THE HILL PROBLEM WITH OBLATE SECONDARY: NUMERICAL EXPLORATION

2006 ◽  
Vol 97 (1-2) ◽  
pp. 127-145 ◽  
Author(s):  
A.E. Perdiou ◽  
V.V. Markellos ◽  
C.N. Douskos
Keyword(s):  
Hill Problem ◽  
Numerical Exploration ◽  
Oblate Secondary ◽  
The Hill

Periodic orbits of the Hill problem with radiation and oblateness

2012 ◽  
Vol 342 (1) ◽  
pp. 19-30 ◽  
Author(s):  
A. E. Perdiou ◽  
E. A. Perdios ◽  
V. S. Kalantonis
Keyword(s):  
Periodic Orbits ◽  
Hill Problem ◽  
The Hill

scholarly journals Hill Problem Analytical Theory to the Order Four: Application to the Computation of Frozen Orbits around Planetary Satellites

2009 ◽  
Vol 2009 ◽  
pp. 1-18 ◽  
Author(s):  
Martin Lara ◽  
Jesús F. Palacián
Keyword(s):  
Fourth Order ◽  
Initial Conditions ◽  
Analytical Theory ◽  
Hill Problem ◽  
Frozen Orbits ◽  
Long Period ◽  
Lie Transforms ◽  
Planetary Satellites ◽  
The Hill ◽  
Order Four

Frozen orbits of the Hill problem are determined in the double-averaged problem, where short and long-period terms are removed by means of Lie transforms. Due to the perturbation method we use, the initial conditions of corresponding quasi-periodic solutions in the nonaveraged problem are computed straightforwardly. Moreover, the method provides the explicit equations of the transformation that connects the averaged and nonaveraged models. A fourth-order analytical theory is necessary for the accurate computation of quasi-periodic frozen orbits.

scholarly journals Orbit classification in the Hill problem: I. The classical case

2017 ◽  
Vol 89 (2) ◽  
pp. 901-923 ◽  
Author(s):  
Euaggelos E. Zotos
Keyword(s):  
Classical Case ◽  
Hill Problem ◽  
The Hill

scholarly journals On the Stability ofL4,5in the Relativistic R3BP with Oblate Secondary and Radiating Primary

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Nakone Bello ◽  
Jagadish Singh
Keyword(s):  
Stability Region ◽  
Body Problem ◽  
Critical Mass ◽  
Mass Ratio ◽  
Three Body Problem ◽  
Triangular Points ◽  
Numerical Exploration ◽  
The Stability ◽  
Oblate Secondary ◽  
Three Body

We consider a version of the relativistic restricted three-body problem (R3BP) which includes the effects of oblateness of the secondary and radiation of the primary. We determine the positions and analyze the stability of the triangular points. We find that these positions are affected by relativistic, oblateness, and radiation factors. It is also seen that both oblateness of the secondary and radiation of the primary reduce the size of stability region. Further, a numerical exploration computing the positions of the triangular points and the critical mass ratio of some binaries systems consisting of the Sun and its planets is given in the tables.

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