Novel orbits of Mercury,Venus and Mars enabled using low-thrust propulsion

Exploration of the inner planets of the Solar System is vital to significantly enhance the understanding of the formulation of the Earth and other planets. This paper therefore considers the development of novel orbits of Mars, Mercury and Venus to enhance the opportunities for remote sensing of these planets. Continuous acceleration is used to extend the critical inclination of highly elliptical orbits at each planet and is shown to require modest thrust magnitudes. This paper also presents the extension of existing sun-synchronous orbits around Mars. However, unlike Earth and Mars, natural sun-synchronous orbits do not exist at Mercury or Venus. This research therefore also uses continuous acceleration to enable circular and elliptical sun-synchronous orbits, by ensuring that the orbit's nodal precession rate matches the planets mean orbital rate around the Sun, such that the lighting along the ground-track remains approximately constant over the mission duration. This property is useful both in terms of spacecraft design, due to the constant thermal conditions, and for comparison of images. Considerably high thrust levels are however required to enable these orbits, which are prohibitively high for orbits with inclinations around 90°. These orbits therefore require some development in electric propulsion systems before becoming feasible.     

圆型限制性三体问题相对运动解析研究

针对圆型限制性三体问题共线平动点附近周期/拟周期轨道下的相对运动问题,提出一种新的、通用的解析研究方法。在周期/拟周期轨道近似解析解的基础上,结合微分修正方法,获得了精确的周期/拟周期轨道。对周期/拟周期轨道的单值矩阵进行分析,同时借鉴Floquet理论核心思想,建立了六个相对运动模态,并将相对运动表示为六个相对运动模态的线性组合,获得了相对运动的近似解析解。最后在地-月系统圆型限制性三体问题下,以L1点作为研究对象,分别以Halo轨道、Lissajous轨道和Lyapunov轨道为参考轨道,对相对运动模态和相对运动进行仿真分析,说明了相对运动模态的正确性以及相对运动近似解析解的有效性。     

Mapping orbits with low station keeping costs for constellations of satellites based on the integral over the time of the perturbing forces

The present paper is concerned with the search for orbits that have potential to require low fuel consumption for station-keeping maneuvers for constellations of satellites. The method used to study this problem is based on the integral over the time of the undesired perturbing forces. This integral measures the change of velocity caused by the perturbation forces acting on the satellite, so mapping orbits that are less perturbed, which generates good candidates for orbits that requires low fuel consumption for station-keeping maneuvers. The integral over the time depends only on the orbit of the spacecraft and the dynamical system considered. The type of engine and the control technique applied to the spacecraft are not considered to search for those orbits. It can be a good strategy to be applied for a first mapping of orbits. For this search, it is analyzed the integral of orbits with different values of the Keplerian elements in order to find the best ones with respect to this criterion. The perturbations considered are the ones caused by the third body, which includes the Sun and the Moon, and the J₂ term of the geopotential. The results presented here show numerical simulations to obtain the integral of those perturbing forces for different orbits. The GPS and the Molniya constellations are used as examples for those calculations.     

月球空间站停泊轨道选择分析

系统梳理了月球附近可用于部署空间站的停泊轨道类型,给出了不同类型轨道的定义及主要参数,通过仿真计算和对比国内外轨道研究结论,分析了不同类型轨道的能量需求、登月任务支持性、空间环境等特点,在此基础上,分析了美国"深空之门"空间站部署轨道选择的主要考虑和依据,并提出了各类轨道的应用建议,可为未来部署月球空间站的停泊轨道选择...     

Fourth-order theories for orbit predictions for low- and high-eccentricity orbits in an oblate atmosphere with scale height dependent on altitude

Two new fourth-order non-singular analytical theories for the motion of near-Earth satellite orbits with air drag are developed for low- and high-eccentricity orbits in an oblate atmosphere with variation of density scale height with altitude. Uniformly regular Kustaanheimo–Stiefel (KS) canonical elements are utilized for low-eccentricity orbits and KS element equations are employed for high-eccentricity orbits. Only two of the nine equations are solved analytically to compute the state vector and change in energy at the end of each revolution, due to symmetry in the equations of motion. The analytical solutions are compared with the numerically integrated values up to 100 revolutions, and found to be quite accurate over a wide range of eccentricity, perigee height and inclination.     

Horseshoe orbits in the Earth–Moon system

Horseshoe orbits in the restricted three-body problem have been mostly considered in the Sun–Jupiter system and, in recent years, in the Sun–Earth system. Here, these orbits have been used to find asteroids that have orbits of this kind. We have built a planar family of horseshoe orbits in the Earth–Moon system and determined the points of planar and 1/1 vertical resonances on this family. We have presented examples of orbits generated by these spatial families.     

考虑地球扁率效应的两圆轨道之间的双共切最优转移

两圆轨道之间的双共切转移轨道是其近地点和远地点分别在这两个圆轨道上的椭圆轨道。本文用两次冲量法给出了沿双共切椭圆轨道实现从一圆轨道向另一圆轨道转移的最优方案，并考虑到地球扁率造成的轨道摄动。文中的所谓圆轨道指的是变轨时刻的密切轨道为圆形的轨道，是对近圆轨道的近似替找。     

Stable spatial orbits around collinear libration points

A technique of generation of spatial periodic solutions to the restricted circular three-body problem from periodic orbits of the planar problem has been used for the families of orbits around collinear libration points L ₁ and L ₂. Developing the families obtained at the 1: 1 resonance, we have obtained stable solutions both in the Earth-Moon system and in the Sun-Earth system. Of course, the term “around the libration point” is rather conventional; the obtained orbits become more similar to the orbits around the smaller attracting body. The further development of the family of orbits “around” the libration point L ₂ in the Sun-Earth system made it possible to find the orbits satisfying the new, much more rigorous constraints on cooling the spacecraft of the Millimetron project.     

太阳帆绕地球周期轨道研究

  地球同步和太阳同步卫星在各个领域有着广泛的应用。静止轨道是一种特殊的地球同步轨道,轨道资源有限。利用化学推进或电推进可以实现轨道高度不同的同步轨道,如悬挂轨道,但需要消耗较多的燃料,工程上无法承受。本文考虑利用太阳帆实现地球同步和太阳同步轨道。太阳光压力在轨道平面内沿拱线方向,选择光压力与平面的夹角使得轨道平面的旋转速率与太阳光同步。研究表明,设计合适的半长轴和偏心率可以使得轨道旋转速率与地球自转速率一致。假设太阳光与赤道平面平行,可以得到准静止轨道,太阳帆将在传统静止轨道的附近运动,星下点的经度将在一个固定值附近振动。实际上太阳光是与黄道面平行,黄道面与赤道面之间存在夹角。考虑黄赤交角的情况下,太阳帆将在一定纬度和经度范围内运动。适合于对某个区域进行长期观测任务。     

A Retrospective Geometric Analysis of the Long-Term Evolution of Orbits and the Ballistic Lifetime for Satellites of the Prognoz Series

We consider the applied aspects of the geometrical analysis of solutions in a restricted circular double-averaged three-body problem that are concerned with the design of high-apogee satellite orbits. Based on the analysis of the long-term evolution and the ballistic lifetime for orbit families of the Prognoz satellites launched into their orbits in the period 1972–1995, we suggest some practical suggestions for choosing long-lived high-apogee orbits with taking into account various requirements for the domain of evolution of the orbital elements.     

Optimization of the trajectory of the spacecraft insertion into the system of heliocentric orbits

The possibility of the spacecraft insertion into the system of operational heliocentric orbits has been analyzed. It has been proposed to use a system of several operational heliocentric orbits. On each orbit, the spacecraft makes one or more revolutions around the Sun. These orbits are characterized by a relatively small perihelion radius and relatively high inclination, which allows one to investigate the polar regions of the Sun. The transition of the spacecraft from one orbit to another has been performed using an unpowered gravity assist maneuver near Venus and does not require the cruise propulsion operation. Each maneuver transfers the spacecraft into the sequence of operational heliocentric orbits. We have analyzed several systems of operational heliocentric orbits into which the spacecraft can be inserted by means of the considered transportation system with electric propulsion (EP). The mass of the spacecraft delivered to these systems of operational orbits has been estimated.     

On the features of long-term evolution of a high-apogee orbit of the SPECTR-R spacecraft

The practical tasks related to qualitative investigation of long-term evolution of high-apogee orbits of artificial Earth satellites (AES), for which the main perturbing factors are gravitational perturbations from the Moon and the Sun, are considered. Attention is given to the problem of the ballistic lifetime of similar orbits, and the issues associated with possibilities of the correction of orbits for ensuring the required duration of their ballistic lifetime are considered. The orbit of the SPECTR-R spacecraft launched in July of 2011 is considered as an example.     

Can solar sails be used to test fundamental physics?

The relative importance of certain general relativistic effects is enhanced by solar radiation pressure (SRP). The observation and study of the trajectories of a solar sail could potentially provide tests of various effects of general relativity. In particular, we study Keplerian and non-Keplerian orbits near the sun as well as escape trajectories for a solar sail, for which general relativistic effects and the solar radiation pressure are considered simultaneously. In contrast with the conventional solar mission, a solar sail allows for non-Keplerian orbits, for which the orbital plane lies above the sun. It is predicted that there is an analog of the Lense–Thirring effect for non-Keplerian orbits. Also the SRP increases the amount of precession per orbit due to the Lense–Thirring effect for polar heliocentric orbits. A solar sail would also enhance the relative importance of effects associated with a possible net charge on the sun and during many rotations this effect may be measurable.     

关于旋进椭圆的讨论

根据Bertrand定理关于轨道闭合的条件,我们知道当中心引力的形式为径向距离的幂次型函数时,并不总能导致闭合轨道,即运动的质点不一定能返回到它自己的轨迹上去。这个定理指出:一切运动质点其初始条件稍微偏离圆轨道的要求条件时,只有当引力满足平方反比律(即牛顿万有引力定律)或线性定律(即虎克定律)时,轨道才是闭合的。 本文试图采用分析力学中作用角变量的方法,对一般情形下的轨道闭合条件进行讨论。这里我们看到使初始轨道接近于圆轨道的假设是不必要的,而且力的类型可推广到包括平方反比和其它幂次型的力。我们证明了轨道闭合的判别公式,并得到在上述情形下轨道非闭合的结论。 最后,如果中心引力包括有r~(-2)项和r~(-3)项时,象相对论性改正后所得到的那样,轨道就不再是闭合的,而是一旋进椭圆形轨道,椭圆的旋进角速度可以容易地计算出来。     

Modeling radiation conditions in orbits of projected system of small satellites for radiation monitoring

Calculated estimates are presented for the accumulated radiation doses behind the shields of various thicknesses in the orbits of projected at Skobeltsyn Institute of Nuclear Physics, Moscow State University system of small satellites for radiation monitoring. The results are analyzed and compared with the calculation data for other actively exploited near-Earth orbits.     

Periodic solutions in three-dimensional restricted three-body problem: 2. Loss of symmetry at the 1:1 resonance

Within the framework of the circular restricted three-body problem a family of inverse periodic orbits around the two attracting bodies (the Egorov’s family) and families generated by it at the 1:1, 2:1, and 3:1 resonances for three-dimensional orbits in the Sun-Earth and Earth-Moon systems are considered. Their relationship with families generated by orbits around the libration points L ₁, L ₂ and L ₃ is investigated. One of the families contains periodic solutions that seem promising as possible orbits for the space radio telescope of the Millimetron project.     

Analysis of the effect of various disturbing factors on high-precision forecasts of spacecraft orbits

The necessity of taking many force components disturbing spacecraft (SC) orbits into account is demonstrated for the example of forecasts of GLONASS ephemerides. The disturbances of SCs in high-earth orbits (HEO) and low-earth orbits (LEO) are systematized, and the degree of their effect on SC motion is estimated. Disturbance models are developed that provide essential increases of the accuracy of one-day forecasts of GLONASS and GPS ephemerides. Modeling results are presented that allow, depending on the required accuracy of SC orbit forecasts, the determination of the necessary list of disturbances included in the model.     

航天器再入制导方法综述

航天器再入制导方法国内外已有不少的学者进行了研究。本文对国内学者这方面的工作作一综述。目前国内研究的大多为有标准轨道的再入制导方法，且从最优原理出发对再入标准轨道进行了优化。对纵向再入制导规律也找出了最佳增益系数。侧向制导采用漏斗型开关曲线其效果良好。预测制导方法也开始了研究工作。     

State transition matrix approximation with geometry preservation for general perturbed orbits

This paper presents a method for approximating the state transition matrix for orbits around a primary body and subject to arbitrary perturbations. The primary objective of this method is to provide an accurate state transition matrix for orbits with realistic perturbations, which has a sufficiently simple form for implementation onboard spacecraft. The averaging method is employed to isolate the high and low frequency spectra of the perturbation terms, and construct a functional form of the approximate state transition matrix composed only of elementary analytic functions. In addition to the methodology of the approximation, it is shown that the symplectic property, which is a fundamental mathematical structure of Hamiltonian systems, can be incorporated into this method. This not only reduces the number of parameters required for approximations but also makes it possible to preserve the physically true structure of the state transition matrix. The resulting state transition matrix approximation is valid for tens of orbital revolutions without having to update the parameters. Numerical simulations show that this method is valid for arbitrary eccentricity orbits with semimajor axis ranging from LEO up to around 10 Earth radii when applied to Earth orbits.     

地球内辐射带核心区环境特征分析及质子屏蔽的蒙特卡罗模拟

辐射带粒子是近地空间卫星总剂量辐射的主要来源。文章分析了内辐射带不同高度轨道的辐射环境特性;并利用Geant4程序,针对内辐射带质子环境进行不同材料的屏蔽效能计算。结果表明:虽然传统的低?高?低原子序数材料三明治屏蔽结构对电子具有较高的屏蔽效能,却并不适用于以质子环境为主的轨道;对于工作在3000 km圆轨道、5年寿命的卫星,若要将总剂量降至30 krad(Si)以下,使用PE屏蔽材料可比Al屏蔽减重28%。