This is a bit of a tricky question that depends on how you define "move". Here's a breakdown:

The Sun doesn't move with the Earth and Moon in the sense that they are all orbiting a common center point. The Earth and Moon orbit the Sun, with the Moon also orbiting the Earth.

However, the Sun does move through space. Our entire solar system is moving within the Milky Way galaxy, and the galaxy itself is also moving.

Here's a more detailed explanation:

* Earth and Moon around the Sun: The Earth and Moon both revolve around the Sun, following an elliptical path. The Sun is at one focus of this ellipse.

* Moon around the Earth: The Moon revolves around the Earth, again in an elliptical path. The Earth is at one focus of this ellipse.

* Solar System's movement: Our entire solar system is moving around the center of the Milky Way galaxy. This movement takes millions of years to complete one cycle.

* Galaxy's movement: The Milky Way galaxy itself is moving within the larger universe, interacting with other galaxies.

So, while the Sun doesn't move along with the Earth and Moon in their orbits, it does move within the larger context of the galaxy and the universe.