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This paper presents an autonomous guidance and control strategy for a satellite swarm that enables scalable distributed space structures for innovative science and business opportunities. The averaged $J_2$ orbital parameters that describe…
Here we present an ergodic theorem which adapts a Theorem by J. Elton to the classical thermodynamical formalism and to ergodic transport. First, we discuss how Elton's theorem can be used to characterise Gibbs measures for expanding maps.…
We have carried out a numerical investigation of the coupled gravitational and non-gravitational perturbations acting on Earth satellite orbits in an extensive grid, covering the whole circumterrestrial space, using an appropriately…
Two new intermediary orbits of the artificial satellite problem are proposed. The analytical solutions include higher order effects of the Geopotential, and are obtained by means of a torsion transformation applied to the quasi-Keplerian…
We study the optimization of ergodic averages for multi-valued dynamical systems, i.e. where points may have multiple different forward orbits. Under upper semi-continuity assumptions, we show that the maximum space average with respect to…
We proposed a learning algorithm for nonparametric estimation and on-line prediction for general stationary ergodic sources. We prepare histograms each of which estimates the probability as a finite distribution, and mixture them with…
Placing satellites in geostationary obital (GEO) is propellant exigeant. It requires large propellant consumption that will take a large part of the total mass. Hence the interest is reduce the mass of propellant loaded both in the rocket…
We study the estimation of the value function for continuous-time Markov diffusion processes using a single, discretely observed ergodic trajectory. Our work provides non-asymptotic statistical guarantees for the least-squares…
We propose a method to account for the Earth oblateness effect in preliminary orbit determination of satellites in low orbits with radar observations. This method is an improvement of the one described in (Gronchi et al 2015), which uses a…
In this paper, the routing in massive low earth orbit (LEO) satellite networks is studied. When the satellite-to-satellite communication distance is limited, we choose different relay satellites to minimize the latency in a constellation at…
Orbital parameters, such as eccentricity and maximum vertical excursion, of stars in the Milky Way are an important tool for understanding its dynamics and evolution, but calculation of such parameters usually relies on…
A major topic of (classical) ergodic theory is to examine qualitatively how the phase space of dynamical systems is penetrated by the orbits of their dynamics. We consider interacting qubit systems with dynamics according to 4-local…
Numerical computation of shortest paths or geodesics on curved domains, as well as the associated geodesic distance, arises in a broad range of applications across digital geometry processing, scientific computing, computer graphics, and…
The long-term dynamics of the geostationary Earth orbits (GEO) is revisited through the application of canonical perturbation theory. We consider a Hamiltonian model accounting for all major perturbations: geopotential at order and degree…
Today's Low Earth Orbit (LEO) satellite networks, exemplified by SpaceX's Starlink, play a crucial role in delivering global internet access to millions of users. However, managing the dynamic and expansive nature of these networks poses…
We statistically compare the relationships between frequencies of digits in continued fraction expansions of typical rational points in the unit interval and higher dimensional generalisations. This takes the form of a Large Deviation and…
Weierstrass elliptic and related functions have been recently shown to enable analytical explicit solutions to classical problems in astrodynamics. These include the constant radial acceleration problem, the Stark problem and the two-fixed…
We propose an addition of known elliptical orbits to the new equatorial O3b satellite constellation, extending O3b to cover high latitudes and the Earth's poles. We simulate the O3b constellation and compare this to recent measurement of…
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 Internet is going through a massive infrastructural revolution with the advent of low-flying satellite networks, 5/6G, WiFi7, and hollow-core fiber deployments. While these networks could unleash enhanced connectivity and new…