An astronaut is traveling in a space vehicle that has a speed of 0.485 c relativ

Question

An astronaut is traveling in a space vehicle that has a speed of 0.485c relative to Earth. The astronaut measures his pulse rate at 77.5 per minute. Signals generated by the astronaut's pulse are radioed to Earth when the vehicle is moving perpendicularly to a line that connects the vehicle with an Earth observer.

A) What pulse rate does the Earth observer measure?  answer = 66.65 (I got this part correct already)

B) What would be the pulse rate if the speed of the space vehicle were increased to 0.990c?

Explanation / Answer

The time between pulses as viewed from earth is the time on the ship, ts / gamma, where

gamma =sqrt[1-(v/c)^2]

for v/c = 0.485, gamma = 0.875 the rate is 1/t so the rate is r/gamma = 77.5*0.875 = 67.8125

For v/c = 0.99, gamma = 0.141, so the rate would be 10.9275

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