Atmospheric Density Uncertainty Quantification for Satellite Conjunction Assessment

Conjunction assessment requires knowledge of the uncertainty in the predicted orbit. Errors in the atmospheric density are a major source of error in the prediction of low Earth orbits. Therefore, accurate estimation of the density and quantification of the uncertainty in the density is required. Most atmospheric density models, however, do not provide an estimate of the uncertainty in the density. In this work, we present a new approach to quantify uncertainties in the density and to include these for calculating the probability of collision Pc. For this, we employ a recently developed dynamic reduced-order density model that enables efficient prediction of the thermospheric density. First, the model is used to obtain accurate estimates of the density and of the uncertainty in the estimates. Second, the density uncertainties are propagated forward simultaneously with orbit propagation to include the density uncertainties for Pc calculation. For this, we account for the effect of cross-correlation in position uncertainties due to density errors on the Pc. Finally, the effect of density uncertainties and cross-correlation on the Pc is assessed. The presented approach provides the distinctive capability to quantify the uncertainty in atmospheric density and to include this uncertainty for conjunction assessment while taking into account the dependence of the density errors on location and time. In addition, the results show that it is important to consider the effect of cross-correlation on the Pc, because ignoring this effect can result in severe underestimation of the collision probability.Comment: 15 pages, 6 figures, 5 table

Synthetic, structural, and spectroscopic studies of sterically crowded tin-chalcogen acenaphthenes

The work in this project was supported by the Engineering and Physical Sciences Research Council (EPSRC) and EaStCHEM.A series of sterically encumbered peri-substituted acenaphthenes have been prepared containing chalcogen and tin moieties at the close 5,6-positions (Acenap[SnPh3][ER], Acenap = acenaphthene-5,6-diyl, ER = SPh (1), SePh (2), TePh (3), SEt (4); Acenap[SnPh2Cl][EPh], E = S (5), Se (6); Acenap[SnBu2Cl][ER], ER = SPh(7), SePh (8), SEt (9)). Two geminally bis(peri-substituted) derivatives ({Acenap[SPh2]}2SnX2, X = Cl (10), Ph (11)) have also been prepared, along with the bromo–sulfur derivative Acenap(Br)(SEt) (15). All 11 chalcogen–tin compounds align a Sn–CPh/Sn–Cl bond along the mean acenaphthene plane and position a chalcogen lone pair in close proximity to the electropositive tin center, promoting the formation of a weakly attractive intramolecular donor–acceptor E···Sn–CPh/E···Sn–Cl 3c-4e type interaction. The extent of E→Sn bonding was investigated by X-ray crystallography and solution-state NMR and was found to be more prevalent in triorganotin chlorides 5–9 in comparison with triphenyltin derivatives 1–4. The increased Lewis acidity of the tin center resulting from coordination of a highly electronegative chlorine atom was found to greatly enhance the lp(E)−σ*(Sn–Y) donor–acceptor 3c-4e type interaction, with substantially shorter E–Sn peri distances observed in the solid state for triorganotin chlorides 5–9 (∼75% ∑rvdW) and significant 1J(119Sn,77Se) spin–spin coupling constants (SSCCs) observed for 6 (163 Hz) and 8 (143 Hz) in comparison to that for the triphenyltin derivative 2 (68 Hz). Similar observations were observed for geminally bis(peri-substituted) derivatives 10 and 11.PostprintPeer reviewe