scholarly journals On the dynamics of Trojan asteroids

1996 ◽  
Vol 172 ◽  
pp. 171-176 ◽  
Author(s):  
B. Érdi
Keyword(s):  
Body Problem ◽  
Three Dimensional ◽  
Dynamical Behaviour ◽  
Three Body Problem ◽  
Orbital Elements ◽  
Orbital Eccentricity ◽  
Trojan Asteroids ◽  
Secular Changes ◽  
Long Time ◽  
Three Body

The author's theory of Trojan asteroids (Érdi, 1988) is developed further. The motion of the Trojans is considered in the framework of the three-dimensional elliptic restricted three-body problem of the Sun-Jupiter-asteroid system including also the secular changes of Jupiter's orbital eccentricity and the apsidal motion of Jupiter's elliptic orbit. An asymptotic solution is derived, by applying the multiple-timescale method, for the cylindrical coordinates of the asteriods and for the perturbations of the orbital elements. This solution is used for the analysis of the long-time dynamical behaviour of the perihelion and the eccentricity of the Trojans.

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 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 Regular and Chaotic Motion in a Restricted Three–Body Problem of Astrophysical Interest

2000 ◽  
Vol 174 ◽  
pp. 281-285 ◽  
Author(s):  
J. C. Muzzio ◽  
F. C. Wachlin ◽  
D. D. Carpintero
Keyword(s):  
External Field ◽  
Body Problem ◽  
Stellar System ◽  
Three Dimensional ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Stellar Orbits ◽  
System A ◽  
Regular And Chaotic Motion ◽  
Three Body

AbstractWe have studied the motion of massless particles (stars) bound to a stellar system (a galactic satellite) that moves on a circular orbit in an external field (a galaxy). A large percentage of the stellar orbits turned out to be chaotic, contrary to what happens in the usual restricted three–body problem of celestial mechanics where most of the orbits are regular. The discrepancy is probably due to three facts: 1) Our study is not limited to orbits on the main planes of symmetry, but considers three–dimensional motion; 2) The force exerted by the satellite goes to zero (rather than to infinity) at the center of the satellite; 3) The potential of the satellite is triaxial, rather than spherical.

scholarly journals Numerical Investigation for Periodic Orbits in the Hill Three-Body Problem

Universe ◽  
2020 ◽  
Vol 6 (6) ◽  
pp. 72 ◽  
Author(s):  
Vassilis S. Kalantonis
Keyword(s):  
Periodic Orbits ◽  
Body Problem ◽  
Numerical Study ◽  
Three Dimensional ◽  
Earth Satellite ◽  
Mission Design ◽  
Special Importance ◽  
Three Body Problem ◽  
Three Body ◽  
The Hill

The current work performs a numerical study on periodic motions of the Hill three-body problem. In particular, by computing the stability of its basic planar families we determine vertical self-resonant (VSR) periodic orbits at which families of three-dimensional periodic orbits bifurcate. It is found that each VSR orbit generates two such families where the multiplicity and symmetry of their member orbits depend on certain property characteristics of the corresponding VSR orbit’s stability. We trace twenty four bifurcated families which are computed and continued up to their natural termination forming thus a manifold of three-dimensional solutions. These solutions are of special importance in the Sun-Earth-Satellite system since they may serve as reference orbits for observations or space mission design.

Resonant Three-Dimensional Periodic Solutions About the Triangular Equilibrium Points in the Restricted Problem

1983 ◽  
Vol 74 ◽  
pp. 235-247 ◽  
Author(s):  
C.G. Zagouras ◽  
V.V. Markellos
Keyword(s):  
Periodic Solutions ◽  
Restricted Problem ◽  
Body Problem ◽  
Equilibrium Points ◽  
Mass Parameter ◽  
Three Dimensional ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Special Values ◽  
Three Body

AbstractIn the three-dimensional restricted three-body problem, the existence of resonant periodic solutions about L4 is shown and expansions for them are constructed for special values of the mass parameter, by means of a perturbation method. These solutions form a second family of periodic orbits bifurcating from the triangular equilibrium point. This bifurcation is the evolution, as μ varies continuously, of a regular vertical bifurcation point on the corresponding family of planar periodic solutions emanating from L4.

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