The Milky Way was once thought to be "murky" or "milky" but is now considereqqcp9 hf;l-a2 3su 0t;tgq,dqd to be made up of point sourcesa;qqqq 3;f90,g-hpud2l tstc . Explain.

A star is in equilibrium when it radiateq/xjcu. jvohu 1tgsnr0j.0xo-4n8 - ts at its surface all the energy generated at its core. What happens when it begins to generate more energy than it radiates? Less energvor 4 0-1tuuc8j.q/x-snn toj .jgxh0y? Explain.

Describe a red giant star. List some of its propertie/ gnfr oz/jws6g 2s-w8s.

Select a point on the H-R diagram. Mark several directions awia+au)8e irr4j3kw 1day from this point. Now describe the changes that would take place in a sta r+4 a8 iu)ijwea1kd3rr moving in each of these directions.

Does the H-R diagram o6 of.e m 0qaj ;grp(:t/ ,ykpnmihv5)+k ago4reveal anything about the core of a star?

Why do some stars end up as white dwarfs, and others as neutron stars or black 0s2qhfiv grprmy 535- holes?hf3v r5p2ms-yqr0 5 gi

  Can we tell, by looking at the population op 9jjkxcijcc o2q5sr2)701 mw*6dbp mn the H-R diagram, that hotter main-ses 12r*oc j7jj6wpc5dcx2q bkm90 i)pmquence stars have shorter lives? Explain.  ----待选择----yesno 

If you were measuring star parallax. vbppcnp4lnn)5 .4 * ul,wckfes from the Moon instead of Earth, what corrections would you have to make? What changes would occur if you were measurupp)pcv4n,w*bnnl4.k5l f.cing parallaxes from Mars?

Cepheid variable stars change in luminosity with a typical per sj+. fi q*/p7zr;ao8s c*hzbkiod of several days. The period has b **pras izjsh+k;fo87 . zc/qbeen 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 ):n. he*/ hxztoiu ob)yw) mk-is its role in General Relativity?

If it were discovered that the redshift of spectral linn(xskju-k4p34 k 8kuy es of galaxies was due to something other than expansion, how might our view of the universe change? Wou(k-4nk3ypku 4 xu8skj ld there be conflicting evidence? Discuss.

  All galaxies appear to be md47 y 2bwg ,(stdqmql3oving away from us. Are we therefore at the center of the universe? E(2qwtb yg4 ,3dlqmd7sxplain.  ----待选择----yesno 

If you were located in a gala5gjhvs0a md pb3nv.; d 3,e4kkxy near the boundary of our observable universe, would galaxies in the direction of the Milky Way appear to be approa s03e4 da3vkbjn.;h k p,vdgm5ching you or receding from you? Explain.

Compare an explosion on Earth to 3,ln;a z.eczj0 yi(d fthe Big Bang. Consider such questions as: Would the debris spread at a higher speed for more distant particles, as i3dlie,y zzf. cj ;n0(an the Big Bang? Would the debris come to rest? What type of universe would this correspond to, open or closed?

If nothing, not even light,w3 0+b0t0pzgsby4 gtw escapes from a black hole, then how can we tell if o3bs ttbw04g00wgpzy+ne is there?

  What mass will give audf: l(9h-cjad2b-rr Schwarzschild radius equal to that of the hydrogen atom in its ground stahc ur2lb d9f(aj- r-d:te? M =    $ \times 10^{16}\ \text{kg}$

The Earth's age is often given as about 4 billion years. Find that time oxmz 15w o+5 rmczp0l9un (Fig. Below). People have lived on Earth on the order of a million yc m1l0mx9uozrz5pw 5+ ears. Where is that on (Fig. Below)?

Explain what the 2.7-K cj5pre ,gv: kt1ifv*l3 osmic microwave background radiation is. Where does it come r,vv:jgt1ei3* fklp5from? Why is its temperature now so low?

Why were atoms, as opposed to bare nuclei, unable to exist until hundrxuy ,twd+s 4d1eds of thousands of yudd+,wsx 41 tyears after the Big Bang?

Under what circumstances would t-w+b(jsl;aog* j 3kq,x7hr xehe universe eventually collapse in on itself?

  Using the definitions of the parsec and the /-s9lc/by upz light-year, show that $1\ \text{pc} = 3.26\ \text{ly}$. D =    ly

  A star exhibits a parallax of 0.38 seconds of arc. */g+wgu qkhz,q sjg/1 fioo42How far away is it? d =    ly

  The parallax angle of a pe(q3o2r. quqmb6 1zistar is $0.00019^\circ$. How far away is the star? d =    ly

  A star is 36 pc away. What is 5j-u7j-lj7wzje/d 4rd k w a 4ndf(t-tits 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 is 55 ly 39ntr.is1, iv ux9 flw959 dr)l0f1 bvxodt aqaway? $\approx$    pc
How many parsecs is this? $\phi $ =    ''

If one star is twice as far )fq1 c(*t/,q uixncakaway from us as a second star, will the parallax angle of the farther star be greater or less than that of taicu/,c)*n qq(1xkfthe nearer star? By what factor?

  A star is 35 pc away. How long does it take for its light to reach:p;l(4.5u af87 ocgcfw fpl rq us?    years

  We saw earlier (Chapter 14) that the rate energy reachxwwzswlcut*- :r xa48b:):b res the Earth from the Sun (the84zbr :xw :w: r* cbausltw-)x "solar 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 avsd07esu4l+8h xy b7a s seen from Jupiter as compared to its brightness from Earth? (Jupiter is 5.2 times farther from the sx4u+vehy bsa l7078dSun than the Earth.) $\dfrac{l_{\text{Jupiter}}}{l_{\text{Earth}}}$    $ \times 10^{-2}$

  Estimate the angular width that our Galaxy would subtend if obso qe9-:l8)ozk*rexw+,gcb ry erved from the nearest galaxy to us (Table 33-1). Compare to t,)o re9g* oyz wbke8xqr+:l-che angular width of the Moon from Earth. $\phi $ =    $ \times 10^{-2} rad$

  When our Sun becomes a red v4: 4nec(3z i2bwgftgz( y;wpgiant, what will be its average density if it expands oupz((w wt ie3g bv zyg44;2:fnct 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, zzxj/ atc upf.3c8g em3t ql0;-mz4-yit is expected to be about the size of the Moon. What angular width will it subtend from the prme z cjt;z-.gp 4l3u0/yz8afqc3 x- mtesent distance to Earth? $\phi = $    $\times 10^{-5}\ \text{rad}$

  Calculate the density of a white dwaro9b63q lux/,aifjs-b f whose mass is equal to the Sun's and whose radiuao9 3b,jbi slu-x6qf/ s is equal to the Earth's. How many 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 mass is 1.5 solar masseu x+ xu-fud4q0-1e ;qm+bwesws has a radius of about 11 km. Calculate its average w0bq us+;uxeq-dxw4-+ 1 m fuedensity 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 i)cl0(iz.igg /cp /cmthe He burning reactions of Eq. 33-2. (The mass of the c(0gi/ pic/.gl)zmci very 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 apparenoul/ (xwf4a* gt 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 dykj a6x (h-(atlfwm sw*(0o0distance from us. Two swwk lt0a0(hm(a* - sxd(oyjf 6uch 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 for a star e*payuxq ka r7uia :d*w+;/z0 with mass equal to that (a) of our Sun is;akri7e z0uqa*auw y:/d+x p *    km, and (b) of Earth is    mm.

  What is the Schwarzschild radius for a typical galaxy (lx3jrf t w,6;ktike ours)? R =    $ \times 10^{14}\ \text{m}$

Describe a triangle, drawn on the surface of a .s704mka v8eks9c3elmas2s b sphere, for which the sum of the angles is (.a42 el8 am0cv9bkm3es sssk 7a) 359º, and (b) 180°.

  What is the maximum sum-of-the-angles for a triangle on a sz 3mg0s z5m99 kof ldq*r.qmq-phere?    $^\circ$

  If a galaxy is traveling aws,f9 xe-2+ ubeen +hsuay from us at 1.0% of the speed of light, roughly how far away is it? v =bsf9 +u xeu+-en h,s2e    Mly

  The redshift of a galaxy indica/ zdmk-oed 1z2tes 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 observablesujrlle4h/ g anm ixy,00)f4nmr (a 8f u1))ig "edge" of the universe, say 12 billiofe4ua0/ )xi80aml4 l)y n,r1mnifj g)s u(grhn light-years away. v =    c

  Estimate the observed wavelength for the 65y/4ynk9hlb+ djc*6no 6-nm line in the Balmer series of hydrogen in the*cnd y 6jby4+ /hk9oln 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 wv 3kp5 eaorr; o*-*h0c fxd/mfor the hydrogen line at 40xwk f o r*he a3rv5*c;pdo/m-34 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 g t3rt(ghw,gz3 alaxy with $z = 0.60$? v =    c

  What would be the redshift parametera;uq .;oe,3laftu/o z $z$ for a galaxy traveling away from us at $v = 0.50c$? z =   

Starting from Eq. 33-3, show that the Doppler shift in wave06a r3a iohw.+q reo3u )rld)klength 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 distributions 3nb9utjucrr+.)+acijnp wc. 9 f4 c7 at 2.7 .ub rcci9+4)+.wn a n 3rjpc7 jtc9fusK using Wien’s law. $\lambda_{\text{P}} =$    $ \times 10^{-3}\ \text{m}$

  The critical density forxj/ gxm:jegrh.m8- /p 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 gal+dd-grcwl rvm:*d*1xe gg v(3(u:prgaxies) at any one moment is believed to have been inver+(rmg gr-3lx* ( dug: c1d:vvreg *dpwsely 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 uu/wgf cda.80 jniverse cooled below the threshold temperature for p/g j0 w8fcau.droducing
(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 starsx7 wn. c830iiheld5gy could undergo the three changes represented by x n370ielc85hdi. gywthe three arrows, 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 toj(hqcx2x c;;i c3v/ kcjo ;vv, us have an absolute luminosity about the same as the Sun's. Their apparent brightness, hovc/qx ;; hicx, o(3kj2vv;jccwever, 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 ae jv9.3so*pnjb69:vv 4 xz uq7h)luox neutron star which has collapsed to a diameter of 20 km, from a star wenvsxhxq o*z6b97. j9uv:4ovu jp l )3hose 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 jbx5ac56h)ci m n/k6qxybb br)r )9j .the rotational kinetic energy change when the star in Problem 56 coj)bh6yib. bj krb9565r/c ac mxx)q )nllapses to a neutron star? $\dfrac{\text{KE}_{\text{final}}}{\text{KE}_{\text{initial}}} = $    $ \times 10^9$

  A certain pulsar, believa23jv)/:p 7f sghmfu* jv1dwsed to be a neutron star of mass 1.5 times that of the Sun, with diameter 20 km, is observedd g1p)3 j2a /7svwhm*vju:ffs 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 Galu*6vl)qy0v-o:y : otpxj ,rccaxy 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 (ipoz/h7*x3t*)s2dg sbj.q.w/ fzy uqh n eV) would provide the critical density to close the universe. Asobu*j 7sdt.qh z2h.fqg 3w s) /xy*/pzsume 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 t8sb( de/mg0 ezw0jc3 nm and 400 nm, respectively, both lie on the main sequence. Use Wien's law, the Ste3de (sj8mtc w0g b0ez/fan-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 100 parsecs. What is our1-dy( evdix hjujf;ngw.gm6+y*h x-ep+-l : f minimum anguldj-juyhpf.n- (g+ *f:x6 x h;1g-v welidme+yar resolution (in degrees), based on this information? $\phi \approx ( $    $\times 10^{-6})^{\circ}$

  Through some coincidence, the Balmer lines from sing 2+)keauyfe) se)r i1fly ionized helium in a distant star happen to ovesu))e+f1ef )ayeir2 krlap with the Balmer lines from hydrogen (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 collisionsdn6 ad b-8ov/)5zbefw at the Fermilab collider? To what era in )e /5fabw-6 d8bvdo zncosmological history does this correspond? [Hint: see (Fig. Below).] T $= $    $\times 10^{16}\ \text{K}$

  Astronomers have recently measured the rotation of gas around what might be a/ar7m,tqt:u kr.x i9j supermassive black hole of about 2 billion solar masses at the center of a galaxy. I.rq,rmia t utx9/7:kjf 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 lin j,ruvo6c k :gv9)ela6e at 434 nm emitted from the galaxy is measured on Ea e6voa vu96r,lc)gk:jrth 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 rz:;7kn;4bn dhuca f),baq1g of stellar evolution, a star (if massive enough) will begin fusing carbon nuclei to formg4)1 , r;cdhnz7 aqfnb;:kbua, for 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 /f kxzst*hc0c*go8q4
$^28\text{Si} + ^28\text{Si} \to ^{56}\text{Ni} + \gamma$
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 critical density of the xgq1+6s ks:e ounivq 6sk e:g1+sxoerse, $\rho_c \approx 10^{-26}\ \text{kg/m}^3$? 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}$