scholarly journals Analysis of Periodic Orbits with Smaller Primary As Oblate Spheroid

10.29007/1r5v ◽  
2018 ◽  
Author(s):  
Niraj Pathak ◽  
V. O. Thomas
Keyword(s):  
Periodic Orbits ◽  
Oblate Spheroid ◽  
Space Mission ◽  
Low Energy ◽  
Negligible Effect ◽  
Second Primary ◽  
Jacobi Constant ◽  
Earth Systems ◽  
Two Systems ◽  
Surface Section

We have studied closed periodic orbits with loops for two systems – Sun – Mars and Sun – Earth systems – using Poincare surface section (PSS) technique. Perturbation due to oblateness for the second primary (Mars or Earth) is taken in to consideration and obtained orbits with loops varying from one to five around both primaries. It is found that the oblateness coefficient A2 and Jacobi constant C has non- negligible effect on the position of the orbits. The model may be useful for designing space mission for low – energy trajectories.

Characterization of Families of Low-Energy Transfers to Cislunar Four-Body Quasi-Periodic Orbits

2022 ◽  
Author(s):  
Brian McCarthy ◽  
Kathleen C. Howell
Keyword(s):  
Periodic Orbits ◽  
Low Energy ◽  
Energy Transfers ◽  
Low Energy Transfers

scholarly journals On Tonelli periodic orbits with low energy on surfaces

2018 ◽  
Vol 371 (5) ◽  
pp. 3001-3048 ◽  
Author(s):  
Luca Asselle ◽  
Marco Mazzucchelli
Keyword(s):  
Periodic Orbits ◽  
Low Energy

scholarly journals Building CX peanut-shaped disk galaxy profiles

2018 ◽  
Vol 612 ◽  
pp. A114 ◽  
Author(s):  
P. A. Patsis ◽  
M. Harsoula
Keyword(s):  
Phase Space ◽  
Periodic Orbits ◽  
Three Dimensional ◽  
Resonance Region ◽  
Space Structure ◽  
Jacobi Constant ◽  
Dynamical Mechanism ◽  
Standard Case ◽  
New Model ◽  
Stable Periodic

Context. We present and discuss the orbital content of a rather unusual rotating barred galaxy model, in which the three-dimensional (3D) family, bifurcating from x1 at the 2:1 vertical resonance with the known “frown-smile” side-on morphology, is unstable. Aims. Our goal is to study the differences that occur in the phase space structure at the vertical 2:1 resonance region in this case, with respect to the known, well studied, standard case, in which the families with the frown-smile profiles are stable and support an X-shaped morphology. Methods. The potential used in the study originates in a frozen snapshot of an N-body simulation in which a fast bar has evolved. We follow the evolution of the vertical stability of the central family of periodic orbits as a function of the energy (Jacobi constant) and we investigate the phase space content by means of spaces of section. Results. The two bifurcating families at the vertical 2:1 resonance region of the new model change their stability with respect to that of most studied analytic potentials. The structure in the side-on view that is directly supported by the trapping of quasi-periodic orbits around 3D stable periodic orbits has now an infinity symbol (i.e. ∞-type) profile. However, the available sticky orbits can reinforce other types of side-on morphologies as well. Conclusions. In the new model, the dynamical mechanism of trapping quasi-periodic orbits around the 3D stable periodic orbits that build the peanut, supports the ∞-type profile. The same mechanism in the standard case supports the X shape with the frown-smile orbits. Nevertheless, in both cases (i.e. in the new and in the standard model) a combination of 3D quasi-periodic orbits around the stable x1 family with sticky orbits can support a profile reminiscent of the shape of the orbits of the 3D unstable family existing in each model.

scholarly journals On the Conley conjecture for Reeb flows

2015 ◽  
Vol 26 (07) ◽  
pp. 1550047 ◽  
Author(s):  
Viktor L. Ginzburg ◽  
Başak Z. Gürel ◽  
Leonardo Macarini
Keyword(s):  
Magnetic Field ◽  
Energy Level ◽  
Periodic Orbits ◽  
Geodesic Flow ◽  
Low Energy ◽  
Contact Manifolds ◽  
Reeb Flows ◽  
Circle Bundles ◽  
Conley Conjecture

In this paper, we prove the existence of infinitely many closed Reeb orbits for a certain class of contact manifolds. This result can be viewed as a contact analogue of the Hamiltonian Conley conjecture. The manifolds for which the contact Conley conjecture is established are the pre-quantization circle bundles with aspherical base. As an application, we prove that for a surface of genus at least two with a non-vanishing magnetic field, the twisted geodesic flow has infinitely many periodic orbits on every low energy level.

Periodic orbits around an oblate spheroid

1981 ◽  
Vol 23 (2) ◽  
pp. 145-158 ◽  
Author(s):  
I. Stellmacher
Keyword(s):  
Periodic Orbits ◽  
Oblate Spheroid

scholarly journals The effect of zonal harmonics on dynamical structures in the circular restricted three-body problem near the secondary body

2020 ◽  
Vol 132 (9) ◽  
Author(s):  
Luke Bury ◽  
Jay McMahon
Keyword(s):  
Periodic Orbits ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Dynamic Environment ◽  
Smooth Transition ◽  
Mission Design ◽  
Jacobi Constant ◽  
Zonal Harmonic ◽  
Outer Planets ◽  
Three Body

Abstract The circular restricted three-body model is widely used for astrodynamical studies in systems where two major bodies are present. However, this model relies on many simplifications, such as point-mass gravity and planar, circular orbits of the bodies, and limiting its accuracy. In an effort to achieve higher-fidelity results while maintaining the autonomous simplicity of the classic model, we employ zonal harmonic perturbations since they are symmetric about the z-axis, thus bearing no time-dependent terms. In this study, we focus on how these perturbations affect the dynamic environment near the secondary body in real systems. Concise, easily implementable equations for gravitational potential, particle motion, and modified Jacobi constant in the perturbed model are presented. These perturbations cause a change in the normalized mean motion, and two different formulations are addressed for assigning this new value. The shifting of collinear equilibrium points in many real systems due to $$J_2$$ J 2 of each body is reported, and we study how families of common periodic orbits—Lyapunov, vertical, and southern halo—shift and distort when $$J_2$$ J 2 , $$J_4$$ J 4 , and $$J_6$$ J 6 of the primary and $$J_2$$ J 2 of the secondary body are accounted for in the Jupiter–Europa and Saturn–Enceladus systems. It is found that these families of periodic orbits change shape, position, and energy, which can lead to dramatically different dynamical behavior in some cases. The primary focus is on moons of the outer planets, many of which have very small odd zonal harmonic terms, or no measured value at all, so while the developed equations are meant for any and all zonal harmonic terms, only even terms are considered in the simulations. Early utilization of this refined CR3BP model in mission design will result in a more smooth transition to full ephemeris model.

scholarly journals Periodic Orbits of the First Kind in the Restricted Three-Body Problem When the More Massive Primary is an Oblate Spheroid

1978 ◽  
Vol 41 ◽  
pp. 355-355
Author(s):  
R.K. Sharma
Keyword(s):  
Analytic Continuation ◽  
Periodic Orbits ◽  
Equatorial Plane ◽  
Body Problem ◽  
Oblate Spheroid ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Canonical Variables ◽  
Three Body

AbstractThe existence of periodic orbits of the first kind using Delaunay’s canonical variables is established through analytic continuation in the planar restricted three-body problem when the more massive primary is an oblate spheroid with its equatorial plane coincident with the plane of motion.

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