Analyze the thermal and electrical performance of a power distribution system for a spacecraft. Given:The spacecraft has a power requirement of $1$ kW$,$ operating in a vacuum environment with an average temperature of $-50$C$.$The power is generated by a solar array with an efficiency of $30\%,$ generating DC voltage at $300$ V$.$The power distribution system includes converters, switches, and relays rated for operation between $-100$C to $+50$C$.$The spacecraft experiences transient thermal conditions during orbit, ranging from direct sunlight to deep space shadow.Design a thermal management system to maintain critical components within safe operating temperatures while maximizing efficiency.Evaluate the impact of thermal cycling and vacuum conditions on the electrical insulation, conductor sizing, and component reliability.Derive equations for thermal dissipation, taking into account the spacecraft's orientation relative to the sun and heat dissipation into space.Analyze the electrical losses due to temperature variations and propose efficiency improvements for the power distribution network.Discuss the integration of thermal sensors and control algorithms to regulate component temperatures dynamically during mission phases.Assess the reliabilit

y of electrical connections and insulation materials under extreme thermal and vacuum conditions, considering long$-$term mission durability.

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