Katar and his wife Shayera possessed at Star-Cruiser, able to travel the expanse between their home and adopted worlds with relative ease. Carter had been gifted at various points in his career with space craft, first while captured and hijacked by Nazis, inexplicably sending him to space, and later when his old friend Elwood Napier gave Hawkman and his Justice Society allies a gravity-motor spaceship.
In order to travel to and fro among the stars, Katar's craft was outfitted with a drive allowing it to access hyperspace. And during Carter's first voyage throughout his solar system, his craft likewise entered hyperspace which led him to an alternate dimension version of Saturn. While it had been said that this was an "alternate universe" version of the planet, the physics of hyperspace in both Earth-One and Earth-Two's universe meant that in fact he arrived at another world within his own universe resembling Earth-Two's Saturn.