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Learn about trajectory optimization in space mechanics through a 28-minute conference talk that demonstrates the application of Julia programming language in scientific computing. Explore how Julia's high-level features and performance capabilities enable efficient solutions for optimal control problems in space mechanics. Discover various approaches from the classic Goddard problem to modern applications developed in collaboration with space agencies like CNES, Thales Alenia Space, and ESA. Examine minimum time orbit transfer and solar sailing implementations while understanding different methodologies including direct transcription and shooting techniques. See how these methods work together to capture solution structures and compute optimal controls with precision. Follow practical demonstrations using the control-toolbox suite of Julia packages, with examples drawn from recent research in orbital mechanics and spacecraft control systems.