Simple self-shadowing in precise orbit determination of Copernicus Sentinel satellites

Numerous non-gravitational accelerations (NGAs) – due to radiation or gas-surface interactions – act on a typical satellite in low Earth orbit. The modeling of these accelerations is a key aspect of (reduced-)dynamic satellite precise orbit determination. Opposed to a purely empirical estimation of NGAs, especially orbit solutions with a high dynamical stiffness require an explicit NGA forward modelling. This is most important, e.g., for altimetry satellites which require utmost orbit accuracy especially in radial direction.

For explicit NGA modelling, a commonly employed strategy is to describe the satellite body in terms of a relatively simple macro model, i.e., a geometry composed of a number of elementary shapes like flat plates, spheres or cylinders, each of which with a specific size, orientation and surface property. During orbit integration, for each individual elementary surface NGAs are then computed based on analytical expressions and the sum over all surfaces yields the total NGA of the satellite at integration epoch. Often each of the elementary surface of the satellite macro model is treated fully independent from the other surfaces and interactions, in particular the (partial) occultation or shadowing of one surface by other surfaces is neglected. In case of satellites with significant non-convex shapes (like the altimetry satellite Sentinel-6A) this can lead to a marked degradation of NGA modeling. On the other hand, very detailed satellite geometry models together with techniques like ray tracing can provide highly accurate NGAs, however, at the price of significantly increased processing times.

In this contribution we assess the performance of a relatively simple self-shadowing algorithm for satellites described by a collection of flat convex polygons. Based on the relative plate locations, for each plate we analytically determine the amount of shadow cast by the other plates. We quantify the cost in terms of processing time and the impact on dynamic orbit solutions for the Copernicus Sentinel satellites in terms of empirical orbit parameters, observation residuals as well as other orbit quality metrics. We compare the so-derived NGAs and orbit solutions to results obtained with different other macro models and alternative approaches to take self-shadowing into account.