28 research outputs found
Towards a sustainable exploitation of the geosynchronous orbital region
In this work the orbital dynamics of Earth satellites about the
geosynchronous altitude are explored, with primary goal to assess current
mitigation guidelines as well as to discuss the future exploitation of the
region. A thorough dynamical mapping was conducted in a high-definition grid of
orbital elements, enabled by a fast and accurate semi-analytical propagator,
which considers all the relevant perturbations. The results are presented in
appropriately selected stability maps to highlight the underlying mechanisms
and their interplay, that can lead to stable graveyard orbits or fast re-entry
pathways. The natural separation of the long-term evolution between equatorial
and inclined satellites is discussed in terms of post-mission disposal
strategies. Moreover, we confirm the existence of an effective cleansing
mechanism for inclined geosynchronous satellites and discuss its implications
in terms of current guidelines as well as alternative mission designs that
could lead to a sustainable use of the geosynchronous orbital region.Comment: Accepted for publication in Celestial Mechanics and Dynamical
Astronom
Drift and its mediation in terrestrial orbits
The slow deformation of terrestrial orbits in the medium range, subject to
lunisolar resonances, is well approximated by a family of Hamiltonian flow with
degree-of-freedom. The action variables of the system may experience
chaotic variations and large drift that we may quantify. Using variational
chaos indicators, we compute high-resolution portraits of the action space.
Such refined meshes allow to reveal the existence of tori and structures
filling chaotic regions. Our elaborate computations allow us to isolate precise
initial conditions near specific zones of interest and study their asymptotic
behaviour in time. Borrowing classical techniques of phase- space
visualisation, we highlight how the drift is mediated by the complement of the
numerically detected KAM tori.Comment: 22 pages, 11 figures, 1 table, 52 references. Comments and feedbacks
greatly appreciated. This article is part of the Research Topic `The
Earth-Moon System as a Dynamical Laboratory', confer
https://www.frontiersin.org/research-topics/5819/the-earth-moon-system-as-a-dynamical-laborator
Accurate modelling of the low-order secondary resonances in the spin-orbit problem
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 this end we extend the perturbative approach introduced in Gkolias et. al.
(2016), based on normal form series computations. This allows to recover
analytically all non-trivial features of the phase space topology and
bifurcations associated with these resonances. Applications include the
characterization of spin states of irregular planetary satellites or double
systems of minor bodies with irregular shapes. The key ingredients of our
method are: i) the use of a detuning parameter measuring the distance from the
exact resonance, and ii) an efficient scheme to `book-keep' the series terms,
which allows to simultaneously treat all small parameters entering the problem.
Explicit formulas are provided for each secondary resonance, yielding i) the
time evolution of the spin state, ii) the form of phase portraits, iii) initial
conditions and stability for periodic solutions, and iv) bifurcation diagrams
associated with the periodic orbits. We give also error estimates of the
method, based on analyzing the asymptotic behavior of the remainder of the
normal form series.Comment: Accepted for publication in Communications in Nonlinear Science and
Numerical Simulatio
Hamiltonian formulation of the spin-orbit model with time-varying non-conservative forces
In a realistic scenario, the evolution of the rotational dynamics of a
celestial or artificial body is subject to dissipative effects. Time-varying
non-conservative forces can be due to, for example, a variation of the moments
of inertia or to tidal interactions. In this work, we consider a simplified
model describing the rotational dynamics, known as the spin-orbit problem,
where we assume that the orbital motion is provided by a fixed Keplerian
ellipse. We consider different examples in which a non-conservative force acts
on the model and we propose an analytical method, which reduces the system to a
Hamiltonian framework. In particular, we compute a time parametrisation in a
series form, which allows us to transform the original system into a
Hamiltonian one. We also provide applications of our method to study the
rotational motion of a body with time-varying moments of inertia, e.g. an
artificial satellite with flexible components, as well as subject to a tidal
torque depending linearly on the velocity.Comment: Accepted for publication in Communications in Nonlinear Science and
Numerical Simulatio
The theory of secondary resonances in the spin-orbit problem
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 being the synchronous one in which most evolved satellites of the
Solar system, including the Moon, are observed. Such primary resonances can be
surrounded by a chain of smaller islands which one refers to as secondary
resonances. Here, we propose a novel canonical normalization procedure allowing
to obtain a higher order normal form, by which we obtain analytical results on
the stability of the primary resonances as well as on the bifurcation
thresholds of the secondary resonances. The procedure makes use of the
expansion in a parameter, called the detuning, measuring the shift from the
exact secondary resonance. Also, we implement the so-called `book-keeping'
method, i.e., the introduction of a suitable separation of the terms in orders
of smallness in the normal form construction, which deals simultaneously with
all the small parameters of the problem. Our analytical computation of the
bifurcation curves is in excellent agreement with the results obtained by a
numerical integration of the equations of motion, thus providing relevant
information on the parameter regions where satellites can be found in a stable
configuration.Comment: Accepted for publication in MNRA
From order to chaos in Earth satellite orbits
We consider Earth satellite orbits in the range of semi-major axes where the
perturbing effects of Earth's oblateness and lunisolar gravity are of
comparable order. This range covers the medium-Earth orbits (MEO) of the Global
Navigation Satellite Systems and the geosynchronous orbits (GEO) of the
communication satellites. We recall a secular and quadrupolar model, based on
the Milankovitch vector formulation of perturbation theory, which governs the
long-term orbital evolution subject to the predominant gravitational
interactions. We study the global dynamics of this two-and-a-half
degrees-of-freedom Hamiltonian system by means of the fast Lyapunov indicator
(FLI), used in a statistical sense. Specifically, we characterize the degree of
chaoticity of the action space using angle-averaged normalized FLI maps,
thereby overcoming the angle dependencies of the conventional stability maps.
Emphasis is placed upon the phase-space structures near secular resonances,
which are of first importance to the space debris community. We confirm and
quantify the transition from order to chaos in MEO, stemming from the critical
inclinations, and find that highly inclined GEO orbits are particularly
unstable. Despite their reputed normality, Earth satellite orbits can possess
an extraordinarily rich spectrum of dynamical behaviors, and, from a
mathematical perspective, have all the complications that make them very
interesting candidates for testing the modern tools of chaos theory.Comment: 30 pages, 9 figures. Accepted for publication in the Astronomical
Journa
Efficient Trajectory Design for Distant Planetary Orbiters
Starting from the Hamiltonian representation of the dynamics in
\cite{rosengren2015chaos,colombo2019long}, this work proposes an innovative
procedure to design fully-analytical maneuvers for post-mission disposal of
HEOs satellites, exploiting the third-body perturbations. The Hamiltonian
representation has been selected to include the external perturbing effects and
to obtain a phase space representation. Notably, the orbit evolution can be
described through the variation of double-averaged orbital elements over the
orbital periods of the spacecraft and the perturbing bodies around the central
planet. this work conveys a two-dimensional Hamiltonian representation under
the third-body perturbations and the central planet's oblateness. The effect of
solar radiation pressure has been neglected in this analysis