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

May 28, 2016

In the absence of significant gravity from other objects, time runs faster in space than on Earth. It takes about 300 years to register seven seconds of time difference.

#### Explanation:

Imagine that you are hovering just above the Earth's surface, letting Earth rotate beneath you while you stay fixed relative to the center of the Earth. I, meanwhile, stay right above you, but many Earth radii away so that Earth's gravitational hold on me is much smaller. If no other massive objects interfere, General Relativity predicts that your watch will run slower than mine, because of gravity curving space-time.

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!