Solar Radiation Pressure Coefficients Research Articles

Satellite Collision and Fragmentation Probabilities Using Radar-Based Size and Mass Estimates

Most conjunctions between Earth-orbiting satellites involve unknown objects, typically debris created by explosions or collisions. This study formulates methods to estimate probabilities of collision and fragmentation for such conjunctions, which depend on the estimated sizes and masses of the unknown objects. Analysis of radar cross-section (RCS) measurements provides estimated sizes, found to be accurate at the 90% confidence level to within a factor of 0.59 for potential underestimations and to within a factor of 3.1 for potential overestimations. For satellites that experience measurable atmospheric drag orbital perturbations, combining RCS data with orbit determination ballistic coefficients provides mass estimates accurate to within factors of 0.47 to 10.9 at the 90% confidence level. For satellites with perigee altitudes above 450 km, combining RCS data with solar radiation pressure coefficients provides mass estimates accurate to within factors of 0.44 to 5.6 at 90% confidence. The collision and fragmentation risk assessment formulation accounts for these size and mass estimation uncertainties. Specifically, conjunction collision probabilities formulated as statistically expected values account for the RCS-based size estimation uncertainties. Fragmentation probabilities, which measure the likelihood of producing more than a threshold number of collision fragments, account for both size and mass estimation uncertainties.

A simulation experiment on the GM estimation for Comet 133P/Elst-Pizarro

In China’s asteroid mission to be launched around 2025, (7968) 133P/Elst-Pizarro (hereafter 133P) will be the second target, after a visit to asteroid (469219) Kamo’oalewa. This paper describes a simulation of precise orbit determination for the spacecraft around comet 133P, as well as estimation of its gravitational parameter (GM) value and the solar radiation pressure coefficient Cr for the spacecraft. Different cometocentric distances of 200, 150 and 100 km orbits are considered, as well as two tracking modes: exclusive two-way range-rate mode (Earth station to spacecraft) and combinations of two-way range-rate and local spacecraft onboard ranging to the comet. Compared to exclusive two-way range-rate, the introduction of local ranging observables improves the final GM uncertainties by up to one order of magnitude. An ephemeris error in the orbit of 133P is also considered, and we show that, to obtain a reliable estimate of the GM for 133P, this error cannot exceed a one km range.

Solar Radiation Pressure Effects on Stability of Periodic Orbits in Restricted Four-Body Problem

In this work, the Hamiltonian of the four-body problem is considered under the effects of solar radiation pressure. The equations of motion of the infinitesimal body are obtained in the Hamiltonian canonical form. The libration points and the corresponding Jacobi constants are obtained with different values of the solar radiation pressure coefficient. The motion and its stability about each point are studied. A family of periodic orbits under the effects of the gravitational forces of the primaries and the solar radiation pressure are obtained depending on the pure numerical method. This purpose is applied to the Sun-Earth-Moon-Space craft system, and the results obtained are in a good agreement with the previous work such as (Kumari and Papadouris, 2013).

Time-varying solar radiation pressure on Ajisai in comparison with LAGEOS satellites

This study aims to investigate solar radiation pressure acting on the spherical geodetic satellites, Ajisai, LAGEOS-1, and LAGEOS-2. The solar radiation pressure coefficients (CR) are derived in two independent ways: (a) through precise orbit determination (POD) using satellite laser ranging (SLR) data, and (b) through modeling using the optical properties of the satellite surface material. The average CR value of Ajisai (1.039), as calculated from the time series of CR POD estimates every 15 days, is consistently smaller than those of LAGEOS-1 (1.140) and LAGEOS-2 (1.103). This difference can be explained by the fact that the surface of Ajisai is mostly covered by mirrors. The Ajisai CR values estimated by POD show remarkable semi-annual variation, which disagrees with the results of a previous study (Sengoku et al., 1995) predicting that the CR of Ajisai varies almost annually. We attribute this semi-annual variation to two physical reasons: the non-spherical additional cross-sectional area due to the “attached fitting ring” and the low reflectivity of the surface material in the polar regions. Furthermore, the solar radiation pressure acting on Ajisai varies annually in a direction perpendicular to the sun-satellite vector. Finally, the two independent CR values of Ajisai agree more when we assume a total solar irradiance of 1361 W/m2, whereas the value 1367 W/m2 has been commonly used in POD.

In-Orbit Tracking of High Area-to-Mass Ratio Space Objects

High area-to-mass ratio space objects at geosynchronous orbits pose a threat to operational satellites because of the difficulty in tracking them from Earth. This paper develops an in-orbit onboard algorithm for tracking high area-to-mass ratio space objects. The design uses relative motion dynamics and a simplified stereocamera measurement model to estimate the tracked object’s position and velocity, as well as its solar radiation pressure coefficient. An underlying assumption is the dominance of the solar radiation pressure perturbation, which is confirmed using an analysis of the relative motion dynamics. Two scenarios are examined: similar orbits and crossing orbits. The simulation results show that the tracking algorithm estimates the tracked object position, velocity, and solar radiation pressure coefficient in both scenarios with high accuracy. The simulations show that, although shape information is lost in the measurement model, the solar radiation pressure coefficient can still be estimated.

Autonomous Formation Keeping of Geostationary Satellites with Regional Navigation Satellites and Dynamics

In this paper, the reduced dynamic autonomous formation control of geostationary-Earth-orbit satellites using Indian Regional Navigation Satellite System observables is presented. Generally, the navigation signal is used to determine the position, velocity, and time kinematically. The kinematic formulation, however, is geometric and vulnerable to data outage and cycle slip. Weak geometry of navigation satellites causes high dilution of precision. In this situation, dynamics can provide the estimates with little degradation in accuracy. This requires combining Indian Regional Navigation Satellite System observables with orbital dynamics of the geostationary-Earth-orbit satellites in an extended Kalman filter setup, resulting in improved position and velocity estimates. Moreover, solar radiation pressure coefficient, ephemeris error, and any other unaccounted minute forces are estimated through an empirical acceleration model, along with receiver clock bias and drift, in a reduced dynamics formulation. Furthermore, it is demonstrated that these position and velocity estimates permit autonomous station and formation keeping of geostationary-Earth-orbit satellites. The classical technique using the sun and moon and solar radiation perturbing accelerations to advantage is used to control eccentricity and inclination vectors of each satellite in the formation. The formation-keeping control maneuvers are performed autonomously, whenever an individual satellite’s eccentricity or inclination limit is exceeded.

GPS-based onboard real-time orbit determination for leo satellites using consider Kalman filter

The use of Global Positioning System (GPS) observables provides the primary and advantageous technique for satellite orbit determination in low earth orbit (LEO), in particular when onboard autonomy is required. A wide range of LEO spacecraft equipped with GPS receivers have been launched into space for different applications. Aiming at determining the position and velocity of the satellite in real-time, a consider Kalman filter (CKF)-based reduced-dynamic orbit determination (RDOD) is introduced in this paper. In the CKF, orbit dynamic model is simplified to meet the space-borne computational limitations. The atmospheric drag and solar radiation pressure coefficients are considered rather than estimated in the conventional RDOD strategy. Only a lower order and degree of an earth gravity model is used in the orbit model. However, the propagation of the covariance of the consider parameters is able to absorb the unmodeled and dismodeled perturbations. Therefore, the filter could become convergent with desirable orbit determination performance. The CKF-RDOD method is implemented with a set of the Gravity Recovery and Climate Experiment flight data. The solutions indicate that this proposed method could achieve satisfactory precision orbit determination with approximately 1.5 m level of three-dimensional root-mean-square error using GPS broadcast messages in real-time scenarios.

Navigation solution for a geostationary satellite based on its dynamic equations and occasional GNSS measurements

The paper offers solution to the problem of geostationary spacecraft navigation by navigation satellite signal measurements using nonlinear dynamic equations, which include perturbing factors such as non-sphericity of the gravitational field of the Earth, gravitational attraction of the Moon and the Sun, and direct solar radiation pressure. This solution uses the iterative Kalman filter based on UD-decomposition and is focused on the onboard implementation with limited computing resources. The estimates of current coordinates and velocity components obtained with the Kalman filter are taken into account when integrating nonlinear equations of a spacecraft motion up to the next solution time moment. With undetermined solar radiation pressure coefficient, the proposed solution proved efficient in terms of accuracy requirements for the spaceborne satellite navigation receiver. The tests were conducted using a GPS signal simulator and a receiver.

Qualitative and analytical results of the bifurcation thresholds to halo orbits

We study the dynamics in the neighborhood of the collinear Lagrangian points in the spatial, circular, restricted three--body problem. We consider the case in which one of the primaries is a radiating body and the other is oblate (although the latter is a minor effect). Beside having an intrinsic mathematical interest, this model is particularly suited for the description of a mission of a spacecraft (e.g., a solar sail) to an asteroid. The aim of our study is to investigate the occurrence of bifurcations to halo orbits, which take place as the energy level is varied. The estimate of the bifurcation thresholds is performed by analytical and numerical methods: we find a remarkable agreement between the two approaches. As a side result, we also evaluate the influence of the different parameters, most notably the solar radiation pressure coefficient, on the dynamical behavior of the model. To perform the analytical and numerical computations, we start by implementing a center manifold reduction. Next, we estimate the bifurcation values using qualitative techniques (e.g. Poincar\'e surfaces, frequency analysis, FLIs). Concerning the analytical approach, following \cite{CPS} we implement a resonant normal form, we transform to suitable action-angle variables and we introduce a detuning parameter measuring the displacement from the synchronous resonance. The bifurcation thresholds are then determined as series expansions in the detuning. Three concrete examples are considered and we find in all cases a very good agreement between the analytical and numerical results.

ESTIMATION OF A GENERAL ALONG-TRACK ACCELERATION IN THE KOMPSAT-1 ORBIT

General along-track acceleration was estimated in the KOMPSAT-1 orbit determination process. Several sets of the atmospheric drag and solar radiation pressure coefficients were also derived with the different spacecraft area. State vectors in the orbit determination with the different spacecraft area were compared in the time frame. The orbit prediction using the estimated coefficients was performed and compared with the orbit determination results. The orbit prediction with the different general acceleration values was also carried out for the comparison

Spectral analyses of the drag-like coefficient Cd from LAGEOS data

From the global SLR data of LAGEOS between 1983 and 1986 inclusive, two series for the drag-like coefficient C D were obtained, the first one using simultaneous estimation of the initial state vector of satellite, C D and the solar radiation pressure coefficient C R for each 15-day arc, the second using multiarc estimation with 10-day orbital state, C D, C R and 5-day ERP. The Marple algorithm for AR spectrum was applied to both series, the first series giving the periods 475.5, 365.2, 216.4, 183.4, 69.0, 39.9 and 32.25 d, the second, 173.3, 152.8, 127.6, 61.3 and 27.64 d. A comparative analysis shows that the periods 475.5, 365.5 and 183.4 d in the first series are a reflection of systematic differences between the x p components of the polar motion derived from the BIH and the SLR data.