Explanation:
The heart rate of the astronaut is 78.5 beats per minute, which means that the time between heart beats is 0.0127 min. This will be the time t measured by the moving observer. The time t' measured by the stationary Earth-based observer is given by
a) If the astronaut is moving at 0.480c, the time t' is
This means that time between his heart beats as measured by Earth-based observer is 0.0145 min, which is equivalent to 69.1 beats per minute.
b) At v = 0.940c, the time t' is
So at this speed, the astronaut's heart rate is 1/(0.0372 min) or 26.9 beats per minute.