Is Tim Peake ageing faster or slower on the ISS?

Dan, London

Special relativity tells us that the faster you’re moving, the slower time will pass for you. It follows this equation.

Where t_{0} is the time for an observer on Earth, t_{f} is the time passing for the astronaut, v is their velocity and c is the speed of light.

General relativity tells us that the closer we are to an object, the slower time passes, compared to an observer who is nowhere near that object. The equation is similar to the previous one, and for a particle in a circular orbit around an object, it looks like this

where G is the constant of Universal Gravitation, M is the Mass of the Earth, r is the distance from the centre of the Earth.

So, special relativity tells us that an astronaut’s clock should slow down as it’s moving pretty fast, but it should also speed up as they’re further away from the Earth.

Both effects are pretty small, but the *gravitational one is more significant.*

**UPDATE: **I got the calculation wrong, I think I got a factor of 10 wrong in the velocity calculation. Dr. Martin Archer pointed out on twitter and I went back to do my calculations. For each second on board of the ISS, an astronaut experience a time dilation of 2.734×10^{-10} seconds.

This is equivalent to becoming 0.08 seconds younger every year.

And to finish, next time you use GPS on your phone, remember that it’s possible for you to find your way around thanks to one of the finest scientific theories of all time.