Modeling satellite drag coefficients with response surfaces

Satellite drag coefficients are a major source of uncertainty in predicting the drag force on satellites in low Earth orbit. Among other things, accurately predicting the orbit requires detailed knowledge of the satellite drag coefficient. Computational methods are an important tool in computing the drag coefficient but are too intensive for real-time and predictive applications. Therefore, analytic or empirical models that can accurately predict drag coefficients are desired. This work uses response surfaces to model drag coefficients. The response surface methodology is validated by developing a response surface model for the drag coefficient of a sphere where the closed-form solution is known. The response surface model performs well in predicting the drag coefficient of a sphere with a root mean square percentage error less than 0.3% over the entire parameter space. For more complex geometries, such as the GRACE satellite, the Hubble Space Telescope, and the International Space Station, the model errors are only slightly larger at about 0.9%, 0.6%, and 1.0%, respectively.     

Drag coefficient modeling for grace using Direct Simulation Monte Carlo

Drag coefficient is a major source of uncertainty in predicting the orbit of a satellite in low Earth orbit (LEO). Computational methods like the Test Particle Monte Carlo (TPMC) and Direct Simulation Monte Carlo (DSMC) are important tools in accurately computing physical drag coefficients. However, the methods are computationally expensive and cannot be employed real time. Therefore, modeling of the physical drag coefficient is required. This work presents a technique of developing parameterized drag coefficients models using the DSMC method. The technique is validated by developing a model for the Gravity Recovery and Climate Experiment (GRACE) satellite. Results show that drag coefficients computed using the developed model for GRACE agree to within 1% with those computed using DSMC.     

Non-conservative forces on LAGEOS I and II

The behavior of the empirically determined along-track accelerations from the LAGEOS satellites has been attributed to a variety of physical phenomena. Of these, the models for Yarkovsky thermal drag, anisotropic reflectivity and Yarkovsky-Schach drag are dependent on the spin axis orientation of the satellite. This investigation explores the utilization of these models in an attempt to recover the spin axis orientation history, particularly for the LAGEOS I satellite.     

Drag and energy accommodation coefficients during sunspot maximum

Conditions appropriate to gas-surface interactions on satellite surfaces in orbit have not been successfully duplicated in the laboratory. However, measurements by pressure gauges and mass spectrometers in orbit have revealed enough of the basic physical chemistry that realistic theoretical models of the gas-surface interaction can now be used to calculate physical drag coefficients. The dependence of these drag coefficients on conditions in space can be inferred by comparing the physical drag coefficient of a satellite with a drag coefficient fitted to its observed orbital decay. This study takes advantage of recent data on spheres and attitude stabilized satellites to compare physical drag coefficients with the histories of the orbital decay of several satellites during the recent sunspot maximum. The orbital decay was obtained by fitting, in a least squares sense, the semi-major axis decay inferred from the historical two-line elements acquired by the US Space Surveillance Network. All the principal orbital perturbations were included, namely geopotential harmonics up to the 16th degree and order, third body attraction of the Moon and the Sun, direct solar radiation pressure (with eclipses), and aerodynamic drag, using the Jacchia-Bowman 2006 (JB2006) model to describe the atmospheric density. After adjusting for density model bias, a comparison of the fitted drag coefficient with the physical drag coefficient has yielded values for the energy accommodation coefficient as well as for the physical drag coefficient as a function of altitude during solar maximum conditions. The results are consistent with the altitude and solar cycle variation of atomic oxygen, which is known to be adsorbed on satellite surfaces, affecting both the energy accommodation and angular distribution of the reemitted molecules.     

Nanosatellite constellation deployment using on-board magnetic torquer interaction with space plasma

One of the advantages that drive nanosatellite development is the potential of multi-point observation through constellation operation. However, constellation deployment of nanosatellites has been a challenge, as thruster operations for orbit maneuver were limited due to mass, volume, and power. Recently, a de-orbiting mechanism using magnetic torquer interaction with space plasma has been introduced, so-called plasma drag. As no additional hardware nor propellant is required, plasma drag has the potential in being used as constellation deployment method. In this research, a novel constellation deployment method using plasma drag is proposed. Orbit decay rate of the satellites in a constellation is controlled using plasma drag in order to achieve a desired phase angle and phase angle rate. A simplified 1D problem is formulated for an elementary analysis of the constellation deployment time. Numerical simulations are further performed for analytical analysis assessment and sensitivity analysis. Analytical analysis and numerical simulation results both agree that the constellation deployment time is proportional to the inverse square root of magnetic moment, the square root of desired phase angle and the square root of satellite mass. CubeSats ranging from 1 to 3?U (1–3?kg nanosatellites) are examined in order to investigate the feasibility of plasma drag constellation on nanosatellite systems. The feasibility analysis results show that plasma drag constellation is feasible on CubeSats, which open up the possibility of CubeSat constellation missions.     

任意偏心率卫星的大气阻力的短周期摄动

通过本文采用的计算方法和CIRA 1972在160～2000公里高度围范的大气密度的分析模型,导出了人造地球卫星大气阻力短周期摄动的一种计算公式,它形式简单,收敛性好,适用于任意偏心率的卫星。     

A detailed spin analysis of the San Marco 5 mission

The attitude of the San Marco 5 satellite flown in 1988 has been monitored by several sensors. Thus the history of the spin period is known with a high degree of accuracy. Because of the simple geometry (spherical body with several extremely long antennas) and the good mass balance (used for the accelerometer aboard) of the satellite it was possible to separate different effects of variations of the spin period. The influence of the drag on the spin period has been modeled. The results are used to derive total gas densities along the trajectory and compare them with model densities, in situ measurements from the drag balance instrument and densities derived by orbital drag methods.     

Determination of basic constants of satellite-atmosphere interaction from the analysis of motion of 1974-70A

The atmospheric drag and lift effects are studied on the orbital data of the satellite 1974-70A. The values of the thermal accomodation coefficient and of the drag coefficient are determined.     

Analysis of the orbit lifetime of CubeSats in low Earth orbits including periodic variation in drag due to attitude motion

It is estimated that more than 22,300 human-made objects are in orbit around the Earth, with a total mass above 8,400,000 kg. Around 89% of these objects are non-operational and without control, which makes them to be considered orbital debris. These numbers consider only objects with dimensions larger than 10 cm. Besides those numbers, there are also about 2000 operational satellites in orbit nowadays. The space debris represents a hazard to operational satellites and to the space operations. A major concern is that this number is growing, due to new launches and particles generated by collisions. Another important point is that the development of CubeSats has increased exponentially in the last years, increasing the number of objects in space, mainly in the Low Earth Orbits (LEO). Due to the short operational time, CubeSats boost the debris population. One of the requirements for space debris mitigation in LEO is the limitation of the orbital lifetime of the satellites, which needs to be lower than 25 years. However, there are space debris with longer estimated decay time. In LEÓs, the influence of the atmospheric drag is the main orbital perturbation, and is used in maneuvers to increment the losses in the satellite orbital energy, to locate satellites in constellations and to accelerate the decay.The goal of the present research is to study the influence of aerodynamic rotational maneuver in the CubeSat?s orbital lifetime. The rotational axis is orthogonal to the orbital plane of the CubeSat, which generates variations in the ballistic coefficient along the trajectory. The maneuver is proposed to accelerate the decay and to mitigate orbital debris generated by non-operational CubeSats. The panel method is selected to determine the drag coefficient as a function of the flow incident angle and the spinning rate. The pressure distribution is integrated from the satellite faces at hypersonic rarefied flow to calculate the drag coefficient. The mathematical model considers the gravitational potential of the Earth and the deceleration due to drag. To analyze the effects of the rotation during the decay, multiple trajectories were propagated, comparing the results obtained assuming a constant drag coefficient with trajectories where the drag coefficient changes periodically. The initial perigees selected were lower than 400 km of altitude with eccentricities ranging from 0.00 to 0.02. Six values for the angular velocity were applied in the maneuver. The technique of rotating the spacecraft is an interesting solution to increase the orbit decay of a CubeSat without implementing additional de-orbit devices. Significant changes in the decay time are presented due to the increase of the mean drag coefficient calculated by the panel method, when the maneuver is applied, reducing the orbital lifetime, however the results are independent of the angular velocity of the satellite.     

低轨卫星的气动特性预测与分析

针对低轨卫星高空自由分子流区的飞行环境特征,采用GOCE卫星典型弹道下的气动数据对DSMC仿真方法进行了算例验证,并就CLL模型下不同物面反射系数对GOCE卫星流场特征及气动特性的预测差异进行了对比分析,给出不同物面反射系数对卫星阻力预测的定量差异.结果表明,本文方法所得气动阻力与文献结果吻合较好,能够在此飞行区域给出合理的气动阻力;当反射系数从0.1逐渐变化至1.0时,卫星流场的驻点区域、尾部方向舵区域压力分布逐渐从带状结构向扇形结构过渡;在所研究的工况下,随着物面反射系数的增加,摩阻系数预测结果偏大,压阻系数预测结果偏小,总阻力先增加后减小,约在反射系数0.8附近达到最大.      

用Schamberg方法计算卫星阻力系数

Schamberg的“超热自由分子流”粒子-表面作用模型比较真实地反映了高空大气分子与空间飞行器材料之间的相互作用,它可以用来计算卫星的阻力系数。本文简要叙述该模型的基本思想,介绍几种常见简单几何形体卫星的阻力系数计算公式,并给出计算曲线。     

基于卫星自旋的纯引力轨道万有引力干扰抑制

一个称为“内卫星”的验证质量块位于外卫星的内部空腔中,不与外卫星接触而自由飞行,由于外卫星的屏蔽,其不受大气阻力、太阳光压等干扰作用,沿着纯引力轨道飞行。外卫星会对内卫星产生万有引力作用,是内卫星纯引力轨道的主要残余干扰。根据卫星相对运动动力学方程,建立了万有引力干扰对内卫星纯引力轨道影响的分析模型;基于将外卫星绕轨道面法向旋转以调制万有引力的策略,建立了外卫星自旋对万有引力干扰影响的抑制模型。以内编队纯引力飞行系统为例,对比计算了外卫星有无自旋时万有引力干扰对内卫星纯引力轨道的影响。基于模型的分析表明,外卫星自旋能够显著抑制万有引力干扰对内卫星纯引力轨道的长期影响;实例计算表明,万有引力干扰的天长期影响能够降低5~7个数量级。     

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.     

Use of two-line element data for thermosphere neutral density model calibration

Traditional empirical thermospheric density models are widely used in orbit determination and prediction of low-Earth satellites. Unfortunately, these models often exhibit large density errors of up to around 30% RMS. Density errors translate into orbit errors, adversely affecting applications such as re-entry operations, manoeuvre planning, collision avoidance and precise orbit determination for geodetic missions. The extensive database of two-line element (TLE) orbit data contains a wealth of information on satellite drag, at a sufficiently high spatial and temporal resolution to allow a calibration of existing neutral density models with a latency of one to two days. In our calibration software, new TLE data for selected objects is converted to satellite drag data on a daily basis. The resulting drag data is then used in a daily adjustment of density model calibration parameters, which modify the output of an existing empirical density model with the aim of increasing its accuracy. Two different calibration schemes have been tested using TLE data for about 50 objects during the year 2000. The schemes involve either height-dependent scale factors to the density or corrections to CIRA-72 model temperatures, which affect the density output based on a physical model. Both schemes have been applied with different spherical harmonic expansions of the parameters in latitude and local solar time. Five TLE objects, varying in perigee altitude between 280 and 530 km, were deliberately not used during calibration, in order to provide independent validation. Even with a single daily parameter, the RMS density model error along their tracks can already be reduced from the 30% to the 15% level. Adding additional parameters results in RMS errors lower than 12%.     

Gravity model development for precise orbit computations for satellite altimetry

Satellite altimeters have been developed which have the capability of measuring the surface topography of the ocean over entire basins for time periods of several years with a precision of a few cm. The combination of these data with accurate satellite position information, subsurface measurements and models of the density field can be used to determine the general circulation of the ocean and its variability. The Topex altimeter oceanographic experiment proposed for the early 1990's requires a radial orbit accuracy approaching 10 cm. Considerable progress has been made at the Goddard Space Flight Center in developing precision orbit determination to support satellite altimetry analysis. This progress is attributed to the development of more accurate models of the earth gravity field, earth and ocean tidal effects, a reference coordinate system as well as improved drag and solar radiation pressure computations. This computational system has been used for the Seasat data acquired during the 1978 time period and has produced an rms radial accuracy of about 50 cm. A first step towards the development of a new Interim gravity model is presented. Global orbit determination accuracies have been improved using these new PGS-T1 and T2 fields.     

行星三体引力摄动对卫星探测器大气制动的影响

考虑行星引力在其卫星探测器大气制动过程中的显著摄动,建立了基于Milankovitch参数的平均轨道动力学模型并对土卫六探测器进行仿真。首先,将轨道参数转换为无奇异的Milankovitch参数,考虑探测卫星的大气阻力、扁率摄动以及行星引力摄动,建立了半解析轨道方程。其次,以土卫六探测器为对象,选择不同的土星初始方位角进行有大气和无大气情况下的数值仿真,并进行比较分析。结果表明,土星初始方位角的选择会引起土卫六大气制动轨道偏心率和近拱点高度在不同范围内震荡,极大地影响大气制动效果。      

Towards accurate atmospheric mass density determination Using precise positional information of space objects

This paper presents a new method of deriving atmospheric mass densities with a high temporal resolution from precise orbit data of low earth orbiting (LEO) space objects. This method is based on the drag perturbation equation of the semi-major axis of the orbit of LEO space objects which relates the change rate of the semi-major axis to the atmospheric mass density. The effectiveness of the new method is evaluated using the GFZ-ISDC GPS rapid science orbit (RSO) products of the CHAMP satellite over a time period of 3 months. The densities derived using this new method and obtained from accelerometer data are compared and good agreements are achieved. An example of using the derived density to generate good orbit prediction for CHAMP is presented.     

近圆低轨卫星星座相位保持方法

主要研究无轨道高度保持要求的近圆低轨卫星星座相位保持方法.首先根据轨道摄动理论，推导了考虑J2摄动和大气阻尼摄动的卫星相位漂移模型，分别给出基于固定基准星和基于虚拟基准星的相位偏差两种表达方法.在此基础上，按照星座各星轨道衰减一致和不一致两种情况，分别提出两种表示方法理论的和考虑实际控制误差的相位保持策略.通过一个walker星座仿真算例验证了两种方法的有效性.仿真结果显示，两种方法在各星轨道衰减一致和不一致两种情况均可有效完成相位维持任务，当各星轨道衰减一致时两种方法在控制次数和控制总量上无明显差异；在各星轨道衰减不一致情况下，基于固定基准星的相位保持策略更优.     

卫星轨道维持方法

人造地球卫星的轨道由于大气阻力和地球引力场等因素的摄动,其形状和近地点位置将不断改变。本文提供一种保持轨道形状和近地点位置不变的控制方法。     

基于会切场推力器无拖曳系统建模及参数优化

随着卫星重力测量技术的突破性进展,对航天器试验环境要求也在不断提高,航天器受到的残余扰动必须尽可能减小。作为中国将来重力场测量卫星备选主推力器的会切场推力器,其推力器的控制精度直接决定了测量的准确性。文章首先通过PID方法设计了位移模式下的无拖曳控制器,该控制器在预估阻力系数、参考质量与卫星本体的位移差、速度差等性能方面有良好的表现,在应对卫星运行时的突发情况时表现出很强的稳定性。但PID参数没有达到最优解,在此基础上对于该模型的控制精度进行优化,用遗传算法对PID控制的参数进行筛选。结果分析表明,会切场推力器的控制精度有所改善,NTW方向上的速度和位移误差均减小;推力阻力和显著减少;控制精度提高,更好地满足使用需求。