Libration point orbits for lunar global positioning systems

With the development of lunar exploration, a lunar global positioning system (LGPS) is demanded for both on-ground and in-flight lunar exploration missions. The traditional configuration of constellation requires at least eighteen satellites to cover the whole lunar surface continuously. In this paper, the configurations of the libration point orbits (LPOs) constellations are investigated. By using the constellations on the Earth–Moon _L1$L_1$ and _L2$L_2$ LPOs, the basic functions of the LGPS can be realized by using eight to fourteen satellites. First, the LPO and the combinations of LPOs, which can be used in the constellations of the LGPS, are investigated. The criteria and procedures of the configuration design are introduced. Second, the configurations of LPOs constellations are investigated in the Earth–Moon circular-restricted three-body problem (CR3BP). The size of the LPOs and the distribution of the satellites on these LPOs are determined by using an exhaustive algorithm and a global optimization method, respectively. The key performance parameters of these constellations are computed. Third, the constellations with good performance in the CR3BP are redesigned in the more accurate Earth–Moon based Sun-perturbed bicircular four-body problem (B4BP). Moreover, in order to avoid the ground coverage problem caused by the perturbation of the Sun, some modifications are implemented, and the configuration of the no blind area LGPS in the B4BP is obtained.     

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.     

High resolution science with high redshift galaxies

We summarize the high-resolution science that has been done on high redshift galaxies with Adaptive Optics (AO) on the world’s largest ground-based facilities and with the Hubble Space Telescope (HST). These facilities complement each other. Ground-based AO provides better light gathering power and in principle better resolution than HST, giving it the edge in high spatial resolution imaging and high resolution spectroscopy. HST produces higher quality, more stable PSF’s over larger field-of-views in a much darker sky-background than ground-based AO, and yields deeper wide-field images and low-resolution spectra than the ground. Faint galaxies have steadily decreasing sizes at fainter fluxes and higher redshifts, reflecting the hierarchical formation of galaxies over cosmic time. HST has imaged this process in great structural detail to z  6, and ground-based AO and spectroscopy has provided measurements of their masses and other physical properties with cosmic time. Last, we review how the 6.5 m James Webb Space Telescope (JWST) will measure First Light, reionization, and galaxy assembly in the near–mid-IR after 2013.     

Analytical expression for distant retrograde orbits around a small natural satellite

An analytical expression for distant retrograde orbits (DROs) is obtained in this study. Owing to the fact that a planar DRO is a closed orbit and can be expressed as an approximately elliptical orbit, respective geometries and periods of DROs are analytically calculated. A switching point, where various properties of planar DROs change abruptly with an increase in the orbital radius, is determined. The Mars–Deimos system is taken as a case study in this work. The proposed method can be applied to cases where the Hill’s approximation of the restricted three-body problem is valid. Numerical calculations are performed to validate the proposed method.     

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.