The Milky Way was once thought to be "murky" or "milky" but is now considav+ 8v8uf +qfb yo;i/ s.cws)eered to be made up of poiey8 fa) f+8 ou .w;qvsi/svb+cnt sources. Explain.

A star is in equilibr x 3cxsk yr398un;cb fleg(+h(ium when it radiates at its surface all the energy generated at its co3 h+cbes k gy9 f;cxnrulx((83re. What happens when it begins to generate more energy than it radiates? Less energy? Explain.

Describe a red giant star. List somc r.nk3prs+ k.e of its properties.

Select a point on the H-R diagram. Mark several directions away fl/oe w,m)cl:nb( ;vufrom this point. Now describe the changes that would take place in a vlub(;mfw/:n )o lc e,star moving in each of these directions.

Does the H-R diagram reveal anything ab i d8mm6x9hnn:out the core of a star?

Why do some stars end up as white dwarfs, and others asccj)-u p2g/uh( yacx1 p2,qul neutron stars or black h)gcu-p2,2luqy ap1 hccj/(u xoles?

  Can we tell, by looking at the population on the H-R diagram, that h5tls9sgw; 1 khotter main-sequence stars have shorter lives? Expla gl1h ;w95tkssin.  ----待选择----yesno 

If you were measuring star parallaxes from the Moon instead of Earth, ke ,/xfa:woy7,s,of yilfvth9m-o)5 f/si u 9what corrections would you have to make? What chf/) yl-kt,am f9hyuo/,si9 oo,5x:v 7isw ef fanges would occur if you were measuring parallaxes from Mars?

Cepheid variable stars change in luminosity with a typical period of .uff 7(8kku2cb n +vkuseveral days. The period has been found to have a definite relationship with uk2 ncf( 8vfk+u7 .bkuthe absolute luminosity of the star. How could these stars be used to measure the distance to galaxies?

What is a geodesic? Wha64, u9suspvwdt is its role in General Relativity?

If it were discovered that the redshift of spectral lines of galaxies wkz5cvs mc av18+2f8 6uc4wi5ci8 dqdgas due to something other than expansion, how might our view of the universe change? Would there be conflicting evidence? Dis8f ivck2s5u8dicv4z g 1dcm8c5+ a 6qwcuss.

  All galaxies appear to be moving away from *i,tc/9sa h gwz x0f-v lm6;xuus. Are we therefore at the center of the univv* ha0lsz-9im,f/u; 6 wtxxgcerse? Explain.  ----待选择----yesno 

If you were located in a galaxy near the:nu wz u10c,na boundary of our observable universe, would galaxies in the direction of the Milky Way appear to be ap a n0:z1uwcnu,proaching you or receding from you? Explain.

Compare an explosion on Earth to the Big Bang. Consider such questtv7e+ *5*nw7x8:hfva eeghbbions as: Would the de7w8v*navgfe ex*e +57t b:hbh bris 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, open or closed?

If nothing, not even ysb0,( yk s(.:fgdtlmlight, escapes from a black hole, then how can we tell if one is the y(ss:yl gmd0b, .k(ftre?

  What mass will give a Schwarzschild radius equal to that of the hyx08y3fzlh zq54jo 1qjdrogen atom in its ground state? M8lq xj zq03jh1z 45yof =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as4,9) m7kxsd ymim)b 11j4t ks /dsmyeo about 4 billion years. Find that time on (Fig. Below). People have lived on Earth on the order of a milli79d1,i144km)xbsk /mmmt e)sjdyoyson years. Where is that on (Fig. Below)?

Explain what the 2.7-K cowue s,pi+o 07xr5ewt)smic microwave background radiation is. Where does it come from? Why is its temperature now s5+i0)rp7wuw , eotxseo low?

Why were atoms, as opposed to bare nuclei, unable to exist until hundredk/r* f hl-ya6y ykft.5s of thousands of yearsr6fy h5fkkl*- y t/.ya after the Big Bang?

Under what circumstances would the universe eventually collapsb ye, +ap4uu2se in on itself?

  Using the definitions of the parsec and the light-year, f,kd57k gw zq/8ysk+xshow that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parall zd2 6dhcb+nb:hi/ s:rax of 0.38 seconds of arc. How far away is it? d =    ly

  The parallax angle of rep bwy4nbu0*tbn+5;a star is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is its parallax ang85ca qseif7flmcz7xfd -lb2 ws+*5vl ,hy-.tle?
State (a) in seconds of arc,$\phi''' \approx $    ($\times 10^{-2}$)''
(b) in degrees. $\approx $(    $\times 10^{-6})^{\circ}$

  What is the parallax angle fd3 dha5v-lacv 0aq85j0ghf5for 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 s, +u:s st.2,thviikabecond star, will the parallax angle of the farther star be h, t stiibk,sv.2u:a+ greater or less than that of the nearer star? By what factor?

  A star is 35 pc away. How lvs 7pe 0-,hesjong does it take for its light to reach us?    years

  We saw earlier (Chapter 1b;qsf gt875*e 06.f/yq fixrpwm hu9r 4) that the rate energy reaches the Earth from the Sun (the "sola*egtm/f9bi0xy;q 5 hfw.pfu r8sq r67r constant") 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 Jupiyl8/1q+ qbg:c n.(co+lfq gdhter as compared to its brightness from Earth? (Jupiter is 5.2 times farther from the Sun than the Earth.dc+1g +oql gnb.c8yqh/:f(ql ) $\dfrac{l_{\text{Jupiter}}}{l_{\text{Earth}}}$    $ \times 10^{-2}$

  Estimate the angular width that oznlu , a,6 k2tiog;1o9 vqfeg2ur Galaxy would subtend if observed from the nearest galax,okntg9 6olv1 e2uzqg;if a ,2y to us (Table 33-1). Compare to the angular width of the Moon from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red giant, what will be its rrth.naml9-iwa0p,fda d: m j;1lt 36 average density if it expands out to the orbit3pr06i alhd-dwanf; at9:, r. l1jmmt 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 exp nwdxhy+kw,nwt0f8/) ected to be about the size of the Moon. What angulw+)tknw8 w,x hynd /0far width will it subtend from the present distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwarf whose mass is equal2( ba:hl9u lgp to the Sun's and whose radius is equal to the Earth's. How many times larger than Earth's density is ph9l:g2 luab( 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 masses odj 7qs6/j9h4j )nses zns1p,)st1th has a radius of about 11 km. Calculate its average density and compare to tq)ept )s jjs ssj nt4 61zhd,7n1s9h/ohat 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 theuy;f o7cgi9ng)*q a+n He burning reactions of Eq. 33-2. (The mass of the very unstabl+;c 9unagyn)og* 7fq ie $^8\text{Be}$ 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 br* sopt2j*9cwuightness $l$ 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 cetk,3b l5, arjertain cluster are assumed to be about the same distance from us. Two53j,k,ra te bl 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 raz ;; qcgre. bfcu 9:k(7bo5w.mrm+zfydius for a star with mass equal to that (a) of our Sun is yucm .z5k;fb7:z w forem b9g+rq.;(c   km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a tpxfo9v 6 2dir3ypical galaxy (like ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a sphere, for whip rfz.z(xgj2-ch the sum of the angles is (a) 359º, and (b) 18. zr-p(f2zg jx0°.

  What is the maximum sum-of-the-angles for a triangle on r0 h5zbsek pv,hfw:c -4d(ru*a sphere?    $^\circ$

  If a galaxy is traveling away from us at 1.0% of the 2ohvbwr0 egm32jy) 8 vx7u1fgspeed of light, roughly how0gv1efxhbm) 28ry3wv ug o7j2 far away is it? v =    Mly

  The redshift of a galaxb2o i8cg(jhp5 y indicates a velocity of $3500\ \text{km/s}$. How far away is it? v =    Mly

  Estimate the speed of a galaxy (relative t :kxaq bp0cb+v0 aso2.9v.aiqo us) that is near the observable "edge" of the universe, say 12 billion light-yearscvi9 02a+ob:.aqb va s.xpq0k away. v =    c

  Estimate the observed wavelength for the 656-nm line i v-/-gpa2 tlry p5a95rbe;anrn the Balmer series of hydrg p-9bpynrr5;a2 el/a 5rtv-a ogen 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 wavee1x( vycjb4xs (l63o jlength for the hydrogen line at 434 ny x((4lsj1cej bo x63vm 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 galaxaxjqf;7 84 cyq2qo,lpy with $z = 0.60$? v =    c

  What would be the redshift paramp -x-f bh(giezl1o n+-d)qyt1eter $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Doppler shift in wavel:d/bi q).abaz9oz0amength is $\Delta\lambda/\lambda \approx v/c$ (Eq. 33-5b) for $v \ll c$. [Hint: use the binomial expansion.]

  Calculate the wavelengsc,20 rk mzgq+th at the peak of the blackbody radiation distribution at 2.7 K using Wien’s law. ,qg2zr+m sck0$\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density for closure of the u8m5hgjiez1/oxnp6 l1 niverse 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 yqa6rk gy 4(/p9heei26 e, dhkdistance between galaxies) at any one moment is believed to have been inversely proportional to the absolute temperature. Estimate the size of the universe, compared to today, at q ie2h /,69k6yeaykgdhr4pe(
(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 thresk h84v.pez ljul2: ij-i(o)xphold temperature for prp.l xl82vhpj):i i -ezk4(j ouoducing
(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 chad)hgne p .,*dvnges represented by the three arrows, A, B, and C, in the H-R diagram of Fig.* e v.hpd)ndg, 33-28. For each case, describe the changes in temperature, luminosity, and size.

  Assume that the nearest stars to usdb /1b)c jkb)y have an absolute luminosity about the same as the Sun's. bb))bj/ 1 kdycTheir 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 vyyxh3/sxx;9ls 0 36n 9 rhqrplelocity of a neutron starl s yqxnpry0h6xrl9;39 3s h/x 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 spv/ pw10b40 m9b i 4xixmht5qxtar in Problem 56 collapses to a neutron star?i4mhvxw9 qi1 5t p4x/bpm00bx $\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 .gv6ormo;e 1cn, with diameter 20 m6v1; erc.oogkm, 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 thju pqdi(ta q0dn b2(8 qdx8-0o 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 cec/b,7 ygb 9eh-ekp- writical density to close the unive ee eg-/y9,bwc7 p-hbkrse. 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, respectively, both linn3 lyyuba8; 8e on the main sequence. Use Wien's law, the Stefan-Boltzmann equation, and the H-R diagram (Fnny38a uy8b; lig. 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. What iscdd7fd pz56* z our minimum angular resolution (in degrees), based on this information? ddcf d*6z5 z7p$\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from singl .2*zr;ywkjfvt aqmefp:49a 8 y ionized helium in a distant star happen to overlap with the Balmer lines from hydrogewt2*rkj.a : 8 yep;m4fav9fzqn (Fig. 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 Fermila,u;x mih2m7ltr1z*g gl3h/5n lctcv 4b collider? To what era in cosmological history does this correspond? [Hint: see (Fig. Belowli1g5mrm lg v/u 3 ,zh;ccnxtlt7*h24).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation of gas arou ;sky,oc w)vk99g4mtxnd what might be a supermassive black hole of about 2 billion solar masses at the center of a gal,k9k9 ;omtcxys)4v g waxy. 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 "bl2m rr v,8f,./aeirl;wt p1yh pue" hydrogen line at 434 nm emitted from the galaxy is measured on Earth to be 650y v2rh,ir1;ppr /f,twam.8l e 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 e6tn/-yc8l4 stxcqnxi vwf -.5 nough) will begin fusing carbon nuclei to form, for qc45clf-xv. s/wt8x -nny6it example, 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 6yknyy4n g 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 eqy+2xkr7,47 , c 3urfpeccc) ku9ohwugualed the critical density of the universe, ccycu47rfk9,r3gw,) e c7 u ohxup+k2 $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$