The treatment of the earth oblateness effect in trajectory optimization in equinoctial coordinates

1997 ◽  
Vol 40 (1) ◽  
pp. 69-82 ◽  
Author(s):  
Jean Albert Kechichian
Keyword(s):  
Trajectory Optimization ◽  
The Earth ◽  
Oblateness Effect

scholarly journals Enhanced Hybrid Differential Evolution for Earth-Moon Low-Energy Transfer Trajectory Optimization

2018 ◽  
Vol 2018 ◽  
pp. 1-17
Author(s):  
Yanyun Zhang ◽  
Lei Peng ◽  
Guangming Dai ◽  
Maocai Wang
Keyword(s):  
Energy Transfer ◽  
Differential Evolution ◽  
Trajectory Optimization ◽  
Transfer Problem ◽  
Low Energy ◽  
Initial Condition ◽  
Transfer Trajectory ◽  
De Algorithm ◽  
The Earth ◽  
Low Energy Transfer

It is known that the optimization of the Earth-Moon low-energy transfer trajectory is extremely sensitive with the initial condition chosen to search. In order to find the proper initial parameter values of Earth-Moon low-energy transfer trajectory faster and obtain more accurate solutions with high stability, in this paper, an efficient hybridized differential evolution (DE) algorithm with a mix reinitialization strategy (DEMR) is presented. The mix reinitialization strategy is implemented based on a set of archived superior solutions to ensure both the search efficiency and the reliability for the optimization problem. And by using DE as the global optimizer, DEMR can optimize the Earth-Moon low-energy transfer trajectory without knowing an exact initial condition. To further validate the performance of DEMR, experiments on benchmark functions have also been done. Compared with peer algorithms on both the Earth-Moon low-energy transfer problem and benchmark functions, DEMR can obtain relatively better results in terms of the quality of the final solutions, robustness, and convergence speed.

Indirect Optimization for Finite-Thrust Orbital Interception Problem

2013 ◽  
Vol 313-314 ◽  
pp. 1051-1054
Author(s):  
Yan Yi Huang ◽  
Guo Dong Chen
Keyword(s):  
Nonlinear Programming ◽  
Trajectory Optimization ◽  
Optimization Problem ◽  
Time History ◽  
Minimum Time ◽  
Programming Method ◽  
The Earth ◽  
Finite Thrust ◽  
Nonlinear Programming Method ◽  
Maximum Thrust

The nonlinear programming method is used to study the finite-thrust minimum-time orbital interception problem. Considering the spacecraft with fixed impulse, the Modified Equinoctial Elements are used to describe the movement of the spacecraft in the attached coordinate, and the model of the orbital interception problem is established. Then the trajectory optimization problem is solved by the nonlinear programming method. The simulations demonstrate that the minimum time orbital interception mission is well accomplished, and the spacecraft fly around the earth with maximum thrust magnitude at whole time history.

scholarly journals A Shape-Based Method for Continuous Low-Thrust Trajectory Design between Circular Coplanar Orbits

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Qun Fang ◽  
Xuefeng Wang ◽  
Chong Sun ◽  
Jianping Yuan
Keyword(s):  
Fourier Series ◽  
Trajectory Optimization ◽  
Lower Cost ◽  
Necessary Conditions ◽  
Trajectory Design ◽  
Low Thrust ◽  
First Order ◽  
The Earth ◽  
Free Case ◽  
Preliminary Phase

The shape-based method can provide suitable initial guesses for trajectory optimization, which are useful for quickly converging a more accurate trajectory. Combined with the optimal control theory, an optimized shape-based method using the finite Fourier series is proposed in this paper. Taking the flight time-fixed case and the time-free case into account, respectively, the optimized shape-based method, which considers the first-order optimal necessary conditions, can guarantee that not only an orbit designed during the preliminary phase is optimal, but also the thrust direction is not constrained to be tangential. Besides, the traditional shape-based method using the finite Fourier series, in which the thrust direction is constrained to be tangential, is developed for the time-free case in this paper. The Earth-Mars case and the LEO-GEO case are used to verify the optimized shape-based method’s feasibility for time-fixed and time-free continuous low-thrust trajectory design between circular coplanar orbits, respectively. The optimized shaped-based method can design a lower cost trajectory.

scholarly journals Trajectory optimization for the Horyu-VI international lunar mission

Astrodynamics ◽  
2021 ◽  
Author(s):  
Federico De Grossi ◽  
Paolo Marzioli ◽  
Mengu Cho ◽  
Fabio Santoni ◽  
Christian Circi
Keyword(s):  
Trajectory Optimization ◽  
Dust Particles ◽  
Gravity Gradient ◽  
The Sun ◽  
The Moon ◽  
Lunar Dust ◽  
The Earth ◽  
Lunar Mission ◽  
Solar Gravity ◽  
Key Parameter

AbstractThe Horyu-VI nano-satellite is an international lunar mission with the purpose of studying the lunar horizon glow (LHG)—a still unclear phenomenon caused by electrostatically charged lunar dust particles. This study analyzes the mission trajectory with the hypothesis that it is launched as a secondary payload of the NASA ARTEMIS-II mission. In particular, the effect of the solar gravity gradient is studied; in fact, depending on the starting relative position of the Moon, the Earth, and the Sun, the solar gradient acts differently on the trajectory—changing it significantly. Therefore, the transfer and lunar capture problem is solved in several cases with the initial Sun-Earth-Moon angle as the key parameter. Furthermore, the inclination with respect to the Moon at capture is constrained to be equatorial. Finally, the problem of stabilization and circularization of the lunar orbit is addressed in a specific case, providing an estimate of the total propellant cost to reach the final orbit around the Moon.

The motion of a lunar orbiter

1966 ◽  
Vol 25 ◽  
pp. 373
Author(s):  
Y. Kozai
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Triaxial Ellipsoid ◽  
The Moon ◽  
Secular Motion ◽  
The Earth ◽  
Close Satellite ◽  
The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

Formation of Lunar Craters and Bright Rays as a Result of Meteorite Impacts

1962 ◽  
Vol 14 ◽  
pp. 415-418
Author(s):  
K. P. Stanyukovich ◽  
V. A. Bronshten
Keyword(s):  
Explosive Charge ◽  
The Moon ◽  
Meteorite Impacts ◽  
The Earth ◽  
Lunar Craters ◽  
The Impact

The phenomena accompanying the impact of large meteorites on the surface of the Moon or of the Earth can be examined on the basis of the theory of explosive phenomena if we assume that, instead of an exploding meteorite moving inside the rock, we have an explosive charge (equivalent in energy), situated at a certain distance under the surface.

The Origin of the Moon

1962 ◽  
Vol 14 ◽  
pp. 149-155 ◽  
Author(s):  
E. L. Ruskol
Keyword(s):  
Chemical Composition ◽  
Solar System ◽  
The Moon ◽  
The Earth ◽  
The Difference ◽  
Origin Of The Moon

The difference between average densities of the Moon and Earth was interpreted in the preceding report by Professor H. Urey as indicating a difference in their chemical composition. Therefore, Urey assumes the Moon's formation to have taken place far away from the Earth, under conditions differing substantially from the conditions of Earth's formation. In such a case, the Earth should have captured the Moon. As is admitted by Professor Urey himself, such a capture is a very improbable event. In addition, an assumption that the “lunar” dimensions were representative of protoplanetary bodies in the entire solar system encounters great difficulties.

The Origin of the Moon and its Relationship to the Origin of the Solar System

1962 ◽  
Vol 14 ◽  
pp. 133-148 ◽  
Author(s):  
Harold C. Urey
Keyword(s):  
Solar System ◽  
The Moon ◽  
The Past ◽  
The Earth ◽  
Short Period ◽  
Origin Of The Moon

During the last 10 years, the writer has presented evidence indicating that the Moon was captured by the Earth and that the large collisions with its surface occurred within a surprisingly short period of time. These observations have been a continuous preoccupation during the past years and some explanation that seemed physically possible and reasonably probable has been sought.

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