The Planetary Disturbing Function

1995 ◽  
pp. 99-119
Author(s):  
Victor A. Brumberg
Keyword(s):  
Disturbing Function ◽  
Planetary Disturbing Function

Expansion of the planetary disturbing function

1971 ◽  
Vol 4 (3-4) ◽  
pp. 490-499 ◽  
Author(s):  
R. Broucke ◽  
G. Smith
Keyword(s):  
Disturbing Function ◽  
Planetary Disturbing Function

Expansion of the first-order planetary disturbing function by Smart's method

1989 ◽  
Vol 47 (3) ◽  
pp. 241-263 ◽  
Author(s):  
Osman M. Kamel ◽  
Adel S. Soliman
Keyword(s):  
Disturbing Function ◽  
First Order ◽  
Planetary Disturbing Function

On the expansion of planetary disturbing function

1988 ◽  
Vol 42 (3) ◽  
pp. 221-226 ◽  
Author(s):  
Osman M. Kamel
Keyword(s):  
Disturbing Function ◽  
Planetary Disturbing Function

scholarly journals A new expansion of planetary disturbing function and applications to interior, co-orbital and exterior resonances with planets

2022 ◽  
Vol 21 (12) ◽  
pp. 311
Author(s):  
Han-Lun Lei
Keyword(s):  
Semimajor Axis ◽  
Disturbing Function ◽  
Circular Orbits ◽  
Mean Motion Resonances ◽  
Mean Motion ◽  
Planetary Disturbing Function ◽  
Resonant Dynamics ◽  
The Mean ◽  
Analytical Expansion ◽  
Orbital Resonances

Abstract In this study, a new expansion of planetary disturbing function is developed for describing the resonant dynamics of minor bodies with arbitrary inclinations and semimajor axis ratios. In practice, the disturbing function is expanded around circular orbits in the first step and then, in the second step, the resulting mutual interaction between circular orbits is expanded around a reference point. As usual, the resulting expansion is presented in the Fourier series form, where the force amplitudes are dependent on the semimajor axis, eccentricity and inclination, and the harmonic arguments are linear combinations of the mean longitude, longitude of pericenter and longitude of ascending node of each mass. The resulting new expansion is valid for arbitrary inclinations and semimajor axis ratios. In the case of mean motion resonant configuration, the disturbing function can be easily averaged to produce the analytical expansion of resonant disturbing function. Based on the analytical expansion, the Hamiltonian model of mean motion resonances is formulated, and the resulting analytical developments are applied to Jupiter’s inner and co-orbital resonances and Neptune’s exterior resonances. Analytical expansion is validated by comparing the analytical results with the associated numerical outcomes.

Expansion of the first order planetary disturbing function by Smart's method

1990 ◽  
Vol 48 (2) ◽  
pp. 165-170 ◽  
Author(s):  
Osman M. Kamel ◽  
Adel S. Soliman
Keyword(s):  
Disturbing Function ◽  
First Order ◽  
Planetary Disturbing Function

scholarly journals Analytical development of the planetary disturbing function on a digital computer

1966 ◽  
Vol 25 ◽  
pp. 230-234 ◽  
Author(s):  
I. G. Izsak
Keyword(s):  
Power Series ◽  
Computer Program ◽  
Trigonometric Series ◽  
Digital Computer ◽  
Disturbing Function ◽  
Planetary Disturbing Function ◽  
Analytical Development

A computer program is described for the analytical development of the planetary disturbing function in the form of a fourfold trigonometric series with threefold power series as coefficients.

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