# How does time in space relate to time on earth?

If gravity is weak, meaning the escape velocity is much below the speed of light, the relative difference in the rate time is observed to pass is about $\frac{{v}^{2}}{2 {c}^{2}}$ where $v$ is the escape velocity and $c$ is the speed of light. In the case of Earth this ratio is about $7 \setminus \times {10}^{- 10}$, or 7\times10^{-8}%, so it would take ${10}^{10}$ seconds or 300 years of total time to register seven seconds of time difference. Yet this differential must be taken into account in GPS devices which operate via space-based satellites, or the GPS calculations are inaccurate!