Answer to Question #203519 in Astronomy | Astrophysics for Ahmed Ayman Mohamm

Question

One of the many exciting phenomena of special relativity is time dilation. Imagine astronauts

in a spaceship that is passing by the Earth with a high velocity.

(c) Are clocks ticking slower for the people on Earth or for the astronauts on the spaceship?

(d) How fast must the spaceship travel such that the clocks go twice as slow?

Answer 1

(c) Clocks are ticking slower for the astronauts on the spaceship.

(d) $\displaystyle \Delta t' = \frac{\Delta t}{\sqrt{1-v^2/c^2}} = 2 \Delta t$

$\Delta t'$ - time on the Earth, $\Delta t$ - on the spaceship.

$\displaystyle \frac{1}{\sqrt{1-v^2/c^2}}= 2$

$\sqrt{1-v^2/c^2} = 0.5$

$1-v^2/c^2 = 0.25$

$v^2/c^2 = 0.75$

$v = 0.866c$

Answer: 0.866c