Brownhall, Indigo; Lavezzi, Giovanni; Jang, Daniel; Lifson, Miles; Bhattarai, Santosh; Linares, Richard; (2024) A Stable Equilibrium for the LEO Orbital Capacity. In: Proceedings of the 22nd IAA Symposium on Space Debris. (pp. pp. 995-1004). International Astronautical Federation (IAF)

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Abstract

This work describes several improvements to pySSEM, the Python version of the open-source MIT Orbital Capacity Assessment Tool - Source-Sink Evolutionary Model (MOCAT-SSEM). First, a novel fragment spreading function, recently introduced in other work, is implemented into the framework. This fragment spreading function deposits collision fragments across multiple shells, based on analysis of the probability distribution of collision-induced changes to fragment velocities. Collisions are simulated based on the NASA Standard Break-up Model for each potential species and altitude collision pair in order to predict the number of fragments created. Then, the velocity change of each fragment is calculated, and mapped to a spread in altitude. This methodology aims to provide a computationally efficient way to address a known limitation of space environment SSEMs: that circular deposition of collision products in the same shell as the parent objects can artificially inflate collision predictions and produce localized runaway conditions not seen in Monte Carlo modeling. Second, an eccentric binning method for SSEM species collision modeling is presented to improve handling of rocket bodies and debris species. For each elliptical orbit species, the time spent in each orbital shell encountered is calculated, and a new coefficient is used to generate collision terms that consider potential cross-shell interactions. In a test scenario, simulations show that this additional capability reduces the number of debris objects, as there are less collisions, particularly between rocket bodies and trackable debris. This is a first step towards full integration of optional consideration of elliptical orbit properties within pySSEM. Finally, the ability to formulate a constrained nonlinear optimization problem is added to support environmental control, economic, and other applications. This capability is demonstrated through a toy problem computing a set of static maximum launch rates for LEO, subject to equality and inequality constraints. All enhancements are openly available as source code or through the pySSEM Python package.

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