Answer
(a) less than
(b) $55~beats/min$
Work Step by Step
(a) The time interval between each heart beat is longer to the Earth-based observer. Thus, the Earth-based observer measures the astronaut's heart rate at less than 72 beats per minute.
(b) We can calculate the required heat beats as follows:
$\frac{1}{\Delta t}=\frac{1}{\Delta t_{\circ}}\sqrt{1-\frac{v^2}{c^2}}$
We plug in the known values to obtain:
$\frac{1}{\Delta t}=(72beats/min)\sqrt{1-\frac{0.65c^2}{c^2}}$
$\implies \frac{1}{\Delta t}=55beats/min$
