Lunar Landing Trajectory Design Based on Invariant Manifold

GONG Sheng-ping; LI Jun-feng; BAOYIN He-xi; GAO Yun-feng

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2007 > 28(2): 183-190

GONG Sheng-ping, LI Jun-feng, BAOYIN He-xi, GAO Yun-feng. Lunar Landing Trajectory Design Based on Invariant Manifold[J]. Applied Mathematics and Mechanics, 2007, 28(2): 183-190.

Citation:

GONG Sheng-ping, LI Jun-feng, BAOYIN He-xi, GAO Yun-feng. Lunar Landing Trajectory Design Based on Invariant Manifold[J]. Applied Mathematics and Mechanics, 2007, 28(2): 183-190.

Citation:

GONG Sheng-ping, LI Jun-feng, BAOYIN He-xi, GAO Yun-feng. Lunar Landing Trajectory Design Based on Invariant Manifold[J]. Applied Mathematics and Mechanics, 2007, 28(2): 183-190.

PDF( 505 KB)

Lunar Landing Trajectory Design Based on Invariant Manifold

School of Aerospace, Tsinghua University, Beijing 100084, P. R. China

Received Date: 2005-09-20
Rev Recd Date: 2006-10-30
Publish Date: 2007-02-15

Abstract

Abstract

The low-energy lunar landing trajectory design using the invariant manifolds of restricted three body problem is studied.Considering angle between the ecliptic plane and lunar orbit plane,the four body problem of Sun-Earth-Moon-spacecraft was divided into two three body problems,the Sun-Earth-spacecraft in the ecliptic plane and the Earth-Moon-spacecraft in the lunar orbit plane.Using the orbit maneuver at the place where the two planes and the invariant manifolds intersect,a general method to design low energy lunar landing trajectory was given.It is found that this method can save the energy by 20% compared with the traditional Hohmann transfer trajectory.The mechanism of the method that can save energy was investigated in the point of view of energy and the expression of the amount of energy saved is given.In addition,some rules of selecting parameters with respect to orbit design were provided.The method of energy analysis can be extended to energy analysis in deep space orbit design.
- three-body problem,
- Lagrange point,
- Halo orbit: invariant manifold,
- lunar landing trajectory,

FullText(HTML)

References(17)

References

[1]	Farquhar R W.The utilization of Halo orbits in advanced lunar operations[R]. Technical Report TN D-6365,NASA,1971.
[2]	Gomez G,Koon W S,Lo M W,et al.Connecting orbits and invariant manifold in the spatial restricted three-body problem[J].Nonlinearity,2004,17(5):1571-1606. doi: 10.1088/0951-7715/17/5/002
[3]	Howell K C,Barden B T,Wilson R S,et al.Trajectory design using a dynamical systems approach with application to GENESIS[A].In:Proceedings of the AAS/AIAA Astrodynamics Conference[C].Idaho:Sun Valley,1997,1665—1684.
[4]	Howell K C,Mains D L,Barden B T.Transfer trajectories from Earth parking orbits to Sun-Earth halo orbits[A].In:Proceedings of the 4th AAS/AIAA Spaceflight Mechanics Meeting[C].Cocoa Beach,Florida,1994，399-422.
[5]	Lo M W,Ross S D.The lunar L1 Gateway: portal to the stars and beyond[A].In:AIAA Space 2001 Conference[C].Albuquerque, NM,2001.
[6]	Lo M W.The interplanetary superhighway and the origins program[A].In:2002 IEEE Aerospace Conference Proceedings[C].Vol 7.Big Sky,MT,2002,3543-3562.
[7]	周天帅，李东，陈新民，等.国外日-地动平衡点卫星应用及转移轨道实现方式[J].导弹与航天运载技术,2004,272(2):29-34.
[8]	郑学塘，郁丽忠，覃一平. 光引力限制性三体问题的平动点[J].应用数学和力学，1994,[STHZ]. 15[STBZ]. (8)：733-739.
[9]	高云峰，龚胜平.编队飞行及拉格朗日平动点在深空探测中的应用前景[J].深空探测研究,2005,1(1):36-41.
[10]	LIU Lin.Evolution on the orbital resonance in restricted 3-body problem[J].Scientia Sinica,1988,31(8):123-128.
[11]	ZHAO Zhang-yin, LIU Lin. The stable regions of the triangular libration points of the planets[J].ICARUS,1992，100(1):136-142.
[12]	Gomez G,Jorba A,Masdemont J J,et al.Study of the transfer from the earth to a halo orbit around the equlibrium point L1[J].Celestial Mechanics and Dynamical Astronomy,1993,56:541-562. doi: 10.1007/BF00696185
[13]	Koon W S,Lo M W,Marsden J E,et al.Low energy transfer to the moon[J].Celestial Mechanics and Dynamical Astronomy,2001,81(5):63-73. doi: 10.1023/A:1013359120468
[14]	Koon W S,Martin W,Lo M W,et al.Shoot the moon[A].In:AAS/AIAA Astrodynamics Specialist Conference[C].Florida, 2000.
[15]	Koon W S,Lo M W,Marsden J E,et al.Constructing a low energy transfer between Jovian Moons[J].Contemporary Mathematics,2000,292(1):129-145.
[16]	Popescu M,Cardos V.The domain of initial conditions for the class of three-dimentional halo periodical orbits[J].Acta Astronautica,1995,36(3):193-196. doi: 10.1016/0094-5765(95)00107-B
[17]	Wilczak D,Zgliczynski P.Heteroclinic connections between periodic orbits in planar restricted circular three-body problem[J].Communications in Mathematical Physics,2004,234(1):37-75.