Estimating the spin axis orientation of the Echostar-2 box-wing geosynchronous satellite

For the first time, the spin axis orientation of an inactive box-wing geosynchronous satellite has been estimated from ground-based optical photometric observations of Echostar-2’s specular reflections. Recent photometric light curves obtained of Echostar-2 over four years suggest that unusually bright and brief specular reflections were occurring twice within an observed spin period. These bright and brief specular reflections suggested two satellite surfaces with surface normals separated by approximately 180°. The geometry between the satellite, the Sun, and the observing location at the time of each of the brightest observed reflections, was used to estimate Echostar-2’s equatorial spin axis orientation coordinates. When considering prograde and retrograde rotation, Echostar-2’s spin axis orientation was estimated to have been located within 30° of either equatorial coordinate pole. Echostar-2’s spin axis was observed to have moved approximately 180° in right ascension, within a time span of six months, suggesting a roughly one year spin axis precession period about the satellite’s angular momentum vector.     

Spin axis orientation of Ajisai determined from Graz 2 kHz SLR data

The Graz 2 kHz Satellite Laser Ranging (SLR) measurements allow determination of the spin axis orientation of the geodetic satellite Ajisai. The high repetition rate of the laser makes it possible to determine the epoch time when the laser is pointing directly between two corner cube reflector (CCR) rings of the satellite. Identification of many such events during a few (up to 3) consecutive passes allows to state the satellite orientation in the celestial coordinate system. Six years of 2 kHz SLR data (October 2003–October 2009) delivered 331 orientation values which clearly show precession of the axis along a cone centered at 14^h56^m2.8^s in right ascension and 88.512° in declination (J2000.0 celestial reference frame) and with an half-aperture angle θ of 1.405°. The spin axis precesses with a period of 117 days, which is equal to the period of the right ascension of the ascending node of Ajisai’s orbit. We present a model of the axis precession which allows prediction of the satellite orientation – necessary for the envisaged laser time transfer via Ajisai mirrors.     

Some comparisons of orbit determination and parameter estimation based on LAGEOS 1 and LAGEOS 2 data

The modelling accuracy of the LAGEOS 1 orbit was continously improved since its launch in 1976. In spite of these experiences the modelling accuracy of LAGEOS 2 is still about 20 per cent worse. Considering e. g. only the influence of different gravity field models it has been shown that the orbital fits for arc lengths of one month is generally about 25 mm for LAGEOS 1 and more than 30 mm for LAGEOS 2. This is mainly due to the fact that LAGEOS 2 has not yet been used for the determination of most gravity field models. The influences of different model parameters on the estimation of station coordinates, Earth rotation parameters, the geogravitational coefficient, the radiation pressure coefficient, and the empirical acceleration has been studied. The differences and peculiarities of both satellites are discussed. Although the analysis of LAGEOS 2 data still does not reach the high level of LAGEOS 1 combination solutions using both satellites allow new insights, higher accuracies, and a higher time resolution for the parameters and phenomena investigated.     

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.     

利用近地点磁场探测数据确定卫星自旋轴参数

阐述了利用近地点磁场探测数据确定卫星自旋轴参数的理论方法和实施步骤,并说明了这种研究对卫星运行和科学探测的重要性.特别强调了需要注意的基本条件,即卫星必须自旋稳定且近地点不很高(1000 km以下).这种方法关键的步骤是,根据卫星轨道数据定出模型磁场数值,比较近地点星载磁强计探测数据和近地点地磁模型数值确定卫星自旋轴的指向.通过对TC-1和TC-2卫星姿态的具体计算,对确定精度和应用效果进行了分析和比较.结果表明,在实际的卫星应用过程中此方法和措施非常有效,在科学分析和将来的卫星运行工程中具有重要的应用意义.      

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.     

Spin rate and spin axis orientation of LARES spectrally determined from Satellite Laser Ranging data

Satellite Laser Ranging (SLR) is a powerful technique able to measure spin rate and spin axis orientation of the fully passive, geodetic satellites. This work presents results of the spin determination of LARES – a new satellite for testing General Relativity. 529 SLR passes measured between February 17 and June 9, 2012, were spectrally analyzed. Our results indicate that the initial spin frequency of LARES is f₀ = 86.906 mHz (RMS = 0.539 mHz). A new method for spin axis determination, developed for this analysis, gives orientation of the axis at RA = 12^h22^m48^s (RMS = 49^m), Dec = −70.4° (RMS = 5.2°) (J2000.0 celestial reference frame), and the clockwise (CW) spin direction. The half-life period of the satellite’s spin is 214.924 days and indicates fast slowing down of the spacecraft.     

Thermal-optical design of a geodetic satellite for one millimeter accuracy

The LAGEOS (LAser GEOdynamic Satellite) satellites use a 1.5 in. uncoated retroreflector (cube corner). Design studies done for LAGEOS-1 showed that using smaller cubes would result in greater accuracy and lower thermal gradients. However, this would require using a larger number of cubes. Simulations showed that the accuracy goal of 5 mm could be met using 1.5 in. cubes by adding a dihedral angle offset. The LARES (LAser RElativity Satellite) satellite launched in 2012 is a smaller version of LAGEOS using the same size cube corner and floating mount as LAGEOS.The recent development of COTS (Commercial Off-The-Shelf) cube corners has eliminated cost as an obstacle to using a larger number of smaller cubes. COTS cubes have no dihedral angle offset. However, no offset is needed if the size is chosen properly. The diffraction pattern of a 1.0 in. uncoated cube with no dihedral angle offset has 6 lobes around the central peak due to total internal reflection, The velocity aberration for LAGEOS is about 32–40 microradians. The OCS (Optical Cross Section) of a one inch uncoated COTS retroreflector is about 0.5 million sq m for the LAGEOS orbit.Testing of 10 inexpensive COTS cubes by Ludwig Grunwaldt and Reinhart Neubert shows good cross section (unpublished work done at GFZ Potsdam, Germany). Measurement of 50 COTS cubes at INFN (Mondaini et al., 2018), shows a loss of cross section of only 33% (Slide 10). Simulations show that systematic range errors on the order of a half millimeter are possible for a spherical geodetic satellite such as LARES. Adjustments for the holding and ejection system result in some loss of accuracy.     

Attitude analysis of space debris using SLR and light curve data measured with single-photon detector

Attitude is the important parameter for active debris removal and collision avoidance. This paper deduced the spin axis orientation and spin period of the rocket body, CZ-3B R/B (NORAD ID 38253), using the satellite laser ranging and light curve data measured with single-photon detector at Graz station. The epoch method and LC & SLR residuals fitting were combined to determine these values. The derived right ascension angle was around 220°, the declination angle was near 64° and the sidereal period was calculated to be 117.724 s, for 2017-07-03. The results derived from the two distinct methods were mutually validated. Rocket bodies are a major contributor to space debris and this work provides a reference for attitude determination and attitude modelling.     

Radiative forces and LAGEOS' orbit

The orbit analysis of LAGEOS satellite has resulted into the discovery and/or reassessment of several very small sources of perturbation on satellite orbits. The analysis of orbital arcs of duration ranging from one month to several years has revealed that perturbative effects are present, having unpredicted long-term or secular components down to the 10⁻¹² m/s² acceleration level. It was soon realized that those perturbations have a non-gravitational origin.

In recent years, we have devoted some effort to the physical modelling of radiative perturbations, caused by momentum exchanges with an appropriate radiative field, and have considered their potential role in the analysis of LAGEOS orbit residuals. These perturbations include: (i) direct solar radiation pressure; (ii) radiation pressure from the Earth's emitted/reflected/diffused radiation flux; (iii) the so-called thermal thrust force.

The main results of this work are reviewed, discussing its relationships with models developed by other research groups. In particular, we present a list of the physical processes which still appear to need more detailed and realistic modelling to reach a better understanding of LAGEOS dynamics at the 10⁻¹² m/s² level.     

Lower thermospheric density structure derived from late decay phases of satellite orbits

In order to obtain new insight into the detailed structure of the lower thermosphere the long-established method of drag analysis again proves to be a powerful tool. For near-circular satellite orbits, in addition to the semi-major axis, the eccentricity and the argument of perigee are strongly influenced by atmospheric drag. With the help of a new computational scheme, which is based on fundamental equations of satellite drag analysis, the amplitudes and phases of global density variations are derived.     

Broglio Drag Balance for neutral thermosphere density measurement on UNICubeSAT

The nanosatellite UNICubeSAT is described, carrying a Broglio Drag Balance Instrument for neutral thermosphere density in situ measurements. The aim of the mission is to contribute to the development of accurate thermosphere models, achieving in situ, real time measurements of atmosphere density, that could be exploited for global atmosphere model validation and accurate short term (1–3 days) real time space weather forecasts. The satellite is inexpensive and swarms could be easily launched operating as a distributed sensor network to get simultaneous in situ local (not orbit averaged) measurements in multiple positions and orbit heights. The nanosatellite is based on the Cubesat standard architecture, weighing about 1 kg for 1-L volume. Atmospheric drag force is measured by the displacement of light plates exposed to the incoming particle flux seen by the spacecraft, applying the original three dimensional Broglio Drag Balance concept to a single nanosatellite axis. The instrument concept and its relation to the satellite bus is depicted, showing that many long term potential measurement error sources and biases can be removed in data processing if the spacecraft is spin stabilized. The expected accuracy in density measurements is 20%. The instrument cost is a fraction of that of accurate accelerometers. The onboard systems are based on commercial off the shelf components, in accordance with the short lifetime typical of aeronomy satellites.     

重力梯度力矩作用下近地卫星自旋运动规律分析

为研究近地卫星自旋运动规律,建立了近地卫星在受摄动影响的轨道上运行并受重力梯度力矩作用下的姿态运动模型,推导了自旋角速率满足一定条件下自旋运动的进动角、章动角、自旋角的解析解,对重力梯度作用下的自旋姿态运动规律进行了仿真分析,并用仿真计算结果验证了解析解的正确性。在轨道面缓慢进动情况下,当卫星绕最大主惯量轴自旋时,给出了自旋角速率取值范围表达式,在该取值范围内卫星自旋运动能够跟随轨道面一起进动,自旋轴以恒定的平均角速率进动,章动角在小范围内波动。建立的自旋姿态运动模型和分析结论可用于近地卫星姿态失控后的姿态确定和预测、在轨姿态设计及在轨备份等。     

Spin parameters of nanosatellite BLITS determined from Graz 2 kHz SLR data

The nanosatellite BLITS (Ball Lens In The Space) is the first object designed as a passive, spherical retroreflector of the Luneburg type, dedicated for Satellite Laser Ranging (SLR). The 2 kHz SLR station Graz measures spin parameters of this satellite, providing information about the rotational dynamics of the body. The measurements obtained during the period from September 26, 2009 to November 24, 2010 show a significant change of the spin configuration. The spin axis was dynamically precessing since the launch and currently is sinus-like behaving between coordinates RA 120°…150°, Dec 30°…60° (J2000 inertial reference frame). The angle between the symmetry axis and the spin axis of BLITS is not constant, but is decreasing since the launch, while its spin period is rather stable with a mean value of 5.613 s (clockwise rotation). The satellite was dynamically changing its attitude during the first three months after deployment; after this time the spin parameters are relatively stable.     

Yarkovsky-Schach effect on space debris motion

The Yarkovsky-Schach effect is a small perturbation affecting Earth satellites and space debris illuminated by the Sun. It was first applied to the orbit of LAGEOS satellites as an explanation of the residuals in orbital elements. In this work, we carry out several numerical integration tests taking into consideration various orbit and rotation parameters, in order to analyse this effect in a broader context. The semi-major axis variations remain small and depend on the spin axis attitude with respect to the Sun. We show that the force amplitude is maximised for orbits inclined with $i\approx$?20–30°. We also observe the influence on other orbital elements, notably on the orbit inclination. However, these effects are clearly observed only on long timescales; in our simulations, we propagated the orbits for 200?y. The Yarkovsky-Schach effect is thus confirmed to have a minuscule magnitude. It should be taken into account in studies requiring high-precision orbit determination, or on expanded timescales.     

一种基于连续星图观测的自旋姿态估计方法

传统的利用地球敏感器和太阳敏感器作为测量仪器的自旋卫星姿态确定方法存在系统误差和安装误差等,从而导致自旋姿态确定误差较大的问题,文章提出了一种利用星敏感器获取的连续星图估计卫星自旋姿态参数的新方法。该方法以卫星的自旋轴和旋转角速度作为状态变量,通过星敏感器连续跟踪拍摄的恒星的成像位置作为观测量,利用无迹卡尔曼滤波估计出卫星的自旋姿态参数。仿真结果表明,在星敏感器的精度为3″时,该方法的自旋轴估计精度为0.3448″,自旋角速度估计精度为10^-4(°)/s数量级。     

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.     

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.     

High accuracy satellite drag model (HASDM)

The dominant error source in force models used to predict low-perigee satellite trajectories is atmospheric drag. Errors in operational thermospheric density models cause significant errors in predicted satellite positions, since these models do not account for dynamic changes in atmospheric drag for orbit predictions. The Air Force Space Battlelab’s High Accuracy Satellite Drag Model (HASDM) estimates and predicts (out three days) a dynamically varying global density field. HASDM includes the Dynamic Calibration Atmosphere (DCA) algorithm that solves for the phases and amplitudes of the diurnal and semidiurnal variations of thermospheric density near real-time from the observed drag effects on a set of Low Earth Orbit (LEO) calibration satellites. The density correction is expressed as a function of latitude, local solar time and altitude. In HASDM, a time series prediction filter relates the extreme ultraviolet (EUV) energy index E_10.7 and the geomagnetic storm index a_p, to the DCA density correction parameters. The E_10.7 index is generated by the SOLAR2000 model, the first full spectrum model of solar irradiance. The estimated and predicted density fields will be used operationally to significantly improve the accuracy of predicted trajectories for all low-perigee satellites.     

Drag balance Cubesat attitude motion effects on in-situ thermosphere density measurements

The dynamics of Cubesats carrying a drag balance instrument (DBI) for in situ atmosphere density measurements is analyzed. Atmospheric drag force is measured by the displacement of two light plates exposed to the incoming particle flow. This system is well suited for a distributed sensor network in orbit, to get simultaneous in situ local (non orbit averaged) measurements in multiple positions and orbit heights, contributing to the development and validation of global atmosphere models. The implementation of the DBI leads to orbit normal pointing spinning two body system. The use of a spin-magnetic attitude control system is suggested, based only on magnetometer readings, contributing to making the system simple, inexpensive, and reliable. It is shown, by an averaging technique, that this system provides for orbit normal spin axis pointing. The effect of the coupling between the attitude dynamics and the DBI is evaluated, analyzing its frequency content and showing that no frequency components arise, affecting the DBI performance. The analysis is confirmed by Monte Carlo numerical simulation results.