Aaowd mnnnoopwTiHH $ @d HHHHff@  d/ Footnote TableFootnote**.\t.\t/ - :;,.!?:0 `$ `TOCHeading1Heading2  EquationVariables&%/( h!~"  <$lastpagenum> <$monthname> <$daynum>, <$year> "<$monthnum>/<$daynum>/<$shortyear> ;<$monthname> <$daynum>, <$year> <$hour>:<$minute00> <$ampm> "<$monthnum>/<$daynum>/<$shortyear> <$monthname> <$daynum>, <$year> "<$monthnum>/<$daynum>/<$shortyear>  <$fullfilename>  <$filename>  <$paratext[Title]>  <$paratext[Heading1]>  <$curpagenum>  <$marker1>  <$marker2>  (Continued) + (Sheet <$tblsheetnum> of <$tblsheetcount>)ono Heading & Page <$paratext> on page<$pagenum> Pagepage<$pagenum>` See Heading & Page%See <$paratext> on page<$pagenum>.dg2  Table All7Table<$paranumonly>, <$paratext>, on page<$pagenum> Table Number & Page'Table<$paranumonly> on page<$pagenum> U e ^  U`` VSSA~ WTTA XUU YVV ZWW [XX \Y]A>$d ]aa ) `  mo a<$  >nu  nda r una   fi    T  a[H     m   r  r  n  htb  ols  o   <   e  Pa  $p>  $ein  %ear % %ppa  2Ta  %apa  % at %aag % %e  % %gbl  %on  % %n  %^ ! % ' '  'A >  " ' ( 'U ( # # #V ) # , # # # , - , -A> , - * ' ) , - , - , - 0 # 1 # . . 4 . 2 - 3 - 3 - / . ' ' ?d / .j / / ?y  . .  / ;{  & .  & 6 + 6 4 7 / ; / / 4 /`  5 .;  B /%<  / /=  C />  9 .?  C . @  . .%A  C .%B  = .C  9 9%D  D 9Q  D <!G  9 9'K  9 .L  D 9>\  9 9"a  8 .(b  . .(c . .#d ! 5 @)qbdq5,XSmA>dq5,VTndq5oH3R `@q6 3H3R `@H RH R hFootnoteHq3@ `@q6 d /Hq3@ `@HzHz h Single LineH'q7{ &Footnote +  r8     H3D `@q9 <H3D `@HH h Double LineH q7A Double Line 9v:!x:ab .H q7 Single Line{:HZq7q TableFootnoteEGVR `@q7 EGVR `@EPwEPw h TableFootnoteod5p5YYpd5::q &HH7 HHj: ` nqCourse Outline  k(handout) 3;` j X` c( Textbooks:Zeilik (lectures,homework) u` cHoff (studios) le` j ` e Grading:Exams10% x 3 ` e Final30% ` eHomework20% ` eb Studios20% #` j @` m# All exams open book / open notes Si]` m tMonday evenings okay? z` j ` u# Homeworks due in Monday lectures ` j ` cTa' Studios due at end of Friday session ` j  ` e% Read studio exercises before class (` e+ vDo you need to bring something along? E` j 5b` m* Class email list:  wastronomy@rpi.edu HH7 HH :Sd aut eHH7 HH okwork) T d a HUV 7 dg:HUV  UUU` i H$ 7 H$ l otes SiV UU` i o ?HUV 7 HUV onq5WUUd ie  eH$ 7 H$  fore claXUUd i t rHH7 5HH(  tronomy@Y  ` n79205 Astronomy C ` k n ohttp://www.rpi.edu/~napolj/ @ o eAstro/course.html  ` l  ` pJim Napolitano  ` q Instructor E ` p p ` pNicolle Zellner  ` q Graduate TA  ` p  ` pSaavik Ford, Dan Holt  ` qUndergraduate TAs 7d5 ZZrSiHH7 ?HH7"UV"Z h j5  d5[[s HH7 HHpfPd i t[ ` nElectromagnetic Radiation ;` j X` c Wavelength yl=2p/ ck u` com Frequency yn=w/2p  fPfP` c8 Speedc y=ln=w/ ck y=3.0010 z8 y  cm/sec o/fP` j fP` e) Wavelength bands have different names: fP` eor*Visible light400 nm  {< l <  e700 nm  fP` eneUltraviolet {l <  e400 nm e T)fP` e Infrared {l >  e700 nm SaFfP` et $Microwave {l  ecentimeters scfP` eRadio {l  emeters fP` eX-ray {l 0.1 e nm fP` {g e-ray {l 0.001  enm 7fP` j "fP` m/ Perpendicular  |E m and  |B m fields fP` m5" }  mLight can be polarized fP` j .fP` u7# Photons: Energy E ~= uh ~n pfPKfP` uX-rayE  ~  u10 keV hfP` ~g u-rayE  ~ u 1 MeV RaF@i}7 &p/cIР7 =2p eed5se]]w fPH3QC ierH3QaWwG=< <aWwGaWwGaWw jWwG= jWwG> 7jWwGjWw |WwG=ers|WwG` |WwG|Ww WwG={WwGfPWwGWw Ww,uB Ww,u Ww,WwWwuBPWwu} mWwWw(Ww,E Ww,Eney Ww,Ww1WwA kWw` WwWwWw}-A7Ww}-WwWw}Ww-=Ww-WwWw)WwGf`=se)WwG_f` WwGqNaGctWwr zCvxwWw~lG@SM5Ww#0gTe+Sy)Ww'Wwf`=w'Ww_f` Ww o4_GPrWwbxC[ۋ6WwhjG@ƯKx3Wwt.g)SP'WwFWw<wFWwFWwaWwjWw<wjWwWwjWwWw>wWwWwWwWw>wWwWwWwaWwÕ#< waWwÕ#aWw1aWw1 lWwvt: ].> wWwvt: ].WwWw dWw} ?$wWw} Ww}Wwd5w\\tHH7 HHfWw~\ ` Ww Diffraction ;` j X` j/Resolution limited by aperture and wavelength. xCu h jh `  jg `  yWw/  cImage of distant object contained within 5`  yWw Z ` r q l/ d <NXw07 Ww&z<)?1@.j69DN&z<)?;'&equal[(*q"Green"q*)char[(*q"Green"q*)lambda],approx[(*q"Green"q*)times[(*q"Green"q*)indexes[(*q"Green"q*)0,1,char[(*q"Green"q*)lambda],num[(*q"Green"q*)0.00000000,"0"]],indexes[(*q"Green"q*)1,0,id[(*i1iq"Green"q*)over[(*q"Green"q*)plus[(*q"Green"q*)num[(*q"Green"q*)1.00000000,"1"],fract[(*q"Green"q*)char[(*q"Green"q*)v],char[(*q"Green"q*)c]]],plus[(*q"Green"q*)num[(*q"Green"q*)1.00000000,"1"],minus[(*q"Green"q*)fract[(*q"Green"q*)char[(*q"Green"q*)v],char[(*q"Green"q*)c]]]]]],fract[(*q"Green"q*)num[(*q"Green"q*)1.00000000,"1"],num[(*q"Green"q*)2.00000000,"2"]]]],times[(*q"Green"q*)indexes[(*q"Green"q*)0,1,char[(*q"Green"q*)lambda],num[(*q"Green"q*)0.00000000,"0"]],id[(*q"Green"q*)plus[(*q"Green"q*)num[(*q"Green"q*)1.00000000,"1"],fract[(*q"Green"q*)char[(*q"Green"q*)v],char[(*q"Green"q*)c]]]]]]]Nw) 7   <?* @ (HwnDN <?;q'dequal[char[nu],approx[times[indexes[0,1,char[nu],num[0.00000000,"0"]],indexes[1,0,id[(*i1i*)over[plus[num[1.00000000,"1"],minus[fract[char[v],char[c]]]],plus[num[1.00000000,"1"],fract[char[v],char[c]]]]],fract[num[1.00000000,"1"],num[2.00000000,"2"]]]],fract[indexes[0,1,char[nu],num[0.00000000,"0"]],id[plus[num[1.00000000,"1"],fract[char[v],char[c]]]]]]]q*HQ C *umHQH{Q C  GenH{QcQ6 C qrecQ6en")1cQQ Q6C qre Q6"Grn"?Q QcQ-\(C 00"cQ-\(c!c! s- jv*Q-\(C *ha*Q-\(*!*! s+ jv*Qu$E.u3rQ>3rQHQQ֎QQ֎Q[QeykrQeykrQoJQyIQyIQQ)4`I IQ_1I>4`_A0_A0 sl 0 s , n 0 QC `I  QC ` M M ~l < l 0 s yQC `I !QC `MM yl > l 0 s ?d$5^^uQKHH7 HHN!v!!]`  Q#Energy Levels in the Hydrogen Atom rQ-`  jK J`  v$Note: Hydrogen is the most abundant 3g` ! vQelement in the universe. k`  {Q,  eExpect to see a lot of it in space.  h j! J@`π#7"#9HH%7 HH0M;q^ ` `Doppler Shift ;`  j IX` j!Electromagnetic Radiation from a u h jMoving Source d]50s__vIHH^7 HHs$5_ ` Astronomical Sources C `  of Electromagnetic Radiation f`  j `   Line sources   jEn'Quantum mechanical transitions between @  j&energy levels in atoms and molecules. `  }& m  tToday (and Fridays studio) `  j  `  s Thermal sources 1`  j"Matter gets so hot that it glows. N`  jBlack Body Radiation k`  }+ m  tNext class (and Fridays studio) H`  j `   Synchrotron radiation   j`)Relativistic electrons moving in circles @  jEl through strong magnetic fields. `  }Mo" m  tLater, when we need it. / Cf @!_"=['/ C^')atop[(*x65536xy1048576yt393216tb1441792b*)equal[(*y-1245184y*)times[char[E],id[char[n]]],times[id[minus[over[times[num[2.00000000,"2"],power[char[pi],num[2.00000000,"2"]],char[m],power[char[e],num[4.00000000,"4"]],power[char[k],num[2.00000000,"2"]]],power[char[h],num[2.00000000,"2"]]]]],over[num[1.00000000,"1"],power[char[n],num[2.00000000,"2"]]]]],equal[(*y-1310720y*)char[n],comma[num[1.00000000,"1"],num[2.00000000,"2"],num[3.00000000,"3"],char[ldots]]],equal[(*y1572864y*)times[indexes[0,1,char[E],times[char[p],char[h],char[o],char[t],char[o],char[n]]],id[rightarrow[char[a],char[b]]]],plus[times[char[E],id[indexes[0,1,char[n],char[a]]]],minus[times[char[E],id[indexes[0,1,char[n],char[b]]]]]],times[char[h],indexes[0,1,char[nu],times[char[a],char[b]]]]],equal[(*y2490368yt327680tq"Red"q*)over[(*q"Red"q*)num[(*q"Red"q*)1.00000000,"1"],indexes[(*q"Red"q*)0,1,char[(*q"Red"q*)lambda],times[(*q"Red"q*)char[(*q"Red"q*)a],char[(*q"Red"q*)b]]]],over[(*q"Red"q*)indexes[(*q"Red"q*)0,1,char[(*q"Red"q*)nu],times[(*q"Red"q*)char[(*q"Red"q*)a],char[(*q"Red"q*)b]]],char[(*q"Red"q*)c]],times[(*q"Red"q*)char[(*q"Red"q*)R],id[(*i1iq"Red"q*)plus[(*q"Red"q*)over[(*q"Red"q*)num[(*q"Red"q*)1.00000000,"1"],power[(*q"Red"q*)indexes[(*q"Red"q*)0,1,char[(*q"Red"q*)n],char[(*q"Red"q*)b]],num[(*q"Red"q*)2.00000000,"2"]]],minus[(*q"Red"q*)over[(*q"Red"q*)num[(*q"Red"q*)1.00000000,"1"],power[(*q"Red"q*)indexes[(*q"Red"q*)0,1,char[(*q"Red"q*)n],char[(*q"Red"q*)a]],num[(*q"Red"q*)2.00000000,"2"]]]]]]]],equiv[(*y1572864yt1376256tq"Red"q*)char[(*q"Red"q*)R],equal[(*nq"Red"q*)over[(*q"Red"q*)times[(*q"Red"q*)num[(*q"Red"q*)2.00000000,"2"],power[(*q"Red"q*)char[(*q"Red"q*)pi],num[(*q"Red"q*)2.00000000,"2"]],char[(*q"Red"q*)m],power[(*q"Red"q*)char[(*q"Red"q*)e],num[(*q"Red"q*)4.00000000,"4"]],power[(*q"Red"q*)char[(*q"Red"q*)k],num[(*q"Red"q*)2.00000000,"2"]]],times[(*q"Red"q*)power[(*q"Red"q*)char[(*q"Red"q*)h],num[(*q"Red"q*)3.00000000,"3"]],char[(*q"Red"q*)c]]],fract[(*q"Red"q*)num[(*q"Red"q*)10.97000000,"10.97"],id[(*q"Red"q*)times[(*q"Red"q*)char[(*q"Red"q*)mu],char[(*q"Red"q*)m]]]]]]]c0g!7qed  us*qJ@πD"7000;Rdes[J@c=h#K'R"qJ@c=h"q*".0J@h?c=h?c=w?c=?c=?c=? ???ω?=?=?=?=?=?ω?? ? ?c=?c=+?c=:?c=:?c=I? X?X?g?ωv?=v?=?=?|=?|=@Ww$$?%)00Ww$[(*ReWwWwWwt#%?$& a(*Wwt#WwdWwd rqerWwG&=%e(*rWwG"Req*rWwGrWw @c=h'E#`[q"@c=hed"")h@;?c=;?c=J?c=Y?c=Y?c=h?w?w??ω?=?=?=?=?=?ω????c=?c=?c= ?c= ?c=?+?+?:?ωI?=I?=X?=g?|=g?|=@@ = (P @ = s[#K'`"q` @A Traveling Wave =@u)Q`* @u@=@= = @=*I)+= @=:?= @=@=w@Ju+L*, =w@Juw@Z=w@Z= A@Ju,L+- A@JuA@Z=A@Z= @nu-L,. @nu@~=@~= L=!.L-/ L=!LĞLĞ t=0@u/L.0 d"@u@=@= ?@=0M/1 ?@=@Ğ@Ğ tJ@H=1Y02=?J@H=c=?J@H=J@Z=w@H=2Y13=?|w@H= =w@H=w@Z=J@Q=-3[24[J@Q=-KJ@Q=w@Q=@8uߡ4[35 nWa@8uߡ@H=@H= Distance traveled = vt@=5=46@=@=@=X@=6=57X@=X@=X@=@=H7I68@=H@=X@=@=H8I79@=H@=@=c -9I8 c -JJ sl=HH:7HHlYZ \@L;L<"1L=6L!H6<c;="2!H6H= !-**3<<ENNi `H6=c<>"=`H624 {{` H6>c=?"?@=@H6e t veʀʀH6?c>@">@=7H6X@ =/&&ӀӀ ӀӀӀH@g?A"=H>?/gH6Ac@B"BC@/gH6 -/88AuJgJgSg\g\gwynUH6BcAC"ACnUH6 Upp~ny/UHCgBD"/UHAB!܀ZDkCE"=!Xm@*!-<6<6E6N6N6W)``e@iir{{܀܀ZEkDF"Xm@HӀӀ@ //LZFkEG"/NXm@&/JJS\\enns@~wpwpcUUQLLUnlGMFH"nln-n8lHoGI"8lc8y IMHJ" y yȔzyȔz E  JoIa" g zz BB ;H Kr" = ;HE6a` @An Electromagnetic Wave Nk LsaM" NkNN k MILN" k 'k NIMO" 'k77 'kOINP" 'k77 kPIOQ" k 'kQIPR" 'k77 H3!tRIQ" 3!tCC jOscillating E and B fieldsHHS7W HHl VȔzHHT7UHHl WHHUV U7VTHUV l XH$ V7UvH$ l YHUV W7XS HUV l ZH$ X7WH$ l [HHY7HHl: \HHZ7kHHl:[ \7HH[7IHHlZ\ \tinHH \77HHl[^ \HH!]77HHl_ \HH"^77THHl\_ \HH#_77UHHl^] \@ = $`P')7S@ = l(( U ;H%arJL"7W ;HlKK ]m}x dmLeftdnRightdo: ReferenceHdpqdqprdrqsdsrt7dtsudutv\dvuw dwv ] :Ff Body. f U Bulleted\t. f CellBody. f   CellHeading. f   Footnote. rf T Heading1Body. f T  Heading2Body. f T   HeadingRunInBody. f  l yIndented. f  g Numbered.\t. f E r Numbered1.\tNumbered. f  f TableFootnote. f T   TableTitleT:Table : .  f P TitleBody. f dT   TableTitleT:Table : . f a  CellHeading. f a CellBody. f  a  CellFooting. f  a Body. @  i lHeader. @  i blaFooter. f  cg.Body. f  k$Body. f  l$Body. f  edy. .Body. f  n$ Body. f  o$Body. f  p$Body. f  q$Body. f  m. .Body. f  mH. .Body. f  n$ Body. f  u. .yBody. f  n$ .Body. f  j. .Body. f c..  .Body. f ! eH..  .Body. f " c.Body. f # j. . .Body. f $ j..Body. f % j. .Body. f & yl. .Body. f ' jH. .Body. f ( c. .Body. f ) e. .Body. f * n$ H. .Body. f + r$l. .Body. $f , e. .Body. $f - j. .Body. f . jl. .Body. f / jl. .Body. f 0 m. .Body. f 1 ml. .Body. f 2 u. .Body. $f 3 u. .Body. f 4 $ l. .Body. $$f 5 vl. .Body. f 6 sl. .Body. f 7 sl. .Body. HHf 8 el. .Body. $$f 9 jl. .Body. f ; k$l. .Body. HHf < jl. .Body. f =  l. .Body. f > jH. .Body. f ?  Body. $$f @ l. .Body. f B $ l. .Body. f C  l. .Body. HHf D ml. .Body. a b+ ڝ aڝ c ) d ڝ e f Emphasis g EquationVariables [ h  ڝ iڝ j$ڝ k$yc> lڝ m$) n $yc> o$ڝ p$tu q$w rw stu tڝ utu vyc> ww yw zw {) | w }w ~$ڝ $)  $w $ڝ w w w  ڝ tu )   ڝ )  )  )  )  5; 56789:< Z= Z> Z? Z@A ZB ZC ZE ZG ZI ZJ ZK ZL ZM ZN ZP ZQ ZY Z[ Zc Zg k Zo Zr Zs Z ) 9 . )Thin *Medium +Double ,Thick@ - Very Thin    ) ) ) ) ) ) ) ) ) + H H H H H Format A   ) * ) ) ) ) ) * H H H H H Format B   Commentd BlackT!WhiteddAReddd Greendd BluedCyandMagentad Yellow Times-Roman9 Times-Bold Helvetica Times-ItalicSymbolSymbolHelvetica-BoldTimes HelveticaSymbol RegularTRegular BoldRegularItalic -|* opaK~AY-m>ɬFN%/4YҚf.EF|snssӴO;yeDf ݛ-(8`KΛ8{$"_( |+|7HG )M[]C.1{>@-