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Satellite drag coefficients are a major source of uncertainty in predicting the drag force on satellites in low Earth orbit. Among other things, accurately predicting the orbit requires detailed knowledge of the satellite drag coefficient. Computational methods are an important tool in computing the drag coefficient but are too intensive for real-time and predictive applications. Therefore, analytic or empirical models that can accurately predict drag coefficients are desired. This work uses response surfaces to model drag coefficients. The response surface methodology is validated by developing a response surface model for the drag coefficient of a sphere where the closed-form solution is known. The response surface model performs well in predicting the drag coefficient of a sphere with a root mean square percentage error less than 0.3% over the entire parameter space. For more complex geometries, such as the GRACE satellite, the Hubble Space Telescope, and the International Space Station, the model errors are only slightly larger at about 0.9%, 0.6%, and 1.0%, respectively. [ABSTRACT FROM AUTHOR]

Ambitious satellite constellation projects by commercial entities and the ease of access to space in recent times have led to a dramatic proliferation of low-Earth space traffic. It jeopardizes space safety and long-term sustainability, necessitating better space domain awareness (SDA). Correct modeling of uncertainties in force models and orbital states, among other things, is an essential part of SDA. For objects in the low-Earth orbit (LEO) region, the uncertainty in the orbital dynamics mainly emanate from limited knowledge of the atmospheric drag-related parameters and variables. In this paper, which extends the work by Paul et al. (2021), we develop a feed-forward deep neural network model for the prediction of the satellite drag coefficient for the full range of satellite attitude (i.e., satellite pitch ∈ (- 90 ° , + 90 °) and satellite yaw ∈ (0 ° , + 360 °)). The model simultaneously predicts the mean and the standard deviation and is well-calibrated. We use numerically simulated physical drag coefficient data for training our neural network. The numerical simulations are carried out using the test particle Monte Carlo method using the diffuse reflection with incomplete accommodation gas-surface interaction model. Modeling is carried out for the well-known CHAllenging Minisatellite Payload (CHAMP) satellite. Finally, we use the Monte Carlo approach to propagate CHAMP over a three-day period under various modeling scenarios to investigate the distribution of radial, along-track, and cross-track orbital errors caused by drag coefficient uncertainty. The key takeaways of this paper are - (a) a constant drag coefficient cannot be used for reliable SDA purposes, and (b) stochastic machine learning models allow for the computation of drag coefficients in a timely manner while providing reliable uncertainty estimates. [ABSTRACT FROM AUTHOR]