Gaia DR2: orbit improvement based on new debiasing of asteroid astrometry

<p><strong>Gaia DR2, validating the debiasing of asteroid astrometry by orbit improvement</strong></p> <p>The optimal exploitation of asteroid astrometry is seminal at many tasks such as the monitoring of impact risks by potentially hazardous asteroids, and the measurement of subtle dynamical effects. These can include, most notably, the Yarkovsky thermal recoil force or perturbations due to other asteroids.</p> <p>The Gaia mission has published astrometry with very high accuracy for 14.099 asteroids in the Data Release 2 (DR2), and about 10 times more are coming in DR3 (end 2021). The level of accuracy of Gaia is unprecedented, reaching 1 mas or better for each epoch, but it deserves unprecedented care to be exploited.<br /> <br />In particular, most archival data (astrometry available at the Minor Planet Center) are the result of a calibration with respect to pre-Gaia catalogues, that are often affected by local systematic errors. Such errors have different possible sources. They can be the result of the tiling of the celestial sphere by a imaging device, whose field of view presents some residual distortion in its astrometric reduction. There can also be effects related to the coupling of two different catalogs, distant in time, used to derive proper motions. Eventually, the adopted reference frame can also introduce other effects.</p> <p>As it has been documented several times in literature such systematic bias, that can vary on spatial scales of a few degrees or less, can also be function of other parameters, such as the magnitude range considered (different bias affect stars of different brightness). </p> <p>To take into account these effects and apply the required corrections, we developed a completely new bias correction computation around on the position of single asteroid observations, instead of the classical approach of computing corrections on fixed grid for each catalogue. Despite being much more time-consuming, our approach allows us to reach a full flexibility on effects related to the field of view size of single surveys, magnitude limit and also epoch-dependent variations. We also implement corrections to the reference frame rotation detected for bright stars (V<12) in Gaia DR2 (Lindegren 2020) necessary to obtain a full consistency.</p> <p>After having completed the debiasing of astrometry archived at MPC for all asteroids in Gaia DR2, we have run an orbit improvement procedure for all of them, that also exploits a refined error model. We illustrate here the results of our processing, in particular investigating the improvement in the ephemeris uncertainty, and the perfomance of the debiasing.<br /> </p>

Efficiency of the piecewise constant acceleration modeling - GOCE case study

<p>One of the valuable products of the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) mission is a centimeter-accuracy orbit of the GOCE satellite called the precise science orbit (PSO). This orbit, delivered by the European Space Agency (ESA), was the reference for the GOCE orbit modeling using the piecewise constant acceleration approach. Besides initial conditions, the piecewise constant accelerations (i.e. empirical accelerations) were estimated in the radial, along-track and cross-track direction, employing the dedicated package called Torun Orbit Processor (TOP). The TOP software is based on the classical least squares adjustment including the Cowell 8-th order numerical integration for an orbit prediction and the orbit improvement module, taking into account the gravity field model and the background models (BM) describing gravitational and non-gravitational perturbing forces. The positions of GOCE satellite on the reduced-dynamic PSO orbit were treated as observations in the orbit improvement process. A measure of the fit of estimated arcs and their accuracy was the RMS of the residuals between the estimated orbits and the corresponding reference ones. Different variants of the orbit estimation were obtained for the shorter  arcs (22.5, 45, 90 and 180 minutes)  and for the longer 1-day arcs. The solution variants were determined for different numbers of the estimated piecewise constant accelerations. Moreover, these numbers were different for the radial, along-track and cross-track direction. The obtained solutions depend on a kind of computational mode – with and without the BM models in the GOCE orbit modeling using the estimated piecewise constant accelerations. Additionally, for selected solutions, the distributions of the residuals in the aforementioned directions along the estimated arcs are presented. </p>

Principles of Orbit Improvement and Generation of Ephemerides for the Global Positloning System Satellites

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Weight Fusion Orbit Determination Method with Multi-Source at Injection Stage

In this paper, according to the theory of differential orbit improvement, the dynamics equations are deduced for the data of different types, and the weight method is introduced to fuse the multi-source data with different precision and form according to the RMS of condition function associated to different data. The results of simulations and real data processing show that the high precise measure data of different orbit measurement have been brought into full play, and the orbit determination precision is improved obviously.