The Sun is the closest star to the earth. It is the center of our solar system, and the energy source that fuels life on Earth. The Sun is not a stationary object by any means. It wobbles around the center of mass of the solar system (a point inside the Sun, but not at its center) and revolves around the center of the Milky Way galaxy.

The Moon

The moon revolves around the Earth with a period of 27.322 days which is why full and new moons come around about once a month. Its synodic period-- the time that it takes for it to return to the same position in the sky, is 29.53059 days. The same face of the moon always faces the Earth because we are tidally locked. We do see different phases of the moon, though, depending on how the moon is illuminated by the Sun.

Planetary motions affect one another as well. Since Jupiter is so massive (the most massive planet in our solar system), it did not allow anything to form between its orbit and Mars's orbit, where the asteroid belt is.
The orbits of the planets are elliptical. Most of them are close to being circular, and most of them are in the same plane, as the cartoon on the right shows.
The planets that are inside the Earth's orbit (Mercury and Venus) are called the inferior, and those outside of the Earth's orbit (Mars, Jupiter, Saturn, Uranus, Neptune, and Pluto) are called superior. Since the Earth is closer to the Sun, it moves faster than the superior planets. When the Earth overtakes a superior planet, and that planet looks like it is looping backward, that is known as retrograde motion.