## Fundamentals of Physics Extended (10th Edition)

$\beta = 0.999 999 50$
First we'll use the time dilation equation and solve for Beta; $\Delta t=\Delta t_0 / \sqrt{1-\beta^2 }$ $\sqrt{1-\beta^2 } \Delta t=\Delta t_0$ $\sqrt{1-\beta^2 } =\Delta t_0 / \Delta t$ $1-\beta^2 =(\Delta t_0 / \Delta t)^2$ $\beta =\sqrt{1-(\Delta t_0 / \Delta t)^2}$ Our journey will take 1 year, ignoring the time it would take to turn around. Also, we would like earth to be 1000 years older. Therefore; $\beta =\sqrt{1-(1year / 1000years)^2}$ $\beta = 0.999 999 50$