Related papers: High-Fidelity Semianalytical Theory for a Low Luna…
The non-integrability of the Hill problem makes that its global dynamics must be necessarily approached numerically. However, the analytical approach is feasible in the computation of relevant solutions. In particular, the nonlinear…
Triple systems with low hierarchical structure are common throughout the Universe, including examples such as high-altitude lunar satellites influenced by the Earth, planetary satellites perturbed by the Sun, and stellar binaries affected…
Consider the action of a connected complex reductive group on a finite-dimensional vector space. A fundamental result in invariant theory states that the orbit closure of a vector v is separated from the origin if and only if some…
Higher-order gravity models have been recently the subject of much attention in the context of cosmic acceleration. These models are derived by adding various curvature invariants to the Einstein-Hilbert action. Several studies showed that…
We propose a general strategy for reduced order modeling of systems that display highly nonlinear oscillations. By considering a continuous family of forced periodic orbits defined in relation to a stable fixed point and subsequently…
Contraction theory for dynamical systems on Euclidean spaces is well-established. For contractive (resp. semi-contractive) systems, the distance (resp. semi-distance) between any two trajectories decreases exponentially fast. For partially…
The planetary dynamics of $4/3$, $3/2$, $5/2$, $3/1$ and $4/1$ mean motion resonances is studied by using the model of the general three body problem in a rotating frame and by determining families of periodic orbits for each resonance.…
With the upcoming launch of large constellations of satellites in the low-Earth orbit (LEO) region it will become important to organize the physical space occupied by the different operating satellites in order to minimize critical…
Using equations of motion accurate to the third post-Newtonian (3PN) order (O(v/c)^6 beyond Newtonian gravity), we derive expressions for the total energy E and angular momentum J of the orbits of compact binary systems (black holes or…
Applying the method of analytical continuation of periodic orbits, we study quasi-satellite motion in the framework of the three-body problem. In the simplest, yet not trivial model, namely the planar circular restricted problem, it is…
Trajectory optimization of low-thrust perturbed orbit rendezvous is a crucial technology for space missions in low Earth orbits, which is difficult to solve due to its initial value sensitivity, especially when the transfer trajectory has…
The Kubo formula for the conductance of a mesoscopic system is analyzed semiclassically, yielding simple expressions for both weak localization and universal conductance fluctuations. In contrast to earlier work which dealt with times…
In this work we present a new methodology for orbit propagation, the hybrid perturbation theory, based on the combination of an integration method and a prediction technique. The former, which can be a numerical, analytical or…
In the framework of the planar and circular restricted three-body problem, we consider an asteroid that orbits the Sun in quasi-satellite motion with a planet. A quasi-satellite trajectory is a heliocentric orbit in co-orbital resonance…
Quasinormal modes describe the ringdown of compact objects deformed by small perturbations. In generic theories of gravity that extend General Relativity, the linearized dynamics of these perturbations is described by a system of coupled…
The aim of this work is to highlight the crucial role that orbital resonances associated with solar radiation pressure can have in Low Earth Orbit. We review the corresponding literature, and provide an analytical tool to estimate the…
We study the orbital evolution of a radiation-damped binary in the extreme mass ratio limit, and the resulting waveforms, to one order beyond what can be obtained using the conservation laws approach. The equations of motion are solved…
Many science missions require an unobstructed view of space and a stable thermal environment but lack the technical or programmatic resources to reach orbits that satisfy these needs. This paper presents a high Earth orbit in 2:1 resonance…
Compact object perturbations, at linear order, often lead in solving one or more coupled wave equations. The study of these equations was typically done by numerical or semi-analytical methods. The WKB method and the associated…
We calculate IR divergent graviton one-loop corrections to scalar correlators in de Sitter space, and show that the leading IR contribution may be reproduced via simple semiclassical consistency relations. One can likewise use such…