Natural highways for end-of-life solutions in the LEO region

Abstract

We present the main findings of a dynamical mapping performed in the Low Earth Orbit region. The results were obtained by propagating an extended grid of initial conditions, considering two different epochs and areato-mass ratios, by means of a singly-averaged numerical propagator. It turns out that dynamical resonances associated with high-degree geopotential harmonics, lunisolar perturbations and solar radiation pressure can open natural deorbiting highways. For area-to-mass ratios typical of the orbiting intact objects, these corridors can be exploited only in combination with the action exerted by the atmospheric drag. For satellites equipped with an area augmentation device, we show the boundary of application of the drag, and where the solar radiation pressure can be exploited.

A frequency portrait of Low Earth Orbits

“…In this paper we studied the evolution of the eccentricity of a large set of orbits both in the time and frequency domains, deepening the work already presented by the authors in [3,4].…”

“…The general results of the LEO dynamical mapping was already extensively described in [3]. In the following, we present the results obtained by assuming the two simplified dynamical models, described in Section 2.1.…”

“…The list of the resonances expected from the theory and found by means of the LEO cartography [3] are shown in Table 1, where the corresponding expression for ψ and the value of α, β, γ are highlighted, together with an index (j = 1, ..11) associated to each resonance. Resonances indexed from 1 to 6 correspond to the conditioṅ ψ =ᾱΩ ±ω ±λ S 0 , withᾱ = 0, 1, and are associated to the zero-order expansion of the SRP disturbing function (e.g., [17,18]).…”

“…Model I is particularly suitable to study the SRP effects on the eccentricity in the case of high A/m objects, when only SRP and drag play a primary role in the evolution. In the case of A/m = 1 m 2 /kg, atmospheric drag is effective in driving a reentry within 25 years for pericenter altitudes up to 1050 km (see [3,22]). Since this is a relatively high value, in order to focus on the effect due to SRP, we have decided to switch off the perturbation due to the atmospheric drag.…”

“…Indeed, the sampling frequency is f s = 1/∆t and, from Nyquist theorem, it follows that f s /2 is the highest frequency we can capture from our analysis. Since the perturbations we are interested in have periodicity of the order of months to years 4 , the sampling ∆t = 1 day, adopted in [11,12,3], is fully reasonable. On the other side, a more critical issue involves the lowest detectable frequency by our analysis, which is limited by 2/T , where T is the duration of the time series.…”