A spacecraft travels a distance of 1.00 ·10^-3 light-years in 20.0 h, as measured by an observe

step 1 To solve this problem, I will use the velocity of spacecraft formula V is equal to D by T. So ju

A spacecraft travels a distance of 1.00 ·10^-3 light-years...

A spacecraft travels a distance of $1.00 \cdot 10^{-3}$ light-years in $20.0 \mathrm{~h},$ as measured by an observer stationed on Earth. How long does the journey take as measured by the captain of the spacecraft?

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Key Concepts

Reference Frames

Reference frames are coordinate systems used by observers to measure physical quantities like time and distance. In problems involving high-speed travel, differences between an Earth-based inertial frame and a moving spacecraft’s inertial frame must be accounted for using the principles of special relativity.

Time Dilation

In special relativity, time dilation is the phenomenon where a clock moving relative to an observer is measured to tick slower than a clock at rest with respect to that observer. This concept is crucial when comparing time intervals measured in different inertial frames, such as between an Earth-based observer and a high-speed spacecraft.

Lorentz Factor

The Lorentz factor, defined as 1/?(1 - v²/c²), is a multiplier that quantifies the amount of time dilation and length contraction experienced by objects moving at relativistic speeds. It bridges measurements between different inertial frames and is central to calculating relativistic effects.

Proper Time

Proper time refers to the time interval measured by an observer who is at rest relative to the event being timed. It is the shortest possible time interval between two events and is measured in the same frame where the events occur at the same location, such as the captain’s measurement aboard the spacecraft.

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