Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://www.kiam1.rssi.ru/pubs/prep_2013_006.pdf Äàòà èçìåíåíèÿ: Tue Oct 8 14:40:35 2013 Äàòà èíäåêñèðîâàíèÿ: Thu Feb 27 19:55:36 2014 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï

. ..

.. , .. , .. , .. , .. , .. , .. , ..

- L2 -

-- 2013


L2 -. ­ - . ­ - ( ) . . . , -. - , , . -. «-» «». : -, L2, , -, . ABSTRACT This work covers ballistic design of the spacecraft transfer to the vicinity of the Sun-Earth system L2 point and halo orbit motion in this area. The following methods and calculation algorithms are described: the algorithm building one impulse transfer trajectories starting at the LEO and ending at the halo orbit implying a swing by maneuver or not. the algorithm calculating the stationkeeping impulses, needed for the transfer to the halo orbit and the for the long term halo orbit motion. For calculation of one impulse flights from the Earth to the halo orbit (with the help of a swing by maneuver or without it) the initial approximation construction algorithm has been implemented. These approximations are calculated by means of two variables' function isolines construction and analysis. The transfer trajectory pericentre height above the Earth surface is considered to be such a function. The arguments of this function are the special parameters describing the halo orbit. The described algorithm provides halo orbits with the given geometrical dimensions in the ecliptics plane and in plane orthogonal to it. The characteristic velocity costs needed for the stationkeeping have been evaluated. These methods were used for construction of the nominal orbits for the "Spectr -RG" and "Millimetron" spacecrafts. Key words: halo orbits, L2 point, isoline method, Spectr-RG, Millimetron.


3

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7

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15

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16

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17

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18




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19

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T


20

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21

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22

4. «-» - L2 .
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5. , . X Y 2014/12/30 18:17:30.000 3.992607214 -5.013255978


23

Z VX VY VZ

-1.540951641 6.676870 2.918931 8.202774

, J2000 , . , /. 4,000 / 7 . . 6. -. 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 015 015 015 015 015 016 016 016 016 016 017 017 017 017 017 018 018 018 018 018 019 019 019 019 019 /03 /05 /07 /10 /12 /02 /05 /07 /09 /11 /02 /04 /06 /09 /11 /01 /04 /06 /08 /10 /01 /03 /05 /08 /10 /1 /1 /2 /0 /1 /2 /0 /1 /2 /2 /0 /1 /2 /0 /1 /2 /0 /1 /2 /3 /0 /1 /2 /0 /1 0 9 8 6 5 3 3 2 0 9 7 8 7 5 4 3 3 2 1 0 8 9 8 6 5 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 :17 :17 :17 :17 :17 :17 :17 :17 :17 :17 :17 :17 :17 :17 :17 :17 :17 :17 :17 :17 :17 :17 :17 :17 :17 :30.000 :30.000 :30.000 :30.000 :30.000 :30.000 :30.000 :30.000 :30.000 :30.000 :30.000 :30.000 :30.000 :30.000 :30.000 :30.000 :30.000 :30.000 :30.000 :30.000 :30.000 :30.000 :30.000 :30.000 :30.000 , / 1.382 0.000 0.986 0.106 0.250 0.940 0.000 0.443 0.125 0.125 0.585 0.928 0.484 0.315 0.062 0.269 0.062 0.000 0.515 0.016 0.016 0.179 0.000 0.096 0.062 L2, . 320.815 250.815 309.196 286.005 244.981 343.854 273.854 321.295 301.526 260.769 265.156 273.353 264.983 317.444 282.751 329.353 350.850 280.850 348.898 353.104 313.182 384.971 314.971 333.644 276.463


24

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23 66 38 31 47 30 29 59 70 21 51 56 97 27

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. 9. - XY XZ . L2. ­ . .


25



B

A

C

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C

, 2014 . 7. 30.09.2014. , , /c , . , . , . , . , . , , X Y Z VX VY VZ 2 3 6 0 4 6 0 1 2 1 014/09/30 04:22:30.000 .265 86.911532 .990397 7.633 5.576533 .218384 360.848407 8.837 92.803

8. , . 2014/09/30 04:22:30.000 -5.160278166 -3.964947978 -1.079258786 5.604056 -5.141350 -7.901425


26

9,000 / 7 . 9. 30.10.2014. , , /c , . , . , . , . , . , , 2 3 6 0 5 6 0 1 2 3 014/10/30 18:07:30.000 .194 82.239417 .990336 1.425 4.908631 .214839 351.507722 57.182 38.161

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27

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5. «» - L2
-, , «». 13. ( 5, ). , 2018/09/15 16:08:31.749 , . 6.587983 0.002851 , . 51.609 , . 88.692813 , . 0.191067 , . 0.228626 , 198.683 , 84.178 14. . , , /c , . , . , . , . , . , , 2 3 7 0 5 6 0 1 1 3 018/09/15 17:05:00.000 .202 12.251380 .990733 1.472 9.238427 .222093 411.524394 98.883 12.243


28

14 / 7 . 15. , . X Y Z VX VY VZ 2018/09/15 17:05:00.000 -5.119120543 1.515577645 -3.881626760 -6.267933 -6.950327 5.711508

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29



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A

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30

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30,840 / 7 .


31

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32

«» , - 800 . . - , , L2. , - L2 600 . . 1. .., .., .. L2 ­ // . .. , 2012, 65. URL: http://keldysh.ru/papers/2012/prep2012_65.pdf 2. .., .., .. L2 ­ // . .. , 2012, 66. URL: http://keldysh.ru/papers/2012/prep2012_66.pdf 3. .., .., .. ­ ­ - L2 ­ // ­ 1992. ­ . 30. 4. ­ .435­454. 4. .. . ­ .: , 1978. ­ 312 . 5. .., .., .. - L2 ­ // . . 1987. . XXV. 2. . 163­185. 6. Eismont N., Dunham D., Jen S.-C., Farquhar R. Lunar Swingby as a Tool for Halo-Orbit Optimization in Relict-2 Project // Proceeding of the ESA Symposium on Spacecraft Flight Dynamic, Germany, 30-4 October, 1991 (ESA SP-326, December 1991), pp.435-439. 7. .., .., .. L2 ­ ( «-2») // . . 1993, . 31, 5. .3­20. 8. .. . . ­ : , 1978. ­ 456 . 9. . . . ­ : , 1982. ­ 656 . 10. .. «» . // ­ 2011. ­ . 48. 3. ­ . 271-278. 11. ., ., . . ­ .: , 1985.