Effect Of Atmospheric Drag Research Articles

Dynamics of highly eccentric and highly inclined space debris

A common condition of many artificial satellites around the Earth is that they orbit on highly eccentric and/or highly inclined orbits. In this work, we study the secular dynamics of these bodies and we present some of their dynamical aspects. Highly eccentric satellites experience different forces along their trajectories, as their orbit tends to cross multiple regions in the space around the Earth, making relevant the effects of atmospheric drag, when the orbit enters the atmosphere, or the solar radiation pressure, when it is further away from the Earth. This means that one needs to take into account different forces, whose magnitude drastically depends on the orbital elements of the satellite. Besides, highly inclined orbits are important in the study of satellite dynamics, as large values of the inclination might provoke an increase of the eccentricity when the satellite is close to a lunisolar resonance. An accurate force model is developed for treating highly eccentric and highly inclined orbits, which includes the geopotential (limited to the most important harmonic coefficients), the effects of Moon and Sun (which are treated as third body perturbations), the secular effects of the atmospheric drag and the solar radiation pressure, using simple models for the density of the Earth’s atmosphere and the Sun’s radiation, respectively. Using canonical transformations we calculate three sets of elements, obtained averaging over different angle variables; we refer to them as mean, averaged mean and proper elements, the latter being quasi integrals of the motion. Using statistical tools, we show that the proper elements of a group of fragments are strongly correlated over time, in contrast to the mean and averaged mean elements, and can be used as an indicator of the group. Finally, we implement machine learning algorithms to efficiently cluster satellite fragments, using their proper elements, and we compare the results to the clusterisation using the averaged mean elements, for highly eccentric orbits, including cases where the dissipation, caused by the atmospheric drag, is relevant for the dynamics.

Novel Source–Sink Model for Space Environment Evolution with Orbit Capacity Assessment

The increasing number of anthropogenic space objects (ASOs) in low Earth orbit (LEO) poses a threat to the safety and sustainability of the space environment. Multiple companies are planning to launch large constellations of hundreds to thousands of satellites in the near future, increasing the probability of collisions and debris generation. This paper analyzes the long-term evolution of the LEO ASO population with the goal of estimating LEO orbital capacity. This is carried out by introducing a new probabilistic source–sink model. The developed source–sink model is a multishell multispecies model, which includes different object species, such as active and derelict satellites, and debris. Furthermore, debris are divided into the following two subgroups: trackable and nontrackable debris, the last ones representing a significant hazard for active satellites. In addition, the proposed model accounts for collision events and atmospheric drag effects, which include the influence of solar activity. Indeed, the Jacchia–Bowman 2008 thermospheric density model is exploited. The results prove that considering untracked debris within the model produces more collisions, and therefore a smaller population of active satellites affecting the safety of LEO and its orbital capacity.

Optimization of constellation deployment using on-board propulsion and Earth nodal regression

Constellation deployment using on-board propulsion is a cost-effective way for distributing multiple satellites into different orbital planes using a minimal number of launches. This paper focuses on the extension of previous studies based on analytical formulations of the problem into a more general numerically-based one, which can be applied to both electric and chemical propulsion systems. Additionally, the formulation is not restricted to in-plane maneuvers only, taking full advantage of the increased mobility capabilities of satellites equipped with high-efficiency propulsion systems. Two deployment methods are analyzed: the first is based on moving the satellites from the injection to the operational orbit sequentially with a properly timed delay between each maneuver so that the difference in nodal regression causes the accumulation of a given spacing; the second is built upon the parallel transfer of satellites into so called “drift” orbits which, once again, exploiting the differential nodal drift, can be used to accumulate orbital plane spacing until a required value is met, and the satellites can be finally moved into their operational orbits. A multi-objective optimization based on the high-fidelity numerical computation of maneuvers using a feedback control law coupled with a genetic algorithm is proposed, presenting a framework capable of generating optimal solutions with respect to total constellation propellant mass needs and deployment time. An example of application based on the FORMOSAT-3/COSMIC mission is presented. The results highlight the potential of the optimization routine which is intended to be applied systematically by mission designers to generate solutions for the deployment problem within the context of constellation design. Some important and un-explored properties of the problem, such as, launcher-related injection constraints, the selection of a suitable propulsion technology and the effects of atmospheric drag are analyzed. The results show the effect of these properties on the optimality of the solutions, and highlight the advantage of a mixed in-plane/out-of-plane maneuver approach.

The Effect of Atmospheric Drag Force on the Elements of Low Earth Orbital Satellites at Minimum Solar Activity

Researching and modeling perturbations is essential in astrodynamics because it gives information on the deviations from the satellite's normal, idealized, or unperturbed motion. Examined the impact of non-conservative atmospheric drag and orbital elements of low-earth-orbit satellites under low solar activity. The study is consisting of parts, the first looks at the effects of atmospheric drag on LEO satellites different area to mass ratios, and the second looks at different inclination values. Modeling the impacts of perturbation is included in each section, and the final portion determines the effects of atmospheric drag at various node values. The simulation was run using the Celestial Mechanics software system's SATORB module (Beutler, 2005), which solves the perturbation equations via numerical integration. The findings were examined using Matlab 2012. Conclusion that the impacts are stronger for retrograde orbits, which is due to the fact that the satellite moves in the opposite direction. The atmospheric drag effects for all orbital elements were increased by increasing the area to mass ratio. When the node value rises, the size parameter changes slightly, but the other orbital elements change. At varying inclinations, it is found that the changes in orbital elements due to atmospheric drug.

A deep learning approach to solar radio flux forecasting

The effect of atmospheric drag on spacecraft dynamics is considered one of the predominant sources of uncertainty in Low Earth Orbit. These effects are characterised in part by the atmospheric density, a quantity highly correlated to space weather. Current atmosphere models typically account for this through proxy indices such as the F10.7, but with variations in solar radio flux forecasts leading to significant orbit differences over just a few days, prediction of these quantities is a limiting factor in the accurate estimation of future drag conditions, and consequently orbital prediction. In this work, a novel deep residual architecture for univariate time series forecasting, N-BEATS, is employed for the prediction of the F10.7 solar proxy on the days-ahead timescales relevant to space operations. This untailored, pure deep learning approach has recently achieved state-of-the-art performance in time series forecasting competitions, outperforming well-established statistical, as well as statistical hybrid models, across a range of domains. The approach was found to be effective in single point forecasting up to 27-days ahead, and was additionally extended to produce forecast uncertainty estimates using deep ensembles. These forecasts were then compared to a persistence baseline and two operationally available forecasts: one statistical (provided by BGS, ESA), and one multi-flux neural network (by CLS, CNES). It was found that the N-BEATS model systematically outperformed the baseline and statistical approaches, and achieved an improved or similar performance to the multi-flux neural network approach despite only learning from a single variable.

A Globally Averaged Thermospheric Density Data Set Derived From Two‐Line Orbital Element Sets and Special Perturbations State Vectors

AbstractWe describe a long‐term data set of global average thermospheric mass density derived from orbit data on ∼7,700 objects in low Earth orbit, via the effect of atmospheric drag. The data cover the years 1967–2019 and altitudes 250–575 km, and the temporal resolution is 3–4 days for most years. The data set is an extension and revision of a previous version. The most important change is the use of more precise orbit data: special perturbation state vectors are now used starting in 2001, instead of mean Keplerian orbital elements. The data are suitable for climatological studies of thermospheric variations and trends, and for space weather studies on time scales longer than 3 days.

Atmospheric drag effects on modelled low Earth orbit (LEO) satellites during the July 2000 Bastille Day event in contrast to an interval of geomagnetically quiet conditions

Abstract. In this work, we simulated the atmospheric drag effect on two model SmallSats (small satellites) in low Earth orbit (LEO) with different ballistic coefficients during 1-month intervals of solar–geomagnetic quiet and perturbed conditions. The goal of this effort was to quantify how solar–geomagnetic activity influences atmospheric drag and perturbs satellite orbits, with particular emphasis on the Bastille Day event. Atmospheric drag compromises satellite operations due to increased ephemeris errors, attitude positional uncertainties and premature satellite re-entry. During a 1-month interval of generally quiescent solar–geomagnetic activity (July 2006), the decay in altitude (h) was a modest 0.53 km (0.66 km) for the satellite with the smaller (larger) ballistic coefficient of 2.2×10-3 m2 kg−1 (3.03×10-3 m2 kg−1). The associated orbital decay rates (ODRs) during this quiet interval ranged from 13 to 23 m per day (from 16 to 29 m per day). For the disturbed interval of July 2000 the significantly increased altitude loss and range of ODRs were 2.77 km (3.09 km) and 65 to 120 m per day (78 to 142 m per day), respectively. Within the two periods, more detailed analyses over 12 d intervals of extremely quiet and disturbed conditions revealed respective orbital decays of 0.16 km (0.20 km) and 1.14 km (1.27 km) for the satellite with the smaller (larger) ballistic coefficient. In essence, the model results show that there was a 6- to 7-fold increase in the deleterious impacts of satellite drag between the quiet and disturbed periods. We also estimated the enhanced atmospheric drag effect on the satellites' parameters caused by the July 2000 Bastille Day event (in contrast to the interval of geomagnetically quiet conditions). The additional percentage increase, due to the Bastille Day event, to the monthly mean values of h and ODR are 34.69 % and 50.13 % for Sat-A and 36.45 % and 68.95 % for Sat-B. These simulations confirmed (i) the dependence of atmospheric drag force on a satellite's ballistic coefficient, and (ii) that increased solar–geomagnetic activity substantially raises the degrading effect of satellite drag. In addition, the results indicate that the impact of short-duration geomagnetic transients (such as the Bastille Day storm) can have a further deleterious effect on normal satellite operations. Thus, this work increases the visibility and contributes to the scientific knowledge surrounding the Bastille Day event and also motivates the introduction of new indices used to describe and estimate the atmospheric drag effect when comparing regimes of varying solar–geomagnetic activity. We suggest that a model of satellite drag, when combined with a high-fidelity atmospheric specification as was done here, can lead to improved satellite ephemeris estimates.

Charting Satellite Courses in a Crowded Thermosphere

As the number of satellites in low Earth orbit grows by leaps and bounds, accurate calculations of the effects of atmospheric drag on their trajectories are becoming critically important.

Linearized model for satellite station-keeping and tandem formations under the effects of atmospheric drag

This work introduces a linearized analytical model for the study of the dynamic of satellites in near circular orbits under the effects of the atmospheric drag. This includes the evaluation of the station keeping required for each satellite subjected to a control box strategy, and also the study of the dynamic of tandem formations between two or more satellites that are located on the same nominal space-track. The model takes into account the effect of the orbit perturbation provoked by the atmospheric drag, while the effects of the Earth gravitation potential are included in the definition of the nominal orbits of the satellites. This allows to easily define the maneuvering strategies for the satellites involved in the tandem formation, and to study their absolute and relative dynamic. In particular, this work focuses on the study of a master–slave scenario and the in plane maneuvers that these satellites require, proposing two different control strategies for the formation.

Spectrophotometric and dynamical properties of the soviet/russian constellation of molniya satellites

We report on the extended observing campaign of the surviving Soviet/Russian spacecraft Molniya, carried out in the years 2014–17 at Mexican and Italian telescopes. Spectrophotometry and astrodynamical analysis have been carried out for all the 43 demised payloads still in uncontrolled HEO orbit at late 2017, in order to assess dynamical and reflectance properties of such a wide family of virtually identical orbiting objects, as well as their long-term orbit evolution, according to full historic Two-Line Elements (TLE) datasets in synergy with mathematical modeling to properly size up the prevailing effect of lunisolar perturbation and atmospheric drag.

Re-entry prediction of objects with low-eccentricity orbits based on mean ballistic coefficients

AbstractDuring re-entry objects with low-eccentricity orbits traverse a large portion of the dense atmospheric region almost every orbital revolution. Their perigee decays slowly, but the apogee decays rapidly. Because ballistic coefficients change with altitude, re-entry predictions of objects in low-eccentricity orbits are more difficult than objects in nearly circular orbits. Problems in orbit determination, such as large residuals and non-convergence, arise for this class of objects, especially in the case of sparse observations. In addition, it might be difficult to select suitable initial ballistic coefficient for re-entry prediction. We present a new re-entry prediction method based on mean ballistic coefficients for objects with low-eccentricity orbits. The mean ballistic coefficient reflects the average effect of atmospheric drag during one orbital revolution, and the coefficient is estimated using a semi-numerical method with a step size of one period. The method is tested using Iridium-52 which uses sparse observations as the data source, and ten other objects with low-eccentricity orbits which use TLEs as the data source. We also discuss the performance of the mean ballistic coefficient when used in the evolution of drag characteristics and orbit propagation. The results show that the mean ballistic coefficient is ideal for re-entry prediction and orbit propagation of objects with low-eccentricity orbits.

Atmospheric drag effect on LAPAN A1 orbit during geomagnetic storm 2017

Satellites moving through the atmosphere and experience a drag force in the opposite direction of their orbital motion. Atmospheric drag is the largest perturbations for low earth orbit satellites beside earth gravitation. We calculate the atmospheric drag on LAPAN A1 in a sun-synchronous circular orbit with an inclination of 97.60°, eccentricity of 0.0014, period of 99.039 minutes and an altitude of 630 km, during September in 2017. Data of orbital elements (Two Line Elements) taken from www.celestrak.com. Geomagnetic activity data (Dst index) taken from https://omniweb.gsfc.nasa.gov. The purpose of this study is to determine the relationship between atmospheric drag, orbital elements, and a geomagnetic storm. In 2017, hourly Dst index had a minimum value of -124 nT at 18:00 UTC, on September 8. But the geomagnetic storm in 2017 didn’t influence significantly to drag acceleration of LAPAN A1. During geomagnetic storm period in 2017, the changes of orbital elements were really small and the data is too scattered to be concluded as the effect of the geomagnetic storm.

REGULUS: A propulsion platform to boost small satellite missions

REGULUS is a propulsion platform for CubeSats. It integrates the Magnetically Enhanced Thruster (MET) and its subsystems (i.e., fluidic line, electronics, and thermo-structural components) in a 2U envelope of weight lower than 3 kg. MET is a RF cathode-less thruster capable of providing thrust in the range 300 μN to 900 μN, with maximum specific impulse of 900 s and maximum operation power of 60 W. The performance has been measured with a dedicated thrust balance, when the thruster is operated with 0.1 mg/s of Xenon gas. REGULUS: (i) is compatible with thermal, mechanical and electrical interfaces of the CubeSat platforms available in the marked, (ii) it relies on COTS components to abate the recurrent costs, and (iii) it is based on a passive thermal control system. The main framework of application of the REGULUS platform is the propulsion of medium-to-large CubeSats (from 6U up to 27U). Such capability is here demonstrated by comparing MET with other thrusters for CubeSats offered in the market. The feasibility of two possible mission scenarios, namely drag compensation and constellation deployment, has been verified through preliminary orbit calculations. The REGULUS platform can compensate the effects of atmospheric drag on a 6U CubeSat in a 400 km altitude orbit for years. Besides, by exploiting the natural drift of the ascending node caused by the second zonal harmonic of the terrestrial gravity field, a CubeSat constellation can be deployed through several planes in some months employing small fractions of the onboard propellant.

Study the Influence of Atmospheric Drag and J2 Effect in a Close-proximity Operation at LEO

In this paper is to assess the mission stability and the influence of J2 effect and aerodynamic forces. To maintain the relative motion of satellites by using a feedback control law for tracking error bound in the presence of J2 perturbation. A constant relative orbit under the effect of earth oblateness and conservative forces is referred as J2 and targeting the presence of atmospheric drag. Although, Schweighart and Sedwick control strategy for satellite relative motion is considering both lift and drag forces. The simulation result shows a better performance with high accuracy than an elliptical orbit under J2 perturbation and atmospheric drag along in-track formation. The algorithm and control strategies is useful tools for analysing a future space mission.

Performance and Applicability of Orbital Transfer with Bare Electrodynamic Tether

Electrodynamic tether technology is a novel way to perform spacecraft orbital transfers. This paper focuses on a bare electrodynamic tether (BEDT) system and evaluates its orbital transfer performance and mission applicability. A nonsingular dynamic model of the BEDT orbital transfer system is developed. In particular, the ambient perturbation forces, including the atmospheric drag and Earth oblateness effect, are taken into account. Numerical simulations are then performed to investigate the orbital transfer performance under various mission parameters involving the initial orbital altitude, initial orbital inclination, tether length, tether diameter, spacecraft mass, and power voltage. An orbital transfer scheme is designed to raise and regulate the orbit. Furthermore, to verify its practicability, the mission applicability of the BEDT system is analyzed for Ariane-4’s H10 upper stage by comparison with the conventional chemical propulsion method. Finally, the conclusions and some discussions are presented to support conducting BEDT-based orbital transfer mission planning in practice.

Motion Modeling of Two Linked Satellites in the Earth’s Gravitational Field for Solving Gravimetric Problems

Motion modeling of two low-orbit linked satellites for measuring the Earth’s gravitational field parameters is presented. The model takes the factors that affect the satellite motion into account, such as nonspherical geopotential, atmospheric drag, tides, and third-body effects from the Moon, Sun, and planets of the Solar System. As a result of modeling, a search for the optimal configuration of satellites for completion of scientific tasks and possibility of technical realization is performed.

Variational and symplectic integrators for satellite relative orbit propagation including drag

Orbit propagation algorithms for satellite relative motion relying on Runge–Kutta integrators are non-symplectic—a situation that leads to incorrect global behavior and degraded accuracy. Thus, attempts have been made to apply symplectic methods to integrate satellite relative motion. However, so far all these symplectic propagation schemes have not taken into account the effect of atmospheric drag. In this paper, drag-generalized symplectic and variational algorithms for satellite relative orbit propagation are developed in different reference frames, and numerical simulations with and without the effect of atmospheric drag are presented. It is also shown that high-order versions of the newly-developed variational and symplectic propagators are more accurate and are significantly faster than Runge–Kutta-based integrators, even in the presence of atmospheric drag.

Efficiency in Carrying Cargo to Earth Orbits: Spaceports Repositioning

Space flights are in these days not any more question of technology, but more question of costs. One way how to decrease cost of launch is change of home spaceport. Change of home spaceport for different rockets is a way to achieve more efficient launches to space. The reason is different acceleration achieved from Earth rotation. We added several mathematical calculations of missions to Low Earth Orbit and Geostationary Earth Orbit to show bonuses from Earth rotation and effect of atmospheric drag on specific rockets used these days. We discussed only already used space vessels. Namely Arianne 5, Delta 4 heavy, Proton-M, Zenit and Falcon9. For reaching GEO we discuss possibility of using Hohmman transfer, because none of aforementioned vessels is available for direct GEO entry. As possible place for launch we discussed spaceports Baikonur, Kennedy Space center, Guyana Space center and Sea Launch platform. We present results in form of additional acceleration for each spaceport, and we also project this additional acceleration in means payload increase. In conclusion we find important differences between vessel effectivity based on spaceport used for launch. Change of launch location may bring significant cost decrease for operators.

Robust control of spacecraft rendezvous on elliptical orbits: Optimal sliding mode and backstepping sliding mode approaches

The problem of relative motion control of spacecraft rendezvous process on elliptical orbit is considered in this paper. Due to the presence of nonlinear dynamics and external disturbances, two robust controllers are developed based on sliding mode control theory. The first one is an optimal sliding mode controller; in which optimal control theory is used to reduce the tracking error and fuel cost, and then integral sliding mode control technique is applied to robustify optimal controller. The other controller is a backstepping sliding mode one that is developed based on nonlinear dynamics of spacecraft rendezvous; having applied the backstepping method to synthesis the tracking errors and Lyapunov functions, a sliding mode controller is developed to guarantee the Lyapunov stability, handling of all nonlinearities, robustness against uncertainties as well as tracking the desired position. It is assumed that the chaser and target spacecraft are in a low Earth orbit and subject to the perturbing effects of J2 and atmospheric drag. In addition, two fault tolerant scenarios, i.e. thruster degradation and short thruster failure are also considered to verify the robustness and efficacy of the control approaches. Simulation results confirm the effectiveness of the proposed controllers in reaching to the desired position in case of actuator fault-free and fault tolerant situations.

Collision Probability Due to Space Debris Clouds Through a Continuum Approach

As the debris population increases, the probability of collisions in space grows. Because of the high level of released energy, even collisions with small objects may produce thousands of fragments. Propagating the trajectories of all the objects produced by a breakup could be computationally expensive. Therefore, in this work, debris clouds are modeled as a fluid, whose spatial density varies with time under the effect of atmospheric drag. By introducing some simplifying assumptions, such as an exponential model of the atmosphere, an analytical expression for the cloud density evolution in time is derived. The proposed approach enables the analysis of many potential fragmentation scenarios that would be time limited with current numerical methods that rely on the integration of all the fragments’ trajectories. In particular, the proposed analytical method is applied to evaluate the consequences of some recent breakups on a list of target objects. In addition, collision scenarios with different initial conditions are simulated to identify which parameters have the largest effect on the resulting collision probability. Finally, the proposed model is used to study the mutual influence among a set of high-risk targets, analyzing how a fragmentation starting from one spacecraft affects the collision probability of the others.