An astronaut is traveling in a space vehicle that has a...

An astronaut is traveling in a space vehicle that has a speed of $0.500 c$ relative to the Earth. The astronaut measures her pulse rate at 75.0 beats per minute. Signals generated by the astronaut's pulse are radioed to Earth when the vehicle is moving in a direction perpendicular to the line that connects the vehicle with an observer on the Earth. (a) What pulse rate does the Earth observer measure? (b) What If? What would be the pulse rate if the speed of the space vehicle were increased to $0.990 c ?$

An astronaut is traveling in a space vehicle that has a speed of $0.500 c$ relative to the Earth. The astronaut measures her pulse rate at 75.0 beats per minute. Signals generated by the astronaut's pulse are radioed to Earth when the vehicle is moving in a direction perpendicular to the line that connects the vehicle with an observer on the Earth.
(a) What pulse rate does the Earth observer measure?
(b) What If? What would be the pulse rate if the speed of the space vehicle were increased to $0.990 c ?$

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Key Concepts

Relativistic Time Dilation

Relativistic time dilation is a fundamental prediction of Einstein's theory of Special Relativity. It states that time measured in a moving system runs slower when compared to the time measured in a stationary system. This effect is especially significant when the relative velocity approaches the speed of light, leading to noticeable differences in time intervals, such as the period between pulses in the astronaut's heart rate when observed from Earth.

Lorentz Factor (?)

The Lorentz factor, denoted as ? and defined by the equation ? = 1/?(1 - v²/c²), quantifies how much time dilation (as well as length contraction) occurs due to relative motion. It is the key parameter used in converting time measurements between different inertial frames, making it essential for calculating the observed pulse rate of the astronaut when the vehicle is moving at relativistic speeds.

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