Orbits around Earth need to be within its Hill sphere. Earth's Hill sphere is the region where Earth's gravity field dominates over the gravity fields of Moon and Sun. For Earth the radius of the Hill sphere is about 1.5 million kilometers. But for long-term stability the satellite needs to be well within the Hill sphere, less than half the maximum radius.
The escape velocity from Earth's surface is about 11.2 km per second. That's the velocity an objects needs at the surface of Earth, relative to a non-rotating coordinate system, to escape the gravity field of Earth, no atmospheric drag assumed.
The escape velocity is dependent of the distance from Earth's center of gravity, the further away from Earth the slower the escape velocity. Its roughly proporional to the inverse of the square root of the distance from Earth's center, as long as points above Earth's surface are considered.
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