Radiation Pressure Parameters Research Articles

Impacts of inter-satellite links on the ECOM model performance for BDS-3 MEO satellites

Inter-satellite link (ISL) plays an essential role in current and future Global Navigation Satellite System (GNSS). In this study, we investigate the impact of ISL observations on precise orbit determination for BeiDou-3 Navigation Satellite System (BDS-3) Medium Earth Orbit (MEO) satellites based on different Extended CODE Orbit Models (ECOM). Thanks to the better observation geometry of the Ka-band ISL data compared to the L-band data for BDS-3 MEO satellites, the ISL solution substantially reduces Orbit Boundary Discontinuity (OBD) errors, except for C30, which suffers from unstable Ka-band hardware delay. From the external quality analysis, ISL significantly enhances the reliability of the orbit of MEO satellites manufactured by the China Academy of Space Technology (CAST). The standard deviation (STD) of the satellite laser ranging (SLR) residuals is approximately 2.5 cm, and the root mean square (RMS) is reduced by 10–23% compared to L-band solutions. Besides, the Sun-elongation angle dependent systematic error in SLR residuals nearly vanishes based on the reduced 5-parameter ECOM (ECOM1) or extended 7-parameter ECOM (ECOM2) with ISL data. This is because the ISL reduces the correlation between state parameters and solar radiation pressure (SRP) parameters as well as those among SRP parameters, leading to a more accurate estimation of both orbit and SRP perturbations, particularly those along B direction. This confirms that the deficiency of the SRP models for BDS-3 CAST satellites can be compensated by using better observation geometry from ISL data. On the other hand, for the satellite manufactured by Shanghai Engineering Center for Microsatellites (SECM), the ISL allows for a more accurate estimation of the Bc1 parameter in the ECOM1 model. This only reduces linear systematic error, possibly because the impact generated by the satellite bus cannot be entirely absorbed by the B-direction parameters.

A Study of Solar Radiation Pressure Model in BDS-3 Precise Orbit Determination

For the BDS (BeiDou Navigation Satellite System) satellites, the solar radiation pressure is the major non-gravitational perturbation the satellites suffer. Due to the influence of multiple factors, accurate modeling the solar radiation pressure acting on these satellites is difficult to accomplish. The solar radiation pressure perturbation is an essential source of error in the precise orbit determination (POD) and orbit prediction processes of the BDS satellites. As the ECOMC (Empirical CODE Orbit Model 1 and 2 Combined) model adopts the advantageous features of the ECOM1 (Empirical CODE Orbit Model 1) model and the ECOM2 (Empirical CODE Orbit Model 2) model, a greater number of parameters have been introduced into the model, leading to strong correlation between the ECOMC model parameters. In response to the deficiency of the ECOMC model, the authors collected the BDS-3 satellite precise ephemeris data that were provided by Wuhan University (WHU) from January 2019 to April 2022. And by these ephemeris data, the ECOMC model’s 13 parameters were obtained through the dynamic orbit fitting method. By conducting these time sequence diagrams analysis of the ECOMC model parameters, this thesis affords the selection strategies of the solar radiation pressure parameters of the ECOMC model for BDS-3 inclined geosynchronous orbit (IGSO) and medium earth orbit (MEO) satellite. And the rationality of the selection strategies of the solar radiation pressure parameters for the ECOMC model was verified by orbit fitting and orbit prediction experiments. The results show that using the improved ECOMC model gains the best orbit fitting effects for BDS-3 IGSO and MEO satellite, and can also enhance the accuracy of medium and long-term orbit prediction of BDS-3 IGSO and MEO satellite.

Estimation of Daily Average Global Solar Radiation with Nonlinear Regression Models Developed Using Some Meteorological and Geographical Parameters

In this study, it is aimed to develop empirical models that can be used in estimation of daily average solar radiation (RS) based on some meteorological and geographical parameters. Seven estimation models were developed by nonlinear regression analysis method using various combinations of air temperature (T), relative humidity (RH), extraterrestrial radiation (Ra), saturated (es) and actual vapour pressure (ea) parameters. The models were created using the long-term average daily meteorological data of Kahramanmaraş province (1938 – 2020). The models were tested both these long-term average data and daily meteorological data measured at Kahramanmaraş Sütçü İmam University (KSU) in 2019 and 2020. Long-term average daily actual RS data varied between 4.99 – 32.56 MJ m-2 day-1. The estimated solar radiation values (("RS" ) ̂) with the highest correlation (r = 0.99) with actual RS data were obtained with the RS_7 model, in which the parameters es, ea, T, RH and Ra were used together. The ("RS" ) ̂ values obtained using this model varied between 6.45 to 33.99 MJ m-2 day-1. For the RS_7, which showed the best performance among the seven models, mean absolute percentage error (MAPE) and root mean square error (RMSE) were determined as 4.17% and 0.69 MJ m-2 day-1, respectively. The daily RS values measured in KSU varied between 7.75 – 33.48 MJ m-2 day-1 and 10.51 – 30.23 MJ m-2 day-1 for 2019 and 2020. The ("RS" ) ̂ values closest to the measured RS values were estimated with the RS_7 model. The estimated ("RS" ) ̂ values by this model varied between 11.74 – 33.93 MJ m-2 day-1 and 13.93 – 31.57 MJ m-2 day-1 for 2019 and 2020, respectively. MAPE values were determined as 11.33% and 7.54%, respectively. It is concluded that this model can be used to estimates daily average solar radiation and will be an excellent alternative since it is compatible with the Kahramanmaraş conditions.

Improving the Orbits of the BDS-2 IGSO and MEO Satellites with Compensating Thermal Radiation Pressure Parameters

The orbit accuracy of the navigation satellites relies on the accurate knowledge of the forces on the spacecraft, in particular the non-conservative perturbations. This study focuses on the Inclined Geosynchronous Orbit (IGSO) and Medium Earth Orbit (MEO) satellites of the regional Chinese BeiDou Navigation Satellite System (BDS-2), for which apparent deficiencies of non-conservative models are identified and evidenced in the Satellite Laser Ranging (SLR) residuals. The orbit errors derived from the empirical 5-parameter Extended CODE Orbit Model (ECOM) as well as a semi-analytical adjustable box-wing model show prominent dependency on the Sun elongation angle, even in the yaw-steering attitude mode. Hence, a periodic acceleration in the normal direction of the +X surface, presumably generated by the mismodeled thermal radiation pressure, is introduced. The SLR validations reveal that the Sun elongation angle-dependent systematic errors were significantly reduced, and the orbit accuracy was improved by 10–30% to approximately 4.5 cm and 3.0 cm for the BDS-2 IGSO and MEO satellites, respectively.

Galileo precise orbit determination with optical two-way links (OTWL): a continuous wave laser ranging and time transfer concept

In this simulation study we analyze the benefit of ground-space optical two-way links (OTWL) for Galileo precise orbit determination (POD). OTWL is a concept based on continuous wave laser ranging and time transfer with modulated signals from and to ground stations. The measurements are in addition to Global Navigation Satellite System (GNSS) observations. We simulate the measurements with regard to 16 Galileo Sensor Stations. In the simulation study we assume that the whole Galileo satellite constellation is equipped with terminals for OTWL. Using OTWL together with Galileo L-band, in comparison with an orbit solution calculated with L-band-only, demonstrates the advantage of combining two ranging techniques with different influences of systematic errors. The two-way link allows a station and satellite clock synchronization. Furthermore, we compare the ground-space concept with the satellite-to-satellite counterpart known as optical two-way inter-satellite links (OISL). The advantage of OTWL is the connection between the satellite system and the solid Earth as well as the possibility to synchronize the satellite clocks and the ground station clocks. The full network, using all three observation types in combination is simulated as well. The possibility to estimate additional solar radiation pressure (SRP) parameters within these combinations is a clear benefit of these additional links. We paid great attention to simulate systematic effects of all observation techniques as realistically as possible. For L-band these are measurement noise, tropospheric delays, phase center variation of receiver and transmitter antennas, constant and variable biases as well as multipath. For optical links we simulated colored and distance-dependent noise, offsets due to the link repeatability and offsets related to the equipment calibration quality. In addition, we added a troposphere error for the OTWL measurements. We discuss the influence on the formal orbit uncertainties and the effects of the systematic errors. Restrictions due to weather conditions are addressed as well. OTWL is synergetic with the other measurement techniques like OISL and can be used for data transfer and communication, respectively.

A long‐term broadcast ephemeris model for extended operation of GNSS satellites

GNSS positioning relies on orbit and clock information, which is predicted on ground and transmitted by the individual satellites as part of their broadcast navigation message. The predictions are typically refreshed at least once per day and partitioned into short-arc ephemeris data sets covering a representative validity period of 0.5-4 h. For an increased autonomy of either the space or user segment, the capability to predict a GNSS satellite orbit over extended periods of up to two weeks is studied. A tailored force model for numerical orbit propagation is proposed that offers high accuracy but can still be used in real-time environments. Aside from Earth-orientation parameters, six state vector components and three empirical solar radiation pressure parameters are employed for each satellite and adjusted to past orbits. Using the Galileo constellation with its high-grade hydrogen maser clocks as an example, global average signal-in-space range errors of less than 25 m RMS and 3D position errors of less than about 50 m are demonstrated after two week predictions in 95% of all test cases over a half-year period. The autonomous orbit prediction model thus enables adequate quality for a rapid first fix or contingency navigation in case of lacking ground segment updates.

Stability of generalized elliptic restricted four body problem with radiation and oblateness effects

This paper studies the existence and stability of non-collinear equilibrium points in the elliptic restricted four body problem with bigger primary as a source of radiation and other two primaries having equal masses as oblate spheroid. In the elliptic restricted four body problem, three of the bodies are moving in elliptical orbit around their common centre of mass fixed at the origin of the coordinate system, while the fourth one is infinitesimal. Three pairs of non-collinear points are obtained symmetric with respect to x-axis. We found the equilibrium points are stable in linear sense. We also investigate the pulsating zero velocity surfaces and basin of attraction for varying value of oblateness coefficient and radiation pressure parameter.

Effects of Triaxiality and Radiation Pressure on Existence of Resonance Stability of Triangular Equilibrium Points in Elliptical Restricted Three-Body Problem

This paper deals with the effects of radiation and triaxiality on linear stability of the triangular librations points for small value of eccentricity ‘\(e\)’ in presence of resonance. The study is carried out for various values of radiation pressure and Triaxiality parameter of both Primaries. It is found that the parametric resonance is only possible at the resonance frequency \(\omega_2 =1/2\) in elliptical case.

Existence of Resonance Stability of Triangular Equilibrium Points in Circular Case of the Elliptical Restricted Three-Body Problem Under Radiating and Triaxial Primaries

The linear stability of the triangular librations points is studied in the presence of resonance considering both the primaries as radiating and triaxial. The study is carried out for various values of radiation pressure and Triaxiality parameter of both Primaries. It is found that the parametric resonance is only possible at the resonance frequency \(\omega_2=1/2\) in circular case.

Empirically derived model of solar radiation pressure for BeiDou GEO satellites

A key limitation in the precise orbit determination (POD) of BeiDou geostationary Earth orbit (GEO) satellites is the relatively static observation geometry, which results in strong correlations between orbital elements, solar radiation pressure (SRP) parameters, and ambiguities. Satellite laser ranging (SLR) residuals of BeiDou G01 satellite orbits display a clear dependence on the Sun elongation angle e, as well as a bias of approximately − 40 cm. These indicate the low performance of BeiDou GEO orbits. In this study, we confirmed that the perturbation caused by the communication antenna generates the e-angle-dependent variation and the bias of approximately − 14.9 cm in BeiDou G01 SLR residuals. Besides, the orbit-normal (ON) attitude mode used by BeiDou GEO satellites as well as an orbital inclination of nearly 0° results in strong linear correlations between the POD estimated parameters, i.e., satellite’s initial position on the Z-axis and the constant Y-bias along the cross-track direction. Hence, the solar pressure models, such as Extended CODE Orbit Model (ECOM) in ON mode, with the Y-axis along the cross-track direction are deficient for SRP estimation of BeiDou GEO satellites. In this study, an empirical a priori SRP model was established for BeiDou GEO satellites to enhance the ECOM using an empirical fitting approach. This proposed model is expressed in DYB frame using eight parameters. With this model, precise BeiDou GEO orbits in 2016 were determined. SLR validation indicated that the systematic e-angle-dependent error was reduced and the large negative bias almost vanished. In general, better than 10-cm root-mean-square of SLR validation was achieved, and also an improvement of 4–5 times over the five-parameter ECOM model was obtained.

Determining characteristics of artificial near-Earth objects using observability analysis

Observability analysis is a method for determining whether a chosen state of a system can be determined from the output or measurements. Knowledge of state information availability resulting from observability analysis leads to improved sensor tasking for observation of orbital debris and better control of active spacecraft. This research performs numerical observability analysis of artificial near-Earth objects. Analysis of linearization methods and state transition matrices is performed to determine the viability of applying linear observability methods to the nonlinear orbit problem. Furthermore, pre-whitening is implemented to reformulate classical observability analysis. In addition, the state in observability analysis is typically composed of position and velocity; however, including object characteristics beyond position and velocity can be crucial for precise orbit propagation. For example, solar radiation pressure has a significant impact on the orbit of high area-to-mass ratio objects in geosynchronous orbit. Therefore, determining the time required for solar radiation pressure parameters to become observable is important for understanding debris objects. In order to compare observability analysis results with and without measurement noise and an extended state, quantitative measures of observability are investigated and implemented.

GPS Satellite Orbit Prediction at User End for Real-Time PPP System.

This paper proposed the high-precision satellite orbit prediction process at the user end for the real-time precise point positioning (PPP) system. Firstly, the structure of a new real-time PPP system will be briefly introduced in the paper. Then, the generation of satellite initial parameters (IP) at the sever end will be discussed, which includes the satellite position, velocity, and the solar radiation pressure (SRP) parameters for each satellite. After that, the method for orbit prediction at the user end, with dynamic models including the Earth’s gravitational force, lunar gravitational force, solar gravitational force, and the SRP, are presented. For numerical integration, both the single-step Runge–Kutta and multi-step Adams–Bashforth–Moulton integrator methods are implemented. Then, the comparison between the predicted orbit and the international global navigation satellite system (GNSS) service (IGS) final products are carried out. The results show that the prediction accuracy can be maintained for several hours, and the average prediction error of the 31 satellites are 0.031, 0.032, and 0.033 m for the radial, along-track and cross-track directions over 12 h, respectively. Finally, the PPP in both static and kinematic modes are carried out to verify the accuracy of the predicted satellite orbit. The average root mean square error (RMSE) for the static PPP of the 32 globally distributed IGS stations are 0.012, 0.015, and 0.021 m for the north, east, and vertical directions, respectively; while the RMSE of the kinematic PPP with the predicted orbit are 0.031, 0.069, and 0.167 m in the north, east and vertical directions, respectively.

Analysis on nonlinear stability of the triangular libration points for radiating and oblate primaries in ER3BP

In this paper we study the non linear stability of the triangular librations points in ER3BP considering both the primaries as radiating and oblate. The study is carried out near the resonance frequency satisfying the conditions  in resonance as well as non resonance case. The study is conducted for various values of radiation pressure and oblateness parameters. It is observed that the case corresponds to the boundary region of the stability for the system Further, it is examined that the system experiences resonance at for different values of radiation pressures and oblateness parameter. In non resonance case, it is observed that the equilibrium points are stable. In resonance case, for and the triangular equilibrium points are unstable. In case, when for some values of radiation pressure and oblateness parameter, it is stable and for some it is unstable. The model is best suited to the binary systems (Achird, Luyten, α Cen AB, Kruger- 60, Xi- Bootis).

Non- linear stability of triangular librations points in circular restricted three body under radiating and oblate primaries in presence of resonance

The nonlinear stability of the triangular librations points is studied in the presence resonance considering both the primaries as radiating and oblate. The study is carried out for various values of radiation pressure and oblateness parameter in general and binary systems in particular. It is found that the normal forms of the Hamiltonian contains both the resonance cases; ω1= 2ω2 and ω1= 3ω2. The case ω1= ω2 corresponds to the boundary region of the stability for the system.It is investigated that for the motion is unstable for third order resonance but stable for fourth order resonance.

Higher order resonance stability of triangular libration points for radiating primaries in ER3BP

<p>The main aim of this paper is to study the existence of resonance and stability of the triangular equilibrium points in the framework of ER3BP when both the attracting bodies are sources of radiation at w<sub>1</sub>=w<sub>2</sub>, w<sub>1</sub>=2w<sub>2</sub>, w<sub>1</sub>=3w<sub>2</sub> in both circular and elliptical cases .A practical application of this model could be seen in the case of binary systems ( Achird, Luyten, α Cen- AB, Kruger 60, Xi Bootis). The study is carried out both analytically and numerically by considering various values of radiation pressures and around binary systems .In both cases (CR3BP and ER3BP) it is found that w<sub>1</sub>=w<sub>2</sub> corresponds to the boundary region of the stability for the system, whereas the other two cases w<sub>1</sub>=2w<sub>2</sub>, w<sub>1</sub>=3w<sub>2</sub> correspond to the resonant cases. In order to investigate the stability, the Hamiltonian is normalized up to the fourth order by using linear canonical transformation of variables. Then KAM theorem is applied to investigate the stability for different values of radiation pressures in general and around the binary systems in particular. Finally, simulation technique is applied to study the correlation between radiation pressures and mass ratio in circular case; mass ratio and eccentricity in elliptical case. It is found that all the binary systems considered are stable. Also, it is found that except for some values of the radiation pressure parameters and for m<=m<sub>c</sub> =0.0385209 the triangular equilibrium points are stable.</p>

Nonlinear Stability of the Triangular Libration Points for Radiating and Oblate Primaries in CR3BP in Nonresonance Condition

This paper investigates the existence of resonance and nonlinear stability of the triangular equilibrium points when both oblate primaries are luminous. The study is carried out near the resonance frequency, satisfying the conditionsω1=ω2, ω1=2ω2, andω1=3ω2in circular cases by the application of Kolmogorov-Arnold-Moser (KAM) theory. The study is carried out for the various values of radiation pressure and oblateness parameters in general. It is noticed that the system experiences resonance atω1=2ω2, ω1=3ω2for different values of radiation pressures and oblateness parameter. The caseω1=ω2corresponds to the boundary region of the stability for the system. It is found that, except for some values of the radiation pressure, and oblateness parameters and forμ≤μc=0.0385209, the triangular equilibrium points are stable.

Stability of triangular lagrangian points in elliptical restricted three body problem under the radiating binary systems

This paper studies the stability of Triangular Lagrangian points in the model of elliptical restricted three body problem, under the assumption that both the primaries are radiating. The model proposed is applicable to the well known binary systems Achird, Luyten, αCen AB, Kruger-60, Xi-Bootis. Conditional stability of the motion around the triangular points exists for 0≤μ≤μ∗, where μ is the mass ratio. The method of averaging due to Grebenikov has been exploited throughout the analysis of stability of the system. The critical mass ratio depends on the combined effects of radiation of both the primaries and eccentricity of this orbit. It is found by adopting the simulation technique that the range of stability decreases as the radiation pressure parameter increases.

An impact analysis of arc length on orbit prediction and clock estimation for PPP ambiguity resolution

Real-time precise orbit and clock products are crucial for real-time high-precision precise point positioning (PPP). The key for precise orbit prediction is to precisely determine the initial conditions (satellite position, velocity at the initial epoch) and the solar radiation pressure (SRP) parameters using an arc of known precise orbits. The optimal arc length will be investigated for precise orbit prediction, with which the high-accuracy satellite clocks can be estimated. The orbit prediction accuracies with different arc lengths and conditions over time are also investigated. The results indicate that the predicted orbit accuracy is governed by the SRP parameters. In addition, the predicted orbits and estimated clocks are evaluated quantitatively with respect to PPP solutions during in and out of eclipses seasons, based on which the optimal arc length is identified. The numerical results show that high-accuracy orbital prediction can be achieved using an arc length between 36 and 48 h and generally an arc length of 42 h is considered to be optimal. With this optimal arc length, the estimated clock accuracy is 0.048 and 0.122 ns for a prediction interval of 6 and 24 h, respectively. The average PPP ambiguity fix-rates with a prediction interval of 6 h are 80.2 and 84.7 % over an observation period of 30 min and 1 h, respectively.

Precise orbit determination of BeiDou constellation based on BETS and MGEX network.

Chinese BeiDou Navigation Satellite System is officially operational as a regional constellation with five Geostationary Earth Orbit (GEO) satellites, five Inclined Geosynchronous Satellite Orbit (IGSO) satellites and four Medium Earth Orbit (MEO) satellites. Observations from the BeiDou Experimental Tracking Stations (BETS) and the IGS Multi-GNSS Experiment (MGEX) network from 1 January to 31 March 2013 are processed for orbit determination of the BeiDou constellation. Various arc lengths and solar radiation pressure parameters are investigated. The reduced set of ECOM five-parameter model produces better performance than the full set of ECOM nine-parameter model for BeiDou IGSO and MEO. The orbit overlap for the middle days of 3-day arc solutions is better than 20 cm and 14 cm for IGSO and MEO in RMS, respectively. Satellite laser ranging residuals are better than 10 cm for both IGSO and MEO. For BeiDou GEO, the orbit overlap of several meters and satellite laser ranging residuals of several decimetres can be achieved.

The sources of the unusual dust jets seen in Comet 103P/Hartley 2

We show that the unusual behavior of dust jets seen embedded in the sunward coma of 103P/Hartley 2 originate in active regions migrating over the two lobes of the nucleus following the Sun. The slowly changing orientation of the jets and their rapid changes in brightness is due to the shape and local topography of the nucleus coupled with the complex spin state. The intermittent appearance of a second jet is due to periodic deviations in the direction of the ejection of dust from the small lobe of the nucleus. The release of dust into the structures is likely due to the sublimation of H2O. The jets are characterized by injection speeds from the nucleus of 50–210m/s, a radiation pressure parameter 0.08<β<1, and a particle life-time near 7h. Within the jets, the average particle size decreases and the injection speed increases with distance from the nucleus.