Impact of the time span selected to calibrate the ballistic parameter on spacecraft re-entry predictions

The trajectory modeling of satellites that are re-entering the Earth’s atmosphere, as a result of natural orbital decay, has always been a challenging task. Residual lifetime estimations and re-entry predictions are affected by substantial uncertainties, associated with atmospheric density models, with the forecasts of the relevant solar and geomagnetic activity indices and with tracking data, which for uncontrolled re-entries are usually sparse and not particularly accurate. Furthermore, modeling the aerodynamic forces that act on low altitude satellites is a formidable task, especially for objects of a complex shape and unknown attitude evolution.     

On the generation of satellite position (and velocity) by a mixed analytical-numerical procedure

The generation of accurate Earth-satellite ephemerides by numerical integration, over a period of perhaps weeks, can consume an inordinate amount of computer time. No satisfactory purely analytical procedure exists, but if short-period components of the standard elliptic elements are removed analytically, the resulting mean elements can be integrated with a step time that is longer than the satellite's orbital period.The definition of the mean elements depends on the particular perturbations included in the orbit generator and regarded as non-resonant. It is best if short-period perturbations are not applied to the orbital elements themselves but to the satellite's position (and velocity if required), expressed in a system of cylindrical polar coordinates, and the paper shows how mean elements can be recovered from position and velocity.A computer program has been written to test the proposed procedure for generating ephemerides, using a truncated potential field. Some results from this program are presented.     

Numerical modeling of propagation of breaking nonlinear acoustic-gravity waves from the lower to the upper atmosphere

Acoustic-gravity waves (AGWs) observed in the upper atmosphere may be generated near the Earth’s surface due to a variety of meteorological sources. Two-dimensional simulations of vertical propagation and breaking of nonlinear AGWs in the atmosphere are performed. Forcing near the Earth’s surface is used as the AGW source in the model. We use a numerical method based on finite-difference analogues of fundamental conservation laws for solving atmospheric hydrodynamic equations. This approach selects physically correct generalized solutions of the wave hydrodynamic equations. Numerical simulations are performed in a representative region of the Earth’s atmosphere up to altitude 500 km. Vertical profiles of temperature, density, molecular viscosity and heat conductivity were taken from the standard atmosphere model MSIS-90 for January. Calculations were made for different amplitudes and frequencies of lower boundary wave forcing. It is shown that after activating the tropospheric wave forcing, the initial pulse of AGWs may very quickly propagate to altitudes of 100 km and above and relatively slowly dissipate due to molecular viscosity and heat conduction. This may increase the role of transient nonstationary waves in effective energy transport and variations of atmospheric parameters and gas admixtures in a broad altitude range.     

Thermal neutrons’ response to the GLEs

Thermal neutrons’ flux near the Earth’s crust is very sensitive regarding different processes and phenomena both in the near-Earth space and in the Earth’s crust by reason of the dual nature of the thermal neutron flux. Its first source is associated with high-energy particles of cosmic rays penetrating into the Earth’s atmosphere and interacting with its elements. The second source originates from the radioactive gases contained in the Earth’s crust. So the contributions of these two sources are specified by the Earth’s crust conditions and its movements, on one hand and variations of high-energy particles flux near the Earth.     

Reentry survival analysis of tumbling metallic hollow cylinder

The survival of orbital debris reentering the Earth’s atmosphere is considered. The numerical approach of NASA’s Object Reentry Survival Analysis Tool (ORSAT) is reviewed, and a new equation accounting for reradiation heat loss of hollow cylindrical objects is presented. Based on these, a code called Survivability Analysis Program for Atmospheric Reentry (SAPAR) has been developed, and the new equation for reradiation heat loss is validated. Using this equation in conjunction with the formulation used in ORSAT, a comparative case study on the Delta-II second stage cylindrical tank is given, demonstrating that the analysis using the proposed equation is in good agreement with the actual recovered object when a practical value for thermal emissivity is used. A detailed explanation of the revised formulation is given, and additional simulation results are presented. Finally, discussions are made to address the applicability of the proposed equation to be incorporated in future survival analyses of orbital debris.     

Improving the orbits of GPS block IIA satellites during eclipse seasons

During Sun-Earth eclipse seasons, GPS-IIA satellites perform noon, shadow and post-shadow yaw maneuvers. If the yaw maneuvers are not properly taken into account in the orbit determination process, two problems appear: (1) the observations residuals increase since the modeled position of the satellite’s navigation antenna differs from the true position, and (2) the non-conservative forces like solar radiation pressure or Earth radiation pressure are mismodeled due to the wrong orientation of the satellite’s surfaces in space.     

Measurements of the radiation quality factor Q at aviation altitudes during solar minimum (2006–2008)

In radiation protection, the Q-factor has been defined to describe the biological effectiveness of the energy deposition or absorbed dose to humans in the mixed radiation fields at aviation altitudes. This particular radiation field is generated by the interactions of primary cosmic particles with the atoms of the constituents of the Earth’s atmosphere. Thus the intensity, characterized by the ambient dose equivalent rate H∗(10), depends on the flight altitude and the energy spectra of the particles, mainly protons and alpha particles, impinging on the atmosphere. These charged cosmic projectiles are deflected both by the interplanetary and the Earth’s magnetic field such that the corresponding energy spectra are modulated by these fields. The solar minimum is a time period of particular interest since the interplanetary magnetic field is weakest within the 11-year solar cycle and the dose rates at aviation altitudes reach their maximum due to the reduced shielding of galactic cosmic radiation. For this reason, the German Aerospace Center (DLR) performed repeated dosimetric on-board measurements in cooperation with several German airlines during the past solar minimum from March 2006 to August 2008. The Q-factors measured with a TEPC range from 1.98 at the equator to 2.60 in the polar region.     

Long-term (50 years) measurements of cosmic ray fluxes in the atmosphere

Since the middle of 1957 till present time the group of researchers of P.N. Lebedev Physical Institute of the Russian Academy of Sciences has carried out the regular balloon borne measurements of charged particle fluxes in the atmosphere. The measurements are performed at polar (northern and southern) and middle latitudes and cover the interval of heights from the ground level up to 30–35 km. Standard detectors of particles (gas-discharged counters) have been used. More than 80,000 measurements of cosmic ray fluxes in the atmosphere have been performed to the present time. In the data analysis the geomagnetic field and the Earth’s atmosphere are used as cosmic ray spectrometers.     

The ground GNSS tomography – unconstrained approach

The GNSS signal along its more than 20,000 km line of sight is bended, attenuated and delayed. These effects are results of the Earth’s atmosphere, and Sun radiation. Amongst all mentioned effects the one considered in this paper is a signal phase delay in troposphere.     

Specification of the Earth’s plasmasphere with data assimilation

In this paper we report on initial work toward data assimilative modeling of the Earth’s plasmasphere. As the medium of propagation for waves which are responsible for acceleration and decay of the radiation belts, an accurate assimilative model of the plasmasphere is crucial for optimizing the accurate prediction of the radiation environments encountered by satellites. On longer time-scales the plasmasphere exhibits significant dynamics. Although these dynamics are modeled well by existing models, they require detailed global knowledge of magnetospheric configuration which is not always readily available. For that reason data assimilation can be expected to be an effective tool in improving the modeling accuracy of the plasmasphere. In this paper we demonstrate that a relatively modest number of measurements, combined with a simple data assimilation scheme, inspired by the ensemble Kalman filtering data assimilation technique does a good job of reproducing the overall structure of the plasmasphere including plume development. This raises hopes that data assimilation will be an effective method for accurately representing the configuration of the plasmasphere for space weather applications.     

Optimising filtering of two-line element sets to increase re-entry prediction accuracy for GTO objects

Predicting re-entry epoch of space objects enables managing the risk to ground population. Predictions are particularly difficult for objects in highly-elliptical orbits, and important for objects with components that can survive re-entry, e.g. rocket bodies (R/Bs). This paper presents a methodology to filter two-line element sets (TLEs) to facilitate accurate re-entry prediction of such objects. Difficulties in using TLEs for precise analyses are highlighted and a set of filters that identifies erroneous element sets is developed. The filter settings are optimised using an artificially generated TLE time series. Optimisation results are verified on real TLEs by analysing the automatically found outliers for exemplar R/Bs. Based on a study of 96 historical re-entries, it is shown that TLE filtering is necessary on all orbital elements that are being used in a given analysis in order to avoid considerably inaccurate results.     

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.     

GNSS reflectometry and remote sensing: New objectives and results

The Global Navigation Satellite System (GNSS) has been a very powerful and important contributor to all scientific questions related to precise positioning on Earth’s surface, particularly as a mature technique in geodesy and geosciences. With the development of GNSS as a satellite microwave (L-band) technique, more and wider applications and new potentials are explored and utilized. The versatile and available GNSS signals can image the Earth’s surface environments as a new, highly precise, continuous, all-weather and near-real-time remote sensing tool. The refracted signals from GNSS radio occultation satellites together with ground GNSS observations can provide the high-resolution tropospheric water vapor, temperature and pressure, tropopause parameters and ionospheric total electron content (TEC) and electron density profile as well. The GNSS reflected signals from the ocean and land surface could determine the ocean height, wind speed and wind direction of ocean surface, soil moisture, ice and snow thickness. In this paper, GNSS remote sensing applications in the atmosphere, oceans, land and hydrology are presented as well as new objectives and results discussed.     

Neutron monitor asymptotic directions of viewing during the event of 13 December 2006

During the recent ground level enhancement of 13 December 2006, also known as GLE70, solar cosmic ray particles of energy bigger that ∼500 MeV/nucleon propagated inside the Earth’s magnetosphere and finally accessed low-altitude satellites and ground level neutron monitors. The magnitude and the characteristics of this event registered at different neutron monitor stations of the worldwide network can be interpreted adequately on the basis of an estimation of the solar particle trajectories in the near Earth interplanetary space. In this work, an extended representation of the Earth’s magnetic field was realized applying the Tsyganenko 1989 model. Using a numerical back-tracing technique the solar proton trajectories inside the magnetospheric field of the Earth were calculated for a variety of particles, initializing their travel at different locations, covering a wide range of energies. In this way, the asymptotic directions of viewing were calculated for a significant number of neutron monitor stations, providing crucial information on the Earth’s “magnetospheric optics” for primary solar cosmic rays, on the top of the atmosphere, during the big solar event of December 2006. The neutron monitor network has been treated, therefore, as a multidimensional tool that gives insights into the arrival directions of solar cosmic ray particles as well as their spatial and energy distributions during extreme solar events.     

The effect of spatial truncation error on integral inversion of satellite gravity gradiometry data

The satellite gravity gradiometry (SGG) data can be used for local modelling of the Earth’s gravity field. In this study, the SGG data in the local north-oriented and orbital frames are inverted to the gravity anomaly at sea level using the second-order partial derivatives of the extended Stokes formula. The emphasis is on the spatial truncation error and the kernel behaviour of the integral formulas in the aforementioned frames. The paper will show that only the diagonal elements of gravitational tensor at satellite level are suitable for recovering the gravity anomaly at sea level. Numerical studies show that the gravity anomaly can be recovered in Fennoscandia with an accuracy of about 6 mGal directly from on-orbit SGG data.     

Application of neural networks to South African GPS TEC modelling

The propagation of radio signals in the Earth’s atmosphere is dominantly affected by the ionosphere due to its dispersive nature. Global Positioning System (GPS) data provides relevant information that leads to the derivation of total electron content (TEC) which can be considered as the ionosphere’s measure of ionisation. This paper presents part of a feasibility study for the development of a Neural Network (NN) based model for the prediction of South African GPS derived TEC. The South African GPS receiver network is operated and maintained by the Chief Directorate Surveys and Mapping (CDSM) in Cape Town, South Africa. Vertical total electron content (VTEC) was calculated for four GPS receiver stations using the Adjusted Spherical Harmonic (ASHA) model. Factors that influence TEC were then identified and used to derive input parameters for the NN. The well established factors used are seasonal variation, diurnal variation, solar activity and magnetic activity. Comparison of diurnal predicted TEC values from both the NN model and the International Reference Ionosphere (IRI-2001) with GPS TEC revealed that the IRI provides more accurate predictions than the NN model during the spring equinoxes. However, on average the NN model predicts GPS TEC more accurately than the IRI model over the GPS locations considered within South Africa.     

基于航天器解体事件的空间碎片寿命算法

研究了针对航天器解体事件所生成的空间碎片的寿命计算方法.给出了基于NASA标准航天器解体模型的航天器解体算法.该算法生成的一系列碎片参数,将作为寿命计算的初始条件.总结了现有求解碎片寿命的算法,并提出了一种半分析算法.该算法运用平均根数法的思路,计算了在J2摄动项的影响下,碎片的半长轴和偏心率的变化率;并采用微分积分法预报半长轴和偏心率随时间的变化.为了适应时变大气模型,该算法限制了计算步长.通过与数值法的比较分析了算法的计算速度和精度.选用了3种大气模型:SA76、GOST和MSIS-00,分析了不同大气模型在计算碎片寿命之间的差异.通过与P-78卫星解体事件的实测数据对比验证了整个算法的正确性.      

Some additional results in the regular balloon monitoring of cosmic rays in the Earth’s atmosphere

The different types of the data recorded in the experiment of the regular balloon monitoring of cosmic rays (carried out since 1957 by Lebedev Physical Institute, Moscow, Russia, in several locations) are described. So called detailed information (the form of each pulse detected by the ground-based receiver) recorded during the last 12 years is discussed in more details. The use of these data both for getting and correcting the standard results of the experiment and for obtaining some additional information on the cosmic rays in the Earth’s atmosphere is considered.     

Numerical modeling of inhomogeneous orographic wave influence on planetary waves in the middle atmosphere

Parameterization of dynamical and thermal effects of stationary orographic gravity waves (OGWs) generated by the Earth’s surface topography is incorporated into a numerical model of general circulation of the middle and upper atmosphere. Responses of atmospheric general circulation and characteristics of planetary waves at altitudes from the troposphere up to the thermosphere to the effects of OGWs propagating from the earth surface are studied. Changes in atmospheric circulation and amplitudes of planetary waves due to variations of OGW generation and propagation in different seasons are considered. It is shown that during solstices the main OGW dynamical and heat effects occur in the middle atmosphere of winter hemispheres, where changes in planetary wave amplitudes due to OGWs may reach up to 50%. During equinoxes OGW effects are distributed more homogeneously between northern and southern hemispheres.     

Antiparticle content in the magnetosphere

In the present work we assess the stable and transient antiparticle content of planetary magnetospheres, and subsequently we consider their capture and application to high delta-v space propulsion. We estimate the total antiparticle mass contained within the Earth’s magnetosphere to assess the expediency of such usage. Using Earth’s magnetic field region as an example, we have considered the various source mechanisms that are applicable to a planetary magnetosphere, the confinement duration versus transport processes, and the antiparticle loss mechanisms. We have estimated the content of the trapped population of antiparticles magnetically confined following production in the exosphere due to nuclear interactions between high energy cosmic rays (CR) and constituents of the residual planetary upper atmosphere.The galactic antiprotons that directly penetrate into the Earth’s magnetosphere are themselves secondary by its nature, i.e. produced in nuclear reactions of the cosmic rays passing through the interstellar matter. These antiproton fluxes are modified, dependent on energy, when penetrating into the heliosphere and subsequently into planetary magnetospheres. During its lifetime in the Galaxy, CR pass through the small grammage of the interstellar matter where they produce secondary antiprotons. In contrast to this, antiprotons generated by the same CR in magnetosphere are locally produced at a path length of several tens g/cm² of matter in the ambient planetary upper atmosphere. Due to the latter process, the resulting magnetically confined fluxes significantly exceed the fluxes of the galactic antiprotons in the Earth’s vicinity by up to two orders of magnitude at some energies.The radiation belt antiparticles can possibly be extracted with an electromagnetic-based “scoop” device. The antiparticles could be concentrated by and then stored within the superimposed magnetic field structure of such a device. In future developments, it is anticipated that the energy of the captured antiparticles (both rest energy and kinetic energy) can be adapted for use as a fuel for propelling spacecraft to high velocities for remote solar system missions.