Dynamics and mission design near libration points, advanced methods for triangular points
Abstract
The final objective of this work is to understand, analyze and compute the kinds of motion that appear on a vicinity (may be a large vicinity) of the geometrically defined equilateral points of the Earth-Moon system, as a source of possible nominal orbits for future space missions.
Full text
! " # $ % &'( )(* " + , " - " " ," ) . &'( , !/ " &'(" 0. - " " $ 1 " 2 . " 3"4"1" , . ." 5 4. " . %.% " - 6 7 -
" " - " # $ 8 " " 5 , . " # 8 " " 67 )(* " " 5 " $ 9 :; < ; " . " # " :; 67 =33 > ! ?33 >" 5 " @ 5 %==1" , < " , " @ 5 " - @5/ . ," 5 @ 5 A 6B ! B 0 * (7 " " - CA "
( # % 3"% B ; " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " % 3"4 D & 5 @ " " " " " " " " " " " " " " " " % 3"4"% - $ &'( " " " " " " " " " " " " " " " " " " " " " " " % 3"4"4 - &'( " " " " " " " " " " " " " " " " " " " " " " " " 1 3"4"1 ' ( " " " " " " " " " " " " " " " " " " " " " " " 1 3"4"E # ! " " " " " " " " " " " " " " " " " " " " " " " " " E 3"1 ! BÆ ( " " " " " " " " " " " " " " " " " " " " " " 8 %"% ! " " " " " " " " " " " " " " " " " " " " " " " " " " " " " F %"4 & & $ ( " " " " " " " " " " " " " " " " = %"1 @ ' ( " " " " " " " " " " " " " " " " " " " %F %"E & @ G )(* ! " " " " " " " " " " " " " 1? %"8 B , " " " " " " " " " " " " " " " " " " " EE ! " 4"% $ 0 - " " " " " " " " " " " " " " " " " " " " " " " " " 83 # $ !%% & % '# 1"% ' ( " " " " " " " " " " " " " " " " " " 81 1"4 , 2 " " " " " " " " " " " " " " " " " " " " " " " " 88 1"4"% , ( & " " " " " " " " " " " 8F 1"1 $ ; ; " " " " " " " " " " " " " " " " " " " " " 93 1"1"% $ ; % G * " " " " " " " " " 9% 1"1"4 $ ; % $ ( ; " " " " " " " 91
1"1"1 & " " " " " " " " " " " " " " " " " " " " " " " " " " 9E 1"E 0 - ; " " " " " " " " " " " " " " " " " " " " " " " " " 98 1"E"% B G - " " " " " " 99 1"E"4 ( # ( 1"% " " " " " " " " " " " " F1 1"E"4"% $ 2 , $, A FE 1"E"4"4 $ 2 , & A " F8 1"E"1 5 ; $ A " " " " " " " " " " " " F? 1"E"E @ , 2 " " " " " " " " " " " " " " " F= 1"8 0 - ; 2 " " " " " " " " " " " " ?% 1"8"% ! " " " " " " " " " " " " " " " " " " " " " " " " " " " " " ?4 1"8"%"% @ " " " " " " " " " " " " " " " " " " " " " " " " ?E 1"8"4 # " " " " " " " " " " " " " " " " " " " " " " " " " " " " ?E 1"8"4"% 5 ! " " " " " " " " " " " " " " " " ?E 1"8"4"4 ! 5 " " " " " " " " " " " " " " " " " " " ?8 1"8"1 & " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " ?8 1"8"E $ A " " " " " " " " " " " " " " " " " " " " " " " ?9 1"8"8 : ' & $ " " " " " " " " " " " " " " " " " " ?9 1"8"8"% 2 " " " " " " " " " " " " " " " " " " " " " ?F 1"8"8"4 $ A " " " " " " " " " " " " " " " " " ?? 1"8"9 $ @ " " " " " " " " " " " " " " " " " " " " " " " " ?= 1"9 5 $ 0 - 5 @ ( ; 0 ' ( " " " " " " " " " " " " " " " " " " " " " " ?= 1"F ; $ G . " " " " " " " " " =4 1"F"% 5 " " " " " " " " " " " " " " " " " =4 1"F"4 ( @ & " " " " " " " " " " " " " " " " " " " =8 1"F"1 B " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " == 1"? ' @ H " " " " " " " " " " " " " " " " " " " " " " " " " %33 1"?"% 5 5 # A - A (. ; " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " %33 1"?"4 @ 5 ( ;" & @ " " %3% 1"?"1 - 5 " " " " " " " " " " " " " " " " " " " " " " " " " " %3% " ( % & E"% * 2 " " " " " " " " " " " " " " " " " " " %%1 E"4 @ G , " " " " " " " " " " " " " " " " " " " " " " " " " " " %%8 E"1 - 5 " " " " " " " " " " " " " " " " " " " " " " " " " " " " " %%? ' ## 8"% # " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " %11 8"4 # & ! " " " " " " " " " " " " " " " " " " " " " " " %1E 8"1 5 ! " " " " " " " " " " " " " " " " " " " " " " " " " %19 8"1"% 2 * & " " " " " " " " " " " " " " " " " " " " " " " " " %19 8"1"%"% #> & " " " " " " " " " " " " " " " " " " %19
8"1"%"4 - " " " " " " " " " " " " " " " " %19 8"1"%"1 ) !, " " " " " " " " " " " " %19 8"1"%"E 0 ! " " " " " " " " " " " " " " " " " " " %19 8"E & 5 ! " " " " " " " " " " " " " " " " " " %1F 8"8 0 & " " " " " " " " " " " " " " " " " " " " " " " " " " " " %1? 8"8"% ( " " " " " " " " " " " " " " " " " " " " " " " " " " " " " %1= 8"8"4 0 ( " " " " " " " " " " " " " " " " " " " " " " " " " " " " %E3 8"9 0 5 ( 0 ( " " " " " " " " %8= ) $ * +% $ )# 9"% $ ; " " " " " " " " " " " " " " " " " " " " %98 9"%"% * 5 $ I(; " " " " " " " " " " " " %98 9"%"%"% $ ; @ 8"8"4 " " " " " " " %99 9"%"%"4 $ ; @ %"E " " " " " " " " %99 9"%"4 $ @ @ " " " " " " " " " " " " " " " " %9? 9"%"1 B :;" $ # " " " " " " " " " %F% 9"%"E : ; " " " " " " " " " " " " " " " " %F1 9"4 @ & " " " " " " " " " " " " " " " " " " " " " " " " " " " %FE 9"4"% ; ! " " " " " " " " " " " " " " " " " " " " " " " " " " %FE 9"4"4 ; @ ; " " " " " " " " " " " " " " " %=E 9"4"4"% * ; @ - " " " " " " %=E 9"4"4"4 * ; @ - " " " " " " %=E , -% ! # , ! '"% # " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " 44F '"4 ! " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " 44? '"4"% B- @ # " " " " " " " " " " " " " " " " " " " " " 44? '"4"4 @ - " " " " " " " " " " " " " " " " " " " " " " " " " " " 414 '"4"1 B -< - 5, " " " " " 41E '"4"E 5 5 ! $ $ Æ " " " " " " " 41E '"4"8 C - " " " " " " " " " " " " " " 418 '"4"9 B -< # " " " " " " " " " 419 '"1 5 5 5 ; & ( " " 41F , % ! $ .%/ &$ " $"% $ $. $. ! " " " " " " " " 4E% $"4 ; 5 $ # ! " " " " " " " " " " " 4E4 $"1 $. $. ! &'( " 4E1
, . % "0 B"% @ 5 " " " " " " " " " " " " " " " " " " " " " " " " " " 4E= B"4 ; ! " " " " " " " " " " " " " " " " " " " " " " " " " " " " " 484 B"1 ; 5 & B @ ! " 481 B"E ; " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " 481 ! '' G & + B @ 5 48F