scholarly journals Effects of the Eccentricity of a Perturbing Third Body on the Orbital Correction Maneuvers of a Spacecraft

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
R. C. Domingos ◽  
A. F. B. A. Prado ◽  
V. M. Gomes
Keyword(s):  
Fuel Consumption ◽  
Low Thrust ◽  
Three Body Problem ◽  
Station Keeping ◽  
Third Body ◽  
Orbital Maneuvers ◽  
Orbital Correction ◽  
Averaged Models ◽  
Three Body ◽  
Averaged Methods

The fuel consumption required by the orbital maneuvers when correcting perturbations on the orbit of a spacecraft due to a perturbing body was estimated. The main goals are the measurement of the influence of the eccentricity of the perturbing body on the fuel consumption required by the station keeping maneuvers and the validation of the averaged methods when applied to the problem of predicting orbital maneuvers. To study the evolution of the orbits, the restricted elliptic three-body problem and the single- and double-averaged models are used. Maneuvers are made by using impulsive and low thrust maneuvers. The results indicated that the averaged models are good to make predictions for the orbital maneuvers when the spacecraft is in a high inclined orbit. The eccentricity of the perturbing body plays an important role in increasing the effects of the perturbation and the fuel consumption required for the station keeping maneuvers. It is shown that the use of more frequent maneuvers decreases the annual cost of the station keeping to correct the orbit of a spacecraft. An example of an eccentric planetary system of importance to apply the present study is the dwarf planet Haumea and its moons, one of them in an eccentric orbit.

scholarly journals Low-Thrust Out-of-Plane Orbital Station-Keeping Maneuvers for Satellites

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Vivian M. Gomes ◽  
Antonio F. B. A. Prado
Keyword(s):  
Main Idea ◽  
Low Thrust ◽  
Station Keeping ◽  
Control Approach ◽  
Orbital Maneuvers ◽  
Hybrid Optimal Control ◽  
The Earth ◽  
Out Of Plane ◽  
Orbital Correction ◽  
Optimal Control Approach

This paper considers the problem of out of plane orbital maneuvers for station keeping of satellites. The main idea is to consider that a satellite is in an orbit around the Earth and that it has its orbit is disturbed by one or more forces. Then, it is necessary to perform a small amplitude orbital correction to return the satellite to its original orbit, to keep it performing its mission. A low thrust propulsion is used to complete this task. It is important to search for solutions that minimize the fuel consumption to increase the lifetime of the satellite. To solve this problem a hybrid optimal control approach is used. The accuracy of the satisfaction of the constraints is considered, in order to try to decrease the fuel expenditure by taking advantage of this freedom. This type of problem presents numerical difficulties and it is necessary to adjust parameters, as well as details of the algorithm, to get convergence. In this versions of the algorithm that works well for planar maneuvers are usually not adequate for the out of plane orbital corrections. In order to illustrate the method, some numerical results are presented.

scholarly journals Searching for Orbits with Minimum Fuel Consumption for Station-Keeping Maneuvers: An Application to Lunisolar Perturbations

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Antonio Fernando Bertachini de Almeida Prado
Keyword(s):  
Numerical Simulations ◽  
Fuel Consumption ◽  
Total Variation ◽  
The Sun ◽  
The Moon ◽  
Station Keeping ◽  
Third Body ◽  
Lunisolar Perturbations ◽  
The Earth ◽  
New Criterion

The present paper has the goal of developing a new criterion to search for orbits that minimize the fuel consumption for station-keeping maneuvers. This approach is based on the integral over the time of the perturbing forces. This integral measures the total variation of velocity caused by the perturbations in the spacecraft, which corresponds to the equivalent variation of velocity that an engine should deliver to the spacecraft to compensate the perturbations and to keep its orbit Keplerian all the time. This integral is a characteristic of the orbit and the set of perturbations considered and does not depend on the type of engine used. In this sense, this integral can be seen as a criterion to select the orbit of the spacecraft. When this value becomes larger, more consumption of fuel is required for the station keeping, and, in this sense, less interesting is the orbit. This concept can be applied to any perturbation. In the present research, as an example, the perturbation caused by a third body is considered. Then, numerical simulations considering the effects of the Sun and the Moon in a satellite around the Earth are shown to exemplify the method.

scholarly journals Boundaries for the Equipotential Curves in the Elliptic Restricted Three-Body Problem

1983 ◽  
Vol 74 ◽  
pp. 317-323
Author(s):  
Magda Delva
Keyword(s):  
Body Problem ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Third Body ◽  
Time Intervals ◽  
The Third ◽  
Circular Problem ◽  
Long Time ◽  
Zero Velocity Curves ◽  
Three Body

AbstractIn the elliptic restricted three body problem an invariant relation between the velocity square of the third body and its potential is studied for long time intervals as well as for different values of the eccentricity. This relation, corresponding to the Jacobian integral in the circular problem, contains an integral expression which can be estimated if one assumes that the potential of the third body remains finite. Then upper and lower boundaries for the equipotential curves can be derived. For large eccentricities or long time intervals the upper boundary increases, while the lower decreases, which can be interpreted as shrinking respectively growing zero velocity curves around the primaries.

scholarly journals Stability of the Sitnikov's circular restricted three body problem when the primaries are oblate spheroid

BIBECHANA ◽  
2014 ◽  
Vol 11 ◽  
pp. 149-156
Author(s):  
RR Thapa
Keyword(s):  
Body Problem ◽  
Equilibrium Points ◽  
Oblate Spheroid ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Third Body ◽  
Independent Variable ◽  
The Stability ◽  
Three Body ◽  
Special Case

The Sitnikov's problem is a special case of restricted three body problem if the primaries are of equal masses (m1 = m2 = 1/2) moving in circular orbits under Newtonian force of attraction and the third body of mass m3 moves along the line perpendicular to plane of motion of primaries. Here oblate spheroid primaries are taken. The solution of the Sitnikov's circular restricted three body problem has been checked when the primaries are oblate spheroid. We observed that solution is depended on oblate parameter A of the primaries and independent variable τ = ηt. For this the stability of non-trivial solutions with the characteristic equation is studied. The general equation of motion of the infinitesimal mass under mutual gravitational field of two oblate primaries are seen at equilibrium points. Then the stability of infinitesimal third body m3 has been calculated. DOI: http://dx.doi.org/10.3126/bibechana.v11i0.10395 BIBECHANA 11(1) (2014) 149-156

Periodic Orbits with Low-Thrust Propulsion in the Restricted Three-body Problem

2006 ◽  
Vol 29 (5) ◽  
pp. 1131-1139 ◽  
Author(s):  
Mutsuko Morimoto ◽  
Hiroshi Yamakawa ◽  
Kuninori Uesugi
Keyword(s):  
Periodic Orbits ◽  
Body Problem ◽  
Restricted Three Body Problem ◽  
Low Thrust ◽  
Three Body Problem ◽  
Three Body

scholarly journals Low-Thrust Minimum-Fuel Optimization in the Circular Restricted Three-Body Problem

2015 ◽  
Vol 38 (8) ◽  
pp. 1501-1510 ◽  
Author(s):  
Chen Zhang ◽  
Francesco Topputo ◽  
Franco Bernelli-Zazzera ◽  
Yu-Shan Zhao
Keyword(s):  
Body Problem ◽  
Restricted Three Body Problem ◽  
Low Thrust ◽  
Three Body Problem ◽  
Fuel Optimization ◽  
Three Body

scholarly journals Phasing Maneuver Analysis from a Low Lunar Orbit to a Near Rectilinear Halo Orbit

Aerospace ◽  
2021 ◽  
Vol 8 (3) ◽  
pp. 70
Author(s):  
Giordana Bucchioni ◽  
Mario Innocenti
Keyword(s):  
Body Problem ◽  
Halo Orbit ◽  
Preliminary Design ◽  
Three Body Problem ◽  
Third Body ◽  
Differential Correction ◽  
Target Station ◽  
The Third ◽  
The One ◽  
Three Body

The paper describes the preliminary design of a phasing trajectory in a cislunar environment, where the third body perturbation is considered non-negligible. The working framework is the one proposed by the ESA’s Heracles mission in which a passive target station is in a Near Rectilinear Halo Orbit and an active vehicle must reach that orbit to start a rendezvous procedure. In this scenario the authors examine three different ways to design such phasing maneuver under the circular restricted three-body problem hypotheses: Lambert/differential correction, Hohmann/differential correction and optimization. The three approaches are compared in terms of ΔV consumption, accuracy and time of flight. The selected solution is also validated under the more accurate restricted elliptic three-body problem hypothesis.

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