The control panel on a spaceship contains a light that blinks every $1\mathrm{.}61$ s as observed by an astronaut in the ship. If the spaceship is moving past Earth with a speed of $0\mathrm{.}653$c$,$ determine the proper time interval between blinks and the time interval between blinks as observed by a person on Earth.

$($a$)$

the proper time interval $($in s$)$ between blinks

s

$($b$)$

the time interval $($in s$)$ between blinks as observed by a person on Earth