Comparison of satellite orbit ephemerides for use in GPS meteorology

This paper discusses GPS (Global Position System) meteorology. The research presented is based on a comparison of values of precipitable water vapour PWV, based on GPS measurements using final and predicted ephemerides of satellite orbits. We analysed recent year’s improvement in predicting ephemerides. We compared the data outputs from a radiosonde using GPS receiver measurements directly from the meteorological station from which the radiosondes were launched. The results indicate a high quality of the predicted ephemerides. This finding makes predicted ephemerides highly usable for near real-time estimations of PWV. To use PWV in meteorological forecast applications, this high speed of PWV values supply is necessary.     

关于Grothendieck代数的特征标

本文用群表示理论和复向量理论证明了Grothendieck代数的一些性质,特别是关于Grothendieck代数基的描述,即设B为K_G(X)的基,Θ={(θ,ρ)|θ是G在X上的轨道,ρ是G_x的一个不可约表示,x∈θ},其中G_x={g∈G|gx=x},则存在1—1对应f:B→Θ使得对于任意V∈B,f(v)=(θ,ρ):V_y≠0<==>y∈θ,且ρ是G_x在V_x上的一个不可约表示,x∈θ,利用这一性质,本文给出了一个求Grothendieck代数的特征标的方法,从而改进了由Luszrig,G.在文[1]中提出的方法,并且给出二面体群D_n关于其一些子群H的Grotheodieck代数的特征标表。     

航天飞机气动力辅助异面轨道变换

本文研究了以气动力作为辅助动力,实现异面圆轨道的最优变换。以目标轨道面倾角最大为优化性能指标,获得了升力和滚转角的最优控制规律。文中提出了优化问题的一种参数搜寻方法,有利于问题的求解。文末对结果作了分析,讨论,并就有关的多种变换模态作了分析、对比,表明在一定条件下,气动力辅助变换有明显的优越性。     

Satellite orbits in Levi-Civita space

In this paper we consider satellite orbits in central force field with quadratic drag using two formalisms. The first using polar coordinates in which the satellite angular momentum plays a dominant role. The second is in Levi-Civita coordinates in which the energy plays a central role. We then merge these two formalisms by introducing polar coordinates in Levi-Civita space and derive a new equation for satellite orbits which unifies these two paradigms. In this equation energy and angular momentum appear on equal footing and thus characterize the orbit by its two invariants. Using this formalism we show that equatorial orbits around oblate spheroids can be expressed analytically in terms of Elliptic functions. In the second part of the paper we derive in Levi-Civita coordinates a linearized equation for the relative motion of two spacecrafts whose trajectories are in the same plane. We carry out also a numerical verification of these equations.     

Equilibrium positions on stationary orbits and planetary principal inertia axis orientations for the Solar System

We present a qualitative analysis in a phase space to determine the longitudinal equilibrium positions on the planetary stationary orbits by applying an analytical model that considers linear gravitational perturbations. We discuss how these longitudes are related with the orientation of the planetary principal inertia axes with respect to their Prime Meridians, and then we use this determination to derive their positions with respect to the International Celestial Reference Frame. Finally, a numerical analysis of the non-linear effects of the gravitational fields on the equilibrium point locations is developed and their correlation with gravity field anomalies shown.     

Asteroid and comet hazard: Identification problem of observed space objects with the parental bodies

This article focuses on the genetic identification of observed small cosmic bodies with alleged parental bodies; namely, comets, asteroids and meteoroid swarms. There is a problem of the upper D-value limit as a measure of proximity between the orbits of the bodies in the five-dimensional phase space (Southworth and Hawkins, 1963). In the study of genetic relationships of the comet and meteor complexes, the D value is usually taken as equal to 0.2 for all meteor showers. However, the upper D limit should be investigated for each meteoroid complex. For example, such investigation was performed for the Taurid meteor complex (Porub?an et al., 2006). In this paper, the upper D-criterion limit value was investigated for the Perseid meteor shower. The 1862 III Swift–Tuttle comet is its parental comet.     

Solar-photon sail hovering orbits about single and binary asteroids

Solar-photon sails can be useful for missions towards and about asteroids. Indeed, for the interplanetary transfer phase, missions to asteroids often require a large variation in inclination and solar-photon sails perform very well for such high energy missions. In the same way, solar-photon sails are also expected to perform well in the phase about the asteroid. This paper studies single and binary asteroids’ hovering regions by using a sailcraft. In order to consider a sailcraft with its own mass and shape, the mutual polyhedral method (usually used to study asteroid dynamics) is used; therefore, the sailcraft is designed by means of tetrahedra. The procedure to obtain the hovering regions about a single asteroid is presented and an accurate analysis of the control variables is carried out. Moreover, control torques required to maintain hovering orbits are obtained by considering the gravitational torques acting on the sailcraft due to the asteroid. In the end, the theory for hovering orbits is extended to binary-asteroid systems and applied to the binary system 1999 KW4.     

Assessing and minimizing collisions in satellite mega-constellations

We aim to provide satellite operators and researchers with an efficient means for evaluating and mitigating collision risk during the design process of mega-constellations. We first introduce a novel algorithm for conjunction prediction that relies on large-scale numerical simulations and uses a sequence of filters to greatly reduce its computational expense. We then use this brute-force algorithm to establish baselines of endogenous (intra-constellation), or self-induced, conjunction events for the FCC-reported designs of the OneWeb LEO and SpaceX Starlink mega-constellations. We demonstrate how these deterministic results can be used to validate more computationally efficient, stochastic techniques for close-encounter prediction by adopting a new probabilistic approach from Solar-System dynamics as a simple test case. Finally, we show how our methodology can be applied during the design phase of large constellations by investigating Minimum Space Occupancy (MiSO) orbits, a generalization of classical frozen orbits that holistically account for the perturbed-Keplerian dynamics of the Earth-satellite-Moon-Sun system. The results indicate that the adoption of MiSO orbital configurations of the proposed mega-constellations can significantly reduce the risk of endogenous collisions with nearly indistinguishable adjustments to the nominal orbital elements of the constellation satellites.     

H-reversal trajectory: A new mission application for high-performance solar sails

The aim of this paper is to quantify the performance of a flat solar sail to perform a double angular momentum reversal maneuver and produce a new class of two-dimensional, non-Keplerian orbits in the ecliptic plane. For a given pair of orbital parameters, the orbital period and the perihelion distance, it is possible to find the minimum solar sail characteristic acceleration required to fulfil a double angular momentum reversal trajectory. This problem is addressed using an optimal formulation and is solved through an indirect approach. The new trajectories are symmetrical with respect to the sun-perihelion line and exhibit a bean-like shape. Two main difficulties must be properly taken into account. On one side the sail is required to perform a rapid reorientation maneuver when it approaches the perihelion. Suitable simulations have shown that such a maneuver is feasible. In the second place the new trajectories require the use of high performance solar sails. For example, assuming an orbital period equal to 5 years, the required solar sail characteristic acceleration is greater than 3.4 mm/s². Such a value, although beyond the currently available sail performance, is comparable to what is required by the original concept of H-reversal maneuvers introduced by Vulpetti in 1996.     

航天飞机最优空间机动轨道

本文对最优空间机动轨道现有的主要研究成果、研究的基本方法及有关结果作了综合评述,并指出有待解决的问题及研究方向。