Related papers: Solution to the main problem of the artificial sat…
The main effects of the Earth's oblateness on the motion of artificial satellites are usually derived from the variation of parameters equations of an average representation of the oblateness disturbing function. Rather, we approach their…
In the context of general perturbation theories, the main problem of the artificial satellite analyses the motion of an orbiter around an Earth-like planet, only perturbed by its equatorial bulge or J2 effect. By means of a Lie transform…
The acclaimed merits of analytical solutions based on a fictitious time developed in the 1970's were partially overvalued due to a common misuse of classical analytical solutions based on the physical time that were taken as reference. With…
Analytical integration in Artificial Satellite Theory may benefit from different canonical simplification techniques, like the elimination of the parallax, the relegation of the nodes, or the elimination of the perigee. These techniques…
Brouwer's solution to the artificial satellite problem is revisited to show that the complete Hamiltonian reduction is rather achieved in the plain Poincar\'e's style, through a single canonical transformation, than using a sequence of…
When dealing with satellites orbiting a central body on a highly elliptical orbit, it is necessary to consider the effect of gravitational perturbations due to external bodies. Indeed, these perturbations can become very important as soon…
Normal form stability estimates are a basic tool of Celestial Mechanics for characterizing the long-term stability of the orbits of natural and artificial bodies. Using high-order normal form constructions, we provide three different…
The merits of a perturbation theory based on a mean to osculating transformation that is pure periodic in the fast angle are investigated. The exact separation of the purely short-period effects of the perturbed Keplerian dynamics from the…
We study the resonant dynamics in a simple one degree of freedom, time dependent Hamiltonian model describing spin-orbit interactions. The equations of motion admit periodic solutions associated with resonant motions, the most important…
This paper is related to our previous works [1][2] on the error estimate of the averaging technique, for systems with one fast angular variable. In the cited references, a general method (of mixed analytical and numerical type) has been…
A popular intermediary in the theory of artificial satellites is obtained after the elimination of parallactic terms from the J2-problem Hamiltonian. The resulting quasi-Keplerian system is in turn converted into the Kepler problem by a…
We provide stability estimates, obtained by implementing the Nekhoroshev theorem, in reference to the orbital motion of a small body (satellite or space debris) around the Earth. We consider a Hamiltonian model, averaged over fast angles,…
This work introduces a Hamiltonian approach to regularization and linearization of central-force particle dynamics through a new canonical extension of the so-called "projective decomposition". The regularization scheme is formulated within…
We develop a rigorous analytical Hamiltonian formalism adapted to the study of the motion of two planets in co-orbital resonance. By constructing a complex domain of holomorphy for the planetary Hamilto-nian, we estimate the size of the…
Over short time intervals planetary ephemerides have been traditionally represented in analytical form as finite sums of periodic terms or sums of Poisson terms that are periodic terms with polynomial amplitudes. Nevertheless, this…
We provide an analytical approximation to the dynamics in each of the three most important low order secondary resonances (1:1, 2:1, and 3:1) bifurcating from the synchronous primary resonance in the gravitational spin-orbit problem. To…
The numerical integration method has been routinely used to produce global standard gravitational models from satellite tracking measurements of CHAMP/GRACE types. It is implemented by solving the differential equations of the partial…
Traditional analytical theories of celestial mechanics are not well-adapted when dealing with highly elliptical orbits. On the one hand, analytical solutions are quite generally expanded into power series of the eccentricity and so limited…
The Galilean satellites' dynamics has been studied extensively during the last century. In the past it was common to use analytical expansions in order to get simple models to integrate, but with the new generation computers it became…
An analytical method for solving the problem of the satellite around the oblated Earth is discussed. Such a method goes back to Dirk Brouwer (1959) and seems to be still widely used in real applications. We reformulate in a more concise way…