You seem to have misconception about the Sun's movement.
First, all movement is relative so different observers from different location will see the Sun have different movement.
From the Galactic center, the Sun is orbiting the galaxy at the speed of 220 km/s moving towards the direction of the star Vega.
From the ground, the Sun appears to circle around Earth every 24 hours with each new day, it doesn't appear to be in the same position at the same hour.
From a stationary observer at the ecliptic pole, the Sun appears to move around background star appearing in a similar location every 365.2536 days.
From a rotating observer (period 1 year) at the ecliptic pole, the Sun would wobble slightly, be larger at January and smaller at July.