Earth revolves around the Sun. It is wrong to say that the Sun revolves around the Earth.

FACT: Motion is relative. There is nothing wrong in saying the Sun revolves around the Earth. The former is more frequently mentioned because the Sun (or more accurately, barycenter) is a better inertial frame, and other planets revolve in a near circle around the Sun as well, but in a bizarre way around the Earth.

By traveling faster than light in the vacuum one can go back to the past.

FACT: No explanation needed.