Related papers: The Long-Term Forecast of Station View Periods for…
Quantifying long-term statistical properties of satellite trajectories typically entails time-consuming trajectory propagation. We present a fast, ergodic\cite{Arnold} method of analytically estimating these for $J_2-$perturbed elliptical…
The propagation time of a signal, emitted by a moving along an elliptical orbit satellite from the GPS (or GLONASS) satellite confi gurations is a very important ingredient of the theory, based on the formalism of the null cone and…
Existing analyses of ergodic capacity in satellite mega-constellations often rely on restrictive serving time assumptions or become intractable under realistic handover strategies. This paper develops a framework for characterising the…
A method is proposed for constraining the Galactic gravitational potential from high precision observations of the phase space coordinates of a system of relaxed tracers. The method relies on an "ergodic" assumption that the observations…
We present a new method of analysis of measure-preserving dynamical systems, based on frequency analysis and ergodic theory, which extends our earlier work [1]. Our method employs the novel concept of harmonic time average [2], and is…
This paper presents a unique approach to the problem of calculating revisit time metrics for different satellite orbits, sensor geometries, and constellation configurations with application to early lifecycle design and optimisation…
We present a computational study of a visualization method for invariant sets based on ergodic partition theory, first proposed in [1,2]. The algorithms for computation of the time averages of observables on phase space are developed and…
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…
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…
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…
Ergodic Optimization is the process of finding invariant probability measures that maximize the integral of a given function. It has been conjectured that "most" functions are optimized by measures supported on a periodic orbit, and it has…
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…
Low Earth orbit (LEO) satellites are being considered for expanding legacy terrestrial cellular networks. The end users may not be able to optimize satellite orbits and constellations, however, they can optimize locations of ground stations…
We form a sequence of oblong matrices by evaluating an integrable vector-valued function along the orbit of an ergodic dynamical system. We obtain an almost sure asymptotic result for the permanents of those matrices. We also give an…
Topical observations of the thermosphere at altitudes below $200 \, km$ are of great benefit in advancing the understanding of the global distribution of mass, composition, and dynamical responses to geomagnetic forcing, and momentum…
This report provides some closed form solutions -- and their inversion -- to a satellite's bounded motion on the equatorial plane of a spheroidal attractor (planet) considering the $J_{2}$ spherical zonal harmonic. The equatorial track 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 primary objective of this paper is to construct an analytical model for determining the total duration of eclipse events of satellites. The approach assumes that the trace formed in the orbital plane, cutting body shadow under the…
We propose a novel scheme for surveillance of a dynamic ground convoy moving along a non-linear trajectory, by aerial agents that maintain a uniformly spaced formation on a time-varying elliptical orbit encompassing the convoy. Elliptical…
In this paper, we overlay a continuum of analytical relations which essentially serve to compute the arc-length described by a celestial body in an elliptic orbit within a stipulated time interval. The formalism is based upon a…