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Dynamics and mission design near libration points, advanced methods for triangular points

Gómez, Gerard,Jorba, Angel,Masdemont Soler, Josep,Simó Torres, Carlos

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          "            "        67    )(*      "           " 5        " $ 9                      :;       < ;                  "             .               " #         "     :;   67          =33 >            !          ?33 >"       5        "                      @ 5  %==1"       ,    <                             "              , "                    @ 5         " -  @5/            .            ," 5                     @ 5      A  6B  ! B 0 * (7  "                       " -             CA   "  (  #  % 3"% B ;  " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " % 3"4 D & 5   @     " " " " " " " " " " " " " " " " % 3"4"% -  $ &'( " " " " " " " " " " " " " " " " " " " " " " " % 3"4"4 -   &'( " " " " " " " " " " " " " " " " " " " " " " " " 1 3"4"1  ' ( " " " " " " " " " " " " " " " " " " " " " " " 1 3"4"E # !  " " " " " " " " " " " " " " " " " " " " " " " " " E 3"1 ! BÆ   ( " " " " " " " " " " " " " " " " " " " " " " 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