Abstract
The motion of an artificial satellite is studied considering geopotential perturbations and resonances between the frequencies of the mean orbital motion and the Earth rotational motion. The behavior of the satellite motion is analyzed in the neighborhood of the resonances 15:1. A suitable sequence of canonical transformations reduces the system of differential equations describing the orbital motion to an integrable kernel. The phase space of the resulting system is studied taking into account that one resonant angle is fixed. Simulations are presented showing the variations of the semi-major axis of artificial satellites due to the resonance effects.
Highlights
The problem of resonance effects on orbital motion of satellites falls under a more categorical problem in astrodynamics, which is known as the one of zero divisors
The following procedure, including a sequence of canonical transformations, enables us to analyse the influence of the resonance upon the orbital elements (Lima Jr., 1998): a) canonical variables (X, Y, Z, Θ, x, y, z, Ө) related with the Delaunay variables are introduced by the canonical transformation described as follows: XL
A sequence of canonical transformations enabled us to analyze the influence of the resonance on the orbital elements of artificial satellites with mean motion commensurable with the rotation
Summary
The problem of resonance effects on orbital motion of satellites falls under a more categorical problem in astrodynamics, which is known as the one of zero divisors. The influence of resonances on the orbital and translational motion of artificial satellites has been extensively discussed in the literature under several aspects. The type of resonance considered is the commensurability between the frequencies of the satellite mean orbital motion and the Earth rotational one. Such case of resonance occurs frequently in real cases. In a survey from a sample of 1818 artificial satellites, chosen in a random choice from the NORAD 2-line elements (Celestrak, 2004), about 85% of them are orbiting near
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