Final answer:
The Earth travels in a nearly circular orbit around the Milky Way's center at a speed of around 200 km/s, taking about 225 million years for a galactic year, and has completed about 20 galactic years over its lifetime. It is surrounded by a halo of dark matter, which influences galactic motion. Additionally, the Earth's axis precesses over a period of about 26,000 years due to solar and lunar gravitational forces.
Step-by-step explanation:
The Earth moves within the Milky Way galaxy in a complex manner. First, our Sun, along with the Earth and other planets in the solar system, orbits the center of the Milky Way in a nearly circular path that lies within the galaxy's disk. This orbit is completed at a speed of about 200 kilometers per second, resulting in a galactic year, which takes approximately 225 million Earth years. During the Earth's lifetime, it has only completed about 20 galactic years.
Additionally, our galaxy itself comprises a giant disk with spiral arms, where Earth resides, and a central bulge. The halo of invisible matter, or dark matter, surrounds this disk, significantly influencing the galaxy's mass and gravitational pull, thus affecting how stars, including our Sun, orbit the galactic center.
Aside from its galactic movement, the Earth also exhibits a precession of its axis—a slow gyroscopic motion, which completes a cycle approximately every 26,000 years due to the gravitational forces from the Sun and Moon acting on Earth's nonspherical shape.