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## Homework Statement

"A star is 5ly away. If an astronaut wants to travel there and back and only age half a year, at what speed β = v/c do they need to travel?"

## Homework Equations

[tex]\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}[/tex]

[tex]\Delta T = \gamma \Delta T_0[/tex]

so [tex]\Delta T = \frac{\Delta T_0}{\sqrt{1 - v^2/c^2}}[/tex]

## The Attempt at a Solution

I'm having problems finding the time elapsed on Earth (T0) without knowing the speed, v/c. I've tried to use [tex]\Delta T_0 = \frac{2l}{c}[/tex] and then put my answer into the equation for delta T, but my answer ended up being 20c which is definitely not right... I've tried it in both ly and in meters. I also tried equating 2d/c and 1/gamma * T but had too many unknowns to solve. Any help with this would be appreciated; this is the first question in a set of problems and whilst I've done the other 'harder' ones, I can't do this one. I feel like I'm missing something really obvious? I've tried to search for other equations for time elapsed on Earth but to no avail. Thank you.