Periodic attitude motions along planar orbits in the elliptic restricted three-body problem

A way to improve the accuracy of the three-body problem model is taking into account the eccentricity of primary attractors. Elliptic Restricted Three-Body Problem (ER3BP) is a model for studying spacecraft trajectory within the three-body problem such that the orbital eccentricity of primaries is reflected in it. As the principal cause of perturbation in the employed dynamical model, the primaries eccentricity changes the structure of orbits compared to the ideal Circular Restricted Three-Body Problem (CR3BP). It also changes the attitude behavior of a spacecraft revolving along periodic orbits in this regime. In this paper, the coupled orbit-attitude dynamics of a spacecraft in the ER3BP are exploited to find precise periodic solutions as the spacecraft is considered to be in planar orbits around Lagrangian points and Distant Retrograde Orbits (DRO). Periodic solutions are repetitious behaviors in which spacecraft whole dynamics are repeated periodically, these periodic behaviors are the main interest of this study because they are beneficial for future mission designs and allow delineation of the system’s governing dynamics. Previous studies laid the foundation for spacecraft stability analysis or studying pitch motion of spacecraft in the ER3BP regime. While in this paper, at first, initial guesses for correction algorithms were derived through verified search methods, then correction algorithms were used to refine calculated orbit-attitude periodic behaviors. Periodic orbits and full periodic solutions are portrayed and compared to previous studies and simpler models. Natural periodic solutions are valuable information eventuate in the longer functional lifetime of spacecraft. Since the problem assumption considered in this paper is much closer to real mission conditions, these results may be the means to use natural bounded motions in the actual operational environment.     

火卫一周期准卫星轨道及入轨分析

围绕火卫一的准卫星轨道（QSOs）因其具有良好的稳定性,是火卫一探测任务最为实用的轨道。在平面圆型限制性三体问题模型下,利用庞加莱截面和KAM环迭代方法探究了准卫星轨道的周期轨道族,并给出不同能量准卫星周期轨道的初始条件。针对火卫一周期准卫星轨道入轨,提出一种转移轨道设计方法:对准卫星周期轨道调整速度后进行反向积分,直至离开火卫一邻近区域,从而得到由火星环绕轨道向火卫一周期准卫星轨道的转移轨道,并调整转移轨道参数对燃料与时间消耗进行优化。研究结果表明,当周期准卫星轨道能量处于特定区间时,存在特定速度脉冲区间,可利用火卫一引力实现较少燃料消耗的轨道转移;在该速度脉冲区间中,通过选取较小的速度脉冲,可缩短转移时间。      

Space-to-space Radio Interferometry System from Medium Earth Orbits

This paper presents a new concept to perform space-to-space Very Long Baseline Interferometry which enables the imaging of cosmic sources at high-resolution and high-sensitivity with small antennas. Several individual apertures are embarked on separate identical satellites staggered in height into Polar or Equatorial Circular Medium Earth Orbits (PECMEO orbits). These orbits are stable and allow GNSS-based on-the-fly centimeter-level relative positioning. Coherent operation is possible by exchanging local oscillator components and measured signals through Inter-Satellite Links (ISL). On-board cross correlation is performed at each satellite over a delay window compatible with the accuracy of the on-the-fly relative positioning and the result sent to the ground. Image reconstruction is completed on the ground thanks to sub-millimeter baseline retrieval from accurate GNSS orbits, ISL ranging and spacecraft attitude information. The application of this concept to image the Super Massive Black Hole Sgr A* is hinted.      

Dynamical evolution of high area-to-mass ratio objects in Molniya orbits

For special demands, some notable orbit types have been developed by human, including the Molniya orbits, which have a relatively high eccentricity up to about 0.7, and a period of 12 h. Considering that space debris with high area-to-mass ratio (A/M) has been discovered, such objects may also exist in Molniya orbits due to spacecraft and upper stages fragmentation events. However, there are not sufficient studies of the complex dynamical phenomena of such orbits. These studies can enrich the knowledge about the long-term evolution of these orbits, be helpful to propose uncatalogued objects observation and identification, and also set the protected region as well as active debris removal. In this paper, the characteristics of 2:1 resonance of Molniya satellite orbits are studied. A large set of numerical simulations, including all the relevant perturbations, is carried out to further investigate the main characteristics, and special attention is payed to the dynamical evolution of objects with high A/M, particularly affected by the direct solar radiation pressure. The long-term dynamical evolution of orbital elements, as well as the dependency of lifetime on the A/M value, is discussed.     

连续波雷达多站跟踪数据的时间对齐与轨道解算

连续波雷达是目前外火箭轨道测量的主要高精度设备。由于各种原因,各测站的时间不能完全一致,导致轨道解算的误差。文章对测量机理和时间不对齐量进行分析,利用轨道参数可以用多项式表述的特点,建立了一个估计时间不对齐量和轨道多项式系数的非线性回归模型,给出了参数估计方法和估计的误差。理论分析和模拟计算表明,用该方法可以给出轨道参数和各站时间不对齐量较高精度的估计。     

航天器双主动交会策略研究

从理论上分析了共面近地圆轨道上的航天器的远程双主动交会的问题.根据轨道动力学基本原理,导出各种情况下特征速度的解析解,为航天器变轨时的燃料消耗分析提供了依据.进一步探讨了航天器轨道转移过程中的时间策略,以保证在不同轨道上运行的航天器在同一时刻、同一空间位置交会.上述理论分析的仿真计算结果表明,双主动交会总特征速度和过程耗时都低于主被动交会情形,单星的燃料消耗大大降低,对大范围快速变轨,优势更加明显.     

Highly Elliptical Orbits for Arctic observations: Assessment of ionizing radiation

The ionizing radiation environment was analyzed for a variety of potential Highly Elliptical Orbits (HEOs) with orbital periods ranging from 6 h to 24 h suitable to continuously monitor the Arctic region. Several models available from the ESA Space Environment Information System (SPENVIS) online tool were employed, including the new-generation AE9/AP9 model for trapped radiation. Results showed that the Total Ionizing Dose (TID) has a well-pronounced local minimum for the 14-h orbit, which is nearly identical to the overall minimum observed for the longest orbital period (24 h). The thickness of slab aluminum shielding required to keep the annual TID below 10, 5 and 3.33 krad (i.e. 150, 75 and 50 krad for 15 years of mission duration) for a 14-h orbit is 2.1, 2.7 and 3.1 mm respectively. The 16-h orbit requires an additional 0.5 mm of aluminum to achieve the same results, while the 24-h orbit requires less shielding in the order of 0.2–0.3 mm. Comparison between the AE8/AP8 and AE9/AP9 models was conducted for all selected orbits. Results demonstrated that differences ranged from −70% to +170% depending on orbit geometry.     

近圆轨道控制的分析方法

应用卫星绝大部分都是近圆轨道的卫星 ,其中又有很多是需要进行轨道控制的。在航天工程的实践中由于各种误差影响 ,实际的轨道控制过程并不是而且也没有必要基于精确的轨道动力学方程来执行。对于近圆轨道控制所用的动力学模型可以按圆轨道进行近似 ,得到一种非常简单的形式 ,基于这种简化的模型可以获得非常有用的分析解。为了从理论上证明这种简化的有效性 ,文中对动力学模型简化过程中所产生的各项误差进行了理论估计。     

Influence of Earth’s shadowing effects on space debris stability

Solar radiation pressure affects the evolution of high area-to-mass geostationary space debris. In this work, we extend the stability study of Valk et al. (2009) by considering the influence of Earth’s shadows on the short- and long-term time evolutions of space debris. To assess the orbits stability, we use the Mean Exponential Growth factor of Nearby Orbits (MEGNO), which is an efficient numerical tool to distinguish between regular and chaotic behaviors. To reliably compute long-term space debris motion, we resort to the Global Symplectic Integrator (GSI) of Libert et al. (2011) which consists in the symplectic integration of both Hamiltonian equations of motion and variational equations. We show how to efficiently compute the MEGNO indicator in a complete symplectic framework, and we also discuss the choice of a symplectic integrator, since propagators adapted to the structure of the Hamiltonian equations of motion are not necessarily suited for the associated variational equations. The performances of our method are illustrated and validated through the study of the Arnold diffusion problem. We then analyze the effects of Earth’s shadows, using the adapted conical and cylindrical Earth’s shadowing models introduced by Hubaux et al. (2012) as the smooth shadow function deriving from these models can be easily included into the variational equations. Our stability study shows that Earth’s shadows greatly affect the global behaviour of space debris orbits by increasing the size of chaotic regions around the geostationary altitude. We also emphasize the differences in the results given by conical or cylindrical Earth’s shadowing models. Finally, such results are compared with a non-symplectic integration scheme.     

Generating precise and homogeneous orbits for Jason-1 and Jason-2

Driven by the GMES (Global Monitoring for Environment and Security) and GGOS (Global Geodetic Observing System) initiatives the user community has a strong demand for high-quality altimetry products. In order to derive such high-quality altimetry products, precise orbits for the altimetry satellites are a necessity. With the launch of the TOPEX/Poseidon mission in 1992 a still on-going time series of high-accuracy altimetry measurements of ocean topography started, continued by the altimetry missions Jason-1 in 2001 and Jason-2/OSTM in 2008. This paper contributes to the on-going orbit reprocessing carried out by several groups and presents the efforts of the Navigation Support Office at ESA/ESOC using its NAPEOS software for the generation of precise and homogeneous orbits referring to the same reference frame for the altimetry satellites Jason-1 and Jason-2. Data of all three tracking instruments on-board the satellites (beside the altimeter), i.e. GPS, DORIS, and SLR measurements, were used in a combined data analysis. About 7 years of Jason-1 data and more than 1 year of Jason-2 data were processed. Our processing strategy is close to the GDR-C standards. However, we estimated slightly different scaling factors for the solar radiation pressure model of 0.96 and 0.98 for Jason-1 and Jason-2, respectively. We used 30 s sampled GPS data and introduced 30 s satellite clocks stemming from ESOC’s reprocessing of the combined GPS/GLONASS IGS solution. We present the orbit determination results, focusing on the benefits of adding GPS data to the solution. The fully combined solution was found to give the best orbit results. We reach a post-fit RMS of the GPS phase observation residuals of 6 mm for Jason-1 and 7 mm for Jason-2. The DORIS post-fit residuals clearly benefit from using GPS data in addition, as the DORIS data editing improves. The DORIS observation RMS for the fully combined solution is with 3.5 mm and 3.4 mm, respectively, 0.3 mm better than for the DORIS-SLR solution. Our orbit solution agrees well with external solutions from other analysis centers, as CNES, LCA, and JPL. The orbit differences between our fully combined orbits and the CNES GDR-C orbits are of about 0.8 cm for Jason-1 and at 0.9 cm for Jason-2 in the radial direction. In the cross-track component we observe a clear improvement when adding GPS data to the POD process. The 3D-RMS of the orbit differences reveals a good orbit consistency at 2.7 cm and 2.9 cm for Jason-1 and Jason-2. Our resulting orbit series for both Jason satellites refer to the ITRF2005 reference frame and are provided in sp3 file format on our ftp server.     

The bistatic radar capabilities of the Medicina radiotelescopes in space debris detection and tracking

An accurate measurement of the position and trajectory of the space debris fragments is of primary importance for the characterization of the orbital debris environment. The Medicina Radioastronomical Station is a radio observation facility that is here proposed as receiving part of a ground-based space surveillance system for detecting and tracking space debris at different orbital regions (from Low Earth Orbits up to Geostationary Earth Orbits). The proposed system consists of two bistatic radars formed by the existing Medicina receiving antennas coupled with appropriate transmitters. This paper focuses on the current features and future technical development of the receiving part of the observational setup. Outlines of possible transmitting systems will also be given together with the evaluation of the observation strategies achievable with the proposed facilities.     

Dynamical evolution of debris clouds in geosynchronous orbit

Optical observations have discovered a substantial amount of decimeter sized objects in orbits close to the geosynchronous altitude. Most of these are probably the result of a still undetermined number of explosions occurred to spacecraft and upper stages. So far, however, only two or three fragmentations have been confirmed near GEO and the identification of further explosions at a so high altitude is made difficult by the long time passed since the occurrence of the events and by the effects of the orbital perturbations on the resulting debris clouds. In order to assist the optical observers in identifying debris clouds due to explosions in proximity of the geosynchronous region, a set of fragmentations has been simulated, taking into account a reasonable range of ejection velocities as a function of the fragment size. The resulting debris clouds have been propagated, including all the relevant orbital perturbations, for several decades and the results obtained are presented as snapshots, at given post-explosion times, in the orbital elements space.     

Symplectic integration of space debris motion considering several Earth’s shadowing models

In this work, we present a symplectic integration scheme to numerically compute space debris motion. Such an integrator is particularly suitable to obtain reliable trajectories of objects lying on high orbits, especially geostationary ones. Indeed, it has already been demonstrated that such objects could stay there for hundreds of years. Our model takes into account the Earth’s gravitational potential, luni-solar and planetary gravitational perturbations and direct solar radiation pressure. Based on the analysis of the energy conservation and on a comparison with a high order non-symplectic integrator, we show that our algorithm allows us to use large time steps and keep accurate results. We also propose an innovative method to model Earth’s shadow crossings by means of a smooth shadow function. In the particular framework of symplectic integration, such a function needs to be included analytically in the equations of motion in order to prevent numerical drifts of the energy. For the sake of completeness, both cylindrical shadows and penumbra transitions models are considered. We show that both models are not equivalent and that big discrepancies actually appear between associated orbits, especially for high area-to-mass ratios.     

Stationkeeping of halo orbits in Jupiter-Europa-Io system

Europa is one of the most promising exploration targets in search for extraterrestrial life. In the observation of Europa, halo orbits are suitable locations, because they are periodic and three-dimensional, and stationary with respect to Europa. However, halo orbits are naturally unstable and thus need stationkeeping. This study addresses the stationkeeping problem of halo orbits in the Jupiter-Europa system perturbated by another Galilean moon Io, in which case Io’s mass and orbital rate are assumed to be unknown. A tight stationkeeping scheme is proposed while accounting for autonomous navigation. To deal with the unknown gravitational perturbation from Io, the mass and orbital rate of Io are estimated during the flight and are then used to enhance the control robustness and stability, and improve the navigation accuracy. The control saturation problem is addressed by introducing adjustable parameters into the control law. The accuracy and error distribution of estimation is evaluated through Monte Carlo simulation.     

Orbit Design for Twin-spacecraft Space VLBI

Space Very Long Baseline Interferometry (S-VLBI) is an aperture synthesis technique utilizing an array of radio telescopes including ground telescopes and space orbiting telescopes. It can achieve much higher spatial resolution than that from the ground-only VLBI. In this paper, a new concept of twin spacecraft S-VLBI has been proposed, which utilizes the space-space baselines formed by two satellites to obtain larger and uniform uv coverage without atmospheric influence and hence achieve high quality images with higher angular resolution. The orbit selections of the two satellites are investigated. The imaging performance and actual launch conditions are all taken into account in orbit designing of the twin spacecraft S-VLBI. Three schemes of orbit design using traditional elliptical orbits and circular orbits are presented. These design results can be used for different scientific goals. Furthermore, these designing ideas can provide useful references for the future Chinese millimeter-wave S-VLBI mission.      

MHD simulation of magnetic field configuration above the active region NOAA 10365

The current sheet (CS) creation before a flare in the vicinity of a singular line above the active region NOAA 10365 is shown in numerical experiments. Such a way the possibility of energy accumulation for a solar flare is demonstrated. These data and results of observation confirm the electrodynamical solar flare model that explains solar flares and CME appearance during CS disruption. The model explains also all phenomena observed in flares. For correct reproduction of the real boundary conditions the magnetic flux between spots should be taken into account. The full system of 3D MHD equations are solved using the PERESVET code. For setting the boundary conditions the method of photospheric magnetic maps is used. Such a method permits to take into account all evolution of photospherical magnetic field during several days before the flare.     

An empirical solar radiation pressure model for satellites moving in the orbit-normal mode

We present a family of empirical solar radiation pressure (SRP) models suited for satellites orbiting the Earth in the orbit normal (ON) mode. The proposed ECOM-TB model describes the SRP accelerations in the so-called terminator coordinate system. The choice of the coordinate system and the SRP parametrization is based on theoretical assumptions and on simulation results with a QZS-1-like box-wing model, where the SRP accelerations acting on the solar panels and on the box are assessed separately. The new SRP model takes into account that in ON-mode the incident angle of the solar radiation on the solar panels is not constant like in the yaw-steering (YS) attitude mode. It depends on the elevation angle of the Sun above the satellite’s orbital plane. The resulting SRP vector acts, therefore, not only in the Sun-satellite direction, but has also a component normal to it. Both components are changing as a function of the incident angle. ECOM-TB has been used for precise orbit determination (POD) for QZS-1 and BeiDou2 (BDS2) satellites in medium (MEO) and inclined geosynchronous Earth orbits (IGSO) based on IGS MGEX data from 2014 and 2015. The resulting orbits have been validated with SLR, long-arc orbit fits, orbit misclosures, and by the satellite clock corrections based on the orbits. The validation results confirm that—compared to ECOM2—ECOM-TB significantly (factor 3–4) improves the POD of QZS-1 in ON-mode for orbits with different arc lengths (one, three, and five days). Moderate orbit improvements are achieved for BDS2 MEO satellites—especially if ECOM-TB is supported by pseudo-stochastic pulses (the model is then called ECOM-TBP). For BDS2 IGSOs, ECOM-TB with its 9 SRP parameters appears to be over-parameterized. For use with BDS2 IGSO spacecraft we therefore developed a minimized model version called ECOM-TBMP, which is based on the same axis decomposition as ECOM-TB, but has only 2 SRP parameters and is supported by pseudo-stochastic parameters, as well. This model shows a similar performance as ECOM-TB with short arcs, but an improved performance with (3-day) long-arcs. The new SRP models have been activated in CODE’s IGS MGEX solution in Summer 2018. Like the other ECOM models the ECOM-TB derivatives might be used together with an a priori model.     

脉冲推力轨道拦截可达性描述及求解方法

针对航天器单脉冲轨道拦截可达性分析问题,基于共面变轨、逆轨拦截假设,考虑能量、时间和交会角约束,提出了拦截航天器可拦截区和可发射区的概念。在航天器单脉冲空间可达范围的基础上,进一步考虑了目标轨道的约束,建立了目标轨道命中区的计算策略,对异面轨道交叉点为燃料最省点做出了解释。把拦截可达性相关的问题归纳为8个基本拦截问题,通过这8个问题的组合,描述了考虑能量、时间和交会角约束下拦截问题的可拦截区和可发射区的计算方法。采用圆轨道共面变轨、逆轨拦截场景进行了仿真验证,结果表明该方法能够快速有效地计算出约束条件下航天器的拦截可达范围,能够用于分析特定任务情况下的拦截可达性。     

基于优化理论的GPS定位解算算法

针对传统定位解算方法存在的问题,基于优化理论的思想提出了一种新的定位解算方法——基于优化理论的最大后验估计算法.介绍了该方法的基本原理,详细给出了算法的推导过程,该方法用优化理论的思路求解系统状态量的最大后验概率估计值.它是从系统状态量、观测量的联合概率密度函数出发,将估计问题转化成优化问题,用优化问题的解法对系统的状态进行估计.在此基础上,用仿真实验验证了该方法进行定位解算的有效性.实验结果表明该方法完全解决了定位解算中的非线性问题,并拥有较高的定位精度.     

Optimal two-impulse rendezvous with terminal tangent burn considering the trajectory constraints

The two-impulse orbital rendezvous problem with a terminal tangent burn between coplanar elliptical orbits is studied by considering a lower bound on perigee radius and an upper bound on apogee radius for the transfer orbit. This problem requires that two spacecraft arrive at the rendezvous point with the same arrival flight-path angle after the same flight time. The admissible range of the final true anomaly that meets the perigee and apogee constraints is obtained in closed form. The revolution number of the transfer orbit is expressed as a function of the true anomaly and the revolution numbers of the initial and final orbits. All the feasible solutions are obtained with a bound on the revolution number of the final orbit. Then, the minimum-fuel one is determined by comparing their costs. Finally, two numerical examples are provided to obtain all the feasible solutions for given initial impulse points and the optimal solution with the initial coasting arc. Numerical results show that the minimum-fuel solution for the terminal tangent burn rendezvous is close to that for the cotangent rendezvous when the rendezvous time is long enough; however, the cotangent rendezvous may not exist when the rendezvous time is short.