(a) How long does it take the astronaut in Example 28.2 to...

(a) How long does it take the astronaut in Example 28.2 to travel 4.30 ly at 0.99944$c$ (as measured by the Earth-bound observer)? (b) How long does it take according to the astronaut? (c) Verify that these two times are related through time dilation with $\gamma=30.00$ as given.

Key Concepts

Lorentz Factor

The Lorentz factor, commonly denoted by gamma (?), is defined as 1 divided by the square root of (1 ? v²/c²), where v is the relative speed between the observers and c is the speed of light. This factor quantifies how much time dilation (and length contraction) occurs when comparing measurements between inertial frames in relative motion.

Proper Time

Proper time refers to the time interval measured by an observer who is at rest with respect to the events being timed. It represents the shortest time interval between two events and serves as the standard against which time in other moving frames is compared, illustrating the effects of time dilation.

Time Dilation

Time dilation is a core concept in special relativity which states that time intervals between events are not absolute but depend on the relative motion of the observer. When an object moves at speeds close to the speed of light relative to an inertial frame, the clock associated with that moving object ticks slower compared to clocks at rest in that frame.

Inertial Reference Frames

Inertial reference frames are coordinate systems in which objects move at constant velocity (or are at rest), meaning there is no acceleration acting on them. The comparison of time measurements between different inertial frames, such as one moving at a high speed relative to another, is fundamental to understanding relativity phenomena like time dilation.

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