Question

Is the Sun stationary?

Answer 1

The Sun is definitely not stationary.

Explanation:

The Sun is constantly in motion. For a start is rotates on its axis. The equator of the Sun rotates about 1.5 times faster than the poles.

Also, the planets don't orbit the Sun. Rather the Sun and all of the planets orbit the Solar System Barycentre (SSB), which is the centre of mass of the solar system. The SSB is in constant motion and can be anywhere from near the centre of the Sun to about a solar radius outside of the Sun. The diagram shows the position of the SSB over several decades.

Also, the Sun is orbiting around the galactic centre of mass.

The galaxy is also moving relative to other galaxies.

So, the Sun is most definitely not stationary, it is in constant motion.