Just to emphasize: There is no limit to the earth's gravitational pull. The formula is F=G*sqrt(m1m2)/r^2.

So as r (the distance between the center of the earth and your satellite) increases, F decreases. But it never hits zero.

Though after a while (a Sun-Earth L point, is it?), the influence of the sun will be greater (by orders of magnitude) than the earths.