AN ANALYTICAL STUDY OF GRAVITY ASSIST IN THREE DIMENSIONS

Jia Jianhua; Wang Qi

doi:10.6052/0459-1879-12-267

Volume 45 Issue 3

Turn off MathJax

Article Contents

Abstract

References

Chinese Journal of Theoretical and Applied Mechanics > 2013 > 45(3): 412-420. > DOI: 10.6052/0459-1879-12-267 CSTR: 32045.14.0459-1879-12-267

Jia Jianhua, Wang Qi. AN ANALYTICAL STUDY OF GRAVITY ASSIST IN THREE DIMENSIONS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(3): 412-420. DOI: 10.6052/0459-1879-12-267

Citation:

Jia Jianhua, Wang Qi. AN ANALYTICAL STUDY OF GRAVITY ASSIST IN THREE DIMENSIONS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(3): 412-420. DOI: 10.6052/0459-1879-12-267

Citation:

Jia Jianhua, Wang Qi. AN ANALYTICAL STUDY OF GRAVITY ASSIST IN THREE DIMENSIONS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(3): 412-420. DOI: 10.6052/0459-1879-12-267

PDF (534 KB)

AN ANALYTICAL STUDY OF GRAVITY ASSIST IN THREE DIMENSIONS

Jia Jianhua^,,
Wang Qi

School of Aeronautic Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China

Funds: The project was supported by the National Natural Science Foundation of China (10832004).

Received Date: September 26, 2012
Revised Date: March 16, 2013

Graphical Abstract

Abstract

Abstract

New analytical equations are derived for the three-dimensional gravity assist based on the patched conics model, including the variations in velocity, angular momentum, energy and inclination of the spacecraft due to the gravity assist. The equations developed here are verified by numerical integrations, using the circular restricted three-body problem, showing a good agreement better than 0.01. The results predicted by these analytical equations and the results computed by the numerical method differ by less than 0.7% under most conditions. This is a good indication that the analytical equations are good approximations and can be used for preliminary mission design. The influence of the parameters on the orbit of spacecraft is discussed based on the simplified equations which are the approximations of the above equations.
- gravity assist in three dimensions,
- analytical equations,
- two-body problem,
- restricted three-body problem

FullText(HTML)

References (21)

References

李俊峰. 2005～ 2009年国际深空轨迹优化竞赛.力学与实践, 2010, 32(4): 130-137 (Li Junfeng. Global trajectory optimization competition from 2005 to 2009. Mechanics in Engeering, 2010, 32(4): 130-137 (in Chinese))

中国科学院空间领域战略研究组.中国至2050年空间科技发展路线图.北京:科学出版社, 2009: 97-97 (Research Group on Space Science & Technology of the Chinese Academy of Science. Space Science & Technology in China: A Roadmap to 2050. Beijing: Science Press, 2009: 97-97 (in Chinese))

Flandro GA. From instrumented comets to grand tours: On the history of gravity assist. In: Proceeding of 39th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, USA, January 8-11, 2001

Battin RH. The determination of round-trip planetary reconnaissance trajectories. Journal of the Aerospace Sciences, 1959, 26(9): 545-567

Strange NJ, Longuski JM. A graphical method for gravity-assist trajectory design. Journal of Spacecraft and Rockets, 2002, 39(1): 9-16

Chen KJ, Kloster KW, Longuski JM. A graphical method for preliminary design of low-thrust gravity-assist trajectories. In: AIAA/AAS Astrodynamics Specialist Conference and Exhibit, Honolulu, Hawaii, USA, August 18-21, 2008

Carnelli I, Dachwald B, Vasile M. Evolutionary neurocontrol: A novel method for low-thrust gravity-assist trajectory optimization. Journal of Guidance, Control and Dynamics, 2009, 32(2): 615-624

Petropoulos AE, Longuski JM. Automated design of low-thrust gravity-assist trajectories. In: Proceedings of AIAA/AAS Astrodynamics Specialist Conference, Denver, CO, Aug, 2000

De Pascale P, Vasile M. Preliminary design of low-thrust multiple gravity-assist trajectories. Journal of Spacecraft and Rockets, 2006, 43(5): 1065-1076

Petropoulos AE, Longuski JM. Shape-based algorithm for automated design of low-thrust, gravity-assist trajectories. Journal of Spacecraft and Rockets, 2004, 41(5): 787-796

Sims JA, Longuski JM, Patel MR. Aerogravity-assist trajectories to the outer planets and the effect of drag. Journal of Spacecraft and Rockets, 2000, 37(1): 49-55

Johnson WR, Longuski JM. Design of aerogravity-assist trajectories. In: Proceedings of AIAA/AAS Astrodynamics Specialist Conference, Denver, CO, Aug, 2000

乔栋, 崔祜涛, 崔平远等. 气动-引力辅助转移轨道研究及在星际探测中的应用. 宇航学报, 2005, 26(5): 541-546 (Qiao Dong, Cui Hutao, Cui Pingyuan. Study of aerogravity assist tranfer trajectory and application in interplanetary exploration missions. Journal of Astronautics, 2005, 26(5): 541-546 (in Chinese))

Armellin R, Lavagna M, Ercoli-Finzi A. Aero-gravity assist maneuvers: Controlled dynamics modeling and optimization. Celestial Mechanics and Dynamical Astronomy, 2006, 95: 391-405

Armellin R, Lavagna M. Aero-gravity assist maneuvers: coupled trajectory and vehicle shape optimization. In: Proceedings of AIAA/AAS Astrodynamics Specialist Conference and Exhibit, Keystone, Colorado, USA, August 21-24, 2006

Broucke RA. The celestial mechanics of the gravity assist. In: Proceeding of AIAA/AAS Astrodynamics Conference, Minneapolis Washington. D. C USA, 1988

Prado AFBA. Close-approach trajectories in the elliptic restricted problem. Journal of Guidance, Control and Dynamics, 1997, 20(4): 797-802

Felipe G, Prado AFBA. Classification of out-of-plane swing-by trajectories. Journal of Guidance, Control and Dynamics, 1999, 22(5): 643-649

乔栋,崔平远,崔祜涛. 基于圆型限制性三体模型的借力飞行机理研究.宇航学报,2009, 30(1): 82-87 (Qiao Dong, Cui Pingyuan, Cui Hutao. Research on gravity-assist mechanism in circular restricted three-body model. Journal of Astronautics, 2009, 30(1): 82-87 (in Chinese))

乔栋,崔平远,尚海滨. 基于椭圆型限制性三体模型的借力飞行机理研究.宇航学报,2010, 31(1): 36-43 (Qiao Dong, Cui Pingyuan, Shang Haibin. Research on gravity-assist mechanism in elliptic restricted three-body model. Journal of Astronautics, 2010, 31 (1): 36-43 (in Chinese))

贾建华,王琪. 三维引力辅助机理分析. 北京航空航天大学学报,2012, 38(7): 981-986 (Jia Jianhua, Wang Qi. Research on gravity-assist mechanism based on three-dimension elliptic restricted three-body model. Journal of Beijing University of Aeronautics and Astronautics, 2012, 38(7): 981-986 (in Chinese))

[1]	Hua Fenfei, Luo Tong, Lei Jian, Liu Dabiao. STUDY OF CONFINED LAYER PLASTICITY BASED ON HIGHER-ORDER STRAIN GRADIENT PLASTICITY THEORY[J]. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(2): 399-408. DOI: 10.6052/0459-1879-23-318
[2]	Zhang Dongjian, Zheng Xitao, Yan Leilei, Lu Tuo, Xu Jianhui, Zhang Cong. FINITE ELEMENT MODEL FOR BUCKLING OF STIFFENED COMPOSITE SANDWICH STRUCTURES BASED ON HIGHER-ORDER THEORY[J]. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(8): 1686-1698. DOI: 10.6052/0459-1879-23-114
[3]	Wang Zhan, Zhu Yuke. THEORY, MODELLING AND COMPUTATION OF NONLINEAR OCEAN INTERNAL WAVES[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(6): 1589-1604. DOI: 10.6052/0459-1879-19-326
[4]	Shen Zhiqiang, Xia Jun, Song Dianyi, Cheng Pan. A QUADRILATERAL QUADRATURE PLATE ELEMENT BASED ON REDDY'S HIGHER-ORDER SHEAR DEFORMATION THEORY AND ITS APPLICATION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(5): 1093-1103. DOI: 10.6052/0459-1879-18-225
[5]	Duan Tiecheng, Li Luxian. STUDY ON HIGHER-ORDER SHEAR DEFORMATION THEORIES OF THICK-PLATE[J]. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(5): 1096-1113. DOI: 10.6052/0459-1879-16-120
[6]	Chen Ling, Shen Jiping, Li Cheng, Liu Xinpei. GRADIENT TYPE OF NONLOCAL HIGHER-ORDER BEAM THEORY AND NEW SOLUTION METHODOLOGY OF NONLOCAL BENDING DEFLECTION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(1): 127-134. DOI: 10.6052/0459-1879-15-170
[7]	Zhao Rujiang. THIRD-ORDER GENERALISED BEAM THEORY AND CALCULATION METHOD[J]. Chinese Journal of Theoretical and Applied Mechanics, 2014, 46(6): 987-993. DOI: 10.6052/0459-1879-14-033
[8]	Jie Zhao, Wanji Chen, Bin Ji. A study on the two second-order strain gradient theories[J]. Chinese Journal of Theoretical and Applied Mechanics, 2010, 42(1): 138-145. DOI: 10.6052/0459-1879-2010-1-2008-517
[9]	Transient Disturbance In A Half-Space Due To Moving Line Heat Source Using Thermoelasticity Without Energy Dissipation[J]. Chinese Journal of Theoretical and Applied Mechanics, 2004, 36(3): 342-347. DOI: 10.6052/0459-1879-2004-3-2003-147
[10]	TIME DOMAIN BEM FOR WAVE PROPAGATION PROBLEMS IN ANISOTROPIC MEDIA AND ITS EXPERIMENTAL VERIFICATIONS[J]. Chinese Journal of Theoretical and Applied Mechanics, 1998, 30(6): 728-736. DOI: 10.6052/0459-1879-1998-6-1995-183

Cited By

Cited by

Periodical cited type(5)

1.	聂隆锋，赵西增，张志杭，童晨奕，王辰. 基于VPM-THINC/QQ模型的波浪高保真模拟. 力学学报. 2019(04): 1043-1053 . 本站查看
2.	张崇伟，宁德志. 基于时域解耦算法的多液舱浮式结构物运动模拟. 力学学报. 2019(06): 1650-1665 . 本站查看
3.	王千，刘桦，房詠柳，邵奇. 孤立波与淹没平板相互作用的三维波面和水动力实验研究. 力学学报. 2019(06): 1605-1613 . 本站查看
4.	李翔，宁德志. 长波波列传播特性的模拟研究. 水动力学研究与进展(A辑). 2018(06): 714-719 .
5.	宁德志，李翔，张崇伟. 聚焦波群对出水截断结构作用的非线性数值模拟（英文）. Journal of Marine Science and Application. 2018(03): 362-370 .

Other cited types(3)

Get Citation

PDF

XML

Article Metrics

Article views (2133) PDF downloads (806) Cited by(8)

AN ANALYTICAL STUDY OF GRAVITY ASSIST IN THREE DIMENSIONS