If you travel 6 month to the future, you are still in the point where you started, but the Earth will be on the other site of the Sun.

Why would you remain spatially locked to the sun? The solar system is moving around the milky way. The Milky way is traveling at around 370 miles per second if we use the universe as a frame of reference. A point is both a place and a moment. Everything is moving relative to everything else. Time travel is also space travel.