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Orbital Mechanics Optimization

#physics #astrophysics #mathematics #optimization

Calculate a Hohmann transfer orbit with inclination change for a specific payload mass.

Solve the following orbital mechanics problem: Calculate the delta-v requirements for a spacecraft to transfer from a 200km Low Earth Orbit (LEO) to a Geostationary Orbit (GEO) including a plane change of 28.5 degrees. Assume a payload mass of 5000kg. Determine the most efficient point to perform the plane change (at perigee, apogee, or combined). Provide the mathematical derivations step-by-step, referencing the Vis-viva equation and the cosine law for non-coplanar maneuvers.