An astronaut wears a new Rolex watch on a journey at a speed of 2.0 ×10^8 m / s with respect to

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An astronaut wears a new Rolex watch on a journey at a speed...

An astronaut wears a new Rolex watch on a journey at a speed of $2.0 \times 10^{8} \mathrm{~m} / \mathrm{s}$ with respect to Earth. According to mission control in Houston, the trip lasts $12.0 \mathrm{~h}$. How long is the trip as measured on the Rolex?

Key Concepts

Special Relativity

Special relativity is a theory in physics that describes the relationship between space and time for observers moving at constant speeds relative to one another. It challenges classical intuitions by showing that measurements of time and distance can vary between observers, especially at velocities close to the speed of light.

Time Dilation

Time dilation is a phenomenon predicted by special relativity in which the elapsed time between two events is longer in a frame of reference that is moving relative to the frame in which the events occur. This means that a moving clock ticks slower compared to a stationary clock, a result that becomes significant at speeds approaching that of light.

Lorentz Factor

The Lorentz factor is a crucial element in the mathematical formulation of special relativity. Represented by ? (gamma), it is defined as ? = 1 / ?(1 - v²/c²), where v is the relative velocity and c is the speed of light. This factor quantifies how much time dilation, length contraction, and relativistic mass increase occur for an object in motion.

Proper Time

Proper time is the time interval measured by an observer who is at rest relative to the clock or the event being observed. In the context of time dilation, it is the shortest time between two events, observed in the reference frame where the events occur at the same spatial location.

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