Answer:
<em>I must travel with a speed of 2.97 x 10^8 m/s</em>
Explanation:
Sine the spacecraft flies at the same speed in the to and fro distance of the journey, then the time taken will be 6 months plus 6 months
Time that elapses on the spacecraft = 1 year
On earth the people have advanced 120 yrs
According to relativity, the time contraction on the spacecraft is gotten from
=
where
is the time that elapses on the spacecraft = 120 years
= time here on Earth = 1 year
is the ratio v/c
where
v is the speed of the spacecraft = ?
c is the speed of light = 3 x 10^8 m/s
substituting values, we have
120 = 1/
squaring both sides of the equation, we have
14400 = 1/
14400 - 14400 = 1
14400 - 1 = 14400
14399 = 14400
= 14399/14400 = 0.99
= 0.99
substitute β = v/c
v/c = 0.99
but c = 3 x 10^8 m/s
v = 0.99c = 0.99 x 3 x 10^8 = <em>2.97 x 10^8 m/s</em>