It may refer to the overriding influence of Earth on man, even when he leaves the Earth. When objects leave Earth and go into orbit around the planet, they are still under the influence of Earth's gravity. Earth's mass exerts a significant force on objects, including spacecrafts and satellites. The moon is a satellite of the Earth and orbits the Earth because of the gravitational pull. One could argue on that basis that Earth is still a major factor for astronauts.
Space travelers orbiting the Earth or living on the moon are under the influence of Earth's gravity.
The distant planet Jupiter and its moons, also feel the tug of Earth's gravity. The effect of Earth on Jupiter and other distant bodies is relatively minuscule but it is still has a measurable influence. Because of a number of factors, Jupiter's moons are prime candidates for space colonies. Thus, travellers within our solar system would still be under the influence of Earth, and may still be obligated to do mitzvot. When we leave the bounds of our solar system and discover planets fit to support life, where Earthly resources will not be needed, we will be free of Earth's gravitational pull and no longer dependent on Earth.