The Milky Way was once thought to be "murky" or "milky" but is now considered tozu55hccn9lxod 6i7g . be made up of point dchc 5u xo.5lgn67 i9zsources. Explain.

A star is in equilibrium when it radiates at i4bej:b k9hmu 7ts surface all the energy generated at its core. What happens when it begins to generate4ehb:9u kmjb7 more energy than it radiates? Less energy? Explain.

Describe a red giantaw2m, zxf 4v.d2cpq6xw nii70 star. List some of its properties.

Select a point on the H-R diagram. Mark several .;-eho5p-6td bjqgrf tum+ 1udirections away from this point. Now describe the changes that would take place in a stajrqu15epd t.u-+- m6fo;g bthr moving in each of these directions.

Does the H-R diagram reveg n kf8c20 *ffkxk flmf6+,dy bx.k(4oal anything about the core of a star?

Why do some stars end up as white xe3d9ad+x r m: 25tnpldwarfs, and others as neutron stars or black hole:d ap2+rm5ldxt9 n e3xs?

  Can we tell, by looking at the populatitzr d1.0a 7n8cv3yv quon on the H-R diagram, that hotter main-sequence stars hdn7varzqvc81 3 0 .ytuave shorter lives? Explain.  ----待选择----yesno 

If you were measuring star parallaxes from the Moon instead of Ear).o5+ zjf mim1 t)p:nktx dfw:,dm 8blth, what corrections would you have to makdpt5 f8mnlzwt :)ij:.1m b ox+dkf)m, e? What changes would occur if you were measuring parallaxes from Mars?

Cepheid variable stars change in luminosity with a typical per(cch8un6f3bh72) ai8afo wpsiod of several days. The period has been founhb8fap7hcaw63(u nic ofs) 2 8d 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 role ip y)xd5vxm7br)u 5)xa n General Relativity?

If it were discovered that the redsmbke25a8od b+ hift of spectral lines of galaxies was due to something other than expansion, how mkm a52 d8oebb+ight our view of the universe change? Would there be conflicting evidence? Discuss.

  All galaxies appear to be moving away from us. Are we therefore at the d 7pbflm5 -uhbsx4)g2y( f(wpcenter of the universe? Ex dslmx((24bfyghu 7f)w-bp p 5plain.  ----待选择----yesno 

If you were located in a galaxy near the boundary of our ob xqfcyb539 i(uservable universe, would galaxies in the direction of the Milky Way appear to be approachinu3(fq95b iycx g you or receding from you? Explain.

Compare an explosion on Earth to the b+ zij)yc4 v9nBig Bang. Consider such questions as: Would the debris spread at a higher speed for more distant particles, as in the Big Bang? Wo4+9bjc ) nvyziuld the debris come to rest? What type of universe would this correspond to, open or closed?

If nothing, not even light, eeer8 64l o6/ *zs)fktkse mn;cscapes from a black hole, then how can we tell if one is thelk/s*ce6o)ter kn sf4 z6;8mere?

  What mass will give a Schwarzschild radius equal to that of the hydrogen atoz) pwe;iwxx/tmda(- 3m in its gxi ; (3w w-xdtmp)ae/zround state? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 w wpr(ko zp2:3c6r(xk billion years. Find that time on (Fig. Below). People havwkrr(c 2(xk p: wpzo36e 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 rz -6,tpyjp-mobm 0x*l adiation is. Where does it come from? Why is its temperatp06mt lbo *mz-- jp,yxure now so low?

Why were atoms, as opposed to bare nuclei, unable to exist until hundreds ofbl), g p;fr ahfdr tx: )dizfk)1pz.,3 thous)gl.r, f, ;dzh :pkp3 )1fzdt f)rxbaiands of years after the Big Bang?

Under what circumstances would the universe eventually collapse in on itsxyebd o27l(i0elf?

  Using the definitions of the parsec and the light-year, show t9dv/ 1t8*9 yo syvxbephat $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.38 seconds of arc. How far away is it? d =wy axct(gn(wgi j;057    ly

  The parallax angle of a st+- 0fc6xspjq tar is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. Whniy m89nx39 edat 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 star that(02gtr :cfq9o4hxo1fs qyhi* is 55 ly away? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far away from us acr)o;0e8gsqhb .hv t )s a second star, will the parallax angle of the farther star be greater or less than th8 vq.s e)ob0;cr gh)htat of the nearer star? By what factor?

  A star is 35 pc away. How long does it take for its light tokprhw7bd (rmfcvs 8b- ,ydk3ih21e/m: x )5gi reach us?    years

  We saw earlier (Chapter 14) that the ratwo) +:r.ormts1 u 4unwe energy reaches the Earth from the Sun (the "solar constant") is an+ rso1to:w m ruu.w4)bout $1.3 \times 10^3\ \text{W/m}^2$. 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 Jupiter as1aai b7++kavt compared to its brightness from Eartha7vabk+ +t 1ai? (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 o/2cqkfrx +-(f w fqopcnm 5h/:ur Galaxy would subtend if observed from the nearest galaxy to us (Table 33-1). Compare to the angular width of the (:2o// f fr5 nwc +hpxc-qqmfkMoon from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, whan dy4;rioz2p ,4;hikk;)zbib zb; h,b t will be its average density if it expands 2kzzih4n;iy,; hrb;doz bk4b ;i)p ,bout 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 b 3 : r5p1w39wycia-kd1k 9xwjwzv4bt the size of the Moon. What angular width will i1zbyw jp339ww:xk r5a4wtvd9-1b ckit subtend from the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whowu 6cl /;j-ztdex0p, xse mass is equal to the Sun's and whose radius is equal to the Earth's. How manycpe0zwx/ x ujd;,-6tl times larger than 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 masspg8. 0gq fiie- is 1.5 solar masses has a radius of about 11 km. Calculate its average density and compare to that for a white dwarf (Problem 13) andg iei0pfq. 8-g 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 t0vwpx: u*(lfx(- urrof Eq. 33-2. (The mass of the very unst*r ( rul uwpf(0x:vxt-able $^8\text{Be}$ 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 3 xzrfl3wh(2ik2zn )xapparent 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 ce.ns:;j )dgaai rtain cluster are assumed to be about the same distance from us. Two sucn.a gsjai;: d)h 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 reo 3*w-0g rfmq +0wjovadius for a star with mass equal to that (a) of our Sun is * 00-qr+fwe goo3vwmj   km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typical galaxy (likp (pl604 fstrje ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surfac oks.p6 :2mbzke of a sphere, for which the sum of the angles is (a) 359º, and (b) 1z 26 ko.p:mskb80°.

  What is the maximum sum-of-the-angles for a triangle on a sphere? ip0/d4n2rwd n   $^\circ$

  If a galaxy is travery +c3kt q 7li+-0pfapling away from us at 1.0% of the speed of light, roughly how far aw7l+ f0p 3rt-q ipca+kyay is it? v =    Mly

  The redshift of a galaxy indicatew2) 5enn ty1;5v nbi +k7yxp3h,cyvh os a velocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxyx0oxnh b + 4ps0ye,sa5/ ;ysyp (relative to us) that is near the observable "edge" of the universe, spoy ne4y;s / s0xyp b0+5ax,hsay 12 billion light-years away. v =    c

  Estimate the observed wavelength for the 6d( 6yqq0e/a mq56-nm line in the Balmer series of hydrogen (/0aqeq md6yq in 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 a galaxy, and its distance from us, if the wavelength for mn6 7mn*:alufthe hydrogen line at 4347n:a*6nmflu m 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 galadv ( u(d;g3 rd2ugwuyn ,u4dp.xy with $z = 0.60$? v =    c

  What would be the redsp( u v(c;p5wu k-.oyeuhift parameter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Doppleroz gp vfl(bft 893.q*i 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 distributrlg+8.ccxwn 8j y7njda9)c+ xion at 2.7 K uacj7rcx8dxgy9. + lnn8cj+ ) wsing Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure ;jcelehoh)v9m .nv-k,ciw.nj)w1p) 0 1sww dof 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 mw2k4 ya70uc4jii+v g homent is believed to h iwc+agi4 v 4k72yh0juave been inversely 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 belodte.+jm k 0f9z wliw;:w the threshold temperature for producing 9+.wj0imtdle;w fz:k
(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 chant)wa,hqau2v *mmk59si1t oq (ges represented by the three arrows, A, B, and C, in the kmhu(1*a 9oasw5mvt,qiq2t) 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 luminos:(aow yk 2y6,, h(v5kloouro,4jqktx ity about the same as the Sun'syay:,uooo l(,q4kv jorw,65xk2(t hk. 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 estimate the angular velocity of a neutehclm u hv3. 1zv83g5yronhm31e lvuh8y5 z 3vgc. star which has collapsed to a diameter 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 kinetic energy change when the stm *yk(umn yg(nl( mi-6-nd2xen*m gh6ar in Problem 56 collapses to h mln(y 2g-y(d-i6(mkmenux* nng* 6ma neutron star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believed to be a neutron star of uj5xo ldj(64)4lpsps mass 1.5 times that of the Sun, with diameter 20 km, is observed to have a 4(5jxul)4d lpp6ss jorotation 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 o*7s8a: f z*w:hkhktiu ur 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 k)ow5c y y1y,umi+1pjcritical density to close the universe. Assu wuyycpjm, oi5yk)11+me 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,10 i8qr mli,wx respectively, both lie on the main sequence. 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 33-4iwmr l80x1, iq and 33-5.] $\dfrac{d_{400}}{d_{600}}$ =   

  Suppose we can measure distances with parallax at 100 parsb17sb 6inwn jow6oq .9ecs. What is our minimum angular resolution (in degrees), based 6on9i7j1 qn.6 wbob swon this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the B wty8g2m(r5 uh3hw-gyalmer lines from singly ionized helium in a distant star happen to overlap with the Balmer lines from hydrogen (Figw5htm3y2(r g-hyug8w . 27-22) in the Sun. How fast is the star receding from us? v =    C

  What is the temperature that corresponds to 1.8-TeV collisions at the Feru tvq* twa09:(eif 4nuue0 n;pmilab collider? To what era in cosmological history does pt:40qwu e*innetv90;f( auu this correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation of gas aru.,smt u 8z +quhx.hs( *gfn8nj19+xpan 2m uround what might be a supermassive black hole of about 2 billion solar8.2ngm 1+tjqar,* snu 9xm 8fup(zh. xn+uush 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 "b/ rvdz9a/x3kp2 1acg3ygk a5t/te xp: lue" hydrogen line at 434 nm emitted from the galaxy is measured on Earth to be 6a cgepza/ 3rd1 9yxk52kg/v p/:atx3t 50 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 evoluz+a t+si(stt4as. j9o-0ss chtion, a star (if massive enough) will begin fusing carbon nuclei to form, for example, magnhiss4.c(saz + -astt +0st9ojesium:
$^12\text{C} + ^12\text{C} \to ^{24}\text{Mg} + \gamma$.
(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 reaction23pl4; 6cbvhqg udu ;q
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 thqb 1jn9c jgs+o;c(v72i zo,sqe critical density of the unic +z7sc2g ji( so qnb91oj;,qvverse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$