a,b a f a = , , r = = r = T

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1 !" #$%" &' &$%( % ) *+, -./01/ :;:; < =>?@ABC>D E E F GF F H I E JKI L H F I F HMN E O HPQH I RE F S TH FH I U Q E VF E WXY=Z M [ PQ \ TE K JMEPQ EEH I VF F E F GF ]EEI FHPQ HI E I JQ PQ ]E H I I F E Q U HI EI E F GF H ^_`abcdebf H U gq hij `d k H EE V I F FHPQ F G F H F l HI ETJ F m E MI E n EE F op VHF S T PQ Gq F F Q HI GTH F H F PQ r E F M PQE H V QE sth JQ E HPQ m E JQ F rj I \ I F [H M u H I F PQ [V J E H I H Q H EE E F v PQV GF ME H I Q EM VF U M v JQ H I F E F GF FHPQ n EE F ] I M F R EM PQ F FHPQ ] I M F I K R EM PQ H F F ]ME H I a,b a f f = a b M PQ M Sw F GF EE F F x EF F P yz{ Nyz V F a F M F EI F I I M a = ,0 1 f = 298, G VHF M[V V F F FJ E[ QE V GEE F E \ [HI TL M H[ Nyz E Q H I F n EE E F x E M E m I { m PQ F H w[ PQ PQ F n FH v JQ H I THI E VF w F EE F FHPQ u EV MEFH I wm F R EM PQ EJ I M PQ F M [H M PQ F I K R EM PQ F E VPQ I Q r = (a 2 b) 1/3 M[V r = 1 3 (2a + b) PQ u E }~ r = ]Q PQ u E r = ]H H F F I I M TE K JMEPQ IE M E ]MMEFH I H M F H F O N PQ F T F G F FH w F \ PQH I [H r = T I V F EE Q I I TE E F GF M JPQ ILK u K M F I EE V F T H F ] I M wm F F [H EE F M F n FH F F IwEI x HK PQ HI E{ M PQ V F F PQ w F M E T E E Iw I \EFTHI E V ƒ ˆ Š Œ Ž Ž Š ˆ Ž Š Ž Œ Œ

2 9:;:9 WXY=Z C>Z C>Z X XDC>D X=>X X?XBX> X = Y=Z S I PQ F S F GF F S I PQ Q PQ u F EE w F E O E F M HPQ PQ F [ JPQ [V PQ H F GF H F F rh F [H U Q F F [ JPQ H I E JKI I N F K PQ F [ Q PQ u F EE H I [ Q b JHK PQ yy [H E F GF EI F K! " # $!! %!! &' ( ' ) * +! ',- EE G HK T H F E F GF F. &' " / '( ' 0! 1 +! ' '!.( ' '2 & )!! 3 0! '. (! 4 '! 2 5 6! 2(.(! 3! 1 ' '2 & ( ' 3 3 ' 7 ' 3 '! 1!!. 1!,. /'( 0 ( ' '! )!! ' )( '3 ' 7 6! 2# ( 1 3 ' 8 3 ' ' 2 42,- E F HK PQ ]H I F 9 F E F GF ] [H T ME M F K HPQ F EH I F H F GF EM GI M F U N EF \ I [H F S EF E lh u U F 9 F F K E rm EE F ]H PQH I F Q PQ F H I H EE E [H PQV EF H F F E T E Q I E [H vu H JPQ EI :;<; =>f`>kc JI yo w F M I vu H JPQ F v?@abc Q F E F Q PQ S HE H I F m ME EPQ SEJPQ [H 9 F [HF I HK I EE V F F K EM H T U PQ F ] Q [H E JHK PQV I [H M Q F E F m ME F Q N PQ ] E I QL H F F Q M LI ]EEI Q M Q PQ I EL VHF ]MV PQH I [V PQ F F H F I I I VJQE GEE F F I I V F M \ F E RLQ EF wm F GEE F M PQ M H F TL n PQ H I M PQ V F F GEE F E u F EE w F E F GF I PQ I H F HPQ T PQ H I I [H H[ ]E \ E Q F n N [ EE F Nyz I F V PQ F U H D oen M F [HI QLI R LQ EF VHF R LQ EF wm n [ EE F }F [HIJ IEPQ ]H T PQ PQ EE PQ F F S I GEE F [H 9 F V EPQ F ]MV N PQH I [V PQ GEE F H F F HPQ FH FHE I w F Q Q M T I PQ u Q F S p S V EF n / H \ E p O\ l u Q No M HQ H E T E u H I 2 G HH IJJKKK H L J H JŒ ŒJŒ MHJŽŠH J H ˆ J H ˆ Hˆ

3 F r MV PQH I H F F r I u EH T H F npqh I F TE R EM PQ V F LK H F E F GEE F l E F FH FHE [H ]E n HE IM PQ E T E M PQE K F GEE F TE R EM PQ [H Q PQ F GF Q H F r FU H I U V F GEE F M HQ [H I K E H GEE FM H I PQ F u Q F F G F F E ] I F QQH F FHPQI wq VHF G VF F HPQ U J FEPQ F K U PQ F E F GF PQ GH U PQ F GEE F V FH I 9 F Q I U PQ u Q F ]H PQV H I H F I GF V F F m M F K F PQV E V F G I M E GF EE F F u EH T F PQV H T F GF [H JEE M Q I Q F TE PQ H F FI MH F HPQ EE M H[H I VHF V Q LIEPQ I PQ u Q F EE F E Q PQ I F u KH T F IE PQ[ I U Q u KN H T H I [ E VF FHPQ TL u K Q wm [ Q V I N F U MH F V F F PQ u Q F EE F E PQV EF F G F ] H ] MV PQH I JPQEPQ SEHIM Q U F U Q M PQ VF H F U EF F G F I PQE 9:;: X?XBX> X X WXY Z = AX C F H F F I I M F U mh T F F I FJN PQ H[M V Q V F F F GFTL U MH F [H VF I E I H V EPQ \ [HI JPQ [ \ H V EPQ GEE F PQ F M [ Q H F V EPQ \ F HH I Q M X >= =Y> 9:; : CXB B DXY Z = AX X?XBX> X B C@ $ F TE PQ FJ V F F U mh T FHPQ F u KV [H v [ U MH F u KV ]M F npqh I M PQ M [H JPQ H F E U r I mh T v [ M FH I [H ] F H I I FJ PQ v [ I VJQE N F VF I ]H H F U n [ H F N H [H I TL w H F G FTL U T m H T r I T F H F R LQ M PQ V F ]H F n [ [ U mh T M [ Q PQ F V H I M EI F M EE [ I I H [H I GH

4 ! }""# $%& '&(!) * +!!,!-./0&1 }23~ 4! &%&( %+ 5+%1 '1!1,++! }"~} 6( +0&&% &%&( %+ 6( +%1( $&! 7++&8 + }2~3 $9!&8& '&(!) 7&+%1% :+%,++! }"~}.( +&-! &%&( %+ ;+% <8=,++! }"~}, &%&( %+ * +!! >%!./0&1 }23~?&( &%&( A % <B <%9 }"C# * 11 &%&( %+ 6!% $&%9-!,++! }"~} D++E& &%&( %+ + F9%+!1,++! }"~}?9E - &(!&%&( %+ 6( +%1( 5+%19%+!1 7++&8 + }2~3 $9!&8& '&(!) 7&+%1% M EE GH u F \ H[H I U PQ F Q N M F F [ I [V S [H I F m ME F H F H [H PQ M I E F r I H I H F M F N F R LQ H I V PQ H H PQ FEPQ H H T m I E F HPQ H PQ FEPQ Q [H O PQH I I RLQ FI [ [H M PQ F H PQE F F V I F E PQ G VPTEH I PQ z H F PQ F F N U IH I [V H PQ FEPQ n [ H F n [ [ U Q F F n VHF v HM H I F F H \ H[H I F F F EI V H FHPQI Q v PQ EI PQV J M I I [H F H PQ G [H Q F E M E H I [ \ FHPQ m M F I HPQ EJ F wm I F R N H I \ PQ F I I Q PQ F K LM NOL PQ R S N w[ PQ H F n [ Nyz F H PQ RTUVLWWN H xm l N E { ] F S E IH I IE M E n [ EE F VF I M ) *), -XY70Z [6.\[- ]X X74630/-3 I Q PQ F F F H F GF I F ^ _ ^ 7 H F F ` 4 9:9 :; X>= =Y> C>Z X C>D EI F VF H EE F K F E F GF FHPQ n EE F M N PQ M VF n PQ PQ F F GEE F [V mh T F E a A C A H F %C A M [ PQ V F WXYDB A= AX b>dx c F H F GEE F E I F R EM EE F TE R EMN PQ v F EN wf E MEF BCB G GE F PQ F u F VF E BCB H I [ PQ G M E MI u F VF FHPQ F T E [V PQ Q H F F vhee F M PQ M T E E T E [V PQ F [HI N Q LI R EM I F PQ H T TEJ

5 p N ]MMEFH I \ H I F rj I T E U [H Q V v F E F JM I I U F I F v HEE F [H I F M PQ u F M \ PQH I F v F E F GEE F U HK Q PQ U npqh I EI F EE I U u K[ QE F T E M PQ M B@ \ B@ rj I F T E U B@ I U WXYDB A= AX BX= X c EI F V F [H JPQ F [ E EE M PQ F K F GEE F HI E 9 F u F Q [ E EE F MN I G [V HU PQ H F HI E VF E PQ U T I E J N E F [ HI E EH T [ HI I E PQ Q E F PT HI E EH TNv F E r ω N = 90 ω/2 r N : Nordrichtung ]MMEFH I \ H F HI E I E J E PQ F H F HI E JPQ H ]H F F E I F F IE PQ \ \ VF FHPQ F E JV T E F Q EM I ELI H I V T E ω I I M F ] I M U PQ U I U U F \ vhee Q K A n FH IE PQ F HI E FH

6 z n P P r N N r N ω = 90 ω/2 r N : Nordrichtung n P : Normalenrichtung durch P ]MMEFH I o \ H F HI E I PQEPQ F \ mh T P H HI E IE PQ F E F T E [V PQ JHK HI E E np P H F F v FPQH I rn F FHPQ F wfnv FFHPQE H E I F ]PQ I I M VF v E PQH I F HI E PQ M Q I u U EH I F HI E M H F [ PQ F FHPQ F U M F I r PQH I V EPQ FHPQ F HI E EH T U EJH npqh I HPQ F m q U wim F F Q PQ Q F EQ RE U rm EE npqh I GF [ QH I T I EE VF BX= X C? ZX < = Y=Z c R HK [V PQ I I Q PQ H F I [ PQ \ H PQ F V B@ mh T P H GEE F VF F 9 FHPQ F E JV T E F T E [V PQ JHK GEE F E n P P H F F v FPQH I rn F FHPQ F wfnv FFHPQE H FHPQ F ]PQ I I M VF ]MMEFH I y \ H F GEE F HPQ F I E PQ VF V @ F 9 ]MM o u ]H Q F m E H F F sth V E PQQ F I I Q PQ \ M I JKI ILK E F I [ PQ \ O PQ H I F F

7 F ]ME H I M IE EI F lh Q I tan b z = (1 f) 2 tan b g Q M bg F I I Q PQ \ bz F I [ PQ \ H F f F ]ME H I I [ F M F \ T E F n Q VPT E V F V M b g b z = m sin(2b g ) 1 2 m2 sin(4b g ) m3 sin(6b g )... m = 1 ( b a 1 + ( ) b 2 a H F F I K R EM PQ F TE R EM PQ F [H H F E I F n [ EE N a b F I PQEPQ Q F I [ M F I I Q PQ \ U z u qh J EPQ ]H F F I I Q PQ \ \ M PQH I P H F M N JPQ F n [ EE F T E F I [ PQ \ H F ]M F F mh T P U u EH T * F GEE F I PQE V F ]MM y cos b g distanz(p,m) = a cos b z cos (b g b z ) AX mh T E rj I F r U H F n [TLN P P F 9 R mh T RLQ H IE PQ vhee F F I I Q PQ F F r HKH T X C>D c u H I I I Q PQ F M HQ H F u H I N PQ V F F Q EM HPQ AA B@! AA I u H I F rj I H PQ F VF H u H I [ FI [ [HwPTI wq V N M H F PQ \ VF H F u H I F RLQ U E ) 2 idealer Polarstern Horizont-Ebene α Erdachse α Äquator ]MMEFH I \ H I F \ R J F GF F E m E F Q Sq F I H H F EJ I H I F GF PQ F H FEPQ I K R E THI E EJI TL F \ PQ E R LQ H HH ƒ Œ Ž H Ž H H Œ ŠŒ

8 F wm F R [ M V F u RE M E MI [TH E EJK PQ F I I Q PQ \ \ M PQH I F PQ E Q PQ u E F RLQ F M H F H HE H T M ]MMEFH I \ H I F \ 9:9 :9 A>D=D X= Y> ZXB X CD AX H F 9 PQEPQ QJ I F I I Q PQ \ H F F R LQ M EE F E \ [HI TL U F QE F L M lh M PQ F K F v E PQH I M T PQ u H I FHPQ F r PQH I M V F H F Q I PQ U EH I G F E H PQ Q I E I \ I U F npqh I M H TL Y DXBC>D c F F H n [TL M [ I F F T F [H r I QE F M [H E wq Q EM w S E w F O PQ H I } U F M I EE V F G \ E F S QE QH I [ I ]MMEFH I G I Q PQ EEH I F r I QE }" IM m HH IJJKKK H L J H JŒ ŒJŒ MHJŽŠH J H ˆ J H ˆ Hˆ HH IJJKKK H L J H JŒ ŒJŒ MHJŽŠH JŒ MJ MH Œ M

9 o K 1 K 2 P P P P * ] MMEFH I S QE M F F U P K1 I M K2 9:9 : BXA>C>D E[ QE U I FJ PQ F \ H[H I }2 F F V IM F v V FIT F F H PQ H I3# O PQ H I EI [ EE PQ EI F ]ME H Q ]MM I M F mh T P FHPQ F rj I \ H F R LQ F N K1 H F GEE F e1 V M rj I H F \ P H e 1 M \ PQ H I F n H T F U P F K1 V M F GEN E F e1 M [ I VF JM I I [H F K2 F Q \ PQ H I F n H T F U P K 2 V EPQ I I wm K 1 O H I U PQ M F ]PQ I I wm K 1 n H I F Q F p \ PQ H I F I I Q PQ F U P H \ PQH I F n [ EN E F e2 F Q rj I H F \ U P HH IJJKKK H L J H JŒ ŒJŒ MHJŽŠH J H ˆ J H Hˆ HH IJJKKK H L J H JŒ ŒJŒ MHJŽŠH J H ˆ J H ˆ Hˆ

10 y K 1 K 2 e 1 P P P e 2 ]MMEFH I ]ME H O PQ H I ) * -./ 70Y-3 F F n [ EE F V H PQ F HI I E I GTEJ F \ II I I 9 PQ rj I H F \ M Q E F H [H I H HK [V PQ U PQ F n [ H I PQ V F V I Q F EPQ \ [HI F H PQE F M HPQ

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