scholarly journals Periodic Orbits Close to That of the Moon in Hill's Problem

2018 ◽  
Vol 5 ◽  
Author(s):  
Giovanni B. Valsecchi
Keyword(s):  
Periodic Orbits ◽  
The Moon ◽  
Hill’S Problem ◽  
Hill's Problem

scholarly journals Encounter in the Keplerian Field: Analytical Treatment

1993 ◽  
Vol 132 ◽  
pp. 289-289
Author(s):  
V.A. Brumberg ◽  
T.V. Ivanova
Keyword(s):  
Point Of View ◽  
Lunar Theory ◽  
Theoretical Point ◽  
The Sun ◽  
The Moon ◽  
Type Solution ◽  
Analytical Treatment ◽  
Hill’S Problem ◽  
Hill's Problem ◽  
Resonance Character

AbstractIn extending the results of Henon and Petit (Celes.Mech., 38,67, 1986) an algorithm is suggested to construct the series representing the general encounter-type solution of the spatial eccentric Hill’s problem. The series are arranged in powers of the eccentricity E of Hill’s problem and two integration constants e and k characterizing eccentricity and inclination of the relative motion. A particular non-periodic solution of Henon and Petit corresponding to E = e = k = 0 is taken as an intermediary. The perturbations to this solution are constructed similar to the Lunar theory of Hill and Brown with; the Universal Poissonian Processor. From theoretical point of view Hill’s problem for the encounter case is of particular interest. In distinction from the Lunar problem we do not have here angular arguments with different frequencies. Moreover, the perturbations related with the external eccentricity E (analogous to the perturbations in the motion of the motion of the Moon caused by the eccentricity of the orbit of the Sun) are of resonance character.

scholarly journals ANALYZING SHELL STRUCTURE FROM BABYLONIAN AND MODERN TIMES

2004 ◽  
Vol 13 (01) ◽  
pp. 247-260
Author(s):  
LIS BRACK-BERNSEN ◽  
MATTHIAS BRACK
Keyword(s):  
Quantum Dots ◽  
Fourier Analysis ◽  
Periodic Orbits ◽  
Shell Structure ◽  
Metal Clusters ◽  
The Moon ◽  
Modern Times ◽  
Fermion Systems

We investigate "shell structure" from Babylonian times: periodicities and beats in computer-simulated lunar data corresponding to those observed by Babylonian scribes some 2500 years ago. We discuss the mathematical similarity between the Babylonians' recently reconstructed method of determining one of the periods of the moon with modern Fourier analysis and the interpretation of shell structure in finite fermion systems (nuclei, metal clusters, quantum dots) in terms of classical closed or periodic orbits.

scholarly journals On The Stability of Stationary Solutions of the Twice-Averaged Hill’s Problem Taking Into Account The Planet Oblateness

1999 ◽  
Vol 172 ◽  
pp. 457-457
Author(s):  
M.A. Vashkovyak
Keyword(s):  
Orbital Evolution ◽  
Stationary Solutions ◽  
Circular Orbits ◽  
Hill’S Problem ◽  
Hill's Problem ◽  
The Stability

The problem of satellite orbital evolution with the combined influence of a distant perturbing body and the planet oblateness is well known (Laplace, 1805; Lidov, 1962, 1973; Kozai, 1963; Kudielka, 1994, 1997). The case of near-circular orbits is investigated in more details in (Sekiguchi, 1961; Allan and Cook, 1964; Vashkovyak, 1974).

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