Relativity of length

Classical Mechanics Level pending

Caught by surprise near a supernova, you race away from the explosion in your spaceship, hoping to outrun the high-speed material ejected towards you. Your Lorentz factor \( \gamma \) relative to the inertial reference frame of the local stars is \( 22.4. \) To reach a safe distance, you figure you need to cover \( 9.00 \times 10^{16} \text{ m} \) as measured in the reference frame of the local stars. Approximately how long does that trip take in your own reference frame?

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