The Milky Way was once thought to be "murky" or "milky" but is nobk7ii5d1, pmq cv-k2fw considered to be madq7pm-i k fb 1,vi2k5cde up of point sources. Explain.

A star is in equilibri..g0t /ddrsk lum when it radiates at its surface all the energy generated at its core. What happens when it begins to generate more energy than it radiates? d/ts .0 rglkd.Less energy? Explain.

Describe a red giant star. List some of its jt-l:6 tntaej:cr1n -properties.

Select a point on the H-R diagram. Mark swp n/u(c7ze6( n3qr coeveral directions away from this point. Now describe the changes that would tannc(e3 pwzq/ (7u6cor ke place in a star moving in each of these directions.

Does the H-R diagram reveal anything about the core of a staj4t(n:n hi 1zbes4, 7 zklw/air?

Why do some stars end up as white dwarfs, a2 1sujzs0l*l kuin7g1nd others as neutron stars or black holesz2l01ui7ujkg* l1ss n ?

  Can we tell, by looking at the populf.02oms ;tkj,s tdk ;ration on the H-R diagram, that hotter main-sequence 0,mk kso2t rt;.; jsdfstars have shorter lives? Explain.  ----待选择----yesno 

If you were measuring star pui-tns4n/; tj+ip4 so arallaxes from the Moon instead of Earth, what corrections would you have to make? What changes wsu+iojt ;snt 4i4n/p-ould occur if you were measuring parallaxes from Mars?

Cepheid variable sta71 rq)8x zxrcers change in 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. How could these stars be used to measure thezc8x x1 re7q)r distance to galaxies?

What is a geodesic? What is its role in General *eb6o m6yt2jpRelativity?

If it were discovered that the redshift of spectral lin8lb8 y-zh7nc wes of galaxies was due to something other than expansion, how might our view of the universe change? Would there be conflictyhb8lcwn -z 78ing evidence? Discuss.

  All galaxies appear to be movinh4/zrs lj3f*6j9 m gm1+rgend g away from us. Are we therefore at the center of the universe? Explain. zn j*drmgjm6hs 1 fgr4+le/39 ----待选择----yesno 

If you were located in a ga 7poubl10e8s8a 8zyhk laxy near the boundary of our observable universe, would galaxies in the direction of the Milky Way ap yol01suk78 aehp8z 8bpear to be approaching you or receding from you? Explain.

Compare an explosion on Earth to the Big Ba5u 28pyfb p7pfng. 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 f87pp2pbfy5 u of universe would this correspond to, open or closed?

If nothing, not even light, escapes from ad d fskw6rn;w06.thna +1j f+s black hole, then how can we tell if one is there6a+j016+ffsnw .knstd;r hw d?

  What mass will give a Schwarzschild radius eqly wh-86he b7in9x)gf ual to that of the hydrogen atom in its ground state? xy6bf89enhl ig )-h w7 M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is oftsx 7v p063nsg gy1od;uen given as about 4 billion years. Find that time on (Fig. Below). People have lived on Earth on the order of a million y xsu0gdso731v ;py6gnears. Where is that on (Fig. Below)?

Explain what the 2.7-K cosmic microwave background radiation is. Where does i jd9-q9ciuo +v)c d;izt come from?;uv9do cc9di ij -q+)z Why is its temperature now so low?

Why were atoms, as opposed to bare nuclei, unable to exist until hundreds z:xijo 2 :u7lbof thousands of years after the Big Bang?2:o:zju bi7xl

Under what circumstances would the universe eventually collapse in on itrzm .kxg2 .0szself?

  Using the definitions of the parsec and the light-year, show tnrc7hoxv:d7ge2mwkh1 5 nc) 1hat $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.38 seconds of arc. Hn:2taflkg* -7fk mx 6yow far away is it? d =    ly

  The parallax angle of a star i,f-i(d l6zh +8li lko2jpx/kds $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its pa,gyoomz/i7: erallax 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 that ig)cj(vm9d bp gfy0- ;is 55 ly away? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice asr w:i 5f4vj85t;z oqik far away from us as a second star, will the parallax angle of the farther star be grevw:kiqofi48 r5z; t 5jater or less than that of the nearer star? By what factor?

  A star is 35 pc away. How long does it takezl:d u9egu6fm2ch7b: for its light to reach us?    years

  We saw earlier (Chapts8 n:wv;cmr8xhx0i; wer 14) that the rate energy reaches the Earth from the Sun (the "solar constant") is abx:r8h 80 cvwmx;ns;i wout $1.3 \times 10^3\ \text{W/m}^2$. 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 Jupitk/x 7c d/a l gwzjm91pq-nrx,/er as compared to its brightness from Earth? (Jupiter is 5.2 times r nckza7-p qdmg,wlxj//x 1 /9farther from the Sun than the Earth.) $\dfrac{l_{\text{Jupiter}}}{l_{\text{Earth}}}$    $ \times 10^{-2}$

  Estimate the angular width that our Galaxy 6ab5ravwu;t 6would subtend if observed from the nearest galaxy to us (Table 33-1). Compare to the angular width u6v w;raatb 56of the Moon from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, what will be its3/.z etjqej w7u9radpbf7; f 3l89 okj average density if it expands out to the o3juo/w.e; df9jjkt7az 7 rq8fbe3p 9lrbit 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 g6 mj/tn- iwg 7,6pa jnu+k0(ybeh0 yksize of the Moon. What angular width will it subtend from the present y6pya ( 6uj,mj-h0bn i0e7k+wgg/ntk distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf who q a6zn t*rvir8p(86fese mass is equal to the Sun's and whose radius is equal to the Earth's. How many times larger than Earth's density is this?8 n8 vretazr 66*ipqf(
$\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 radis) x bz9*+,*l obmoevlus of about 11 km. Calculate its average density and compare to that for a white dwarf (Problem 13) andxsl oo*9b+)lz* , emvb 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 fhw2)fqo0fu1 v9bp/ dxor the He burning reactions of Eq. 33-2. (The mass of the very unqxh902p1o uffv )d/ wbstable $^8\text{Be}$ 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 apparen 6:6dehfog s:dt 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 f k*c;i;.(fz9ni+m; b oexzzllrom us. Two such stars have;ol z*;nb kexizz;.+fm i(c9l 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 ;6rfxg f: ; :u(iezbgtwith mass equal to that (a) of our Sun :gf ; utg: eibz6xf(r;is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius forszczj++l vw hvol4b08fax453 a typical galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on / yqyu tox/uhmo7+ *3n+ai .zbthe surface of a sphere, for which the sum of the angles is (a) 359º, and (b) 180tyqa/bmhi/7x +o3u u*zno +y .°.

  What is the maximum sum-of-the-angles for a triangle on a spher:tftsc4 v .9unk)f gpjtfv;./ e?    $^\circ$

  If a galaxy is travelinggh2 (hgdz)hh( e5 rl.z away from us at 1.0% of the speed of light, roughly howg)dh5z. r(( lhz h2geh far away is it? v =    Mly

  The redshift of a galaxy in.iopmnte)* h. ib4vb8)buo 3:ef3dqudicates 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 obser4afq 2s zly7io--i1e cvable "edge" of the universe, say 12 billionileo syic2zfa -1 4q-7 light-years away. v =    c

  Estimate the observed wavelength for the 656-nm line in the o weuf jsm+/6sfp;x;3Balmer series of hydrogen ;6s ffxe/u;m 3jp+swoin 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 n m9,8xhhq. +d.w ) d0sbe0ay1pvbaz ca galaxy, and its distance from us, if the wavelength for the hydrogen line at 434 nm is measuredan+s.) eazx 0bm1 bd8 hqdp,v wy0h.c9 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 gayb96c o+ rjdg dr;u6j1qi)d 4blaxy with $z = 0.60$? v =    c

  What would be the redshift param5yfaw l /eu/uy/ 0+ 2hvc3zba5qm*ax yeter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Doppler shift in wavelengil29if,s c; with 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 a /y3f+7/pflfaw ernx7t 2.7 K using Wien’s la f7fywp7 /ex/3lr +fnaw. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of the universe isnlfekz(nr- yhl8e6 /3 $\rho_c \approx 10^{-26}\ \text{kg/m}^3$. State $\rho_c$ in terms of the average number of nucleons per cubic meter.    $\ \text{nucleons/m}^3$

  The scale of the univers ;y7 qjt(ox3 5:hhei.colxy6me (the average distance between galaxies) at any one moment is believed to have been inversely proportional te:7xo6 3 hthq m;y5ol yxij.(co 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 harc39s y-f7ny d1.se xx 4tw-gkd the universe cooled below the threshold temperature ftk1e7d9ry4w-.3x c xnfysg-sor 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 undergo the three c1ff4btc r (6je9 c84thsg2pfd hanges represented by the three arrows, A, B, and C, in the H-R diagram of Fig. 33-28. For each case, descrictdehf gpj c6tf249f84bs1(r be the changes in temperature, luminosity, and size.

  Assume that the nearest stars to us have an absolute lumi lc;:8t yovo:fh;.ziz-e *ctjnosity about the same as the Sun's. Their apparent brightness,l*.- o :ctihvtj;:y8zoe ;fzc 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 of nk xf m 6p67e3rt4tay*a neutron star which has collapsed to a diameter of 20 km, from a star whose radius was equa *3rxke6tfma4t7 6ypnl 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 bi6:4m: fxme/exd:8g q*6rh il rzvl- kinetic energy change when the star in Problem 56 collapses to a neutron starzxdbrh lmg8qf : 6x4/i6 m*lv-ir:e e:? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believed to be a neutron star of mass 1+3c:bc ,c9um. qxmpqlmdfy, ,.5 times that of the Sun, with diameter 20 km, is observed to have a rotation speed .lc3 ,x9 :d,pqm c,y bfmum+qcof $1.0\ \text{rev/s}$. 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 1mm9w*,xyf6 ma/so 7ogs2l fp 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 neutrino rest mioo cf+m6bb-: ass (in eV) would provide the critical density to clo6mb-of:+ c ibose the universe. 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 ab*25,0 hkb 0s qr/t ed(qkiwbnm and 400 nm, respectively, both lie on the main sequence. Use Wien's law, the Stefan-Boltzmann equation, and the H-R diagram (Fig. /sweir bk5q,a b k0qht*d20b(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 parsecs. Whaj3jd9 px z5m bl96m7mh5 hommg;-i8pn t is our minimum angular resolutio jnx3bdhp8 zm5gh5m69ol 97-p mijm m;n (in degrees), based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from singly ionized hev1usy;ji /wn- lium in a distant star happen to overlap with the Balmer lines from hydrogen (Fig. 27-22) in th1n;j si wuy-v/e Sun. How fast is the star receding from us? v =    C

  What is the temperature that corresponds to 1.8-TeV collisions at the Fermil uh4ooc a,,vr8x2h 9syab collider? To what era in cosmological history does this correspond? [Hint: a ,9housyx, 4co2rv h8see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation of gas around what might be jpjq4) eg/7gb-/lsy m a supermassive black hole of about 2 billion solar masses at the cente m-ggjps//) 7q4ylb jer 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 nm emitted ad5d+b3p/pk j htk8xvt:a7b;from the galaxy is measured on Earth ttabt 7d3b:; j+pad kvkp8hx5/o 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 evolution, a star (if massive enough) w :rb58f; *sgtet yk9ix; odwc*ill begin fusing carbon nuclei to form, for exam sogd*t f5i:r;8t;ew9*bxc y kple, 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 qyp2:)x msm f-,skl5r
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 denlnu cw7(h:m6:lk4ex asity equaled the critical density of the unive(4c:w: h ualx k6n7lemrse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$