Yes, it is true that all the solar systems within the Milky Way, including our own, are moving in relation to the central supermassive black hole known as Sagittarius A*.
The motion of stars and solar systems in the Milky Way is influenced by the combined gravitational forces from all the matter within the galaxy, including the stars, gas, dust, and the central black hole. This gravitational interaction leads to various orbital motions, both around the galactic center and within the galactic disk.
In general, stars and solar systems in the outer regions of the Milky Way, like our Sun, orbit the galactic center in a roughly circular or elliptical path. The speed of their motion depends on their distance from the center, with objects farther out moving at slower speeds.
However, it is important to note that the gravitational pull of the central black hole alone is not the dominant factor determining the overall motion of stars and solar systems in the Milky Way. The collective gravitational forces from the galaxy's entire mass distribution play a significant role.
Therefore, while all the solar systems within the Milky Way are affected by the gravitational forces of the central black hole, their motion is primarily determined by the overall gravitational dynamics of the galaxy rather than being directly pulled toward the black hole itself.