Semi-analytical investigations of high area-to-mass ratio geosynchronous space debris including Earth’s shadowing effects

This paper investigates the long-term perturbations of the orbits of geosynchronous space debris influenced by direct radiation pressure including the Earth’s shadowing effects. For this purpose, we propose an extension of our homemade semi-analytical theory [Valk, S., Lemaître, A., Deleflie, F. Semi-analytical theory of mean orbital motion for geosynchronous space debris under gravitational influence. Adv. Space Res., submitted for publication], based on the method developed by Aksnes [Aksnes, K. Short-period and long-period perturbations of a spherical satellite due to direct solar radiation. Celest. Mech. Dyn. Astron. 13, 89–104, 1976] and generalized into a more convenient non-singular formalism. The perturbations accounting for the direct radiation pressure with the Earth’s shadow are computed on a revolution-by-revolution basis, retaining the original osculating Hamiltonian disturbing function. In this framework, we compute the non-singular mean longitude at shadow entry and shadow exit at every orbital revolution in opposition to classical approaches where the singular eccentric anomalies at shadow entry and shadow exit are computed. This new algorithm is developed using non-singular variables. Consequently, it is particularly suitable for both near-circular and near-equatorial orbits as well as orbits which transit periodically around null eccentricities and null inclinations.The algorithm is tested by means of numerical integrations of the equations, averaged over the short periods, including radiation pressure, J₂, the combined Moon and Sun third body attraction as well as the long-term effects of the 1:1 resonance occurring for geosynchronous objects. As an extension of [Valk, S., Lemaître, A., Anselmo, L. Analytical and semi-analytical investigations of geosynchronous space debris with high area-to-mass ratios influenced by solar radiation pressure. Adv. Space Res., doi:10.1016/j.asr.2007.10.025, 2007b], we especially apply our analysis to space debris with area-to-mass as high as 20 m²/kg. This paper provides numerical and semi-analytical investigations leading to a deep understanding of the long-term evolution of the semi-major axis. Finally, these semi-analytical investigations are compared with accurate numerical integrations of the osculating equations of motion over time scales as high as 25 years.     

Evolution of the orbital elements for objects with high area-to-mass ratios in geostationary transfer orbits

A new population of uncatalogued objects in geosynchronous Earth orbits (GEO), with a mean motion of about 1 rev/day and eccentricities up to 0.6, has been identified recently. The first observations of this new type of objects were acquired in the framework of the European Space Agency’s (ESA) search for space debris in GEO and the geostationary transfer orbit (GTO) using the ESA 1-m telescope on Tenerife. Earlier studies have postulated that the perturbations due to the solar radiation pressure can lead to such large eccentricities for GEO objects with a high area-to-mass ratio (A/M). The simulations showed that the eccentricities of GEO objects with large A/M exhibit periodic variations with periods of about one year and amplitudes depending on the value of A/M. The findings of these studies could be confirmed by observations from the ESA 1-m telescope on Tenerife.     

On the practical exploitation of perturbative effects in low Earth orbit for space debris mitigation

This paper presents the results of a numerical evaluation of the natural lifetime reduction in low Earth orbit, due to dynamical perturbations. The study considers two values for the area-to-mass ratio, a nominal ratio which resembles a typical value of spacecraft in orbit today, and an enhanced ratio which covers the surface augmentation. The results were obtained with two orbit propagators, one of a semi-analytical nature and the second one using non-averaged equations of motion. The simulations for both propagators were set up similarly to allow comparison. They both use the solar radiation pressure and the secular terms of the geopotential ($J_2,J_4$ and $J_6$). The atmospheric drag was turned on and off in both propagators to alternatively study the eccentricity build up and the residual lifetime. The non-averaging case also covers a validation with the full 6?×?6 geopotential. The results confirm the findings in previous publications, that is, the possibility for de-orbiting from altitudes above the residual atmosphere if a solar sail is deployed at the end-of-life, due to the combined effect of solar radiation pressure and the oblateness of the Earth. At near polar inclinations, shadowing effects can be exploited to the same end. The results obtained with the full, non-averaging propagator revealed additional de-orbiting corridors associated with solar radiation pressure which were not found by previous work on space debris mitigation. The results of both tools are compared for specific initial conditions. For nominal values of area-to-mass ratio, instead, it is confirmed that this resonance effect is negligible.The paper then puts the findings in the perspective of the current satellite catalogue. It identifies space missions which are currently close to a resonance corridor and shows the orbit evolution within the resonances with a significantly shorter residual orbital lifetime. The paper finishes with a discussion on the exploitation of these effects with regards to the long-term simulation of the space debris environment and a flux and collision probability comparison.     

Analytical and semi-analytical investigations of geosynchronous space debris with high area-to-mass ratios

This paper provides a Hamiltonian formulation of the averaged equations of motion with respect to short periods (1 day) of a space debris subjected to direct solar radiation pressure and orbiting near the geostationary ring. This theory is based on a semi-analytical theory of order 1 regarding the averaging process, formulated using canonical and non-singular elements for eccentricity and inclination. The analysis is based on an expansion in powers of the eccentricity and of the inclination, truncated at an arbitrary high order.     

Global dynamics of high area-to-mass ratios GEO space debris by means of the MEGNO indicator

In this paper we provide an extensive analysis of the global dynamics of high-area-to-mass ratios geosynchronous (GEO) space debris, applying a recent technique developed by Cincotta and Simó [Cincotta, P.M., Simó, C.Simple tools to study global dynamics in non-axisymmetric galactic potentials–I. Astron. Astrophys. (147), 205–228, 2000.], Mean Exponential Growth factor of Nearby Orbits (MEGNO), which provides an efficient tool to investigate both regular and chaotic components of the phase space.     

加工装配误差影响下偏转射流压力伺服阀静态特性分析

电液压力伺服阀是电液压力伺服控制系统的核心控制元件,广泛应用于航空、航天、军事等领域。区别于流量伺服阀,压力伺服阀在滑阀放大器的设计上多采用带有压力控制容腔的三通阀结构,不同的滑阀结构使得现有的偏转射流流量伺服阀仿真模型难以满足压力伺服阀性能预测的需求。本文基于AMESim平台建立了偏转射流压力伺服阀的仿真模型,并通过实验对仿真模型进行了验证,验证结果表明仿真模型能够准确地描述压力伺服阀的静态特性。最后,通过仿真模型分析了加工装配误差影响下压力伺服阀输出性能差异,仿真结果可为偏转射流压力伺服阀的性能预测和结构设计提供参考。