Here's why:

* Gravity: The Milky Way's gravity is strong enough to hold the Sun and all the other stars in the galaxy.

* Orbital Motion: The Sun orbits the Milky Way's center at a speed of about 220 kilometers per second. This orbital motion is what keeps the Sun from flying off into space.

* Cosmic Speed Limit: For the Sun to escape the Milky Way's gravity, it would need to reach escape velocity. This is much faster than the Sun's current orbital speed.

The Sun's Future:

While the Sun won't leave the Milky Way, it will eventually become a red giant star, expand, and consume the inner planets (including Earth). However, this is billions of years in the future.

In summary: The Sun is safely bound to the Milky Way galaxy by its gravitational pull and its orbital motion. It will remain within the galaxy for a very long time.