L$10-1[10$ marks$]$ A spaceship travels away from earth with a speed of $\backslash (\backslash$frac$\{3\}\{5\}$ c $\backslash ).$ When an astronaut on the spaceship observes that $2$ hours have elapsed according to his clock, the spaceship sends an electromagnetic wave signal back to earth.

$($a$)$ According to the clocks of an observer on earth, when was the signal sent?

$($b$)$ According to the clocks of an observer on earth, when the signal is received, how much time has elapsed since the spaceship left?

$($c$)$ According to the astronaut on the spaceship, how much time has elapsed since the spaceship left earth?