scholarly journals A Quantized Hill’s Dynamical System

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Elbaz I. Abouelmagd ◽  
Vassilis S. Kalantonis ◽  
Angela E. Perdiou
Keyword(s):  
Dynamical System ◽  
Body Problem ◽  
Equations Of Motion ◽  
Quantum Corrections ◽  
Mass Ratio ◽  
Three Body Problem ◽  
Hill’S Problem ◽  
Hill's Problem ◽  
Three Body ◽  
Do So

In this paper, we present a modified version of Hill’s dynamical system that is called the quantized Hill’s three-body problem in the sense that the equations of motion for the classical Hill’s problem are now derived under the effects of quantum corrections. To do so, the position variables and the parameters that correspond to the quantum corrections of the respective quantized three-body problem are scaled appropriately, and then by taking the limit when the parameter of mass ratio tends to zero, we obtain the relevant equations of motion for the spatial quantized Hill’s problem. Furthermore, the Hamiltonian formula and related equations of motion are also derived.

scholarly journals On the Stability of Collinear Points of the RTBP with Triaxial and Oblate Primaries and Relativistic Effects

2021 ◽  
pp. 56-73
Author(s):  
S. E. Abd El-Bar
Keyword(s):  
Characteristic Equation ◽  
Body Problem ◽  
Equilibrium Points ◽  
Equations Of Motion ◽  
Relativistic Effects ◽  
Three Body Problem ◽  
Total Potential ◽  
The Mean ◽  
The Stability ◽  
Three Body

Under the influence of some different perturbations, we study the stability of collinear equilibrium points of the Restricted Three Body Problem. More precisely, the perturbations due to the triaxiality of the bigger primary and the oblateness of the smaller primary, in addition to the relativistic effects, are considered. Moreover, the total potential and the mean motion of the problem are obtained. The equations of motion are derived and linearized around the collinear points. For studying the stability of these points, the characteristic equation and its partial derivatives are derived. Two real and two imaginary roots of the characteristic equation are deduced from the plotted figures throughout the manuscript. In addition, the instability of the collinear points is stressed. Finally, we compute some selected roots corresponding to the eigenvalues which are based on some selected values of the perturbing parameters in the Tables 1, 2.

Orbits of Trojan Asteroids

1974 ◽  
Vol 62 ◽  
pp. 63-69 ◽  
Author(s):  
G. A. Chebotarev ◽  
N. A. Belyaev ◽  
R. P. Eremenko
Keyword(s):  
Solar System ◽  
Body Problem ◽  
Equations Of Motion ◽  
Orbital Evolution ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Trojan Asteroids ◽  
Actual Motion ◽  
Three Body

In this paper the orbital evolution of Trojan asteroids are studied by integrating numerically the equations of motion over the interval 1660–2060, perturbations from Venus to Pluto being taken into account. The comparison of the actual motion of Trojans in the solar system with the theory based on the restricted three-body problem are given.

scholarly journals Progression of bifurcated family f type periodic orbits in the circular restricted three-body problem

2017 ◽  
Vol 5 (2) ◽  
pp. 69
Author(s):  
Nishanth Pushparaj ◽  
Ram Krishan Sharma
Keyword(s):  
Solar Radiation ◽  
Periodic Orbits ◽  
Radiation Pressure ◽  
Body Problem ◽  
Solar Radiation Pressure ◽  
Restricted Three Body Problem ◽  
Mass Ratio ◽  
Three Body Problem ◽  
Semi Major Axis ◽  
Three Body

Progression of f-type family of periodic orbits, their nature, stability and location nearer the smaller primary for different mass ratios in the framework of circular restricted three-body problem is studied using Poincaré surfaces of section. The orbits around the smaller primary are found to decrease in size with increase in Jacobian Constant C, and move very close towards the smaller primary. The orbit bifurcates into two orbits with the increase in C to 4.2. The two orbits that appear for this value of C belong to two adjacent separate families: one as direct orbit belonging to family g of periodic orbits and other one as retrograde orbit belonging to family f of periodic orbits. This bifurcation is interesting. These orbits increase in size with increase in mass ratio. The elliptic orbits found within the mass ratio 0 < µ ≤ 0.1 have eccentricity less than 0.2 and the orbits found above the mass ratio µ > 0.1 are elliptical orbits with eccentricity above 0.2. Deviations in the parameters: eccentricity, semi-major axis and time period of these orbits with solar radiation pressure q are computed in the frame work of photogravitational restricted Three-body problem in addition to the restricted three-body problem. These parameters are found to decrease with increase in the solar radiation pressure.

scholarly journals Orbital stability of high inclination asteroids

1996 ◽  
Vol 172 ◽  
pp. 187-192
Author(s):  
N. A. Solovaya ◽  
E. M. Pittich
Keyword(s):  
Solar System ◽  
Body Problem ◽  
Equations Of Motion ◽  
Orbital Stability ◽  
Dynamical Model ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Three Body

The orbital evolutions of fictitious asteroids with high inclinations have been investigated. The selected initial orbits represent asteroids with movement, which corresponds to the conditions of the Tisserand invariant for C = C (L1) in the restricted three body problem. Initial eccentricities of the orbits cover the interval 0.0–0.4, inclinations the interval 40–80°, and arguments of perihelion the interval 0–360°. The equations of motion of the asteroids were numerically integrated from the epoch March 25, 1991 forward within the interval of 20,000 years, using a dynamical model of the solar system consisting of all planets. The orbits of the model asteroids are stable at least during the investigated period.

scholarly journals Stationary solutions, critical mass, Tadpole orbits in the circular restricted three-body problem with the more massive primary as an oblate spheroid

2020 ◽  
Vol 13 (39) ◽  
pp. 4168-4188
Author(s):  
A Arantza Jency
Keyword(s):  
Body Problem ◽  
Equilibrium Points ◽  
Critical Mass ◽  
Equations Of Motion ◽  
Oblate Spheroid ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Mean Motion ◽  
The Mean ◽  
Three Body

Background: The location and stability of the equilibrium points are studied for the Planar Circular Restricted Three-Body Problem where the more massive primary is an oblate spheroid. Methods: The mean motion of the equations of motion is formulated from the secular perturbations as derived by(1) and used in(2–4). The singularities of the equations of motion are found for locating the equilibrium points. Their stability is analysed using the linearized variational equations of motion at the equilibrium points. Findings: As the effect of oblateness in the mean motion expression increases, the location and stability of the equilibrium points are affected by the oblateness of the more massive primary. It is interesting to note that all the three collinear points move towards the more massive primary with oblateness. It is a new result. Among the shifts in the locations of the five equilibrium points, the y–location of the triangular equilibrium points relocate the most. It is very interesting to note that the eccentricities (e) of the orbits around L1 and L3 increase, while it decreases around L2 with the addition of oblateness with the new mean motion. The decrease in e is significant in Saturn-Mimas system from 0.95036 to 0.87558. Similarly, the value of the critical mass ratio mc, which sets the limit for the linear stability of the triangular points, further reduces significantly from 0:285: : :A1 to 0:365: : :A1 with the new mean motion. The mean motion sz in the z-direction increases significantly with the new mean motion from 9A1/4 to 9A1/2.

scholarly journals Retrograde Satellites in the Circular Plane Restricted Three-Body Problem

1974 ◽  
Vol 62 ◽  
pp. 129-129
Author(s):  
D. Benest
Keyword(s):  
Body Problem ◽  
Restricted Three Body Problem ◽  
Mass Ratio ◽  
Three Body Problem ◽  
Three Body ◽  
Circular Plane

Characteristics and stability of simple-periodic retrograde satellites of the lighter body are presented for Hill's case and for all values of the mass ratio m2/(m1+m2) between 0 and 0.5.

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