How far must one travel to escape the earth's gravitational field?
Somewhere past the moon.
The moon at 400,000 kilometers only orbits the earth because of the earth's gravitational pull.
The scientific answer is 1 over r squared where r = the distance in question. And since this equations will never reach zero there is no exact distance. But some where well beyond the orbit of the moon the strength of the earth's gravity is negligible.