Mark Vincent, Raytheon; Francois Rogez, Jet Propulsion Laboratory
https://doi.org/10.64861/NHOI5955
Keywords: atmospheric drag predictions, uncertainties in Pc calculations, drag make-up maneuvers, F10.7 solar flux, geomagnetic indices
Abstract:
It is well known that the major contributor to the orbital state uncertainty used in calculating the Probability of Collision (Pc) of two LEO space objects is atmospheric drag prediction error. Past analyses1 have shown that the majority of the future uncertainty in atmospheric drag (50 to 75%) comes from the prediction of the solar indices that are used as inputs to neutral density atmospheric models. This paper will first overview recent efforts to improve the prediction of these indices, for example, the use of helioseismology. However, the bulk of the paper will concentrate on the empirical aspects of the remainder of the problem, namely the inadequacies of the atmospheric models to produce a density that is reflected in the real-life drag accelerations experienced by the space objects. In other words, investigating the case when the solar indices are predicted perfectly and how well the atmospheric drag can be modeled in the future with such predictions. The second section of the paper will present different methods for modeling the stochastic aspects of the future drag. The simpler methods assume one stochastic parameter and most often the Coefficient of Drag (Cd) is used as a proxy for this purpose. The paper will discuss the misconceptions and nuances of adopting this method. The orbital characteristics of the Orbiting Carbon Observatory 2 (OCO-2) and the NASA/ISRO SAR (NISAR) missions whose data are used in the analysis, are described in the paper. The data from October and November 2025 was used. The October data is shown in Figure 1. The following is a brief description of each data set (details are in the paper): NISAR Acc: The orbit-averaged drag acceleration on NISAR that is estimated during the orbit determination process. Flux/500: The definitive F10.7 solar flux values obtained from NOAA. Divided by 500 for plotting purposes. Ap/200: The definitive Ap geomagnetic index values obtained from NOAA. Divided by 200 for plotting purposes. OCO2 Cd/10: The daily estimate of Cd for OCO-2 using definitive solar indices. Divided by 10 for plotting purposes. NISAR Cd/10: As explained in the paper this is actually the product of two stochastic parameters, but here consider it to be the Cd estimated once per orbit for NISAR. Divided by 10 for plotting purposes. B10.7/500: A recently-coined term for the Bremsstrahlung component of the F10.7. It is a better proxy for the EUV radiation that actually heats the atmosphere. This will be discussed in the paper. Divided by 500 for plotting purposes. A somewhat surprising result was observed just with the raw data. The variation in Cd for the two spacecraft was well correlated as seen in Figure 1. This was encouraging since it meant the errors in the atmosphere models was similar in both cases even though their orbits were at different altitudes and different orientations with respect to the Sun. However, both sets of Cd values can be used to calculate the inherent error in the atmosphere models. Results are shown in Figure 2, depicted as relative R = model/truth (its derivation is in the paper). After some research and trial-and-error, two fitting/predicting models were chosen either: log(Cd) = a + b*B10.7 +c*(Ap or a p ) + d* or log(1+Acc) = a + b*B10.7 +c*(Ap or a p ) + d* The log (base 10) values were used since prior analyses2 indicated log of the atmospheric density (which is linearly related to Cd and acceleration) was proportional to the solar flux value. The “1+” term was just added for plotting purposes. The daily averaged geomagnetic index Ap was used for non-storm days while the 3-hour a p values were used during storms. Analysis confirmed the log values were also proportional to these geomagnetic indices. The term represents the integrated effect of the solar flux heating the atmosphere (a 7-day average was chosen). Other models included a persistence term, for example with only 1-day steps: Cd(i) = a * Cd(i-1) + b * [a + b*B10.7 +c*Ap + d*] where Cd(i), F10.7 and Ap are on Day i. The a and b terms are normalized weighting coefficients. For example, using 3-hour steps and a = 0.917 and b = 0.083 is analogous to an exponential decay with a half-life of one day, since (0.917)8 = 0.5. An example of the fit and prediction are shown in Figure 3. Note the geomagnetic storm starting near November 12 (Day 43) and that the 26 days of fitting included a smaller storm neat October 18. The paper discussing the overall results of fitting both Cd and Acc, as well as the trade-offs for implementing them into mission operations. Results indicate that either formulation predicted better than, for example, using a constant value of Cd for predictions. Acknowledgment: The work described in this paper was carried out in part at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. References: [1] Mesalles-Ripoll, P.; Rositani, R.; Duncan, M., “Low-Earth Orbit Prediction Accuracy Review of Modern Empirical Atmospheric Models,” Proceeding of the AMOS Conference, 2023 [2] Vincent, M.A., ““Explanation and History of the New Solar Cycle/ Atmospheric Model used in Mars Planetary Protection Analysis,” Proceedings of the AAS/AIAA Astrodynamics Specialists Conference, Quebec City, Quebec, Canada, July 30-Aug. 2, 2001 (also JPL document D-21422) Figure 1. Input Data used in the Analysis Figure 2. Relative Error in the Atmosphere Models Figure 3. The November Storm: 26-Day Fit and 3-Day Predict of Drag Acceleration
Date of Conference: September 15-18, 2026
Track: Atmospherics/Space Weather