Satellite In Circular Orbit Research Articles

Modelling Earth’s lithospheric magnetic field using satellites in low-perigee elliptical orbits

SUMMARYThe sensitivity of magnetic measurements taken by satellites in elliptical orbits to the lithospheric magnetic field is studied by comparing the formal error variances of the lithospheric Gauss coefficients for various satellite orbital constellations. Analytical expressions are presented for the variances of the Gauss coefficients when either all three magnetic vector components or only the radial component are used. We compare the results obtained using a satellite in a near-polar circular orbit at 350 km altitude with those from a satellite in an elliptical orbit with perigee at 140 km (and apogee at 1500 km) and find that the latter leads to Gauss coefficient variances at spherical harmonic degree n = 180 (corresponding to a horizontal wavelength of λ = 220 km) that are 104 times smaller compared to those derived from a similar number of data measured at 350 km altitude. The improvements in variance ratio at degree n = 145 (λ = 275 km) and n = 110 (λ = 360 km) are 103 and 102, respectively. These findings are supported by an analysis of synthetic magnetic data along simulated satellite orbits from which the lithospheric Gauss coefficients are estimated and compared with the original ones used to generate the synthetic data. Coefficients at degree n are successfully determined if the power of the difference between retrieved and original coefficients at that degree is smaller than the power of the lithospheric field (i.e. of the input coefficients). Using 3 yr of simulated data we conclude that magnetic measurements from a satellite in an elliptical orbit with perigee at 140 km allow for a reliable determination of the lithospheric field up to spherical harmonic n ≈ 170 while a satellite in a circular orbit at 350 km height only enables lithospheric field modelling up to n ≈ 100. The analysis demonstrates that low-altitude magnetic data collected by satellites in low-perigee elliptical orbits—although only available for a fraction of each orbit—enable improved global lithospheric field modelling at spatial wavelengths well beyond what is currently possible with data from satellites in circular orbits that do not reach such low altitudes. We applied the approach to the orbital configuration proposed for the Daedalus satellite mission (140 km perigee); the method will however also help in the preparation for other satellite missions in near-polar low-perigee elliptical orbits like the Macau Science Satellite pair MSS-2A and MSS-2B (perigee of 200 km or lower).

On the stability of additional moons orbiting Kepler-1625 b

ABSTRACT Since it was proposed, the exomoon candidate Kepler-1625 b-I has changed the way we see satellite systems. Because of its unusual physical characteristics, many questions about the stability and origin of this candidate have been raised. Currently, we have enough theoretical studies to show that if Kepler-1625 b-I is indeed confirmed, it will be stable. Regarding its origin, previous works indicated that the most likely scenario is capture, although conditions for in situ formation have also been investigated. In this work, we assume that Kepler-1625 b-I is an exomoon and study the possibility of an additional, massive exomoon being stable in the same system. To model this scenario, we perform N-body simulations of a system including the planet, Kepler-1625 b-I, and one extra Earth-like satellite. Based on previous results, the satellites in our system will be exposed to tidal interactions with the planet and to gravitational effects owing to the rotation of the planet. We find that the satellite system around Kepler-1625 b is capable of harbouring two massive satellites. The extra Earth-like satellite can be stable in various locations between the planet and Kepler-1625 b-I, with a preference for regions inside $25\, R_{\rm p}$. Our results suggest that the strong tidal interaction between the planet and the satellites is an important mechanism to ensure the stability of satellites in circular orbits closer to the planet, while the 2:1 mean motion resonance between the Earth-like satellite and Kepler-1625 b-I would provide stability for satellites in wider orbits.

A Coastal Experiment for GNSS-R Code-Level Altimetry Using BDS-3 New Civil Signals

High temporal and spatial resolutions are the key advantages of the global navigation satellites system-reflectometry (GNSS-R) technique, while low precision and instabilities constrain its development. Compared with conventional Ku/C band nadir-looking radar altimetry, the precision of GNSS-R code-level altimetry is restricted by the smaller bandwidth and the lower transmitted power of the signals. Fortunately, modernized GNSS broadcast new open-available ranging codes with wider bandwidth. The Chinese BDS-3 system was built on 31 July 2020; its inclined geostationary orbit and medium circular orbit satellites provide B1C and B2a public navigation service signals in the two frequency bands of B1 and B2. In order to investigate their performance on GNSS-R code-level altimetry, a coastal experiment was conducted on 5 November 2020 at a trestle of Weihai in the Shandong province of China. The raw intermediate frequency data with a 62 MHz sampling rate were collected and post-processed to solve the sea surface height every second continuously for over eight hours. The precisions were evaluated using the measurements from a 26 GHz radar altimeter mounted on the same trestle near our GNSS-R setup. The results show that a centimeter-level accuracy of GNSS-R altimetry—based on B1C code after the application of the moving average—can be achieved, while for B2a code, the accuracy is about 10 to 20 cm.

ON THE CHARACTER OF AN ARTIFICIAL SATELLITE DRAG UNDER VARIOUS STATES OF SOLAR AND GEOMAGNETIC ACTIVITY

Purpose: The artificial satellites drag in the atmosphere remains an urgent problem to date. In this work, the artificial satellites data are used in order to study the atmosphere state under various manifestations of solar and geomagnetic activity. The selected satelites were moving uncontrollable being good indicators of the upper atmosphere state. The B-star (drag term) drag coefficient is used in this work. This term is used in the SGP and SDP models to take into account the resistance of the atmosphere to the satelite orbital motion. The data of the drag of two artificial satellites, one moving in elliptical and the other in circular orbits at midlatitudes (orbital plane angles of 58°-60°) were considered. These data include the end of the 23rd solar activity cycle, as well as the growth, the maximum and the decay phases of the 24th solar cycle (years 2005–2017). Seven periods of anomalous drag of the satellites were analyzed. They are: 4 monthly periods (two in 2005 and two in 2011) and 3 yearly periods (within 19.07.2014 to 22.08.2015), five-year long (2005–2010) and six-year long (2011–2017) periods. Design/methodology/approach: The periodogram analysis was made. This allowed to reveal the periodic processes in changes in the state of the atmosphere of different duration. The correlation coefficients of the B-star drag term with the indices of solar and geomagnetic activity were calculated. The analysis of extreme drag of the satellites in the periods of the increased solar and geomagnetic activity (intervals of observation lasting a month) was made. Findings: Using the solar and geomagnetic data we found that some month-long part of the anomalous drag periods were followed by flares on the Sun and the arrival of the coronal mass ejections into the near-Earth space. At time intervals of yearlong observations the highest values (0.5-0.7) were obtained for the coefficients of the B-star parameter correlation with the solar activity indices – solar radiation at the wavelength of 10.7 cm, F10.7, and Lyman alpha radiation, Lα. At monthly time intervals, the largest values of the correlation coefficients were obtained for the B-stars with the electron fluxes with energies above 0.6 and 2 MeV, E, (0.3-0.5), the Lyman alpha radiation, Lα, (0.58–0.73 for a сircular orbit satellite), and the solar constant, TSI, (0.3–0.6), as well as the geomagnetic storms intensity index, Dst , (0.66–0.69). Periodogram calculations show the presence of a whole spectrum of periods in the deceleration of a circular orbit satellite and a dedicated period for an elliptical orbit satellite. Conclusions: The B-star drag term dependences on the indices of solar and geomagnetic activity during some periods of their intensification for the 23–24 cycles of solar activity are considered. The periodogram analysis made together with the analysis of the conditions and parameters of space weather allows to see the general and more detailed picture of the solar and geomagnetic activity influence on the change in the motion of the satellite in the atmosphere. The B-star drag term helps to consider only the atmosphere influence on the artificial satellite movement in the near-Earth space. Key words: artificial satellite, atmosphere, artificial satellite drag, solar activity, geomagnetic activity, space weather

Basic performance and future developments of BeiDou global navigation satellite system

The core performance elements of global navigation satellite system include availability, continuity, integrity and accuracy, all of which are particularly important for the developing BeiDou global navigation satellite system (BDS-3). This paper describes the basic performance of BDS-3 and suggests some methods to improve the positioning, navigation and timing (PNT) service. The precision of the BDS-3 post-processing orbit can reach centimeter level, the average satellite clock offset uncertainty of 18 medium circular orbit satellites is 1.55 ns and the average signal-in-space ranging error is approximately 0.474 m. The future possible improvements for the BeiDou navigation system are also discussed. It is suggested to increase the orbital inclination of the inclined geostationary orbit (IGSO) satellites to improve the PNT service in the Arctic region. The IGSO satellite can perform part of the geostationary orbit (GEO) satellite’s functions to solve the southern occlusion problem of the GEO satellite service in the northern hemisphere (namely the “south wall effect”). The space-borne inertial navigation system could be used to realize continuous orbit determination during satellite maneuver. In addition, high-accuracy space-borne hydrogen clock or cesium clock can be used to maintain the time system in the autonomous navigation mode, and stability of spatial datum. Furthermore, the ionospheric delay correction model of BDS-3 for all signals should be unified to avoid user confusion and improve positioning accuracy. Finally, to overcome the vulnerability of satellite navigation system, the comprehensive and resilient PNT infrastructures are proposed for the future seamless PNT services.

Ionospheric Sounding and Tomography Using Automatic Identification System (AIS) and Other Signals of Opportunity

AbstractNumerical modeling has demonstrated that Automatic Identification System (AIS) signals can be used not only to estimate vertical total electron content (TEC) to supplement current TEC maps and data assimilation models but also to reconstruct two‐dimensional (2‐D) electron density maps of the ionosphere using computerized tomography. A ray tracing model was used to determine the characteristics of individual linearly polarized waves transmitted by ships to satellites in circular orbits at 780‐ and 1,000‐km altitude, including the wave path and the state of polarization at the satellite receiver. The modeled Faraday rotation was computed and used to calculate the TEC along the ray paths. The resulting TEC was used as input for computerized ionospheric tomography using the algebraic reconstruction technique. This study concentrated on reconstructing mesoscale structures 25–100 km in horizontal extent. The primary scientific interest of this study was to show that AIS signals can be used as a new source of input data for computerized ionospheric tomography to image the ionosphere and to obtain a better understanding of magneto‐ionic wave propagation.

Dynamics of Reusable Tether System with Sliding Bead Capsule for Deorbiting Small Payloads

This paper is devoted to the problem of a small payload delivery from an orbit to the Earth by a reusable space tether system consisting of a satellite in circular orbit, a tether, and a bottom module. The payload is placed in a dynamically symmetrical bead capsule, which can slide along the tether. Three scenarios for the payload delivery are proposed: an uncontrolled sliding of the capsule, a soft docking with the bottom module following separation, and a soft docking and the tether spin-up. The objectives of the paper are developing a mathematical model of the system, conducting a numerical analysis of its behavior, and comparison of the descent scenarios. The mathematical model that takes into account the friction between the bead capsule and the inextensible three-segment tether is developed using the Lagrange formalism. The results show that high-frequency oscillations of the bead capsule, its sharp stop, and the tether tangling can be observed. The scenario comparison allows concluding that the third scenario is more effective in terms of the capsule’s orbit perigee radius minimizing, but it requires considerable time. The first scenario, compared with the second one, yields a significant decrease in perigee altitude, but it is more dangerous.

Conservative Term Constrained Kalman Filter for Autonomous Orbit Determination

This paper presents a novel constrained Kalman filter framework for autonomous orbit determination. By using Lagrangian multiplier techniques, the conserved terms of orbit motion are incorporated into the estimation routines to reconstruct the Kalman filter, and then the orthogonal and multipartial-norm-constrained Kalman filters are developed for the satellite in circular orbit and eccentric ones, respectively. Finally, scenarios of both circular and eccentric orbits with unknown measurement bias are simulated by using the proposed constrained Kalman filter; the simulation results show that the estimation accuracy is significantly improved after introducing the conservative terms as constraint.

Validation of Galileo orbits using SLR with a focus on satellites launched into incorrect orbital planes

The space segment of the European Global Navigation Satellite System (GNSS) Galileo consists of In-Orbit Validation (IOV) and Full Operational Capability (FOC) spacecraft. The first pair of FOC satellites was launched into an incorrect, highly eccentric orbital plane with a lower than nominal inclination angle. All Galileo satellites are equipped with satellite laser ranging (SLR) retroreflectors which allow, for example, for the assessment of the orbit quality or for the SLR–GNSS co-location in space. The number of SLR observations to Galileo satellites has been continuously increasing thanks to a series of intensive campaigns devoted to SLR tracking of GNSS satellites initiated by the International Laser Ranging Service. This paper assesses systematic effects and quality of Galileo orbits using SLR data with a main focus on Galileo satellites launched into incorrect orbits. We compare the SLR observations with respect to microwave-based Galileo orbits generated by the Center for Orbit Determination in Europe (CODE) in the framework of the International GNSS Service Multi-GNSS Experiment for the period 2014.0–2016.5. We analyze the SLR signature effect, which is characterized by the dependency of SLR residuals with respect to various incidence angles of laser beams for stations equipped with single-photon and multi-photon detectors. Surprisingly, the CODE orbit quality of satellites in the incorrect orbital planes is not worse than that of nominal FOC and IOV orbits. The RMS of SLR residuals is even lower by 5.0 and 1.5 mm for satellites in the incorrect orbital planes than for FOC and IOV satellites, respectively. The mean SLR offsets equal -44.9, -35.0, and -22.4 mm for IOV, FOC, and satellites in the incorrect orbital plane. Finally, we found that the empirical orbit models, which were originally designed for precise orbit determination of GNSS satellites in circular orbits, provide fully appropriate results also for highly eccentric orbits with variable linear and angular velocities.

Three‐Axis Global Magnetic Attitude Control of Earth‐Pointing Satellites in Circular Orbit

AbstractThis paper addresses the controllability and global stability issues of a magnetically actuated satellite in the geomagnetic field. The variation of the geomagnetic field along the orbit, which is time varying in nature, makes the dynamics of the satellite time varying also. Sufficient conditions for controllability of such a time varying magnetic attitude control system are given. As a major contribution, it is proven that the three‐axis controllability of the spacecraft actuated by the magnetic actuators is possible and it does not depend on the initial angular velocity of the spacecraft. Global controllability is a precursor to global stability. Therefore, exponential stability for an arbitrarily high initial angular velocity and an arbitrary initial orientation is proven next for a proportional‐derivative control law using averaging theory. It is also proven that even an iso‐inertial satellite can be stabilized using the time invariant feedback control, which was hitherto not possible, even using time variant conventional control. Simulation results are presented under different initial orientations and angular velocities of the satellite in the presence of favorable and unfavorable gravity gradient torques to validate the proposed control method.

Коррекция траектории перехода космического аппарата на круговую орбиту спутника при использовании торможения в атмосфере в условиях неопределенности ее параметров

Коррекция траектории перехода космического аппарата на круговую орбиту спутника при использовании торможения в атмосфере в условиях неопределенности ее параметров

Moon’s influence on the plane variation of circular orbits

The long-term orbital plane motion of a satellite in circular orbit has been investigated, taking into account the influence of the Earth’s oblateness and luni-solar perturbations, to determine solutions characterised by initial conditions (in terms of Right Ascension of the Ascending Node and orbit inclination) which guarantee quasi-frozen orbital planes. The Moon’s influence has been investigated considering the real motion of the lunar pole around the ecliptic pole, also evaluating the differences with respect to the simplified case in which these poles are considered as coincident at 23.445deg of inclination. After having studied in detail the case of geosynchronous orbits, where at low inclination differences in the order of ±1.5deg have been found for the optimal initial inclination with respect to the above-mentioned simplified case, the analysis has been extended to the range of altitude 20,000–60,000km. The study has highlighted how the optimal initial conditions are strictly correlated to the launch date and how the differences between the real and the simplified cases increase with satellite altitude.

LAPLACE PLANE MODIFICATIONS ARISING FROM SOLAR RADIATION PRESSURE

The dynamical effects of solar radiation pressure (SRP) in the solar system have been rigorously studied since the early 1900s. This non-gravitational perturbation plays a significant role in the evolution of dust particles in circumplanetary orbits, as well as in the orbital motion about asteroids and comets. For gravitationally dominated orbits, SRP is negligible and the resulting motion is largely governed by the oblateness of the primary and the attraction of the Sun. The interplay between these gravitational perturbations gives rise to three mutually perpendicular planes of equilibrium for circular satellite orbits. The classical Laplace plane lies between the equatorial and orbital planes of the primary, and is the mean reference plane about whose axis the pole of a satellite's orbit precesses. From a previously derived solution for the secular motion of an orbiter about a small body in a SRP dominated environment, we find that SRP acting alone will cause an initially circular orbit to precess around the pole of the primary's heliocentric orbital plane. When the gravitational and non-gravitational perturbations act in concert, the resulting equilibrium planes turn out to be qualitatively different, in some cases, from those obtained without considering the radiation pressure. The warping of the surfaces swept out by the modified equilibria as the semi-major axis varies depends critically on the cross-sectional area of the body exposed. These results, together with an adiabatic invariance argument on Poynting–Robertson drag, provide a natural qualitative explanation for the initial albedo dichotomy of Saturn's moon, Iapetus.

MODELING THE FLYBY ANOMALIES WITH DARK MATTER SCATTERING: UPDATE WITH ADDITIONAL DATA AND FURTHER PREDICTIONS

We continue our exploration of whether the flyby anomalies can be explained by scattering of spacecraft nucleons from dark matter gravitationally bound to the Earth, with the addition of data from five new flybys to that from the original six. We continue to use our model in which inelastic and elastic scatterers populate shells generated by the precession of circular orbits with normals tilted with respect to the Earth's axis. With 11 data points and eight parameters in the model, a statistically meaningful fit is obtained with a chi-squared of 2.7. We give plots of the anomalous acceleration along the spacecraft trajectory, and the cumulative velocity change, for the five flybys which exhibit a significant nonzero anomaly. We also discuss implications of the fit for dark matter–nucleon cross-sections, give the prediction of our fit for the anomaly to be expected from the future Juno flyby, and give predictions of our fit for flyby orbit orientation changes. In addition, we give formulas for estimating the flyby temperature increase caused by dark matter inelastic scattering, and for the fraction of flyby nucleons undergoing such scatters. Finally, for circular satellite orbits, we give a table of predicted secular changes in orbit radius. These are much too large to be reasonable — comparing with data for COBE and GP-B supplied to us by Edward Wright (after the first version of this paper was posted), we find that our model predicts changes in orbit radius that are too large by many orders of magnitude. So the model studied here is ruled out. We conclude that further modeling of the flyby anomalies must simultaneously attempt to fit constraints coming from satellite orbits.

Modified iterated extended Kalman particle filter for single satellite passive tracking

Single satellite-to-satellite passive tracking techniques have great significance in space surveillance systems. A new passive modified iterated extended Kalman particle filter (MIEKPF) using bearings-only measurements in the Earth-Centered Inertial Coordinate System is proposed. The modified iterated extended Kalman filter (MIEKF), with a new maximum likelihood iteration termination criterion, is used to generate the proposal distribution of the MIEKPF. Moreover, a new measurement update equation of the MIEKF is derived by modifying the objective function of the Gauss--Newton iteration. The approximated second-order linearized state propagation equation, Jacobian matrix of state transfer, and measurement equations are derived in satellite 2-body movement. The tracking performances of the MIEKPF, iterated extended Kalman particle filter (IEKPF), extended Kalman particle filter (EKPF), and extended Kalman filter (EKF) are compared via Monte Carlo simulations through simulated data from STK8.1. The simulation results indicate that the proposed MIEKF is capable of passively tracking a low earth circular orbit satellite with a high earth orbit satellite using bearings-only measurements and has higher tracking precision than the traditional algorithms.

Passive tracking from the combined set of bearings and frequency measurements by single satellite

In this paper, a new passive modified iterated extended Kalman filter (MIEKF) using the combined set of bearings and frequency measurements in Earth Centered Inertial (ECI) coordinate is proposed. A new measurement update equation of MIEKF is derived by modifying the objective function of the Gauss-Newton iteration. A new gain equation and iteration termination criteria are acquired by applying the property of the maximum likelihood estimate. The approximated second order linearized state propagation equation, Jacobian matrix of state transfer and measurement equations are derived in satellite two-body movement. The tracking performances of MIEKF, iterated extended Kalman filter (IEKF) and extended Kalman filter (EKF) are compared via Monte Carlo simulations through simulated data from STK8.1. Simulation results indicate that the proposed MIEKF is possible to passively track low earth circular orbit satellite by a high earth orbit satellite, and has higher tracking precision than the IEKF and EKF.

Study of Stability of Rotational Motion of Spacecraft with Canonical Variables

This work aims to analyze the stability of the rotational motion of artificial satellites in circular orbit with the influence of gravity gradient torque, using the Andoyer variables. The used method in this paper to analyze stability is the Kovalev‐Savchenko theorem. This method requires the reduction of the Hamiltonian in its normal form up to fourth order by means of canonical transformations around equilibrium points. The coefficients of the normal Hamiltonian are indispensable in the study of nonlinear stability of its equilibrium points according to the three established conditions in the theorem. Some physical and orbital data of real satellites were used in the numerical simulations. In comparison with previous work, the results show a greater number of equilibrium points and an optimization in the algorithm to determine the normal form and stability analysis. The results of this paper can directly contribute in maintaining the attitude of artificial satellites.

Spin‐Stabilized Spacecrafts: Analytical Attitude Propagation Using Magnetic Torques

An analytical approach for spin‐stabilized satellites attitude propagation is presented, considering the influence of the residual magnetic torque and eddy currents torque. It is assumed two approaches to examine the influence of external torques acting during the motion of the satellite, with the Earth′s magnetic field described by the quadripole model. In the first approach is included only the residual magnetic torque in the motion equations, with the satellites in circular or elliptical orbit. In the second approach only the eddy currents torque is analyzed, with the satellite in circular orbit. The inclusion of these torques on the dynamic equations of spin stabilized satellites yields the conditions to derive an analytical solution. The solutions show that residual torque does not affect the spin velocity magnitude, contributing only for the precession and the drift of the spacecraft′s spin axis and the eddy currents torque causes an exponential decay of the angular velocity magnitude. Numerical simulations performed with data of the Brazilian Satellites (SCD1 and SCD2) show the period that analytical solution can be used to the attitude propagation, within the dispersion range of the attitude determination system performance of Satellite Control Center of Brazil National Research Institute.

Hohmann-Hohmann and Hohmann-Phasing Cooperative Rendezvous Maneuvers

We consider the problem of cooperative rendezvous between two satellites in circular orbits, given a fixed time for the rendezvous to be completed, and assuming a circular rendezvous orbit. We investigate two types of cooperative maneuvers for which analytical solutions can be obtained. One is the case of two Hohmann transfers, henceforth referred to as HHCM, while the other, henceforth referred to as HPCM, is the case of a Hohmann transfer and a phasing maneuver. For the latter case we derive conditions on the phasing angle that make a HPCM rendezvous cheaper than a cooperative rendezvous on an orbit that is different than either the original orbits of the two participating satellites. It is shown that minimizing the fuel expenditure is equivalent to minimizing a weighted sum of the ΔVs of the two orbital transfers, the weights being determined by the mass and engine characteristics of the satellites. Our results show that, if the time of rendezvous allows for a Hohmann transfer between the orbits of the satellites, the optimal rendezvous is either a noncooperative Hohmann transfer or a Hohmann-phasing cooperative maneuver. In both of these cases, the maneuver costs are determined analytically. A numerical example verifies these observations. Finally, we demonstrate the utility of this study for Peer-to-Peer (P2P) refueling of satellites residing in two different circular orbits.

Optimal Servicing of Geosynchronous Satellites

Optimal Servicing of Geosynchronous Satellites