Dynamical cartography of Earth satellite orbits

We have carried out a numerical investigation of the coupled gravitational and non-gravitational perturbations acting on Earth satellite orbits in an extensive grid, covering the whole circumterrestrial space, using an appropriately modified version of the SWIFT symplectic integrator, which is suitable for long-term ($～$120?years) integrations of the non-averaged equations of motion. Hence, we characterize the long-term dynamics and the phase-space structure of the Earth-orbiter environment, starting from low altitudes ($～$400?km) and going up to the GEO region and beyond. This investigation was done in the framework of the EC-funded “ReDSHIFT” project, with the purpose of enabling the definition of passive debris removal strategies, based on the use of physical mechanisms inherent in the complex dynamics of the problem (i.e., resonances). Accordingly, the complicated interactions among resonances, generated by different perturbing forces (i.e., lunisolar gravity, solar radiation pressure, tesseral harmonics in the geopotential) are accurately depicted in our results, where we can identify the regions of phase space where the motion is regular and long-term stable and regions for which eccentricity growth and even instability due to chaotic behavior can emerge. The results are presented in an “atlas” of dynamical stability maps for different orbital zones, with a particular focus on the (drag-free) range of semimajor axes, where the perturbing effects of the Earth’s oblateness and lunisolar gravity are of comparable order. In some regions, the overlapping of the predominant lunisolar secular and semi-secular resonances furnish a number of interesting disposal hatches at moderate to low eccentricity orbits. All computations were repeated for an increased area-to-mass ratio, simulating the case of a satellite equipped with an on-board, area-augmenting device. We find that this would generally promote the deorbiting process, particularly at the transition region between LEO and MEO. Although direct reentry from very low eccentricities is very unlikely in most cases of interest, we find that a modest “delta-v” ($\mathrm{\Delta }V$) budget would be enough for satellites to be steered into a relatively short-lived resonance and achieve reentry into the Earth’s atmosphere within reasonable timescales ($～$50?years).     

Earth and ocean tides from long-term analysis of satellite orbits

Precision laser tracking data on three close-earth satellites (Geos 1, Geos 2, and Lageos) are analyzed to obtain measurements of ocean tides, core-mantle resonance, and other mass displacements.Mean elements are computed for 6.0 years for Geos 1, 4.9 years for Geos 2, and 2.1 years for Lageos. Ocean tides T2, S2, K2, P1, K1, and φ1 are measured, along with the core-mantle resonance at the K1 and P1 frequencies, as predicted by Molodensky. Also measured are the Sa and Ssa tides and radiation-pressure area-to-mass ratios.     

Analytical expression for distant retrograde orbits around a small natural satellite

An analytical expression for distant retrograde orbits (DROs) is obtained in this study. Owing to the fact that a planar DRO is a closed orbit and can be expressed as an approximately elliptical orbit, respective geometries and periods of DROs are analytically calculated. A switching point, where various properties of planar DROs change abruptly with an increase in the orbital radius, is determined. The Mars–Deimos system is taken as a case study in this work. The proposed method can be applied to cases where the Hill’s approximation of the restricted three-body problem is valid. Numerical calculations are performed to validate the proposed method.     

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.     

Impact of GPS antenna phase center variations on precise orbits of the GOCE satellite

The first European Space Agency Earth explorer core mission GOCE (Gravity field and steady-state Ocean Circulation Explorer) has been launched on March 17, 2009. The 12-channel dual-frequency Global Positioning System receiver delivers 1 Hz data and provides the basis for precise orbit determination (POD) on the few cm-level for such a very low orbiting satellite (254.9 km). As a member of the European GOCE Gravity Consortium, which is responsible for the GOCE High-level Processing Facility (HPF), the Astronomical Institute of the University of Bern (AIUB) provides the Precise Science Orbit (PSO) product for the GOCE satellite. The mission requirement for 1-dimensional POD accuracy is 2 cm. The use of in-flight determined antenna phase center variations (PCVs) is necessary to meet this requirement. The PCVs are determined from 154 days of data and the magnitude is up to 3-4 cm. The impact of the PCVs on the orbit determination is significant. The cross-track direction benefits most of the PCVs. The improvement is clearly seen in the orbit overlap analysis and in the validation with independent Satellite Laser Ranging (SLR) measurements. It is the first time that SLR could validate the cross-track component of a LEO orbit.     

The motion of an artificial satellite under the terrestrial radiation pressure

The terrestrial infrared radiation pressure effects on the motion of an artificial satellite are investigated. The radiative field is described by a series of spherical harmonics. The equations for the changes of the elements are found and numerical examples for the case of the satellite D-5-B (1975 39 B) are given.     

Optimal H∞ robust output feedback control for satellite formation in arbitrary elliptical reference orbits

A two degree-of-freedom signal-based optimal H_∞ robust output feedback controller is designed for satellite formation in an arbitrary elliptical reference orbit. Based on high-fidelity linearized dynamics of relative motion, uncertainties introduced by non-zero eccentricity and gravitational J2 perturbation are separated to construct a robust control model. Furthermore, a distributed robust control model is derived by modifying the perturbed robust control model of each satellite with the eigenvalues of the Laplacian matrix of the communication graph, which represent uncertainty in the communication topology. A signal-based optimal H_∞ robust controller is then designed primarily. Considering that the uncertainties involved in the distributed robust control model have a completely diagonal structure, the corresponding analyses are made through structured singular value theory to reduce the conservativeness. Based on simulation results, further designs including increasing the degrees of freedom of the controller, modifying the performance and control weighted functions, adding a post high-pass filter according to the dynamic characteristics, and reducing the control model are made to improve the control performance. Nonlinear simulations demonstrate that the resultant optimal H_∞ robust output feedback controller satisfies the robust performance requirements under uncertainties caused by non-zero eccentricity, J2 perturbation, and varying communication topology, and that 5 m accuracy in terms of stable desired formation configuration can be achieved by the presented optimal H_∞ robust controller. In addition to considering the widely discussed uncertainties caused by the orbit of each satellite in a formation, the optimal H_∞ robust output feedback control model presented in the current work considers the uncertainties caused by varying communication topology in the satellite formation that works in a cooperative way. Other new improvements include adopting a new method to more accurately describe and analyze the effects of the higher-order J2 perturbation, combining all the uncertainties into a diagonal structure, and utilizing a structured singular value to synthesize and analyze the controller.     

Evaluation of geomagnetic field models using magnetometer measurements for satellite attitude determination system at low earth orbits: Case studies

In this study, different geomagnetic field models are compared in order to study the errors resulting from the representation of magnetic fields that affect the satellite attitude system. For this purpose, we used magnetometer data from two Low Earth Orbit (LEO) spacecraft and the geomagnetic models IGRF-12 (Thébault et al., 2015) and T89 (Tsyganenko, 1989) models to study the differences between the magnetic field components, strength and the angle between the predicted and observed vector magnetic fields. The comparisons were made during geomagnetically active and quiet days to see the effects of the geomagnetic storms and sub-storms on the predicted and observed magnetic fields and angles. The angles, in turn, are used to estimate the spacecraft attitude and hence, the differences between model and observations as well as between two models become important to determine and reduce the errors associated with the models under different space environment conditions. We show that the models differ from the observations even during the geomagnetically quiet times but the associated errors during the geomagnetically active times increase. We find that the T89 model gives closer predictions to the observations, especially during active times and the errors are smaller compared to the IGRF-12 model. The magnitude of the error in the angle under both environmental conditions was found to be less than 1°. For the first time, the geomagnetic models were used to address the effects of the near Earth space environment on the satellite attitude.     

Evolution of artificial ion clouds in the ionospheric F-region in CRRES satellite experiments from radiophysical sounding data

In the paper the results of the G-09 and G-12 Caribbean CRRES experiments radiophysical probing of artificial barium ion clouds in the ionosphere carried by ionosonde and vertical Doppler sounder are considered.     

Quiet time distribution of plasma pressure in the inner earth's magnetosphere

Trapped particles of the radiation belts provide a considerable part of plasma pressure at low L-shells. The evaluations of this part during quiet times can be made on the basis of existing trapped radiation models. The radial profiles of plasma pressure at 1.2 < L < 7 were obtained by using the empirical AP8MAX model of trapped radiation (L < 6.6) and the theoretical model of the distribution of the proton fluxes in the Earth's radiation belts (L < 7) developed on the basis of the numerical solution of the radial diffusion equation with dissipation processes. The calculations were compared with AMPTE/CCE data. The contribution of quiet-time plasma pressure profile producing the quiet-time ring current to D_st-variation was obtained about 15 nT which is comparative with the magnetic field disturbances during weak and moderate magnetic storms (D_st = −40 ≈ −100 nT).     

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.     

Long-term predictability of orbits around the geosynchronous altitude

For a family of simulated geostationary, geosynchronous and super-geostationary orbits we compute the indicator called MEGNO in order to find out which orbits are chaotic and the timescale of their exponential divergence. A symplectic integrator of the Wisdom–Holman type was used for this purpose, with an integration span of 40 years. The results indicate that chaotic orbits exist only at the separatrix between geostationary libration and circulation and that they are relatively rare. The super-geostationary region seems to be entirely regular and quasi-periodic on the timescale of few decades.     

Determination of orbits with Torun Orbit Processor system

The Torun Orbit Processor system (TOP) is a multipurpose system designed to provide the research requirements of the various orbital problems for artificial satellites. The analysis of mathematical model for the TOP system began in 1991 and coding for the IBM PC and Sun SparcStation 10 computers was completed in 1993. TOP was first used for laser data processing of Lageos satellite and for simulations of satellite-to-satellite tracking technique (SST). This paper gives an overview of TOP system and highlights some problems connected with orbit recovery.     

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.     

LET-distributions and doses of HZE radiation components at near-Earth orbits.

Among cosmic rays, the heavy nuclei ranging from carbon to iron provide the principal contribution to the dose equivalent. The LET-distributions and absorbed dose aid dose equivalent have been calculated and are presented as a function of shielding and tissue self-shielding. At solar minimum, outside the magnetosphere, the unshielded dose equivalent of nuclei with atomic number Z > or = 6 is about 47 rem/year. The contribution of the target nuclei adds 7 rem/year. With 4 g/cm2 aluminum shielding, and at a depth of 5 cm in a biological phantom of 30 cm diameter, the respective values are 11 and 10 rem/year. Corresponding dose rates for orbits with various inclinations are presented, as well as the LET distributions of various components of cosmic rays.     

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.     

Configuration space and stability analysis of solar sail near-vertical earth-trailing orbits

Regions outside the reach of traditional propulsion systems or the ones that require significant propellant, may be reached by harnessing the solar radiation pressure and leveraging coupled dynamics to maneuver a sail-based spacecraft. Earth-trailing orbits have recently been investigated for getting a unique perspective of the Sun while maintaining the spacecraft in close proximity to Earth. Vertical orbits trailing the Earth exhibit the additional capability to view the Sun from above and below the ecliptic plane. In this work, families of sail-based orbits are explored for varying Earth-trailing angles and Z amplitudes in the Sun-Earth circular restricted three-body problem. Optimization is carried out to ensure that the non-traditional vertical orbits exhibit a constant pitch angle control history, as well as symmetry across the X-Y plane. The stability of the resulting orbit families is assessed using an extension of Flouquet theory to Differential Algebraic Equations. Results indicate that sail-based Earth-trailing vertical orbits can be more stable than traditional sub-L₁ sail-based vertical orbits.