scholarly journals Collinear Equilibrium Points in the Relativistic R3BP when the Bigger Primary is a Triaxial Rigid Body

2017 ◽  
Vol 11 ◽  
pp. 45-56 ◽  
Author(s):  
Bello Nakone ◽  
Aminu Abubakar Hussain
Keyword(s):  
Rigid Body ◽  
Equilibrium Points ◽  
Numerical Approach ◽  
Observable Effect ◽  
Moon System ◽  
The Earth ◽  
Numerical Exploration ◽  
Relativistic Factor ◽  
Triaxial Rigid Body ◽  
Frame Work

This study examines the effect of the relativistic factor as well as the triaxiality effect of the bigger primary on the positions and stability of the collinear points in the frame work of the post-Newtonian approximation. Using semi-analytical and numerical approach the collinear points are found to be unstable. A numerical exploration in this connection, with the Earth-Moon system, reveals that the relativistic factor has an effect on these positions. It is also found that under the combined effect of relativistic factor and triaxiality, the collinear point L1 moves towards the primaries with the increase in triaxiality, while L2 and L3 move away from the bigger primary. It is also seen that in most of the cases in the presence of triaxiality, the effect of relativistic factor on the positions of L1 and L3 is not observable; however it has an observable effect on the position of L2 in the presence of triaxiality except for the case 2.

scholarly journals Pulsating curves of zero velocity for infinitesimal mass around oblate and triaxial rigid body of triangular equilibrium points in elliptical restricted three body problem

2017 ◽  
Vol 5 (1) ◽  
pp. 29
Author(s):  
Nutan Singh ◽  
A. Narayan
Keyword(s):  
Rigid Body ◽  
Body Problem ◽  
Equilibrium Points ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Zero Velocity ◽  
Triaxial Rigid Body ◽  
Three Body ◽  
Infinitesimal Mass

This paper explore pulsating Curves of zero velocityof the infinitesimal mass around the triangular equilibrium points with oblate and triaxial rigid body in the elliptical restricted three body problem(ER3BP).

Chaotic Dynamics in a Low-Energy Transfer Strategy to the Equilateral Equilibrium Points in the Earth–Moon System

2015 ◽  
Vol 25 (05) ◽  
pp. 1550077 ◽  
Author(s):  
F. J. T. Salazar ◽  
E. E. N. Macau ◽  
O. C. Winter
Keyword(s):  
Equilibrium Points ◽  
Low Energy ◽  
The Moon ◽  
Gravity Assist ◽  
Moon System ◽  
Keplerian Orbits ◽  
The Earth ◽  
Chaotic Region ◽  
Gravity Assist Maneuver ◽  
Three Body

In the frame of the equilateral equilibrium points exploration, numerous future space missions will require maximization of payload mass, simultaneously achieving reasonable transfer times. To fulfill this request, low-energy non-Keplerian orbits could be used to reach L4 and L5 in the Earth–Moon system instead of high energetic transfers. Previous studies have shown that chaos in physical systems like the restricted three-body Earth–Moon-particle problem can be used to direct a chaotic trajectory to a target that has been previously considered. In this work, we propose to transfer a spacecraft from a circular Earth Orbit in the chaotic region to the equilateral equilibrium points L4 and L5 in the Earth–Moon system, exploiting the chaotic region that connects the Earth with the Moon and changing the trajectory of the spacecraft (relative to the Earth) by using a gravity assist maneuver with the Moon. Choosing a sequence of small perturbations, the time of flight is reduced and the spacecraft is guided to a proper trajectory so that it uses the Moon's gravitational force to finally arrive at a desired target. In this study, the desired target will be an orbit about the Lagrangian equilibrium points L4 or L5. This strategy is not only more efficient with respect to thrust requirement, but also its time transfer is comparable to other known transfer techniques based on time optimization.

scholarly journals Rotation of the Earth as a triaxial rigid body

2007 ◽  
Vol 10 (2) ◽  
pp. 85-90 ◽  
Author(s):  
Wenbin Shen ◽  
Wei Chen ◽  
Wenjun Wang ◽  
Yiqiang Liang
Keyword(s):  
Rigid Body ◽  
The Earth ◽  
Triaxial Rigid Body ◽  
Rotation Of The Earth

scholarly journals Effects of Radiation Pressure on the Elliptic Restricted Four-Body Problem

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Sahar H. Younis ◽  
M. N. Ismail ◽  
Ghada F. Mohamdien ◽  
A. H. Ibrahiem
Keyword(s):  
Radiation Pressure ◽  
Body Problem ◽  
Equilibrium Points ◽  
Equations Of Motion ◽  
Numerical Approach ◽  
The Earth ◽  
Families Of Periodic Orbits ◽  
Four Body Problem ◽  
The Stability ◽  
Effects Of Radiation

In this paper, under the effects of the largest primary radiation pressure, the elliptic restricted four-body problem is formulated in Hamiltonian form. Moreover, the canonical equations are obtained which are considered as the equations of motion. The Lagrangian points within the frame of the elliptic restricted four-body problem are obtained. The true anomalies are considered as independent variables. An analytical and numerical approach had been used. A code of Mathematica version 12 is constructed to truncate these considerations and is applied on the Earth-Moon-Sun system. In addition, the stability and periodicity of the motion about the equilibrium points are studied by using the Poincare maps. The motion about the collinear point L2 is presented as an example for the obtained results, and some families of periodic orbits are presented.

scholarly journals Some Special Types of Orbits around Jupiter

Aerospace ◽  
2021 ◽  
Vol 8 (7) ◽  
pp. 183
Author(s):  
Yongjie Liu ◽  
Yu Jiang ◽  
Hengnian Li ◽  
Hui Zhang
Keyword(s):  
Gravity Model ◽  
Small Perturbation ◽  
Equilibrium Points ◽  
Major Axis ◽  
Semi Major Axis ◽  
Ground Track ◽  
The Earth ◽  
Degenerate Equilibrium ◽  
The Mean ◽  
Element Theory

This paper intends to show some special types of orbits around Jupiter based on the mean element theory, including stationary orbits, sun-synchronous orbits, orbits at the critical inclination, and repeating ground track orbits. A gravity model concerning only the perturbations of J2 and J4 terms is used here. Compared with special orbits around the Earth, the orbit dynamics differ greatly: (1) There do not exist longitude drifts on stationary orbits due to non-spherical gravity since only J2 and J4 terms are taken into account in the gravity model. All points on stationary orbits are degenerate equilibrium points. Moreover, the satellite will oscillate in the radial and North-South directions after a sufficiently small perturbation of stationary orbits. (2) The inclinations of sun-synchronous orbits are always bigger than 90 degrees, but smaller than those for satellites around the Earth. (3) The critical inclinations are no-longer independent of the semi-major axis and eccentricity of the orbits. The results show that if the eccentricity is small, the critical inclinations will decrease as the altitudes of orbits increase; if the eccentricity is larger, the critical inclinations will increase as the altitudes of orbits increase. (4) The inclinations of repeating ground track orbits are monotonically increasing rapidly with respect to the altitudes of orbits.

Transfers between NRHOs and DROs in the Earth-Moon system

2021 ◽  
Author(s):  
Yue Wang ◽  
Ruikang Zhang ◽  
Chen Zhang ◽  
Hao Zhang
Keyword(s):  
Moon System ◽  
The Earth
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