arXiv subjects

Yacob Medhin

Publications and source records attributed to Yacob Medhin.

3 recordsLinked to original sources

arXiv2026

Beyond the Cube: Overlapping Grid Methods for Debris Collision Risk Assessment

The cube method reduces conjunction screening in orbital debris simulations to $\mathcal{O}(N)$ cost by evaluating only object pairs sharing the same grid cell at each snapshot, but systematically assigns zero collision probability to pairs separated by a cell boundary at that epoch, a failure known as boundary blindness. This paper introduces the Double Cube (DC) method, which recovers boundary-crossing conjunctions through a spatially shifted secondary grid using bin-index lookup alone, preserving $\mathcal{O}(N)$ complexity. Validated across 8,000 Monte Carlo seeds, DC reduces the blindness rate from $\beta_{\mathrm{Cube}} = 9.70\%$ to $\beta_{\mathrm{DC}} = 4.21\%$; a synchronized experiment confirms the residual is temporal in origin by reaching exactly $0.00\%$. Removing blindness reveals a systematic per-pair overestimation in the cube formula that blind zero-probability assignments had been masking, suppressing the overall predicted collision rate below the true rate. Two independent corrections are derived and validated: a power-law correction motivated by the Direct Simulation Monte Carlo kinetic theory analogy reduces the calibration error from $12.9\%$ to $1.9\%$ at $k = 1$ and $4.0\%$ at $k = 2$, bracketing perfect calibration from opposite sides; a parameter-free Gaussian correction derived from the pair-distance distribution geometry achieves a residual of $0.08\%$. Both corrections have been implemented in MOCAT-MC.

astro-ph.EP↗

arXiv2026

Multidisciplinary Design Optimization of a Low-Thrust Asteroid Orbit Insertion Using Electric Propulsion

Low-thrust electric propulsion missions are often designed under simplifying assumptions such as constant thrust or fixed specific impulse, neglecting the strong coupling between trajectory dynamics, spacecraft power availability, and propulsion performance. In deep-space environments with reduced solar irradiance, these assumptions can lead to suboptimal or infeasible designs, underscoring the need to simultaneously optimize the trajectory and power subsystem. This paper presents a multidisciplinary design optimization (MDO) framework for the simultaneous design of low-thrust trajectories and spacecraft power systems, with explicit coupling to electric propulsion performance. The framework incorporates a high-fidelity variable-specific impulse model of the SPT-140 Hall thruster, in which thrust and efficiency are directly constrained by time-varying solar power availability and solar array degradation, rather than treated as fixed parameters. The coupled problem is posed as a time-optimal control problem and addressed using a framework built on top of OpenMDAO and Dymos toolchains, where Dymos employs a collocation-based direct-transcription approach for trajectory optimization. OpenMDAO provides accurate analytic partial derivatives, enabling efficient gradient-based optimization. A Fast Fourier Series shape-based method is used to generate dynamically feasible initial guess trajectories, and the resulting nonlinear programming problem is solved using IPOPT. The proposed framework is demonstrated through a low-thrust orbit insertion scenario around asteroid 16-Psyche, a regime in which reduced solar irradiance makes power-aware trajectory design particularly critical. Simulation results demonstrate the framework's ability to capture key power-propulsion-trajectory trade-offs, highlighting the importance of integrated power optimization for realistic electric propulsion mission design.

eess.SY↗

arXiv2025

The Sustainability of the Leo Orbit Capacity via Risk-Driven Active Debris Removal

The growing number of space debris in Low Earth Orbit (LEO) jeopardizes long-term orbital sustainability, requiring efficient risk assessment for active debris removal (ADR) missions. This study presents the development and validation of Filtered Modified MITRI (FMM), an enhanced risk index designed to improve the prioritization of high-criticality debris. Leveraging the MOCAT-MC simulation framework, we conducted a comprehensive performance evaluation and sensitivity analysis to probe the robustness of the FMM formulation. The results demonstrate that while the FMM provides superior identification of high-risk targets for annual removal campaigns, a nuanced performance trade-off exists between risk models depending on the operational removal cadence. The analysis also confirms that physically grounded mass terms are indispensable for practical risk assessment. By providing a validated open source tool and critical insights into the dynamics of risk, this research enhances our ability to select optimal ADR targets and ensure the long-term viability of LEO operations.

eess.SY↗