps1lp.7ppo -rb v1+-4 whose mass is equal to the Sun's and whose radius is equal to the Earth's. How many times larger pa1-v 1m -r4.s+pmfozlp7pbgthan 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 masszwnmg-u - df6 7-5ehckes has a radius of about 11 km. Calculate its average density and compare to that for a white du 57d 6m-k zgcn--ewhfwarf (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 ma7/+7 s t bz1eg(ivtqrbss of the vbqr/( iz+t gs1 evt7b7ery 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 apparent xcfl sh;tnlo687,7f a 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 assumed to be about the same distance cuho-jl5 5hn8 from us. un5ol5 hh-8c jTwo 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 radius mdxfhk52cf . +lw)grr ft/92 ofor a star with mass equal to that (a) of our Sud og2/lr92)hx c . ffrw+fk5tmn is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typi+,y 2eba -0pas43. 8tdlifp auvo9h xdcal galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a sphere, for which the sum of 5y6pgn/ y3/ywu / icjcsj6jo5the angles is (pcoy/6 35sg//nujw6yji cyj5a) 359º, and (b) 180°.

  What is the maximum sum-of-the-angles for a tr e opwkah3;5 x*lk4n03p0mvdiiangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the speed of lighox*u2: gyx2p , yycki9,t4hght, roughly how far ahc*2xug:9x k py igh2y,4t,yoway is it? v =    Mly

  The redshift of a galaxy indic91rroee) o5kqates a velocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a gadm k:qj7gxq0gh y)4 c;laxy (relative to us) that is near the observable "edge" of the universe, say 12 billion light-years away. hxg; j70)gd4cqmk yq: v =    c

  Estimate the observed wavelen j7f kl 8sp mp3bd:4*tiszc(8ugth for the 656-nm line in the Balmer series of hydrogen in the spectrum of a galaxy whose distance f8f*d:7mpjszt8kp4 (bc 3uls irom 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, ,(ky82r 8 l+l t)/ *fcp9otvixmuszny and its distance from us, if the wavelength for the hydrogen l8(i nz/tvy29*+lpstk)lr mc fyu8 o ,xine 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 ,qh3cs9u zo5ywith $z = 0.60$? v =    c

  What would be the redshift paqbr1clpz- 2r3(q 0:b :hxyi eqrameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Doppler sso4 cn1x ywm/ ea.wvv)zx*m /(jlx8u4hift 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 distribg6+3 xt*0ycvgh9 nrofkz5f 2cution at 2.7 Krg* 2ctnof0yfvkzgc x5 39+ h6 using Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closh1 ey8-8ddd*fws; n jowys8 c5cu9l q9ure 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 (tht c *xnxo6/e m, 77cqi.juvppci1:3rme average distance between galaxies) at any one moment is believed to have been inversely proportional to the absolute temperature. Estimate the spe ru61x q3*:.7j/ix 7 ,pmvnoctccmi ize 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 wha 8iu8 l3ivpjx)t/,m(xhgl vnjd/7n3ct time had the universe cooled below the threshold temperature for produc jd/ic( hij,xn/u8g)p37vv 3lnl8t m xing
(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 change 2 (ktipsp;+tus represented by the three arrows, A, B, and C, in the H-R diagram ofpt;ki+sp ( 2tu 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 the sam ;, b(tostgq*be as the Sug ;,( otb*tbqsn's. Their apparent 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 angu chqxw :6;c lky.) h,5lygbc,zlar momentum to estimate the angular velocity of a neutron star which has collapsed to a diamylcl . y6ch5hx),c ,;wq:zgb keter 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 rotational b06hl)m(uhb -cpf/l g l1 x*.vz-c9n rxaqgw;kinetic energy change when the star in Problem 56 collapses to a neut */;acl) bc-h v9g(xlr-m1 wgnxph q0.z 6buflron star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believed to be a neutron star of mass 1.5 times that of the Su,gi w )gkl )kkr+mav81* vkka;wocn,9n, with diameter 20 km, is obse kn go,r),i*kk9+kvmawwl8)g 1kvca; rved 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 about ohvoj0 mociy:mj(a 9b) 8q b.wve3eo5hon98 )$2 \times 10^6\ \text{ly}$ 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) w 9hnp+w6iy45 z a.libcould provide the critical density to close the univc +9hw4 6p .nlbiz5yaierse. Assume the neutrino 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 400 nm, respect 8iqu;z fe ug2afan.5tf5,cv3 ively, both lie on the main seq,28gef; i3uacua vf n5tqfz. 5uence. Use Wien's law, the Stefan-Boltzmann 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 paralla.zd3/ e ecuv4.c9gfr ,xwur:b, t6j elx at 100 parsecs. What is our minimum angular r .t4gj3be,ucr:wdul,fc6ve / re z.9xesolution (in degrees), based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines fle8(4.jbtszn e .l;t9hzys /xrom singly ionized helium in a distant star happen to overlap with the Balmer lines from hydrogen (Fig. 27-22) in the Sun. Ht/9s zelxz8;jeb st. n.yh(l4ow fast is the star receding from us? v =    C

  What is the temperature that corresponds to 1.8-TeV collisions at the Fermilabiw*gxwozz bm)taaxn.m 2+2a+a4 x1 t( collider? To what era in cosmological hist xxtb+mmgx4oa )zazaawit1n. (w 2*+2 ory does this correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation of gas 7izbxl x08m) varound what might be a supermassive black hole of about 2 billion solar masses at the center of a galaxy. If the radius from the 8)xvb7lx0m izgalactic 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 fr(el o1axti 3fyc9(mm )om Earth. The "blue" hydrogen line at 434 nm emitted from the galaxy is measured on Earth to be 650 nm. mi(xaoet) 1l y(cm93f
(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 enoughoy1+1 tr ;t,f lzcg:ad) will begin fusing carbon nuclei to form, for example, magnesium: :;at1tg+ 1rcfozy,l d
$^12\text{C} + ^12\text{C} \to ^{24}\text{Mg} + \gamma$.
(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 reactioj0whvwg8 r/6i7,jur38e wj nna7 n zw;n
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 criticx73 m,jmada s2al density of the unisjd, 3xmm7 aa2verse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$