What path does an asteroid travel in space?
The Asteroids travel in a somewhat elliptical & inclined path inside the Asteroid belt between Mars & Jupiter.
Once you have reached space, build a new spaceship at the Holopad on the Pewter Moon. You will need to travel to the three planets (Jungle, Ice, and Fire) and defeat the mechanical creatures there. Once you have all three of the Space Knights with you, you can travel to the Giant Asteroid in the asteroid belt, and battle the Binary Bard to save the Princess. (see related questions)