Multi-GNSS Combined Orbit and Clock Solutions at iGMAS

Global navigation services from the quad-constellation of GPS, GLONASS, BDS, and Galileo are now available. The international GNSS monitoring and assessment system (iGMAS) aims to evaluate the navigation performance of the current quad systems under a unified framework. In order to assess impact of orbit and clock errors on the positioning accuracy, the user range error (URE) is always taken as a metric by comparison with the precise products. Compared with the solutions from a single analysis center, the combined solutions derived from multiple analysis centers are characterized with robustness and reliability and preferred to be used as references to assess the performance of broadcast ephemerides. In this paper, the combination method of iGMAS orbit and clock products is described, and the performance of the combined solutions is evaluated by various means. There are different internal precisions of the combined orbit and clock for different constellations, which indicates that consistent weights should be assigned for individual constellations and analysis centers included in the combination. For BDS-3, Galileo, and GLONASS combined orbits of iGMAS, the root-mean-square error (RMSE) of 5 cm is achieved by satellite laser ranging (SLR) observations. Meanwhile, the SLR residuals are characterized with a linear pattern with respect to the position of the sun, which indicates that the solar radiation pressure (SRP) model adopted in precise orbit determination needs further improvement. The consistency between combined orbit and clock of quad-constellation is validated by precise point positioning (PPP), and the accuracies of simulated kinematic tests are 1.4, 1.2, and 2.9 cm for east, north, and up components, respectively.

Iterative Lambert’s Trajectory Optimization for Extrasolar Bodies Interception

Interception of extrasolar objects is one of the major current astrophysical objectives since it allows gathering information on the formation and composition of other planetary systems. This paper develops a tool to design optimal orbits for the interception of these bodies considering the effects of different perturbation sources. The optimal trajectory is obtained by solving a Lambert’s problem that gives the required initial impulse. A numerical integration of a perturbed orbital model is calculated. This model considers the perturbations of the joint action of the gravitational potentials of the Solar System planets and the solar radiation pressure. These effects cause a deviation in the orbit that prevents the interception from taking place, so an iterative correction scheme of the initial estimated impulse is presented, capable of modifying the orbit and achieving a successful interception in a more realistic environment.

A Hybrid ECOM Model for Solar Radiation Pressure Effect on GPS Reference Orbit Derived by Orbit Fitting Technique

A hybrid ECOM (Empirical CODE Orbit Model) solar radiation pressure (SRP) model, which is termed ECOMC in this work, is proposed for global navigation satellite system (GNSS) orbit modeling. The ECOMC is mainly parameterized by both ECOM1 and ECOM2 models. The GNSS orbit mainly serves as a reference datum not only for its ranging measurement but also for the so-called precise point positioning (PPP) technique. Compared to a complex procedure of orbit determination with real tracking data, the so-called orbit fitting technique simply uses satellite positions from GNSS ephemeris as pseudo-observations to estimate the initial state vector and SRP parameters. The accuracy of the reference orbit is mainly dominated by the SRP, which is usually handled by either ECOM1 or ECOM2. However, the reference orbit derived by ECOM1 produces periodic variations on orbit differences with respect to International GNSS Service (IGS) final orbit for GPS IIR satellites. Such periodic variations are removed from a reference orbit formed using the ECOM2 model, which, however, yields large cross-track orbit errors for the IIR and IIF satellites. Such large errors are attributed to the fact that the ECOM2 intrinsically lacks 1 cycle per revolution (CPR) terms, which stabilize the estimations of the even-order CPR terms in the satellite-Sun direction when the orbit fitting is used. In comparison, a reference orbit constructed with the ECOMC model is free of both the periodic variations from the ECOM1 and the large cross-track orbit errors from the ECOM2. The above improvements from the ECOMC are associated with (1) the even CPR terms removing the periodic variations and (2) the 1 CPR terms compensating for the force mismodeling at = 90° and 270°, where the is the argument of the latitude of the satellite with respect to the Sun. The parameter correlation analysis also presents that the direct SRP estimation is sensitive to the 1 and 2 CPR terms in the ECOMC case. In addition, the root-mean-square (RMS) of orbit difference with respect to IGS orbit is improved by ~40%, ~10%, and ~50% in the radial, along-track, and cross-track directions, respectively, when the SRP model is changed from the ECOM2 to the ECOMC. The orbit accuracy is assessed through orbit overlaps at day boundaries. The accuracy improvements of the ECOMC-derived orbit over the ECOM2-derived orbit in the radial, along-track, and cross-track directions are 13.2%, 14.8%, and 42.6% for the IIF satellites and 7.4%, 7.7%, and 35.0% for the IIR satellites. The impact of the reference orbit using the three models on the PPP is assessed. The positioning accuracy derived from the ECOMC is better than that derived from the ECOM1 and ECOM2 by approximately 13% and 20%, respectively. This work may serve as a reference for forming the GNSS reference orbit using the orbit fitting technique with the ECOMC SRP model.

Validation of Multi-Year Galileo Orbits Using Satellite Laser Ranging

Satellite laser ranging (SLR) observations provide an independent validation of the global navigation satellite system (GNSS) orbits derived using microwave measurements. SLR residuals have also proven to be an important indicator of orbit radial accuracy. In this study, SLR validation is conducted for the precise orbits of eight Galileo satellites covering four to eight years (the current longest span), provided by multiple analysis centers (ACs) participating in the multi-GNSS experiment (MGEX). The purpose of this long-term analysis (the longest such study to date), is to provide a comprehensive evaluation of orbit product quality, its influencing factors, and the effect of perturbation model updates on precise orbit determination (POD) processing. A conventional ECOM solar radiation pressure (SRP) model was used for POD. The results showed distinct periodic variations with angular arguments in the SRP model, implying certain defects in the ECOM system. Updated SRP descriptions, such as ECOM2 or the Box-Wing model, led to significant improvements in SLR residuals for orbital products from multiple ACs. The standard deviation of these residuals decreased from 8–10 cm, before the SRP update, to about 3 cm afterward. The systematic bias of the residuals was also reduced by 2–4 cm and the apparent variability decreased significantly. In addition, the effects of gradual SRP model updates in the POD were evident in orbit comparisons. Orbital differences between ACs in the radial direction were reduced from the initial 10 cm to better than 3 cm, which is consistent with the results of SLR residual analysis. These results suggest SLR validation to be a powerful technique for evaluating the quality of POD strategies in GNSS orbits. Furthermore, this study has demonstrated that perturbation models, such as SRP, provide a better orbit modeling for the Galileo satellites.

Influence of non-gravitational effects on the Centaur upper stage of the Surveyor 2 spacecraft

A small near-Earth asteroid, discovered by the Panoramic Survey Telescope and Rapid Response System (Pan-STARRS) on September 17, 2020, turned out to be a part of the Centaur upper stage of the Surveyor 2 spacecraft launched by NASA on September 20, 1966 and subsequently crashed. This object had moved in a heliocentric orbit until it was under the influence of Earth’s gravitational field. As a result, a close approach to the Earth took place at a distance of about 50000 km on December 1, 2020. Despite the fact that the Centaur escaped back into a new orbit around the Sun in March 2021, it is of special interest for research, in particular, to consider the impact of non-gravitational effects on its orbital characteristics. Thus, it was calculated that the maximum displacement of the object trajectory due to the influence of solar radiation pressure over 15 years (the next close approach will take place in 2036) can be about 10.3-13.5 km, depending on the albedo. Estimations of the Yarkovsky effect showed that the magnitude of the expected change in the semi-major axis of Centaur’s orbit is from -8.1 • 10−13 to 1.6 10−13, depending on the angle of its rotation.

Constraints on the Occurrence of ‘Oumuamua-Like Objects

At present, there exists no consensus in the astronomical community regarding either the bulk composition or the formation mechanism for the interstellar object 1I/2017 U1 (‘Oumuamua). With the goal of assessing the merits of the various scenarios that have been suggested to explain ‘Oumuamua's appearance and observed properties, we report a number of new analyses and provide an up-to-date review of the current hypotheses. We consider the interpretations that can reconcile ‘Oumuamua's observed non-Keplerian trajectory with the nondetection of traditional cometary volatiles. We examine the ability of these proposed formation pathways to populate the galaxy with sufficient interstellar objects such that the detection of ‘Oumuamua by Pan-STARRS would be statistically favored. We consider two exotic ices, hydrogen and nitrogen, showing that the frigid temperature requirement for the former and the necessary formation efficiency of the latter pose serious difficulties for these interpretations. Via order-of-magnitude arguments and hydrodynamical cratering simulations, we show that impacts on extrasolar Kuiper Belt analogues are not expected to generate N2 ice fragments as large as ‘Oumuamua. In addition, we discuss observational tests to confirm the presence of these ices in future interstellar objects. Next, we examine the explanations that attribute ‘Oumuamua's properties to other compositions: ultraporous dust aggregates and thin membranes powered by solar radiation pressure, among others. While none of these hypotheses are perfectly satisfactory, we make predictions that will be testable by the Vera Rubin Observatory to resolve the tension introduced by ‘Oumuamua.

Forced Resonance Orbit Analysis of Binary Asteroid System

The solar radiation pressure becomes one of the major perturbations to orbits in the study of binary asteroid system, since asteroids have relatively weak gravity fields. In this paper, based on the idea of treating the solar radiation pressure as periodic external excitation, one novel family of orbits due to primary resonance and another novel family of orbits due to both primary resonance and internal resonance have been found by the classical perturbation method. The two types of steady-state orbits due to external resonance with different area-to-mass ratios have been determined and discussed by the frequency-response equations. Five binary asteroid systems, 283 Emma-S/2003 (283) 1, 22 Kalliope-Linus, 31 Euphrosyne-S/2019 (31) 1, 2006 Polonskaya-S/2005 (2006) 1 and 4029 Bridges have been taken as examples to show the validity of the proposed mechanism in the explanation of orbits formation due to resonance.

ON THE EFFECTS OF SOLAR RADIATION PRESSURE ON THE DEVIATION OF ASTEROIDS

In this work, we study the effects of solar radiation pressure (SRP) on the problem of changing the orbit of an asteroid to support planetary defense, scientific research, or exploitation of materials. This alternative considers a tethered reflective balloon (or a set of reflective balloons) attached to the asteroid, with a high area-to-mass ratio, to use the SRP to deflect a potentially hazardous asteroid (PHA) or to approximate the target asteroid to Earth. The tether is assumed to be inextensible and massless, and the motion is described only in the orbital plane of the asteroid around the Sun. The model is then used to study the effects that the tether length, the reflectivity coefficient, and the area-to-mass ratio have on the deviation of the trajectory of the asteroid.

Hybrid propulsion spacecraft formation control around the planetary displaced orbit

This paper aims to investigate the feasibility of using the combination of solar radiation pressure and Coulomb force as a propellantless control method for spacecraft formation around the planetary displaced orbit. Firstly, the dynamical equation of spacecraft formation is derived and linearized. Based on the linearized dynamic model, an integral sliding mode controller (ISMC) is designed. Aimed to stabilize the spacecraft formation, the control method is proposed to adjust the product of the charge and the attitude angles of two spacecrafts. Finally, numerical simulations are conducted and the results show that the controller can make the formation achieve the desired configuration with favorable control performances.