A spaceship is traveling away from Earth at 0.87 c . The...

A spaceship is traveling away from Earth at $0.87 c .$ The astronauts report home by radio every $12 \mathrm{h}$ (by their own clocks). At what interval are the reports sent to Earth, according to Earth clocks?

Key Concepts

Special Relativity

Special relativity is the theory that describes the physics of objects moving at constant speeds near the speed of light. It introduces concepts such as the invariance of the speed of light in all inertial frames and shows that measurements of time and space are relative, depending on the motion of the observer, which is essential for understanding phenomena occurring at high velocities.

Time Dilation

Time dilation is the phenomenon predicted by special relativity where a moving clock ticks more slowly compared to a stationary one. This effect means that time intervals measured in the moving frame (the proper time) appear longer when observed from a different inertial frame. It is a crucial concept when comparing time intervals between observers in relative motion.

Proper Time

Proper time refers to the time interval between two events as measured by an observer for whom both events occur at the same location. This measurement represents the shortest possible time interval between events and is used as the standard for comparing how time is experienced in different frames of reference, particularly when taking into account time dilation.

Relativistic Doppler Effect

The relativistic Doppler effect describes how the observed frequency (or time interval) of signals changes due to the relative motion between the source and the observer, combining the effects of time dilation with the additional delay caused by the movement of the source. It is instrumental in explaining how signals emitted at regular intervals in one frame are received at different intervals in another, particularly when the source is receding or approaching.

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