Question

Suppose you are planning a trip in which a spacecraft is to travel at a constant velocity for exactly six months, as measured by a clock on board the spacecraft, and then return home at the same speed. Upon return, the people on earth will have advanced exactly 90 years into the future. According to special relativity, how fast must you travel

Answer 1

Answer:

v = 0.99 c = 2.99 x 10⁸ m/s

Explanation:

From the special theory of relativity:

$t = \frac{t_o}{\sqrt{1-\frac{v^2}{c^2} } }$

where,

v = speed  of travel = ?

c = speed of light = 3 x 10⁸ m/s

t = time measured on earth = 90 years

t₀ = time measured in moving frame = 6 months = 0.5 year

Therefore,

$90\ yr = \frac{0.5\ yr}{\sqrt{1-\frac{v^2}{c^2} } } \\\\\\\sqrt{1-\frac{v^2}{c^2}} = \frac{0.5\ yr}{90\ yr}\\ 1-\frac{v^2}{c^2} = 0.00003086\\\frac{v^2}{c^2} = 1-0.00003086$

v = 0.99 c = 2.99 x 10⁸ m/s