Effects of Self-Shadowing on Nonconservative Force Modeling for Mars-Orbiting Spacecraft Erwan Mazarico * and Maria T. Zuber Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 and Frank G. Lemoine † and David E. Smith † NASA Goddard Space Flight Center, Greenbelt, Maryland 20771 DOI: 10.2514/1.41679 Modeling improvements of nonconservative forces affecting Mars-orbiting spacecraft are presented in this study. Recent high-resolution gravity fields enable the recovery of smaller signals in the radio tracking data, previously obscured by mismodeled gravitational anomalies. In particular, the estimation of the atmospheric drag experienced by the spacecraft benefits from the new force models. More precise calculations of the spacecraft cross-sectional areas entering the equations for the atmospheric drag and direct solar radiation pressure are possible by accounting for the interplate self-shadowing of the spacecraft physical model. The relevant surface areas can change by as much as 20% on average, and the effects can be very variable within one orbit (10%). The benefits of these updated models are assessed with two spacecraft, the Mars Odyssey and the Mars Reconnaissance Orbiter. The changes in the nonconservative forces can significantly impact the reconstructed spacecraft trajectory and the estimated model parameters depend on the spacecraft geometry and orbit. The atmospheric density estimated by the Mars Odyssey is much improved with self-shadowing applied to the solar radiation, but improvements to both the drag force and the solar radiation are important in this case of the Mars Reconnaissance Orbiter. I. Introduction I N RECENT years, several NASA Mars orbiter missions provided valuable tracking data with the aim to improve the knowledge of the Martian gravity field. The Mars Global Surveyor (MGS) was tracked extensively over nearly 10 years. The Mars Odyssey (launched in early 2001) and Mars Reconnaissance Orbiter (MRO, launched in late 2005) are still operational and continue to be tracked nearly continuously. The designs of the three spacecraft included movable high-gain antennae, so that acquisition of radio tracking and downlink of telemetry to Earth would not interfere with science data collection. In contrast, the sparse tracking of the ESA Mars Express spacecraft is due to its fixed high-gain antenna on the spacecraft bus. These recent NASA missions considerably improved the spatial resolution of the estimated Martian gravity field compared with earlier models [1–3]. The level of the unmodeled gravity anomalies decreased consi- derably as a result, and the nongravitational forces have a more noticeable impact on the adjusted trajectory. This enables the esti- mation of previously unadjustable parameters, such as the atmo- spheric drag [3–6]. Because the nonconservative forces are small and generally of the same order of magnitude, improvements of the orbit reconstruction and of the confidence in the adjusted force parameters depend on better modeling of all of them. The results of modeling efforts focused on the spacecraft cross section calculations are presented. Better models of atmospheric density structure or seasonal surface tempera- tures are of course important for the estimation of the nonconservative forces, but the surface area affects all these small forces. The current modeling scheme of the nonconservative forces is first presented and its limitations are addressed. The new algorithm used to accurately estimate the spacecraft cross section is explained in detail, followed by an assessment of its computational performance and its implementation in the precision orbit determination (POD) workflow. Sample trajectory arcs of the Mars Odyssey and MRO spacecraft are used to show the differences that arise with the new modeling, including changes in the cross-sectional areas and nonconservative accelerations. The effects on a larger scale, covering most of the missions of both spacecraft, are presented as well. The more detailed study of the MRO shows how the modeling improvements can affect, for the better, the ability to recover small signals in the tracking data. The physical configuration of the MGS spacecraft and the phasing of the orbit were such (early afternoon) that the ensuing self-shadowing is much smaller than for the other two spacecraft, and so it is not discussed in further detail. Finally, the modeling of the planetary radiation pressure accele- ration modeling is discussed, both in terms of practical difficulties and of potential future beneficial improvements. In all this work, the POD program “GEODYN II” developed at NASA Goddard Space Flight Center (GSFC) [7] was used. The orbit of the spacecraft is forward integrated using accurate force models, and the radio tracking data are compared with values predicted from the computed trajectory. The differences (residuals) are used along with the partial derivatives of all the adjustable parameters in order to obtain the parameters’ values for a new iteration until convergence is attained. Here, contrary to other studies where the focus was gravity field estimation, only the initial state, measurement biases, and of course the atmospheric drag and solar radiation scale factors, are adjusted. The density model for the Martian upper atmosphere is a modified Stewart–Culp model [4], which was used in previous Mars orbiters’ radio tracking data studies at NASA GSFC [2,5,6]. II. Model Description A. Principle and Algorithm Although spacecraft with simple geometries can be very useful for geodetic studies (Starlette, LAGEOS), many spacecraft missions with more general scientific instruments have more complex Presented as Paper 7201 at the AIAA/AAS Astrodynamics Specialist Conference and Exhibit, Honolulu, HI, 18–21 August 2008; received 28 October 2008; revision received 18 February 2009; accepted for publication 6 March 2009. Copyright © 2009 by Erwan Mazarico. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; include the code 0022-4650/ 09 $10.00 in correspondence with the CCC. * Currently NASA Postdoctoral Program Fellow, NASA Goddard Space Flight Center; Erwan.M.Mazarico@nasa.gov. † Solar System Exploration Division. 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