Characterization and hazard mitigation of resonant returning Near Earth Objects Authors: Arnaud Bourdoux. Supervisor: Dario Izzo, Advanced Concepts Team (ESTEC). Contacts: Dario Izzo Tel: ++31 (0)71565 – 3511 Fax: ++31 (0)71565 – 8018 e-mail: [email protected] Final Stage Report Study length: 3 months ACT internal report: ACT-RPT-4100-AB-CHMRRNEO05 Available on the ACT net (www.esa.int/act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ª ## 1 + & C ++D? ½ " (K " " ( K " " ( 6 ++? 4 2 " * " I " " " " (! " ' ( ½ +8 " ? ½ ½ #+ ½ ½ C+#D 1 + & 6 +8? 6! 6 " ? ½ ½ ½ C++D " " (! " " 0 " " 6 * 5 A " " " ! ' )" " " 0 ! ( * " ! >" #8 1 + & 6 +-? ! A " " ! !* !* ! !* ! " " !* !* * ? C+8D 6 " " " ? C+-D C+/D C+9D R& " ? " & " " .2 " " #- 1 + & * 6 * " &" ! " " " ! " @ C !* " D " " !* !* " * " &" 0 " C+%D " ! " 3 0 C+;D " " " !* & .2 " " .2L ! " .2 ? !"! "!# $ % $ # "! &' # ! & & ( !)#* $ $ !% ' * +## ,! ! % * - !& " # % $! ' $ $ & * ' !& " " " ( " 0 " " * " " " " * 0 " I " " ( " #/ 1 + & " ! * " & " 5 5 & " " " 7 " * ! " " & ! ! * ¼ & " " > " ! # " ? C+$D " A C+$D " &" ¼ ! " " & " & " ! !! 0 " ? C+#,D ¼ " 6 * " & " " " ' +8# & ! ! * ¼ " > " C" * D " ? ¼ ¼ C+##D & ! C ++8 " & ! " * " " + , ¾ #9 1 + & " " # * " C R& D ¼ ¼ " (! ! ¼? ¼ C+#+D C+#8D +#8 ( " " " ! " " " " ( ( ? C+#-D C+#/D @ +#8 C+9D " ? ¼ ¼ C+#9D +#9 ( C+#- +#/D = " " ? ¼ ¼ ¼ C+#%D ! !* " " # !* " ? # # " #% C+#;D 1 + & @ " ! ! ? ¼¼ ¼¼ ¼ ¼ !"#$% +#% " " I )" * ! " ! .* 1C#$$$D ! " & ! ! 7 & ! " ' & ! " ' H " " @ & " " ( ( # $ % & ! " & & ! ! & "? & " ! C ++8DK " ¼¼ ¼¼ #; 1 + & " 6 ' .2 3 ¼¼ 6 ' " 3 .2 3 ¼¼ A +8+ ! 0 " " " & E#F # & '( ! " " > .2 " " 6 " E#F " .2 " 0 " " " .2 " " ? & " >3 ! C +-8D " ! " " ! E-F G E#F 3 & .2 I ¼¼ " A ? $ ¼¼ ¼ % C++,D $% >" .2 " " 3 = "" " " ! " " .2 & " * & " " & $ ¼¼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Æ %$% % C+8,D . , +8 1 + & +8, ( C ++%D " " ? % / C+8#D + , " ( ( ! ) ( ! ( ( ! ( " ! " !* ++8 * ( ! ' " ++8 " ! " " !* ! " ? C+8+D " " " ( ++# " * ( " H A " " & ( ! ( ? + C+88D ( ! (? , +- % / C+8-D " " " " ! 6 " " * . " ' 1 1 % .2 " " " " H . 2 " " " " .2 & & 4) .2 0 E+F & .2 " " A " ! * .2 " " " ' * " * " " 0 " & +/ 1 8 " " & ++# * & 0 & 0 & C8#D C8+D C88D >" " 3 0 1 C8-D " 1 " ¼ ¼ C8/D !* " " ¼ # ¼ ¼ ¼ C89D ¼ C8%D " " ? # 1 1 C8;D C8;D " " * " C8#D C8+D C88D C8;D & & " +9 1 8 6 & .2 " C8#D C88D C8;D? # 1 & 0 & 0 C8$D " .2 ! ' " * .2 8$ " " " " 'A " H " " 4) " .2 ,,/ 'A & 6 & " " " = 98%; & / 'A " / 'A " " " * " " " & ¼ &¼ 0¼ ¼ * " 8## " " " 8% * # ¼ ¼ ¼ ¼ & 0 & 0 1 * 8; " " & & ++ " & " " &" " " !* " !* ! ? # 1 " " C8#,D * 6 5+,,, %2!!! % 2!!! 2 3 +% 1 8 8# 8+ " " " .2 547 ! * 5+,,, " " " * " Comparison between Circular and Elliptical findMOID functions on PHO data 0.2 Circular Earth Orbit Elliptical J2000 Earth Orbit Elliptical Earth Orbit at Epoch 0.18 0.16 Error Distribution Function 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 -6 10 -5 10 -4 10 -3 -2 10 10 Deviation from JPL MOID, AU -1 10 0 10 1 10 6 8#? 4) .2 6 8# 4 )3 " .2 C ,,/ 'AD * C* " 0 "D " 8 'A " " ; = " " " 4) 8+ " & &" .2 " 'A * " &" .2 " = * 0 " +; 1 8 Comparison between Circular and Elliptical findMOID functions on NEO data 0.14 Circular Earth Orbit Elliptical J2000 Earth Orbit Elliptical Earth Orbit at Epoch 0.12 Error Distribution Function 0.1 0.08 0.06 0.04 0.02 0 -6 10 -5 10 -4 10 -3 -2 10 10 Deviation from JPL MOID, AU -1 10 0 10 1 10 6 8+? .2 & 1 " " " . " " '1 . * > )" " .2 " .2 ' " * . > . " " +$ 1 8 * " " " " " . . . C8##D . . . " " " " " " C8#+D " 2 " C D # " " I I ! ( 5 ' " 5 ( & "! ++# ' * " . 88 8- +,,8 0O +/ & 5 ' " 8- 5 ( " " " , 4 8, 1 8 Eccentricity Inclination 0.73 0.12 0.72 0.1 Radians 0.71 0.7 0.08 0.06 0.69 0.04 0.68 0.67 2000 2010 2020 2030 2040 years 2050 2060 0.02 2000 2070 2010 RAAN 2030 2040 years 2050 2060 2070 2060 2070 Argument of perihelion 1.6 1.4 1.4 1.2 1 Radians 1.2 Radians 2020 1 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 2000 2010 2020 2030 2040 years 2050 2060 0 2000 2070 2010 2020 2030 2040 years 2050 6 88? +,,8 0O +/ Semimajor Axis 3.12 3.1 AUs 3.08 3.06 3.04 3.02 3 2.98 2000 2010 2020 2030 2040 2050 2060 2070 years Perturbations induced by planets 0.014 Venus Earth Mars Jupiter Saturn Adimentional units 0.012 0.01 0.008 0.006 0.004 0.002 0 2000 2010 2020 2030 2040 2050 2060 2070 years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x 10 2 1.5 AUs 1 0.5 0 -0.5 -1 2000 2010 2020 2030 years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years Resonance chart 150 100 Zeta (Earth Radii) 50 0 -50 -100 -150 -150 -100 -50 0 Xi (Earth Radii) 50 100 150 () 2004 MN4 - 7 years Resonance chart 15 10 Zeta (Earth Radii) 5 0 -5 -10 -15 -20 -5 0 Xi (Earth Radii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Æ " " ( & 3? 9 ? " I I ! ! * I " & I ! * " " " !* ,? ) 3 " 2 " Æ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arth - 2004 mn4 transfer : Trajectory x 10 1.5 1 (km) 0.5 Thrust arc Arrival at 2004 MN4 20/02/2014 0 Coast arc Earth escape 11/04/2011 -0.5 -1 2004 MN4 orbit Earth orbit -1.5 -2 -1.5 -1 -0.5 0 (km) 0.5 1 1.5 8 x 10 6 /#? =3 " /# /+ ! /8 /- " " 3 " " 3 6 /+ " 88 .- ! " /# 1 / ' ( 8 x 10 1.5 1 0.5 0 -0.5 -1 -1.5 -2 -1.5 -1 -0.5 1.5 0 1 0.5 8 x 10 0.5 0 1 -0.5 1.5 8 x 10 -1 -1.5 6 /+? =3 ? 1 -5 4.5 Earth - 2004 mn4 transfer : Thrust intensity x 10 4 3.5 2 Thrust (kg km/s = kN) 3 2.5 2 1.5 1 0.5 0 4000 4200 4400 4600 Time (Mean Julian Date 2000) 4800 5000 6 /8? 3 /+ 5200 1 / ' ( 8 2.5 Earth - 2004 mn4 transfer : Approach x 10 S/C - Asteroid distance (km) 2 1.5 1 0.5 0 4000 4200 4400 4600 Time (Mean Julian Date 2000) 4800 5000 5200 6 /-? ! ' 3 3 "? / ? ## ' +,## 1! ! ? # &N ) ? %,, & 9 ? +; ? +, 6 +,# ? ,# &N = !? %, & ) ! - @ * " "! !G! ' " 6 !G "" ' +,#+ " " ( ' +,#8 " ( H #, &N * ( C +8-D // /8 1 / ' ( 8 Earth - Venus - Earth gravity assists for a 350 kg impactor x 10 1 2004 MN4 orbit Venus flyby 19/9/2012 0.5 Earth orbit Impact 28/1/2015 (km) 0 Earth escape 6/4/2012 -0.5 Venus orbit -1 Earth flyby 26/8/2013 -1.5 -2 -2 -1.5 -1 -0.5 0 (km) 0.5 1 1.5 6 //? "? / ? 9 ' +,#+ 1! ! ? 8 &N ) ? 8/, & ; % ? #$ +,#+ ; % * ? /;8 &N ; % ? /,, & , % ? +9 ' +,#8 , % * ? $/8 &N , % ? 9,;,, & ! ? +; 5 +,#/ ! ? #8$9 &N 9 ? +% % >!? #; & /- 2 8 x 10 1 / ) ' ( ( @ 2 : & ? ## "" H "& " 6 " " )" " " * 2 : ( & " +,,- .- " 4 ( ( #; & ' -- " " / " H " " " " ( C +8-D? / " " 6 8/ 2 " ' / " " "! " " 2 : " ? 2' & &- &&& # 3 &! " #% ! ! !&! ' ' &-% * # * &!&% # &! ( ' # &' !' "!# !% & #' "3 &- " " "! * )" // 1 / ' ( " #( * 1 %) % )# ! & /8# #/, & " " "! " ( " /9 8 500 kg impactor - Ion propulsion x 10 2004 MN4 orbit 1 Earth orbit 0.5 (km) Venus flyby 02/09/2012 0 Impact 16/07/2014 Earth escape 27/03/2012 -0.5 Venus orbit -1 -1.5 -1.5 -1 -0.5 0 (km) 0.5 1 6 /9? 6 " "? / ? +% . +,#+ 1! ! ? 8- &N ) ? /,, & ; % ? + +,#+ /9 1.5 8 x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mpactor : Direct transfer x 10 2004 MN4 orbit 1 Earth orbit 0.5 (km) Impact 17/10/2012 0 -0.5 Earth Departure 03/08/2009 -1 -1.5 -1.5 -1 -0.5 0 (km) 0.5 1 1.5 8 x 10 6 /%? +/+ * # ' /% @ " ' " /%9 & * ' !+,,$ CD " " " 0 " )) +,,- .- #% +,#+ * " ,# &N 6 " ? " " * * +,,$ " +/ /$ 1 / ' ( A +,,$ "" 3 " " " /; " C /#D +,,- .- & " * * 8 2009 Rendezvous trajectory x 10 1.5 1 Rendezvous with 2004 MN4 18/02/2012 (km) 0.5 0 -0.5 Earth departure 20/07/2009 -1 2004 MN4 orbit Earth orbit -1.5 -2 -1.5 -1 -0.5 0 0.5 (km) 1 1.5 8 x 10 6 /;? " ? / ? +, 5 +,,$ 1! ! ? # &N ) ? %,, & 9 ? +9 ? #; 6 +,#+ ? ,# &N = !? #,8 & 9, 1 / ' ( & $ " H 8, & " ! "" ' " & ( & " " I " ( & ( " " !! 3L "3 4 ( ? / C/+D ) % " % / " )" " " * " /$ 0 6 +,,$ ( I "? #++ & " ) / C /$CDD #+// & " ) / C /$CDD #+9 & " ) % / C /$CDD " " " % " % " * " I " " " " 9# 1 / ' ( ' & +,,$ " "? # 4 " K + " ) / " 6 " K 8 " " " & K - " " " " & ( " 9+ 1 / ' ( 8 8 2009 Impactor : U.V objective function 2009 Impactor : M U.V objective function x 10 1 1 0.5 0.5 (km) (km) x 10 0 0 -0.5 -0.5 -1 -1 -1.5 -1.5 -1.5 -1 -0.5 0 (km) 0.5 1 -1.5 1.5 -1 -0.5 8 x 10 () 0 (km) 0.5 1 1.5 8 x 10 () 8 x 10 2009 Impactor : M T U.V objective function 1 (km) 0.5 0 -0.5 -1 -1.5 -1.5 -1 -0.5 0 (km) 0.5 1 1.5 8 x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
© Copyright 2026 Paperzz