The Milky Way was once ) rnxjb to(.)mthought to be "murky" or "milky" but is now considered to be made up of point sources. Explain.j).xrb) mto n(

A star is in equilibrium when it radiates aih*r swmczvytu 8ci :/8,v+7ut its surface all the energy generated at its core. What happens when it begins to generate morvzci 88:u*im/y uthc+w s ,7rve energy than it radiates? Less energy? Explain.

Describe a red giant star. List some of nxwwm8p-u1mmah p 08: its properties.

Select a point on the H-R diagram. Mark several directions away from this poi*cj x1b 2t))uunvaq3snt. Now describe the changes that would take place in a star moving in each of these 2b3 *nj 1tqc)xvua)usdirections.

Does the H-R diagram,)(vw l i-ukjlzqh7ly3p7:w,.u oh uc reveal anything about the core of a star?

Why do some stars end up as wdv1k truwy/v26(q* rhhite dwarfs, and others as neutron stars or black hole1/vt qhrrv2y6duk*( ws?

  Can we tell, by looking at the population on the H-R kgzac;+d cuf j/ek.28 diagram, that hotter main-sequence stars have short ;dg.k k/ c+ueaf2czj8er lives? Explain.  ----待选择----yesno 

If you were measuring sta r1suws -iq:v ,hd4n: iapks 691wlp:kr parallaxes from the Moon instead of Earth, what corrections would av l4 1iusr -pdh:s6k,qinsw:k1: 9 wpyou have to make? What changes would occur if you were measuring parallaxes from Mars?

Cepheid variable stars change in luminosity with a taezl*( *lda 9 einu qbu32n8n3ypical period of several days. The period has been found to have a definite relationship with the absolu 9n3*enunal8auqe3d2bl * (izte 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 Relativity?du uwr2-cas r4v6uw1 0nnxx230: lsso

If it were discovered that the redshift of spectral lines pu*iv2 u-fu5xcy dbr 05i,z5aof galaxies was due to something other than expansion, how miguxaz5b*dv-r0yc ,f p2u5 5iiuht our view of the universe change? Would there be conflicting evidence? Discuss.

  All galaxies appear to be moving away from us. Are wem 5i)8o *,ahfqwih d5n therefore at the center of the univer w)afqi5 5dn*oim,8hhse? Explain.  ----待选择----yesno 

If you were located in a galaxy near the boundary of our blmf/0 rq1emffl nja/1 f2:3sobservable universe, would galaxies in the direction of the Milky Way appear to be approaching you or recedinl21 nsef :1b f ammjf3r0//qflg from you? Explain.

Compare an explosion on Earth to the Big Bang. C(1 1sre og 5laweab54jb l8bl;onsider 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 1e8(1eolbr 5 bg4blj;w s l5aawould this correspond to, open or closed?

If nothing, not even light, es 4 3c/ae5 pv m)j/(qh fn5xxu;mzo,sbecapes from a black hole, then how can we tell if one is thereosmvqx ezmf(h45)j / /p3a5,ue;xcb n ?

  What mass will give a Schwarzschild radius equal to that of thet 802cm) t +pt nl/qb6zoaz7ue hydrogen atom in its ground state?2t87)ab0tzl u6z e+ qmcnot p/ M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billioj8/v1 9nort4uv.pb w yn years. Find that time on (Fig. Below). People have8 9oypbr/vjwu.4 1nt v 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 radiatnr* um shbks9n.3+n 7tion is. Where does it come from? Why is its temperature n b3*7n u hnstn9.smrk+ow so low?

Why were atoms, as opposed to bare nuclei, unable to exist untilw;s+( navq py /avbl(mq 5uwiu a*/l9. hundreds of thousands of years after the Big Banvs9 .al( u w5q (avqnup+bmy*/ ;wial/g?

Under what circumstances would the universe eventually collapse in on its(em:wm z9lul f7hm3*a elf?

  Using the definitions of thqr5)luy9 )uv(u typ,oe parsec and the light-year, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.3 8-xx;, owbz+oypmkq4h1 9 lpj8 seconds of arc. How far away is it? d =    ly

  The parallax angle of a stq5seue1u/c+e4 mf)os nd vj9 6ar is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its parallax angle? q r pouvf5bh x+w/12) z+oigi/
State (a) in seconds of arc,$\phi''' \approx $    ($\times 10^{-2}$)''
(b) in degrees. $\approx $(    $\times 10^{-6})^{\circ}$

  What is the parallax angle f 3ryawxsuqe-*cc +lo 43 i+ u9fb5anb9or a star 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 t7ftpbx,s+yt1tx0,, uy hr ,hangle of the farther star be greater t,+tpyhyt ,ur, ,01xtx7hfbsor less than that of the nearer star? By what factor?

  A star is 35 pc away. How long does it take for its light to reach9;7lgikm, nh j us?    years

  We saw earlier (Chapter 14) that the rate energy reaches the Earth from thntcee njw,-hv2g) :1i8x;kdn e Sun (the "solar constant")ngjk 8c-ne,:dhev in wx; )21t 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 wgsivry w1yq16b7j.c0 da+v 0as seen from Jupiter as compared to its brightness from Earth? (Jupiter is 5.2 times farther from thw7yrq v.101 cswvi + a0dygb6je Sun than the Earth.) $\dfrac{l_{\text{Jupiter}}}{l_{\text{Earth}}}$    $ \times 10^{-2}$

  Estimate the angular width that our Galaxy would subtend if observed froldhi6p)6)s qf4 hr n7km the nearest galaxy to us (Table 33-1). Compare to the angular width of hd4ri)6)shlf7q pk n 6the Moon from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, what will be its average;vlba92r jr5zca 6vu ) density if it expands out to the orbit of Eab5uv)raj; v2r9 a lzc6rth ($1.5 \times 10^{11}\ \text{m}$ from the Sun)? $\rho = $    $ \times 10^{-4}\ \text{kg/m}^3$

  When our Sun becomes a white dwarf, it is expected to be about t lyz,9y dj3t 11tl/sodhe size of the Moon. What angular width will it sut1t o,19sydzy3l l/ djbtend from the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density o)/h8e3x ne ijo(2 7hjame seumok0,o)f a white dwarf whose mass is equal to the Sun's and whose radius is equal to the Earth's. How many times larger than Earth's densitems(8m2a0xi)eo 7oe jjn3keh ,oh/)u y 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 1u14- wdrg ec71-itfy g.5 solar masses has a radius of about 11 km. Calculate its averagt gif714w ygr-deu-c1 e density and compare to that 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 reactions of Eq. 3ckpq .akwtdnx/ n,053e ht.f)3-2. (The mass of the very kpdqka.c). 3 ,hnn x05fwe/ttunstable $^8\text{Be}$ 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 brighuhfs)4l(b p jxqf)34t5ow 3qk tness $l$ 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 assu7;gq + einc yjk3ndg6+med to be about the same distance from us. Two such stars have spectra that pe+ e3qn6cnikd7j ;g+g yak 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 eq0cdcqm:nhm zjk) ;-ya9zx +8g wg4(ekual to that (a) of our Sun+k8j9zcemkx)-(zgngdy a0hcq 4:wm ; is    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typical galaxy (like ours)? R =or:ckk -37obo    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the su:zy me(jy;sf)i aq7 2g3jbf*dttt)) i rface of a sphere, for which the sum of the angles isyazt ()*fyig tj)i32jbf qsm7e t:;d) (a) 359º, and (b) 180°.

  What is the maximum sumanupoik6e7 0+ -of-the-angles for a triangle on a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the speed of lighu:,si / m 4k/z4cnq;(nxjct/a2wm+9nxxg ycat, roughly how far away is it? na;(y/a,4w 2 nmct/ uc/z4ijnkm9gx:+xcx q s v =    Mly

  The redshift of a galaxy ,qgl/cm5 zz gem8zl/+ indicates a velocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a gazr1k )9mo o:gdlaxy (relative to us) that is near the observable "edge" of the universe, say 12 billion light-years km1go:)9do zr away. v =    c

  Estimate the observed w7ffj4rg; n:gwosn7 iw 36 jzy0avelength for the 656-nm line in the Balmer series of hydrogen in the spectrum of a gal fg:joww jfr 7n;4zn6i3gs70yaxy 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 its distance 07j fgv5(jrj ;oq+bjefrom us, if the wavelength for the hydrogen line at 434 nm ijj0ev ;+fjqorb5g j (7s 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 withejudm/r2;jd9)2 sfzxq3xh ;w $z = 0.60$? v =    c

  What would be the redshift pari;a yr6ev;i/l3cu+u wameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Doppler shift in (ux2b6g:k3a j5hgjum 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 tef vj.c-n.tt1cwqc3 ;k:s- orhe blackbody radiation distribution at 2.7 K uscocc :tk.n.3sf1 q--jtew ;rving Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical densityh ::34ofyqr9mwqli *g for closure 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 galaxies) at any one mvxrp)e024p uy su(u6coment is believed to have been inversely proportional to the absolute temp2pesy)4vucu rx( up 06erature. 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 timk7 m8 bvch r3kmp5+p2ke had the universe cooled below the threshold temperature for producing p2c k +phm53krbv8mk7
(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-seqta 2. dj.jo3x 3z +qgsr6*lfw r2jwlc9uence stars could undergo the three changes represented by the three al lr2j6x2 jjsr3+*gc .9f3 d.zwqawtorrows, A, 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 stars to us hjeh,o y) 4ll-n+weg4/xxkm y(ave an absolute luminosity about the same aw4y e(lyx,le/k-)og n x4 j+hms the Sun'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 angular momentum to 9v4 tdaih+l9w estimate the angular velocity of a neutron star which has collapsed to a diameter of 20 km, from a star whose radius was equal to that ow v4tidh9+ l9af 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 rot **suphp:gc6l:6ioiao +i ,i zxxkc4+ational kinetic energy change when the star in Problem xp*k , i+z4u:6spii6l +:aco*xiochg56 collapses to a neutron star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believed to be a neutwr6 7h eh8kta4ron star of mass 1.5 times that of the Sun, with diameter 20 km, is observed to have a rotation spt 4rewa7 6hhk8eed 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 ga cnd;(;6n/b caq0eor dlaxy to our 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 mass (in eV) would provide the critical density tonx6y3+ f(h a d1em0hpg close the universe. Assume the neutrino density isx 0d1g( p+e 3h6hynafm, 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 nmbx5c3b4lay y:h hy1- p, respectively, both lie on the main sequench3hyyy1x-: 5blab p 4ce. 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 parallax at 18,9 a (o gxx-hn+)zddvgp*s bl00 parsecs. What is our minimum angular resolutio8bpzv l- )*ns,9ghddx(aog+xn (in degrees), based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from singly ionized helium in a dig+a/gbrr tx /6stant star happen to overlap with the Balmer li r6 txg/+b/granes from hydrogen (Fig. 27-22) in the Sun. How fast is the star receding from us? v =    C

  What is the temperature that corre3.l n(uee)6m7oh yhefsponds to 1.8-TeV collisions at the Fermilab collider? To what era in cosmological history does this correspond? [Hint: see uh3ee).me n 6hy lfo7((Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation of gas around what might bq3fg0)4b gisdr/d -c be a supermassive black hole )c-qfb g3/40gdsid rbof 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, 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" hyev4v+a c 8dq0sud95;7 mqdc epx)u9hydrogen line at 434 nm emitted frou dhex8;qp9mys9)0u deq 4v5ca7v+dcm the 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 stellar evolution, a star (if massive enough) wil)x iiy/pwc 7t*l begin fusing carbon nuclei to form, for exampi/p 7*i cw)ytxle, 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 ;g6 71)wq;dkt aaphck
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 de0e6vh dindl*2nsity equaled the critical density of the unn62e vdidh*0l iverse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$