???????? ??????????? ????????? ? ???????????????????? ??????? ? ??????????? ????????-?????? ????? ???????? L1 ? L2. (LCD on LPO)

1
???????? ??????????? ????????? ?
???????????????????? ??????? ? ???????????
????????-?????? ????? ???????? L1 ? L2.(LCD on
LPO)

• ?.?.???????, ?.?.???????, ?.?.???????

2
???????????? ???????.

• ????????????????.
• ???????? (????????) ????? ????????.
• ????? ???????? ??????? ???? ???????? ?.?????????
  (1736-1813) ??????? ??????????? ???????????,
  ??????? ????? ???? ??????? ??? ?????????
  ?????????? ? 19 ??? ? ?????????????? ???????.
• ?????? ????? ??????? ? ??????. ?? ?????
  ??????????? ????????? ??? ?????? ?? ?????????
  ???????? (??????? ????? ??? ??????).

??? ????? ????? ????????. ??????????? ????????
?????????? ??????? (?? ?.????). ?? ???????????
??????? ????????? ? ??????? ? ?????? ? ????,
?????????? ????? ????? ?????, ??? ????? ????
????????? ? ??????????, ?.?. ?????? ??
?????????. ???????????? ????? ???????? L1, L2,
L3. ??????????? ????? ???????? L4, L5. ? 1890 ?.
?.????????, ???????? ???????????? ?????????
???????, ?????????, ??? ??????????? ?????
???????? ?????????, ? ????????????
???. ????????????? ???????????? ??????????? ?????
??????? ????? ???? ? ???????????? ???? ?????
(?????????? ????? 1900 ??? ??????? ??????? ? 5
??? ???????).
3
???????????? ???????.

• ??????? ??????? ? ?????? ????????.
• ?????? ??????? ???????? ???? ??????????? ??????
  ?????? ?? ????-?????? ? ??????????? ?????
  ???????? L1.
• ?????? ???????? ISEE-3 ????????? ? ??????? 1978
  ?.
• ? 1982 ?. ??? ????????? ? L2, ? ????? ?
  ?????????? 15 ????????? ????????? ? 5
  ?????????????? ???????? ? ???? ??? ????????? ?
  ??????? 1983 ?. ?? ?????????? ?????? ? ??????
  Giacobini-Zinner ????? ??????? ?????? ?????? ?
  1985 ?. ??????? ????????? ?????? ? ?????? ??????
  ?????? ? ????? 1986 ?.
• ? ????? ????? ??????? ???????? ? ??????? 2014 ?.

?????????? ?????? ?????? 2 ???? ?????
???????????? ??????????? ????????? ? ?????
???????????? ???????? ? ??????????? ?????
???????? L2. ??? ?????????? ????????? ?????? ?
800000 ?? ?? 250000 ?? ????????????? ??????????
??????????????? ??????? ? ????. ?????? ???
??????? ? ???? ??????????? ??????????????.
4
???????????? ???????.

• ????????? ???????????? ????? ????????
  ???????????? ? ????????????? ?????????? ?? ????
  ???????????? ??????????? ??????? ? ??????.
• Flown and Planned Libration-Point Missions.
  "Acronyms ISEE (International Sun-Earth
  Explorer SOHO (Solar Heliosphere Observatory)
  ACE (Advanced Composition Explorer) MAP
  (Microwave Anisotropy Probe) GAIA (Global
  Astrometric Interferometer for Astrophysics)
  NGST (Next Generation Space
• Telescope) renamed as
• JWST TPF (Terrestrial
• Planet Finder ) XEUS
• (X-ray Evolving Universe
• Spectroscopy)

Mission Sun-Earth Lib. Point Date of Orbit Insertion Mission Purpose
ISEE-3 (NASA) L1, L2 1978, 1983 Solar wind, cosmic rays, plasma studies
SOHO (ESA/NASA) L1 1996 Solar observatory
ACE(NASA) L1 1997 Solar wind, energetic particles
WIND (NASA) L1 1995 Solar-wind monitor
MAP (NASA) L2 2001 Cosmic microwave background
Genesis (NASA) L1 2001 Solar-wind composition
Herschel (ESA) L2 2007 Far infrared telescope
Plank (ESA) L2 2007 Cosmic microwave background
Eddington (ESA) L2 2008 Stellar observations
NGST (NASA) L2 2010 Deep space observatory
Constellation-X (NASA) L2 2011 X-ray astronomy
GAIA (ESA) L2 2012 Galactic structure, Astrometry
TPF(NASA) L2 2012 Detection of distant planets
XEUS(ESA) L2 2014 X-ray astrophysics
DARWIN (ESA) L2 2014 Detection of Earth-like planets
5
???????????? ???????.
SOHO
6
???????????? ???????.
Herschel
7
???????????? ???????.
GAIA
8
???????????? ???????.

• ??????? ???????????? ????????????? ????????????
  ???????????? ????? ????????
• ??????????? ???? ?? ??????? ???????????? ??????
  ? ????????? ?????, ????????? ? ????????
  ?????????? ????????? ?? ???????? ??????
  ??????????
• ???? ?????????? ???????? ????? ????????????
  ????????, ? ??? ????? ?? ????? ???????? ? ????
  ?????
• ??????????? ??????????? ??????????? ??????????
  ????? ??? ?????? ? ??????????? L1 ? ??? ???
  ?????, ??????? ????????? ?????
• ???????? ?????????? ??????????? ???????????
  ????????? ? ???? ???????????? ?????? ?????????
  ???? ???????.
• ????? ???????? ???????? ??????? ????????
  ??????????? ????????? ? ???????????? ????????????
  ????? ????????.

9
???????? ?????? ??????????? ????????? ?
??????????? ????? ????????.????? ?????,
????????? ? ??????????.

• ? ???????? ????????????? ??????? ????????? ?
  ??????? ? ????? ???????? (??? X ?? ??????, Z
  ? ????? ?????????) ??????????????? ?????????
  ???????? ???????? ????? ???????? ? ????
• ,??? K ???????????? ??????????? ?????? ? ?????.
• ??????? ???? ??????? ?????????????? ?????????
  ???????
• ????????? Ai ???????????? ?????????? ?????????
  ????????.

10
???????? ?????? ??????????? ????????? ?
??????????? ????? ????????.????? ?????,
????????? ? ??????????.

• ? ????? ?????? ?? ????? ?????? ???????.

11
?????????? ? ???????.

• ??? ???????, ???? ??????????? ?? ????????? ??????
  ????? ??? Y. ??? ??????????? ????????????? ???
  100-250 ???. ??, ?????? ???? ???????, ???????????
  ???????????? ????????? (800 ???. ??).
• ???????????? ????????? ?????????? ???
  ?????????????? ???????? ?? ?????? ? ???????????
  ????? ????????, ????? ???????? ?????????? ??????
  ???? ???????, ??????????? ??? ? ?????????????
  ??????????? ?????? ?? ?????? ? ??????????? ?????
  ????????.
• ????? ?????????? ????????? ?????? ???????? ??
  ?????? ? ??????? ??????????.
• ??????????? ???????????????? ????????
  ???????????? ???????? ?????? ???????? ????????.
• ????????? ????? ??????? ???? ??????????? ?????
  ? ??????, ?.?. ??????????? ????????, ???????
  ????????????? ????????????? ??? ?????????? ?
  ????????????? ???????????
• ??? ????????? ???????? ?? ?????? ??????? ??????
  ???????? ? ???? ???????????.
• ???? ????? ??????????? ? ???? X ?????????? 28,6?.

??? ????????, ?????????? ? ?????????,
????????????? ????? ???????????, ????????
????????? ??????, ???????????? ???????? ????????
???????. ????????? ??????????? ????????
?????????? ????? ??????. ?????? ????????
?????????? ???????? ??? ????????? ????????? AX
(AY) ??????? ?? ????? ???????. ??? ?????
????????? ?????? ??? X.
12
?????????? ? ???????.

• ?????? ?????????? ????????? ???????? ??? ????
  ???? ?????, ???? ?????? ? ??????????? L2 ??? ???
  ???? ?????????? ?? ?????? (???? ?????
  ????????????? ?? ?????? ????? ?? ?????? ? ??
  ??????? ?? ?????? ???? ????? 3?).
• ??? ?????????? ????? ???? ????????? ???? ?? ????
  ???????????????? ?????? ????????? ?????? (??? ???
  ??????? ? ??????? Planck, ??? ??????? ?? ???????
  ? ???? ? ??????? 6 ??? ????? ???????), ???? ??
  ???? ?????????? ??????????????? ??????????????
  ????????.
• ? ???? ?????? ???????????? ??? ??????????
  ????????? ???????? ????? ?????? ??????
  ???????????? ?? ?????? ?????????? Y.
  ?????????????? ??????? ????? 15 ?/? ?????????
  ???????? ?????? ? ???? ? ??????? 6 ???.
• ?????????? ?????????????? ?????? ????????????
  ?????????? ?????? ???????????????? ???????????? ?
  ?????????? ????????.
• ?????? ??? ???????? ?????????? ???? ??? ? 1-2
  ??????, ?????? ? ??????? ???????? 5 ?/? ? ???.
• ??? ????, ??? ???????, ????????? ?????????? ?? ?
  ??????????? ??????????? (28,6? ? ??? X), ? ?????
  ??? X, ?.?. ????? ??????????? ?? ??????.

13
??????? ? ??????????? ????? ???????? ? ??????????
??????? ?????.

• ????????????? ???????????? ????? ????? ?????
  ???????? ???????? ?? ??????? ????? ?????????????
  ????????? ?????. ??? ????????, ??? ??? ?????????
  ????????, ???????????? ?? ??????????? ??????,
  ???????? ????? ??????? ???????? ???
  ??????????????? ?????? ???????? ???????? ? ?????
  ??????? ??????? ????????? ?? ?????? ????? ?????
  ???????? ??? ?????????????? ???????? (?
  ??????????? ??????). ??? ???? ????? ??????????
  ????????? ?????????? ?????????? ???????, ??? ???
  ??????? ?????? ???????? ??? ???????????????????.

14
??????? ? ??????????? ????? ???????? ? ??????????
??????? ?????.

• ? ???????? ???????? ????????? ???????? ??????
  ????? ???????????? ??????? ??????? ?????? (???
  ???????? ? ???????). ????????? ?????????
  ?????????? ?? ?????????? ?????????, ?????????????
  ???????????? ????????????? ??? ?????????????
  ?????????????? ?????????.
• ?????????? ????? ??????? ?????? ????? ?????
  ???????? ???????? ???????? ? ?????????????
  ??????????? ? ????????? XY (800000 ?? ? ?????).
• ??????? ??????? ?????? ???????? ?? ???? ??????
  ??????? ??????? ???????, ??? ???? ??????? ??????
  ????? ????????, ????? ?????????? ????????
  ?????????? ? ????? (???????) ? ????? ???????
  ?????? ?? ????? ?? ????????? ???????? ??? ???????
  ?????? ??????? (????).

15
???? ?????????? ?????????? ?????? ??? ??????? ?
??????????? ????? ???????? L

• ????? ?????? L1 ???? ??????????? ????????????????
  ?????????? ?????????? ????? ? ?? ?????, ?????
  ??????????? ??????? ????????? ? 1,5 ???. ?? ??
  ?????. ??? ????????? ??????????????? ????????????
  ??????????????? ?????? ? ????????? ?????????.
• ??????? ??????? ? ?????, ????????????? ??????,
  ??? L1 ?? ?????, ????? ????????? ????? ??
  ??????????? ?????????? ? ????????? ????? ??
  ??????????? ??????????? ??????? ? ????????????
  ?????.
• ?????????? ?????????? ?????? ????? ?????
  ????????, ????????? ????? ???? ?????? ??????????
  ?????????? ??????, ??? ??? ??????? ?? ???????????
  ????
• ??? ?????? ??????? ?????????? ????? ????????????
• ??????????? ???????? m/S ??? ????????? ????????
  ?? ?????????? d ?? ????? ?????? ????????.

d, ???. ?? 1500 2000 2500 3000 4000
, ??/?2 - 0.03468 0.02018 0.01502 0.01042
16
???? ?????????? ?????????? ?????? ??? ??????? ?
??????????? ????? ???????? L

• ??? ???????? ??????????? ????????? ?? ?? ????????
  ??????????? ??? ??????? ?????? ????? ???????,
  ???? ????? ????? ??????????? ???????????.
• ???? ????????? ?? ???? ????? ?????????? ????? ?
  ???????? ?????????? ??????? ????????????????????
  ??????, ?? ??????? ? ?????? ?????????????
  ?????????? ?? ??????, ????? ???????? ??
  ???????????? ?, ?????????????? ???? ???????????
  ?????.

???? ????? ????? ??????????? ????????
????????????? ?????????????? ?? ???????-????
????????? ?? ??????? ??????????, ?? ??????????
??????????? ???????????????? ????????? ????
???????? ?????. ? ??-?????? ??????????? ??????
????????? ???????????? ????????????????????
????-?? ? ?????????? ?????????????.
2F
F
???????????????????? ?????? (?????????? ?????????)
???????????????????? ?????? (????????????
?????????)
2F
?????????? ??????
F
?????????? ??????
17
?????? ?????? L1 ????????? ? ???????.

• ??? ???????????? ???????????? ?????????? ?????
  ????????? ? ?????????? ??????? ??????? ???
  ???????? ??? ?? ??????, ??? ? ??? ????????? ???
  ??????, ?.?. ? ????????? ??????? ??????????
  ???????????? ?????????? ?????????? ???????
  ???????, ??????????????? ???????? ???????? ??
  ?????? ????? L1.
• ??? ???? ?? ??????????? ?? ????? ?? 1,3 ???. ??
  ??????????????, ??? ????? ?? ???????, ????? ?????
  ???????????, ? ????? ???? ?????????? ????????
  ?????????????? ??????????????? ???????????
  ?????????, ? ????? ???????? ???????????????
  ???????????? ??????????? ?? ??????.
• ????????? ?????? ???????? ?????????? ???????????.
• ??? ????? ?? ?????????? ????????, ??????????
  ?????? ???????? ? ???????? ?????? ?????? ?? ?????
  (??? ? ???????????), ?????????? ???????? ?????? ?
  ??????? ???????? ?? ??????.
• ? ??????? ??????, ??? ?????????? ???????? ??????
  ? ????? ??????? ?????? ??????, ??? ? ?????????
  ???????, ????????? ? ???????????? ??????? ?????.

18
?????????? ????????? ? ??????? ?????????? ??????.

• ???? ???????????????? ??????????? ??????????
  ?????? ??? ????? ?????????? ?????????.
  ??????????????, ??? ????? ????????? ??????????
  ?????? ? ??? ????????????? ????????????. ??????
  ?????????? ??? ??? ???? ??????????? ??????? ?
  ??????????? ?????? ???????????? ?????????, ??????
  ??? ????????? ????????? ??????????? ???????
  ??????????? ? ????? ??????? ?????? (?????????????
  ????? - ?????????).
• ??????????? ??????? ????????? ???????????
  ????????
• ??? T0 - ?????? ????????? ????????, ???????????
  ????? ???????? ?????????? ?????
• k -????????? ????????? ??????????? ??????? ??
  ???? ??????? ??????
• ? - ???? ????? ???????? ??????????? ?? ?????? ?
  ???????? ? ????????
• N0 - ????????? ??????, ????????????? ???????????
  ??????.
• ? ??????????? ?????? ? 0, k 0.

??????? ?????????? ????????? ? ????????? XY
?????????????? ?????? ?? ??????????? ???
????????? ??? ??????, ? ????? ? ?????????????,
??? ?? ????? ?????? ????????? ???? ??????????
????????, ?.?. ??????????? ?????? ??????????
?????????.
19
?????????? ????????? ? ??????? ?????????? ??????.

• ?????????? ??????? ???????????? ??????????
  ???????, ???????????????? ?????????, ???????? ???
  ?????? ????????? ??? ??????. ??????????? ???
  ???????, ?????? ??? ????????????? ?? 30 ????,
  ?????? - 10 ????. ????? ??????????? ?????
  ???????, ??? ??????? ? ??? ??????????? ???????? ?
  ????????? ????????? (????????? ?? ???????? ???? -
  ??? ???? ??????? ? ???????????? ?? ?????? ?
  ?????????? ?????????).
• ??? ????? ?? ????????, ??????? ??????? ?????????
  ? ??? ?????? ????????? ???????? ????????? ??????
  ????? ??? Y?? ???????? 2200 ???. ?? ?? 550 ???.
  ?? ??? ???????? ?? ?????? 0.07 ??/? ? ?? 3400 ??
  1200 ???.?? ??? ???????? ?? ?????? 0.054 ??/?.
• ????????? ??????? ???????????? ???????????
  ????????? ????????? ????? ??? Z.

20
?????????? ????????? ? ??????? ?????????? ??????.

• ? ???? ?????? ??????????????? ?????????? ??????
  ?? ???????????? ?????????, ??? ????? ???????
  ???????????? ?? ??????? ? ????????? (13.5 ???????
  ?????????? ??????? ? ?????? ?? ?????????
  ?????????) ???????? ? ????????? ???????????
  ???????? ???????? ?????? ??? X ??
  ???????????????. ?????? ?????????? ? ??????
  ??????, ??? ?????????? Y ?? ?????? ?????? ?
  ????????????.

21
?????????? ?????? ??? ?????????????? ????????
????????? ???????? ?? ?????? ? ??????????? ?????
????????.

• ?????? ???????? ????????? ??????????????????
  ???????? ??? ????????? ???????? ?? ??????
  ???????? ? ???????? ????? 5 ?/? ? ??? ???
  ????????????? ?????? (??? ??????).
• ? ?????? ??????? ??????? ???????? ?? ????????
  ??????, ????? ??????????? ?????? ???????????? ???
  ?????? ? ????????????, ?????????? ?? ?? 100.
• ? ?????? ??????? ??????? ?????? ? ??????????
  ????????????? ???????????? ?????? ????????????
  ???????? (??????? ???????? ????????? ???????)
  ????? ????????? ??????????? ?????? ??????????
  ?????????????? ???????? ????????? ???????? ??
  ??????.

22
?????????? ?????? ??? ???????? ? ???????????
??????????? ? ??????????? ????? ????????.

• ???????? ??? ????????????? ????????,
  ?????????????? ???????? ??????????? ? ???????????
  ????? ???????? L2 (XEUS,TPF, Darvin). ??????????
  ?????? ? ?????????? ????????????? ????????????
  ????? ???? ??????? ????????????? ?????????????
  ?????????? ??????????.

XEUS
23
?????????? ?????? ??? ???????? ? ???????????
??????????? ? ??????????? ????? ????????.
TPF
24
?????????? ?????? ??? ???????? ? ???????????
??????????? ? ??????????? ????? ????????.
DARWIN
25
??????????.

• ????????? ?????????? ?? ??????? ? ???????????
  ????? ????????.
• Proceedings of the Libration Point Orbits and
  Application, Aiguablava, Spain,10-14 June
  2002,World Scientific Publishing Co.Pte.LTD.
  2003,
• http//www.ieec.fcr.es/libpoint/viewgraph.html
• ?????? ???????????? ???????????? ?????????
  http//www.esa.int
• N.A.EismontR.R Nazirov Solar Sails as a Tool for
  Spacecraft Motion Control Near Solar -Terrestrial
  Libration Points. Proceedings of the 18th
  International Symposium on Space Flight Dynamics.
  11-15 October 2004, Munich, Germany, ESA SP-548,
  December 2004.
• Novikov D., Nazirov R., Eismont,N. Spacecraft
  formation control in vicinity of libration points
  using solar sails. Small Satellites for Earth
  Observation. Selected Proceedings of the 5th
  International Symposium of the Interntional
  Academy of Astronautics. Berlin, April 4-8, 2005.
  Ed.by Hans-Peter Roezer,Rainer Sandau,Arnoldo
  Valenzuela. Walter de Gruyter, Berlin, New York